Links – Special Issue 1 Unconventional Computing Andrew Adamatzky (Ed.)

LINKs – Special Issue 1 Unconventional Computing Andrew Adamatzky (ed.)

Irina Petrova, Deep Down the Rabbit Hole. Installation with Macrolepiota procera fungi, 2020.

Louis-José Lestocart (dir.) LINKs – Special Issue 1 – Unconventional Computing

Andy Adamatzky Preface, 5

Thoughts on Unconventional Computing

Selim G. Akl Computational Nonuniversality: Philosophical and Artistic Perspectives, 8 Bruce MacLennan Swarms of microscopic agents self-assemble into complex bodies, 16 Bernd Ulmann Exploring chaos with analog computers, 21 Olga Kosheleva and Vladik Kreinovich Are There Traces of Megacomputing in Our Universe, 25 Dawid Przyczyna, Marcin Strzelecki, Konrad Szaciłowski Communication, information and music, 28 Zoran Konkoli Unconventional sensing: doing it unusual way in unusual settings, 34 Mark Burgin Induction versus Deduction in Science, Computing, Literature and Art, 40 Andrew Adamatzky and Irina Petrova Fungal Grey Matter, 44 Alessandro Chiolerio Le vignoble cosmique, 51 Kenichi Morita Novel reversible logic elements for unconventional computing, 56 Nancy Salay An Unconventional Look at AI: Why Today’s Machine Learning Systems are not Intelligent, 62 Jordi Vallverdú The benefits of being wrong: bonding epistemic and cognitive incompleteness for natural and artificial intelligent systems, 68 Richard Mayne Collapsing the wave function on postquantum unconventional computing, 71 Pier Luigi Gentili How to face the Complexity of the 21st Century Challenges? The contribution of Natural Computing, 77 Dan V. Nicolau, Jr. The Quantum Computing Delusion, 82 Genaro J. Martínez, Andrew Adamatzky, Marcin J. Schroeder The art of unconventional computing with cellular automata, 87 Andrew Adamatzky, Anna Nikolaidou, Antoni Gandia, and Alessandro Chiolerio Living wearables from slime mould and fungi, 93 Stefan Höltgen Brain Lego. Toy Computing with Lego Bricks, 99 Catarina Pombo Nabais Intelligent technological tattoos. Science, Art and Technology on and under the skin, 104 About the authors, 110

2 3 Thoughts on Unconventional Computing: Preface

There is no strict definition of unconventional computing. Being an unconventional computist is not a matter of training but thinking and living. Phenomenologically most works on unconventional computing are about implementation of computing in novel substrates (chemical, physical, biological), development of computing schemes and algorithms not fitting into the mainstream framework, or designing of computing architectures inspired by chemical or biological systems. This special issue of LINKs gives a snapshot of the unconventional computing field. Articles presented are punchy and well illustrated. I don’t feel there is a need to introduce each article because they all are short and self-contained and as well can be seen as extended abstracts or essays of the authors research profiles. All articles of the issue are authored by the world-leading experts in the field. The issue will serve well as a light-touch introduction to unconventional computing for people not familiar with computing and might inspire artists and humanitarians to enter the field.

Andrew Adamatzky, Bristol January 2021

4 5 Thoughts on Unconventional Computing

Photograph of the IBM Q 53 qubit quantum computer. Image courtesy of IBM. https://newsroom.ibm.com/image-gallery-research. 2. A proof by contradiction, in which it is 3. Returning the value of a fixed-size var- Computational Nonuniversality: Philosophical and Artistic Perspectives assumed that there indeed exists a ‘uni- iable to the outside world (for example, Selim G. Akl1 versal’ computer, and this assumption is displaying an output, setting a physical then shown to lead to an absurd situation quantity, and so on). whereby this computer embarks on an un- This paper draws connections from the science of computation to philosophy and the visual ending computation. Each of these operations can be performed on arts. The motivation for this endeavor is computational nonuniversality, a fundamental the- every conceivable machine that is referred to orem in theoretical computing established relatively recently. Two distinct mathematical These two approaches to disproving the ex- as a computer. Together, they are used to de- proofs of this result are offered, one proof by counterexample, and one proof by contradic- istence of a universal computer are reviewed fine, in the most general possible way, what in this paper. The role of philosophy in inter- is meant by to compute: the acquisition, the tion. Both proofs show that simulation, upon which rests the principle of universality, is not preting these results is highlighted. The equal- transformation, and the production of informa- always possible, thereby making the existence of a universal computer a myth. Both proofs ly important contribution of the visual arts in tion. are inspired by philosophy of science. Both are illustrated using an artist’s conception. illustrating the proofs is put in evidence. Now all computers today (whether theoretical or practical) have V(t) = c, where c is a Nonuniversality and incompleteness constant (often a very large number, but still a Introduction any other computer. And yet, it seems natural In this section we draw an analogy between constant). In order to make the nonuniversali- The science of computation has witnessed a to ask: is simulation always possible? Gödel’s Incompleteness Theorem in mathe- ty result even stronger, in what follows we do tremendous success since its inception in the In reality, the principle of universality is but matical logic, and the impossibility of achiev- not restrict V(t) to be a constant. Thus, V(t) is middle of the 20th century. Today, computers a conjecture, sometimes referred to as the ing a Universal Computer in computer science, allowed to be an increasing function of time, t are crucial in every aspect of modern society, Church-Turing thesis. This conjecture is im- that illustrates the similarities in the formal such as V(t) = t, or V(t) = 22 , and so on. transforming communication, transportation, possible to prove in general because an all structure and philosophical implications of Finally, U1 is allowed to have an unlimited education, business, health care and enter- encompassing and agreed upon definition of the two results. Specifically, Gödel proved that memory in which to store its program, as well tainment, to name just a few of the areas ben- what constitutes a computation does not ex- there exist formal systems of mathematics that as its input data, intermediate results, and efiting from information technology. The idea ist. This is the case, despite the overwhelming are consistent but not complete. In the same outputs. Furthermore, no limit whatsoever is behind this extraordinary impact is a simple number of instances providing evidence of its way, we show that there does not exist a gen- placed on the time taken by U1 to perform a one, namely, universality. The principle of uni- validity. An abundance of examples confirm- eral-purpose computer that is universal in the computation. versality states that given sufficient time and ing a claim is not a proof, however. By con- sense of being able to simulate any computa- memory space, any computation that can be trast, it is actually possible to disprove the uni- tion executable on another computer. Nonuniversality Theorem: U1 cannot be a performed by a general-purpose computer versality conjecture, and this is precisely what universal computer. can, through simulation, be performed by any this paper is about. Proving nonuniversality in computation by coun- Proof: Let us define a computation P1 re- other general-purpose computer (regardless terexample quiring W(t) operations during time unit of any architectural differences between the It was shown recently that, in fact, the princi- Let U1 be a general-purpose computer. For the number t, for t = 1, 2, 3, … If these opera- simulating and simulated computers, or how ple of universality is false in general; it does purpose of this proof, we suppose further that tions are not performed by the end of time efficient or inefficient is the simulation). This not apply to all computations. The reason for time is divided into discrete time units, and unit t, the computation P1 is said to have is accomplished by having the second com- this is that, as it turns out, simulation is the that U1 is capable of V(t) elementary opera- failed. Let W(t) > V(t), for some t. Clearly, puter simulate (that is, imitate exactly in order weakest link, the Achilles heel in the quest for tions at time unit number t, where t is a posi- U1 cannot perform P1. However, P1 is suc- to obtain the same effect) every step execut- universality in computation. Put simply, sim- tive integer, t = 1, 2, 3, … Here, an elementary cessfully completed by another computer ed by the first computer, using its own (hard- ulation is not always possible. It immediately th computational operation may be any one of U2 capable of W(t) operations during the t ware and software) resources. Thus, for exam- follows that a universal computer cannot ex- the following: time unit, for t = 1, 2, 3, … ple, an email program that runs on a laptop ist. This result, to which we refer as compu- can be made to run equally well on a mobile tational nonuniversality (or nonuniversality in 1. Obtaining the value of a fixed-size var- It is important to note that, by the definition phone. This applies to far more complex com- computation) is established using two distinct iable from an external medium (for exam- of universality, U1, once its features have been putations, from studying the subatomic realm approaches: ple, reading an input, measuring a physi- specified, is fixed and cannot change during to exploring the far reaches of our universe. cal quantity, and so on), the computation. Despite being allowed ex- It is indeed fair to say that simulation is the 1. A proof by counterexample, whereby an traordinary powers (such as, for example, the engine that would make universality possible. otherwise computable function, cannot be 2. Performing an arithmetic or logical op- ability to increase the number of operations it Consequently, according to the principle of computed on a putative ‘universal’ com- eration on a fixed number of fixed-size can do at every consecutive time unit), U1 still universality, every general purpose computer puter, that is, on a computer that is finite variables (for example, adding two num- fails to perform P1. The computer U2 on the is universal, capable of carrying out through and fixed once and for all. bers, comparing two numbers, and so on), other hand is especially tailored to carry out simulation any computation that is possible on and P1 and succeeds in doing so. This establishes

8 9 An algorithm for a computer M capable of n/2 Stepping outside of A1, Gödel proved that G1

operations per time unit solves the aforemen- cannot be proved within A1. Indeed, prov-

tioned variant of the sorting problem handily ing it true within A1 would mean that a false in n steps, by means of predefined pairwise statement is true, while proving it false within

swaps applied to the input array S, during A1 would mean that a true statement is false.

each of which S[j] and S[k] exchange positions Since G1 cannot be proved within A1, it fol-

(using an additional memory location for tem- lows that G1 is true. This means that A1 is in- porary storage). Thus, for example, the input complete as it contains a true statement that

array cannot be proved within A1. 7 6 5 4 3 2 1 0 To appreciate the significance of this result, would be sorted by the following sequence of consider adding the recalcitrant proposition

comparison/swap operations (each pair of un- G1 to A1, thus obtaining a new system A2. Is derlined numbers are compared to one anoth- the latter now complete? Surely not, for now

er and swapped if necessary to put the smaller we can create a proposition G2 not provable

first): within A2. We can prove G2 in a new system

7 6 5 4 3 2 1 0 A3, which in turn has its own problem prop-

6 7 4 5 2 3 0 1 osition G3 not provable within it, and so on 6 4 7 2 5 0 3 1 forever. This result became known as Gödel’s Fig. 1. Computing a function of N clocks. 4 6 2 7 0 5 1 3 Incompleteness Theorem.

4 2 6 0 7 1 5 3 The infinite ascent of formal systems A1, A2, that P1 is definitely computable. Yet surprising- per time unit, and claiming to be ‘universal’, 2 4 0 6 1 7 3 5 A3, …, in the Incompleteness Theorem, is di- ly, U1 is unable to simulate the actions of U2, readily solves the problem. It does so by read- 2 0 4 1 6 3 7 5 rectly paralleled by the infinite ascent of aspir- notwithstanding the fact that no limit is placed ing the times displayed by the N clocks, and 0 2 1 4 3 6 5 7 ing ‘universal’ computers U1, U2, U3, …, in the on its memory or the time it is allowed to run. computing a function of these values all in 0 1 2 3 4 5 6 7 Nonuniversality Theorem.

Would U2 be the new Universal Computer? Of one time unit (before time unit T + 1 when the However, an alleged ‘universal’ computer ca- It is interesting to note in passing the way in course not, as we can easily define a computa- clocks update their displays). This computer, pable of fewer than (n/2) operations per time which various philosophical movements took tion P2 requiring X(t) > W(t) operations during however, is thwarted if even one clock is add- unit, cannot solve the problem consistently. hold of the result as a validation of their agen- time unit t, that U2 cannot perform. A more ed to the wall! Confronted with the input array shown above, da. Thus, for example, to the postmodernists, powerful computer U3 can execute P2, but is it fails to satisfy the requirement that at no time Gödel’s Incompleteness Theorem implied that in turn defeated by a third computation P3, and An algorithmic counterexample to universality three consecutive values are listed in decreas- no firm foundation exists for any system of so on forever. Consider the well-known quintessential coming order. Is M universal? Certainly not, for it logic. The existentialists saw in it an end to ra- putational problem of sorting a sequence of too cannot solve the sorting problem when the tional and objective thought. Some mathema- A pictorial example numbers stored in the memory of a computer. input sequence has length greater than n.2 ticians and an assortment of thinkers in various As shown in Fig. 1, N clocks are hanging on a For a positive even integer n, where n ≥ 8, let disciplines argued, on the strength of the the- wall, N > 1. The clocks are digital, each display- n distinct integers be stored in an array S with A philosophical precursor to nonuniversality orem, that humans are superior to machines. ing the time as a quadruple of digits AB:CD; n locations S[1], S[2], …, S[n], one integer per In 1931, the twenty-five year old Austrian lo- One physicist even suggested that, thanks to for example, 19:48. All the clocks are working, location. Thus S[j], for all 1 ≤ j ≤ n, represents gician Kurt Gödel published his famous In- Gödel’s work, it is now obvious that the hu- ticking away synchronously. At every tick, each the integer currently stored in the jth location of completeness Theorem, arguably the most man brain is not a deterministic computer; clock displays a new, but random, quadruple S. In a variant of the standard sorting problem, important result in the history of mathematical rather, it is a quantum computer. AB:CD—a time perhaps different from the ones it is required to sort the n integers in place into logic. The theorem established that there exist displayed by the other N – 1 clocks. No clock increasing order, such that: nontrivial formal systems of mathematics that, Nonuniversality and unending recursion has a memory; therefore, when at the following if consistent, cannot be complete.3 Here the philosophical concept of infinite re- tick a new time is generated and displayed, the 1. After step i of the sorting algorithm, for In order to make his point, Gödel chose the gress is used to develop a proof of nonuniver- previous quadruple is lost forever. The wall is all i ≥ 1, no three consecutive integers sat- formal system of simple arithmetic, that is, sality that is distinct from the proof by counter- long at will, allowing N to be big at will. The isfy: the natural numbers with equality, addition, example. The proof itself is presented within problem to be solved is the following: For an S[j] > S[j + 1] > S[j + 2], and multiplication. Denoting this system by the general framework of logic known as proof arbitrary number of clocks N, it is required to for all 1 ≤ j ≤ n − 2. A1, consider the following proposition G1, ex- by contradiction. When invoking contradic- compute a function (for example, the average) pressible within A1: tion to prove a theorem, we begin by assum- of the N times displayed at a given moment T. 2. When the sort terminates we have: G1 = < This statement cannot be proved ing that the claim in the theorem is false; we

A computer capable of exactly N operations S[1] < S[2] < … < S[n]. within A1 >. then show that this assumption leads logically

10 11 to an absurdity (hence the Latin name reductio U1[C]. This means that U1 is executing the ad absurdum for this style of proof in mathe- actions of itself (U1, the computer), on the matics). simulation (U1[C], the input); we write:

U1[U1[C]] = U1(U1, U1[C]). Proving nonuniversality in computation by The right hand side of the above expres- contradiction sion, has three U1s: the first is the simula- An alternative proof of the Nonuniversality tor, the second is the computer being sim- 4 Theorem is provided in what follows. Let U1 ulated, and the third, U1[C], is the input. be a general-purpose computer. We therefore have: Fig. 2. Self reference and unending recursion. U1[U1[C]] = U1(U1,U1[C])

Nonuniversality Theorem. U1 cannot be a = U1(U1[U1[C]])

universal computer. = U1(U1(U1,U1[C]))

Proof: Let us assume, as is commonly the = U1(U1(U1[U1[C]]))

case in computer science, that there exists = U1(U1(U1(U1,U1[C]))) a ‘universal’ computer capable of simulat- … ing any possible computation C, the latter This leads to a self-referential infinite re-

being the result of another computer M gress, with U1 simulating itself, simulating executing a certain program on an input I. itself, simulating itself,… The computation For brevity, in what follows we use M to just described is a non-terminating process represent both the computer as well as the (one could say that it is not even a compu- program being simulated. tation, by definition, since it does not halt, the assumption regarding the existence of addressed the International Congress of Math-

but that is not important for our purpose). a universal computer U1 is false. No com- ematicians assembled at the Sorbonne in Paris.

In order to be specific, and without any loss It follows that U1 has failed to simulate it- puter is universal. Hilbert presented his colleagues with a list of of generality, let the assumed ‘universal’ com- self, while executing a terminating compu- problems on which, he believed, they should puter be U1. We write U1 (M, I) to express the tation C. Absolute idealism and self-referential cartography spend their time in the new century. Among th fact that U1 takes M and I as input and sim- As the sun was setting on the 19 century, these problems was the question of whether ulates the computation C by performing the Option 2. We can stipulate the existence idealist philosopher Josiah Royce proposed there exists a fixed set of true mathematical actions of M on I. Note that U1 is used here, of a more powerful universal computer U2 an interesting thought experiment. Imagine, statements that can be used to prove auto- by definition, as a simulating computer. Such that simulates U1[C]. Again, this leads, in he suggested, we could draw a detailed map matically any new mathematical statement. a computer needs the description of another turn, to an ascending infinite regress, fea- of England. The map would be so precise as Hilbert’s objective was the formalization of computer (M) in order to simulate that com- turing a sequence of ever more powerful to contain every road, every river, every hill, mathematics. puter as it runs a program on its input (I). In computers U2, U3, U4, … , Un, Un+1, Un+2, every plain, and so on. A flat terrain will be The purpose of Hilbert’s program in formal- other words, U1 does not act directly on an …, performing simulations C1, C2, C3, … , chosen and the map inscribed on the surface izing mathematics was twofold. The first goal input (such as I). Cn, Cn+1, Cn+2, … of the English countryside. But then something was to contain infinity. Proofs for all true state- In what follows, let C = (M, I) be a terminating Formally, unexpected would happen. Since the map is ments of a formal system were to be produced computation, meaning that M runs on I and C1 = U2[U1[C]], now part of the landscape, in order for it to from a finite set of axioms. The second goal halts in a finite number of computational steps. C2 = U3 [U2[U1[C]]], be exact, it would necessarily have to contain was to eliminate intuition from mathematics.

We write U1 [C] as a shorthand for U1 (M, I), the C3 = U4 [U3[U2[U1[C]]]], a copy of itself. That copy would therefore in- By mechanizing proof generation, serendipity simulation of C by U1, the latter also a termi- … evitably contain a copy of itself as well, and would no longer be part of the process of do- nating computation. Cn+1 = Un+2[Un+1 ... U4[U3[U2[U1[C]]]]...], the copy of the copy a copy, …; the process ing mathematics. Gödel’s work demonstrated It is evident, from the principle of universality, … will continue indefinitely. This self-referential that, on the contrary, infinity is an integral part that the actions of U1 itself should be possible and so on ad infinitum. In the unending map-within-a map construction is known as of mathematics and cannot be tamed. Math- to simulate. The question is: ‘Who’ is to simu- sequence of computations described here, the map of England problem and is sometimes ematicians will always use their intuition to 5 late a computation performed by a universal computer Un+1 is needed to simulate Un, used in studies of consciousness. A whimsical reason about the infinite. computer? Specifically, how are the actions of for n = 1, 2, 3, …, given that computer Un illustration of self-reference and the potential Likewise, the Nonuniversality Theorem shows

U1–as it simulates C, that is, U1 [C]–themselves cannot simulate itself (as shown in Option for infinite regress is shown in Fig. 2. that no finite computer can be universal. A to be simulated? 1 for U1). new machine will always be needed to cope There are two options. Conclusion with the next challenge. The resemblance be-

Option 1. U1 simulates itself. We write Both Option 1 and Option 2 are computa- On a hot August day in the year 1900, the il- tween the Nonuniversality Theorem and the

U1[U1[C]] to indicate that U1 is simulating tionally absurd, leading to one conclusion: lustrious German mathematician David Hilbert Incompleteness Theorem is captured by the

12 13 Fig. 3. Nonuniversality and incompleteness.

Fig. 4. Self-simulation and the ensuing infinite regress. drawing in Fig. 3. For every computer thought computations are taking place everywhere, all to be universal, there exists a computational the time. The genie simply does not fit in the problem that it cannot solve, even if given bottle. computers, chemical computers, and so on. plexity and Systems Science, New York, Springer, unbounded time and space; a more powerful By contrast with the proof by counterexample, Like the Halting Problem in Computer Sci- 2018, 631-639. computer is required. Similarly, for every set of the proof of nonuniversality in computation ence, Incompleteness in Mathematics, and the 3 K. Gödel, “Über formal unentscheidbare Sätze der axioms thought to be complete, there exists a by contradiction is a more recent result. It was Uncertainty Principle in Physics, Nonuniver- Principia Mathematica und verwandter Systeme I,” proposition that it cannot prove; an augment- motivated when an obvious and logical ques- sality in Computation is a limiting theorem, an Monatshefte für Methematik und Physik 38, 1931, ed set of axioms is required. tion was asked, apparently for the first time 173-198. impossibility result. 4 ever: If simulation is the bedrock of comput- S. G. Akl, “A map of England, the simulator simulat- The idea of nonuniversality in computation is ing, and the supposed ‘universal’ computer ed, and nonuniversality in computation,” to appear I am grateful to my daughter Sophia for the beautiful in: International Journal of Unconventional Comput- not a new one. Several proofs by counterexam- can simulate any computation, how can the drawings in this paper. ing. ple of the non-existence of a universal com- actions of the ‘universal’ computer itself be 5 J. Royce, The World and The Individual, First Series: puter have been presented since early in this simulated? The answer led once again to the The Four Historical Conceptions of Being, New York, century. They described different unconven- collapse of the notion of universality. This, in 1 School of Computing, Queen’s University, King- Dover Publications, 1959, 504-505. tional computational paradigms that falsify the turn, leads here to the following interesting ob- ston, Ontario K7L 3N6, Canada, [email protected]. idea of a universal computer. Examples of such servation. The invention in 1899 of the self-ref- 2 S. G. Akl, “Unconventional computational prob- paradigms include computations with: time erential map-of-England metaphor, bringing lems,” in R. A. Meyers (ed.), Encyclopedia of Com- varying variables, time varying computational about an inevitable infinite regress along with complexity, rank varying computational com- it, predates by 121 years the discovery of a plexity, interacting variables, uncertain time proof, by self-simulation, of computational constraints, mathematical constraints, glob- nonuniversality. Miraculously, the former (old al variables, and so on. These computational result) serves as a striking illustration of the lat- problems imply that computation is a funda- ter (new result), as demonstrated in Fig. 4. mental category of Nature, and as such it has We note in closing that nonuniversality in com- no bounds. Its parameters are limitless. Time putation applies to all known computational passes, inexorably, changing everything in its models and existing conventional computers, path. The constituents of our physical space both sequential and parallel, as well as apply- constantly interact with one another, mutual- ing to all future unconventional computers, ly affecting each other. As our world evolves, including quantum computers, biomolecular

14 15 Swarms of microscopic agents self-assemble into complex bodies Bruce MacLennan1

Nature produces living bodies of magnificent beauty and complexity, which are not the work of an external artist, but of a self-organized dance of a vast number of microscopic cells communicating and coordinating with each other. We can learn the dance scores from nature and use them to control massive swarms of microscopic artificial agents to assemble complex structures organized at many hierarchical levels, from the nanoscale up to the macroscale. Simulations demonstrate the application of these ideas in artificial Fig. 1. Depictions of large-scale neurocomputer.4 To left, external connections to artificial cortex. In center, computational mi- intelligence and artificial life. crostructure of artificial cortex. To right, example of three massive fiber bundles connecting functional regions of cortex.

The Problem about 20W of power. If we want to achieve applications in medicine, such as prosthetic may be considered one approach to morpho- As Richard Feynman said, “there is plenty of human-scale artificial intelligence, it is reason- limbs and sense organs. Surely, we would like genetic engineering, which applies principles room at the bottom,”2 and we are discover- able to suppose that we may need to construct prosthetic eyes with the sensitivity and acuity of morphogenesis to the creation of form.6 In ing ways to organize matter and processes at artificial brains similarly organized from the of natural eyes, and prosthetic hands with the artificial morphogenesis, very large numbers the microscopic scale — and even at the na- microscale to the macroscale (Fig. 1). dexterity and sense of touch of natural hands, of microscopic agents cooperate to assemble noscale — that have macroscopic effects that Continuing the example of artificial intelli- but these require vast numbers of components themselves and inanimate microscopic com- are relevant to technology, medicine, and art. gence, we now understand much better the to be assembled in precise ways. ponents into a desired structure (Fig. 2). Under But to date, nanotechnology has been limit- importance of embodiment as a foundation some conditions, they can disassemble such a ed to the creation of simple structures with a for intelligence.3 Brains have evolved to con- Artificial Morphogenesis structure in order to reassemble it into a new relatively small number of components, or to trol physical bodies in their physical environ- Assembling many millions of components into form. structures with a large number of components ments, although, of course, we also use them complex systems, structured from the nanoscale The agents, which may be wholly artificial or with either a highly regular or a random organ- for abstract thought and contemplation. Nev- up through the macroscale, might seem impos- produced by synthetic biology, have relatively ization. For many purposes, however, we need ertheless, control of our mechanically com- sible, but developmental processes in embryos simple capabilities for motion, signaling, and to be able to create complex structures hierar- plex bodies by means of rich sensorimotor prove that it is possible. An embryo develops information processing and control. Agents chically organized at many spatial scales from feedback provides the foundation from which from a single cell, which divides repeatedly need to be able to signal their immediate the microscopic to the macroscopic. Consider language and abstract thought can emerge. producing an exponentially growing cell mass. neighbors, but also more distant agents in or- these examples. Large numbers of sensory neurons embedded These cells differentiate and orchestrate a com- der to coordinate their behavior. Cells in a de- The contemporary, most successful approach- in our muscles, joints, and skin provide rich, plex dance that assembles the tissues, organs, veloping embryo accomplish this by emitting es to artificial intelligence are inspired by the high-dimensional input that allows our (quite and limbs of a complete organism (3.7x1013 chemical morphogens, which diffuse in the brain; they strive to model massive neural net- slow) neurons to coordinate complex behavior cells in a human adult). A foetus may comprise intercellular environment and can be detect- works at a level of abstraction that preserves in real time. Future robots with physical com- a trillion cells, which have self-organized into ed by other cells. Likewise, in artificial mor- their information processing capabilities while petence comparable to that of animals will be innumerable structures at many spatial scales phogenesis, agents communicate by chemical omitting irrelevant biological detail. Research facilitated by similarly complex artificial sense spanning five orders of magnitude. In this ro- and other signals. Agents also need to be able in cognitive neuroscience and artificial neural organs, skin, and muscles (actuators). Al- bust process, cells migrate, following chemical to move, either through a fluid medium or networks has revealed that much of the flex- though macroscopic in size, they will be com- waystations to distant destinations, signaling as a viscoelastic mass. This movement is ac- ible, context-sensitive information process- plex structures of many microscopic parts. For each other to coordinate their movement and complished by a variety of simple mechanical ing of our brains depends on large numbers example, the human eye has approximately trigger context-sensitive differentiation into mechanisms. Finally, the behavior of agents of massively interconnected neurons (9x1010 100 million retinal cells, which preprocess the hundreds of cell types. Masses of cells flow is governed by relatively simple, primarily neurons in a human brain, with perhaps 1015 visual image in real time, reducing its dimen- viscously, forming intricately structured tissues analog control mechanisms. connections). Moreover, these neurons are not sion so that it can be transmitted on about one that stretch, fold, and grow. This is our inspi- Progress in microrobotics is ongoing, and we arranged and interconnected in either a reg- million optic nerve fibers. It is not unreasona- ration. anticipate that there will soon be sub-millime- ular or a random pattern; there are complex ble to suppose that an artificial eye, with sim- Artificial morphogenesis applies the principles ter-scale autonomous robots with the capabil- organizations both within individual brain re- ilar visual acuity and information processing of embryological morphogenesis to coordi- ities required for artificial morphogenesis. An- gions and among the regions. All this within a capacity to ours, will have similar complexity. nating very large numbers of simple agents to other attractive option is to use the techniques volume of 1100 to 1300 cm3, and consuming Such robotic devices will have important assemble complex hierarchical structures.5 It of synthetic biology to modify microorganisms

16 17 nature. Thus we are using a natural process a pacemaker in the tail bud produces a pulse both for a purpose that it served in nature of a third morphogen, which is propagated (spinal segmentation) and also for a purpose through the tissue toward the head. As it pass- it does not serve in nature (leg segmentation). es through a region of relatively low concen- The number and lengths of the segments are trations of the first two morphogens, it leads parameters that we can control in each case. to differentiation of a new spinal segment. The In brief, morphogenesis proceeds as follows. length of the segments is determined by the Agents are recruited to assemble between the ratio of the growth rate and the pacemaker fre- spine and the tail bud, which is moved right- quency; the number of segments is controlled ward. Both the tail bud and completed spinal by the product of pacemaker frequency and segments produce morphogens which diffuse the growth time. This same process is used to into the undifferentiated spinal region. Peri- grow segmented legs on the spinal segments. odically (and this is the temporal patterning),

Fig. 2. Artistic depiction of microrobots. To the left, a single microrobot attached to a surface. To the right, a swarm of microrobots assembling into a layer of an artificial tissue.

to implement the required agents. Genetic Our first example (Fig. 3) shows how an in- regulatory circuits are essentially analog con- definite but very large number of agents can trol mechanisms, and they can be modified be coordinated to lay down neural fiber bun- to implement the behavior required of a mor- dles between selected regions of an artificial phogenetic agent. Another advantage of bio- brain.8 In this morphogenetic algorithm the logical agents is that they can reproduce, thus bundles are grown one at a time. A massive eliminating the need to manufacture artificial swarm of agents (equal in number to the num- agents in large numbers. ber of nerve fibers in the bundle) is injected at Agents move in coordinated masses and dif- the origin region, and they follow the gradient ferentiate under the influence of signaling sub- of a morphogen diffusing from the destination stances that diffuse in the environment. Since region, depositing fiber material as they go. our goal is to have very large numbers of very Once a bundle has been created, its material small agents moving en masse, we describe absorbs the attractant, and this causes agents morphogenetic processes by partial differen- to steer around already created bundles, Fig. 3. To the left, simulation of swarms of 5000 agents depositing neural fiber bundles between randomly chosen origins and desti- tial equations (PDEs), which treats the agent avoiding collisions. Moreover we can allow nations. To the right, simulation of massive swarm of agents creating paths around obstacles from lower right to upper left. mass as a continuous fluid or tissue. Embry- fiber bundles to split to go around obstacles ologists often use PDEs for the same reason, when that is required. and we can use their equations in artificial Our second example (Fig. 4) shows how nat- morphogenesis. Mathematically, we treat our ural morphogenetic processes —in this case agents as infinitesimal particles moving under spinal segmentation — can be used for both Fig. 4. Simulation of assem- the influence of forces and morphogen con- similar and different applications in artificial bly of insect-like robot body frame using clock-and-wave- centrations. This approach helps to ensure that morphogenesis, in this case, assembling an front process. Head end to our algorithms scale up to very large num- insect-like robot body frame.9 The example ex- left, tail end to right. Red co- bers of very small agents, but also keeps them ploits the idea that in morphogenesis, patterns lor denotes wave of segmen- largely scale-invariant, that is, independent of in time can create patterns in space. In this case tation morphogen propagating to left, which has just the exact size of the agents relative to the mac- we use the clock-and-wavefront model of spi- passed through and diffe- roscopic object being constructed. nal segmentation, which was first proposed in rentiated the right-most tan 1976 but finally confirmed in 2008.10 We use segment. Similar processes this process to assemble the spine of a robot, are simultaneously assem- Examples bling and differentiating leg Since the required microscopic agents are not which is similar to its function in vertebrate segments. yet available, we test our morphogenetic algo- development, but we also use it to assemble rithms through simulation.7 segmented legs, which develop differently in

18 19 Conclusions communication,” Nano Communication Networks 1, Morphogenetic processes in nature can be im- 2010, 199-208, and B. J. MacLennan, “The morphoge- Exploring chaos with analog computers itated and adapted to control massive swarms netic path to programmable matter,” Proceedings of Bernd Ulmann1 of microscopic agents to assemble complex, the IEEE 103, 2015, 1226-1232. 6 On morphogenetic engineering, see for example hierarchically structured systems. Describing R. Doursat, H. Sayama, O. Michel, “A review of mor- these processes by partial differential equa- This article shows how chaotic systems and their behaviour can be explored using analog phogenetic engineering,” Natural Computing 12, computers instead of the now prevalent digital approach. tions describing masses of infinitesimal parti- 2013, 517-535, and H. Oh, A. R. Shirazi, C. Sun, Y. cles helps to ensure that they scale up to very Jin, “Bio-inspired self-organising multi-robot pattern large numbers of microscopic agents, which formation: A review,” Robotics and Autonomous Sys- Many natural systems, even very simple ones computers but exploring this parallelism and is what will be required for the self-assembly tems 91, 2017, 83-100. such as a damped pendulum with an exter- achieving a high degree of parallelism is typi- of very complex structures, organized from the 7 B. J. MacLennan, A. C. McBride, “Swarm intelligence nal driving force exhibit chaotic behaviour. cally at least difficult and most problems won’t microscale up to the macroscale. In this way, for morphogenetic engineering,” in A. Schumann (ed.), One of the main characteristics of such sys- scale well with this respect.) we may hope to produce artifacts of a similar Swarm Intelligence: From Social Bacteria to Human tems is their extreme sensitivity to changes in In contrast to this, an analog computer has no Beings, Boca Raton, Taylor & Francis / CRC, 2020, sophistication to those in nature. initial conditions, something often called the fixed internal structure, it even has no memory 9-54. 8 “Butterfly Effect.” Although these systems are at all and is not programmed by a sequence B. J. MacLennan, “A morphogenetic program for path formation by continuous flocking,” International Jour- fully deterministic and thus can be described of instruction to be executed. At its heart an 1 Associate Professor Emeritus, Department of Elec- nal of Unconventional Computing 14, 2019, 91-119. mathematically in closed form, which implies analog computer consists of a number of com- trical Engineering & Computer Science, University of 9 B. J. MacLennan, “Coordinating swarms of micro- that their future behaviour is completely deter- puting elements, each of which implements a Tennessee. scopic agents to assemble complex structures,” in Y. mined by their past and thus their initial con- basic operation such as summation, integra- 2 R. P. Feynman, “There’s plenty of room at the bottom,” Tan (ed.), Swarm Intelligence, Vol. 1: Principles, Cur- ditions, they are nonetheless not predictable. tion, multiplication, etc. Values are typically Engineering and Science 23, 1960, 22-36. https://re- rent Algorithms and Methods, PBCE 119, Institution The term “chaos” was characterised by Edward represented in a (basically) continuous form as solver.caltech.edu/CaltechES:23.5.1960Bottom of Engineering and Technology, 2018, Chap. 20, 583- Norton Lorenz, one of the founders of mod- voltages or currents and not as sequences of 3 See, for example, A. Clark, Being There: Putting 612. ern chaos theory, as follows: “Chaos: When bits. (There are, indeed, “digital analog com- 10 Brain, Body, and World Together Again, Cambridge, J. Cooke, E. C. Zeeman, “A clock and wavefront the present determines the future, but the puters,” so-called “Digital Differential Analy- model for control of the number of repeated struc- MIT Press, 1997, and G. Lakoff, M. Johnson, Philos- approximate present does not approximately sers,” DDAs for short, but these are outside the ophy in the Flesh: The Embodied Mind and its Chal- tures during animal morphogenesis,” Journal of The- determine the future.”2 Interestingly, Lorenz scope of this article.) Programming an analog lenge to Western Thought, New York, Basic Books, oretical Biology 58, 1976, 455-476. M.-L. Dequéant, 1999. O. Pourquié, “Segmental patterning of the vertebrate did his groundbreaking work on a tiny digi- computer means to devise a scheme by which 3 4 B. J. MacLennan, “The U-machine: A model of gener- embryonic axis,” Nature Reviews Genetics 9, 2008, tal computer, a Royal McBee LGP-30 which the various computing elements are intercon- alized computation,” International Journal of Uncon- 370-382. is only marginally suited for exploring chaotic nected in order to form a “model,” an “ana- ventional Computing 6, 2010, 265-283. systems at best. logue” for the problem to be solved. 5 On artificial morphogenesis, see for example B. J. To introduce the idea of an analog computer, a Although analog computers have been largely MacLennan, “Morphogenesis as a model for nano short recapitulation of the basic operation of a forgotten for the last decades due to the low stored-program digital computer might help: A price and ubiquity of stored program digital modern digital computer (typically) has a fixed computers, they have some advantages over internal structure, i.e. there are one or more their digital rivals, most notably they are ex- arithmetic logic units (ALU), there is a central tremely energy efficient (in most modern memory system (nowadays supplemented by applications for analog computers this high a hierarchy of cache memory subsystems to degree of energy efficiency will be the main speed things up), and there is a central con- driver for their application), they interface well trol unit in addition to a number of input/ to our analog world, and they are inherent- output channels, etc. All of this is controlled ly interactive. This interactivity is one of the by means of a stream of instructions, an “al- key advantages when it comes to the study of gorithm,” stored in memory. At every moment dynamic systems in general and chaotic sys- such a machine executes one or more instruc- tems in special, where a researcher can easily tions from memory and may decide which change some parameters and “see” the effect instruction to read and process in the next in realtime on some output device such as an step based on the result of prior instructions oscilloscope.4 executed. So the execution of a program on Figure 1 shows a modern analog computer, such a digital computer is basically strictly se- an Analog Paradigm Model-1 in its basic con- quential. (There are, of course, parallel digital figuration. The top chassis contains (among

20 21 power supplies) four comparators which can Figure 2 shows part of a typical analog com- be used to model discontinuities, eight manual puter setup. What looks like an intricate maze precision potentiometers which can be used of wires is the actual program (at least part of it to set coefficients and initial conditions for a as the overall program spans many more com- simulation, and a manual control unit which puting elements) which directly resembles the allows the machine to operate either in a man- mathematical problem being solved. This is in ual mode where its operation is controlled by contrast to a stored-program digital computer Fig. 2. Typical analog comput- a human operator, or in repetitive-mode where where the underlying mathematical problem er setup (partial) – shown are one simulation run is repeated over and over has to be translated into a suitable algorithm some computing elements such again at (typically) high speed in order to get a yielding the desired solution. This additional as quad-integrators (on the flicker free picture on an oscilloscope screen. and often rather error prone and convoluted right side), manual potentiometers (upper middle), multipliers The lower chassis contains eight multipliers, step can be skipped altogether with an analog (left) eight summers, and four integrators. (This is computer, the mathematical formulation of a part of the real “magic” of an analog computer problem is basically sufficient to program an – integration is one of its basic functions!) analog computer (sans scaling, which is out of scope here as well). One of the simplest systems exhibiting chaotic behaviour is a damped pendulum such as a swing being exhibited to an external driving force that might be of a harmonic nature in the most general case. The behaviour of this the behaviour of the system, as shown in the The three equations involved are parameter- oscillatory system can then be rep- following figure. The chaotic nature of the pen- ised by three coefficients. The original param- resented by a “phase space plot,” dulum’s movement can be easily seen. eter set yields the attractor shown in figure 4. i.e. a graphical description of the A figure like in figure 3 is called an “attractor”, time-dependent variation of two which is basically a subset of a phase space, or more variables involved in the i.e. a set of values a dynamic system will final- problem. In the case of a pendu- ly evolve to. lum, its angle, the angular veloc- Performing a simulation like this on an ana- ity, and the angular acceleration log computer has the advantage that chang- could be of interest. Typically, the es in parameters such as the damping or the angular velocity and acceleration excitation frequency, etc., can be performed are used as x- and y-coordinates manually by setting potentiometers during run for the phase-space plot describing time. This allows one to gain a real “feel” of Fig. 1. Small scale analog computer. the behaviour of complex systems as parameter changes take immediate effect and can be Mathematically, dynamic systems can be de- directly observed on an oscilloscope. scribed by so-called differential equations The next example is the already mentioned (DEQ for short), i.e. equations in which the un- original chaotic system first described by Lo- known is not a value (this would be typically renz, a result of early research in atmospheric quite simple to solve) but instead a time-vary- sciences. He discovered the chaotic nature of ing function. Such DEQs are the tool of choice this problem through simulations on a digital when it comes to modelling natural systems computer, which was slow and tedious back and are notoriously hard to solve, in fact most then. (It is not clear as of now why he did not differential equations have no analytical solu- use an analog computer for his research as tion, i.e. there is no closed mathematical ex- the advantages would have been even more Fig. 4. Typical display of the Lorenz attractor. pression describing the solution to such an profound in his days than they are now.) The equation. Thus the only viable way to gain an system treated by Lorenz is described by three understanding of the underlying system is by coupled differential equations and represents a means of simulation, be it digital or analog. simplified model for atmospheric convection. Fig. 3. Phase space plot of a damped pendulum exhibited to an external force. 22 23 This so-called “Lorenz attractor” is a special 1 Professor for business informatics at the “Hoch- form of an attractor as it is a “strange attractor,” schule für Oekonomie und Management” in Frank- Are There Traces of Megacomputing in Our Universe i.e. it exhibits a fractal structure. The state of furt/Main, Germany, and a guest professor and lec- 1 turer at the Institute of Medical Systems Biology at Olga Kosheleva and Vladik Kreinovich the system at every point in time can be char- Ulm University, [email protected]. A acterised by its corresponding point on this number of application notes, including the chaot- (rather beautiful) graph. The interesting thing is ic systems described here can be found at http:// The recent successes of quantum computing encouraged many researchers to search for that even tiniest deviations in the initial condi- analogparadigm.com/documentation.html, and the other unconventional physical phenomena that could potentially speed up computations. tions will lead the system to points far apart on author is happy to answer your questions on analog computing. Several promising schemes have been proposed that will – hopefully – lead to faster com- the attractor, so it is not possible to predict the 2 C. M. Danforth, “Chaos in an Atmosphere Hang- putations in the future. Some of these schemes – similarly to quantum computing – involve future behaviour of the system. On the other ing on a Wall,” on line: http://mpe.dimacs.rutgers. using events from the micro-world while others involve using large-scale phenomena. If hand, the system cannot “leave” its attractor edu/2013/03/17/chaos-in-an-atmosphere-hanging- (at least not for its parameters and initial values on-a-wall/ some civilization used micro-world for computations, this will be difficult for us to notice, 3 within suitable intervals), so the attractor faith- E. N. Lorenz, “Deterministic Nonperiodic Flow,” but if they use mega-scale effects, maybe we can notice these phenomena? In this paper, Journal of the the Atmospheric Sciences 20, 1963, we analyze what possible traces such megacomputing can leave – and come up with rather fully describes the system behaviour without 130-141. the chance of actually predicting it from mea- 4 For more background information and the history surprising conclusions. surements or the like. of analog computers, see B. Ulmann, Analog Com- puting, München, De Gruyter Oldenbourg, 2013. All in all, electronic analog computers are ideal Modern computers are fast. By performing bil- that. Many of such problems are related to or- tools to explore the behaviour of chaotic (and lions of computational steps, we can reason- ganic chemistry and biochemistry. So it is not other dynamic) systems and modern develop- ably well predict tomorrow’s weather – and surprising that, e.g. in our university, the main ments in this field will lead to highly integrat- when the prediction is not perfect, the problem users of high-performance computers are not ed analog computers, which will form hybrid is usually not with the computers, but with the – as one may think – computer scientists, but computers when combined with classic digital fact that we do not have enough weather-re- folks from the Department of Chemistry and computers thus bringing the advantages of ana- lated sensors in many geographic areas. On- Biochemistry. log computing to a rather wide audience. board computers allow missiles to fly close to How can we make computers faster? Journal- the ground at astronomical speeds without hit- ists writing about science often express an op- ting the ground. A recent quarantine enables timistic belief that human ingenuity will solve billions of people to be connected by reason- all the problems. We are optimistic too, but ably reliable video-connection, helping many with computers, we cannot be to optimistic: people continue to work, to study, and even to we are currently reaching the bounds set by enjoy (remotely) their favorite operas. fundamental physics. This bound is very sim- But for many practical applications, comput- ple to explain. According to modern physics, ers are still too slow. For example, a large part nothing can travel faster that the speed of light of the US is threatened by destructive torna- – i.e. faster than 300 000 km/sec, or 300 000 000 does, and we still do not have a reliable means m/sec. How does this affect computations? A to predict where a tornado will be moving. As usual laptop of which we are typing this ar- a result, in tornado-prone areas, alarms sound ticle is about 30 cm in diameter, i.e. 0.3 m. This so often – and usually, with no actual tornado means that for a signal to go from one side of the coming – that when the actual deadly tornado computer to another, we need 0.3/300 000 000 comes, people do not react to the warning, do sec, i.e. 0.000 000 001 seconds. This may sound not evacuate – and the consequences may be like a very small time, but even on the cheap- disastrous. Here, we know the equations that est 4 GigaHerz computer, the processor can would describe the tornado’s dynamics – they perform 4 operations while a signal is still trav- are largely the same equations that allow us to elling. predict tomorrow’s weather. Experiments have To make computers faster, we need to shrink shown that by spending the same computation their processing elements even more – this time (several hours) on a supercomputer, we is why we enter the realm of quantum com- can predict where a tornado will go in the next puting.2 But there is a limit to this shrinkage. 15 minutes – but that is too late. This is just one Already, a processing element may consist of example, there are many other problems like a few thousand atoms. We can theoretically

24 25 shrink more, to the level of a single atom – but hour for us – and this is exactly what we want. By observing a humongous black hole that 1 Olga Kosheleva and Vladik Kreinovich, University then what? Then we are stuck. In other words, instead of speeding up comput- our previous astrophysical theories did not ex- of Texas at El Paso, El Paso, TX 79968, USA, olgak@ So what can we do? In this long-term prospec- ers, we can slow down ourselves, our whole plain. utep.edu, [email protected] 2 See for instance M. A. Nielsen & I. L. Chuang, tive, quantum physics does not seem to help, so civilization. How can we do it? As we men- Sounds familiar? It should. According to mod- Quantum Computation and Quantum Information, let us look at other possible physical phenom- tioned, there are two ways to do it: we can start ern astrophysics, there is indeed a very mas- Cambridge, Cambridge University Press, 2000. ena. It would help if we could find a way to travelling with a speed close to the speed of sive black hole in the center of our Galaxy 3 See for instance R. Feynman, R. Leighton, and M. speed up all the processes – that will speed up light, and/or we can place ourselves in a strong – and in the centers of many other galaxies. Sands, The Feynman Lectures on Physics, Boston, computations as well. Unfortunately, in mod- gravitational field. Let us consider these two op- So maybe these black holes are also traces of Addison Wesley, 2005, and K. S. Thorne & R. D. landford 5 B , Modern Classical Physics: Optics, Fluids, ern physics, there is no known way to speed up tions one by one, starting with fast travel. megacomputing civilizations? Plasmas, Elasticity, Relativity, and Statistical Physics, all the processes – there are only ways to slow We cannot immediately go from 0 to 300 000 Who knows? Princeton, Princeton University Press, 2017. them down. km/sec: we can only survive the acceleration 4 See ibidem. 5 According to Einstein’s Special Relativity Theo- similar to the Earth’s gravitational acceleration This work was supported in part by the US Nation- Readers interested in technical details can look ry, 3 processes slow down when we travel with a of 9.81 m/sec2. So we need to start going slow- al Science Foundation grants 1623190 (A Model into O. Kosheleva & V. Kreinovich, “Relativistic effects can be used to achieve a universal square-root speed close to the speed of light. Actually, they ly. We cannot travel on the same orbit around of Change for Preparing a New Generation for Professional Practice in Computer Science) and (or even faster) computation speedup,” in A. Blass, P. also slow down when we fly on a plane, but the Sun – if we start travelling with too high a HRD-1242122 (Cyber-ShARE Center of Excel- Cegielsky, N. Dershowitz, M. Droste, and B. Finkbein- that slow-down is so miniscule that often su- speed, centrifugal forces will squeeze us, so lence). er (eds.), Fields of Logic and Computation III, Spring- per-precise clocks can detect it, while for the we need to go further and further away from er, to appear. particles in a particle accelerator (that move the Sun. We cannot simply travel away on a practically at speed of light), the time slows straight line – this way, we will reach a high down so much that their average decay time speed, but by that time, we will be so far away increases by orders of magnitude. from the left-behind computers that communi- According to General Relativity Theory,4 pro- cation time will eat up all the advantages. So cesses also slow down when we are in a strong the only way to reach the desired effect is to gravitational field – e.g. near a massive black make circles which are becoming wider and hole. Yes, they also slow done when a usual wider – in other words, to follow a spiral tra- gravitational field becomes a little stronger, but jectory. this change is also minuscule. This acceleration requires a lot of energy. Is the situation hopeless? Good news is that, Where can we get this energy? We have to by the very name of relativity theory, many get it as we travel, from the interplanetary and things are relative. There is no absolute time then interstellar particles and gases – and other with respect to which we want computers to objects. As we follow this spiral trajectory, we be faster, all we want is that the computers be will burn whatever we can, leaving practically faster with respect to our time. In other words, nothing. So what will remain? What will re- what we want is to make sure that computers main is empty spaces forming a spiral. Sounds are in one environment, and we are in another familiar? It should: this is exactly how our own environment, and all the processes in the com- Galaxy and many other galaxies look like. puter-containing environment should be much So maybe the spiral shape of our Galaxy is in- faster than all the processes in our environment. deed the trace of an ancient megacomputing We cannot achieve this by staying on Earth civilization? But wait, there is more. and placing computers somewhere else – the As we have mentioned, another way to speed only thing we would then achieve is that, in up is to place oneself in a strong gravitational comparison to our time, computers will be field – e.g. near a massive black hole. At first, even slower than they are now. But what we we can use existing black holes, but what if we can do is leave computers where they are – want to perform even faster computations? The and place ourselves in situations where time only way to do that is to make the black hole will go slower. If we manage to slow down bigger and bigger – thus increasing its gravita- our own time by a factor of ten, then the same tional field and slowing us down even more. An example of a spiral galaxy, the Pinwheel Galaxy problem that requires five hours of compu- So how will be known that a supercivilization (also known as Messier 101 or NGC 5457). tation in computer-time will feel like half an used this idea to perform megacomputations?

26 27 contexts (according to pragmatic rules) and Music is the only form of natural communi- Communication, information and music used to transport biologically relevant infor- cation, that is created and perceived only by Dawid Przyczyna,1 Marcin Strzelecki,2 Konrad Szaciłowski3 mation. Almost all kingdoms of life use mol- humans (however studies on animals indicate ecules as the only available communication some aspects of sensitivity to music). Music tool, whereas animals add vocal and visual belongs to human universals, i.e. elements, In this brief article, we would like to take the reader on a journey through the fields of communication tools to their repertoire of patterns, features, or notions that are common information, communication and music, as well as the places where these domains inter- available signs. to all human cultures worldwide, however, ac- sect. As it turns out, contemporary and seemingly abstract concepts related to information cording to some opinions, it does not convey processing can be conveyed in an accessible form through music. To spice things up, the In humans, these evolutionary novelties dom- any biologically-relevant information. Accord- thoughts in this article are supplemented with pictures of postage stamps, which include inate, almost completely, over the molecular ing to the mathematician and musicologist all of the above-mentioned concepts. language, however “molecular senses” of olfac- Guerino Mazzola “music embodies meaning- tion and gustation are still significantly impor- ful communication and mediates physically tant. Most of animals use senses of vision and between its emotional and symbolic layers.”4 hearing for most of their communication pur- The importance of music is exemplified by the poses. Whereas our own (human) senses seem discovery of Paleolithic musical instruments. to be impaired (as compared with some pred- Whereas most probably music at early times atory birds), their ability to process signals is had no direct effect on the economy or a re- still amazing. We have also developed unique productive success, it may have had provided ways of communication: music and language, medium of social integration (Fig. 1). As of to- Fig. 1. Paleolithic musical instruments: upper manifested sonically as speech, and graphically day, the influence of muzak on our decisions Paleolithic from Geissenklösterle (a), middle as writing. These tools provide an unprecedent- in supermarkets and retail centres proves its Paleolithic flute, ca. 35000-40000 years, (b) and neandertalic flute from Divje Babe Cave (Slove- ed opportunity to communicate language and impact on real profits from these businesses. nia, 55000 years ago, c). emotions using graphical symbols and aesthet- Nowadays music is one of the most ubiquitous Photos courtesy José-Manuel Benito (a), Marco ic, religious and cultural feelings via organized human activity, independently on any social Ciamella (b) and Jean-Pierre Dalbéra (c). sounds of different parameters like pitch, dura- and cultural attributes or intellectual abilities. tions, and timbral qualities, arranged in melodic, rhythmic, and harmonic (tonal) patterns.

Communication between organisms is an between individual organisms. In most cases ubiquitous phenomenon, both at intraspecies the intracellular and intraorganismic commu- and interspecies level in all kingdoms: Ar- nication is based on signalling molecules, the chaea, Bacteria, Protista, Fungi, Plantae and same concerns most of the interorganismic Fig. 3. Important political changes depicted on postage Animalia. Surprisingly, primitive communica- and interspecies communication protocols. stamps : socialistic revolution in Bavaria (1918), Upper tion was detected even between individual Communication in general can be described Fig. 2. Prominent musical personalities : Sayed Silesia plebiscite (1921), Jordanian annexation of the West Bank (1948), the fall of the Nazi Germany (1945), forma- virions. All these organisms possess both in- as a sign-mediated interaction between at Darwish, Jim Morrison and Frederic Chopin portrayed on postage stamps of United Arab tion of the Soviet Occupation Zone (1948), and the inde- tracellular, intraorganismic and transorganis- least two living entities, which share the com- Republic, Germany and Soviet Union. pendence of Ukraine (1991). mic communication protocols, however the mon repertoire of signs representing a form of most complex and interesting ones, from the natural language. These signs may be com- point of view of information theory, are those bined according to syntactic rules in various

28 29 The importance of music in modern society is unquestionable – composers, performers and musical instruments are leading motifs of numerous postage stamps (Fig. 2), along with monarchs, dictators, religion, nature and sport. Interestingly, in the past postage stamps (first introduced in 1840 by the United Kingdom) were considered as a very effective medium of communication. Therefore, each political or territorial change was (and still is) immediately Fig. 7. Circulation of goods and information as a decorative reflected in postage stamps (Fig. 3). Year 1985 motif of postage stamps of Germany and Greece. was announced European Year of Music (this fact was commemorated by a numerous series of stamps issued by European countries), and sciences, machine learning and artificial neu- 2019 was announced the Smithsonian Year of ral networks significantly influences musical Music. creativity.11 Unconventional computing is a natural consequence of research towards new Fig. 5. Tjlempung, totobuang, gangsa and ka- computational paradigms and application of lintang: traditional musical instruments used new materials and systems as computation- in gamelan music. Fig. 6. Sultan’s tughra on old Saudi (1934) 12 and Ottoman (1898) postage stamps. al platforms. Therefore, some time ago, the composer Eduardo Miranda has initiated the organized while at the same time lacking of multidisciplinary research and creative activ- audible regularities. Finally, there also exist specific genres. The simplest musical message, ity in the field at the border of music and un- genres, avant-garde, experimental music, and melody, can be defined as an appropriate time conventional computing.13 Among the newest anti-music movements, which aim at breaking sequence of quantized frequencies, usually computational paradigms, reservoir comput- traditional regularities. Such exceptions and noted as a musical score (Fig. 4). ing is one of the latest discoveries. declared negation of musical syntax also con- firms the existence of one. Music is a domain These frequencies, called steps, are strictly Reservoir computing is a computational par- of human artistic and entertaining activity, but defined by tuning systems. Most of musical adigm that explores the internal dynamics of also a field of vigorous studies. Information systems are founded on a concept of the oc- physical systems for information processing. In alike, music is a very difficult notion to define tave: an interval between frequencies of f and principle, any physical system with internal dy- in precise terms; dislike speech, it is not meant 2f. Octave is an interval between the first and namics can serve as a foundation for reservoir for direct communication purposes, especial- second harmonics of the harmonic series. computing.14 Dynamics at the edge of chaos ly of biological importance.5 Conversely, it is Therefore, octave is considered as a natural renders a perfect medium for computation as meant to trigger various emotional responses Fig. 4. Examples of musical scores: Die Meis- phenomenon that has been referred to as the it is the most sensitive for any perturbation of tersinger von Nürnberg (R. Wagner) and 2nd in recipients due to aesthetical feelings. On “basic miracle of music”, the use of which is external signals (input data). Graphical rep- Brandenburg Concerto (J.S. Bach) as depict- the other hand, music is a very well-organized “common in most musical systems.”7 There ex- resentation of such dynamic behaviour usually ed on German postage stamps. structure. Even the denial of the existence of ist many different tuning systems,8 and octave resembles tughra, a calligraphic signature of a such structure, conceptually declared by the divisions (like Balinese and Javanese gamelan sultan, frequently found on postage stamps of Music and language are created and processed author, proves the existence of specific “musi- systems, Fig. 5). Other musical systems, both Ottoman Empire and Saudi Arabia (Fig. 6). in distinctly different neural structures but cal language” with appropriate grammar, syn- traditional (e.g. the Middle East, India and Far have some common features: they are specific tax and vocabulary – the harmony, rhythmical East), as well as modern experimental musical Reservoirs must be also equipped with input forms of communication, they have specific patterns, timbres and their mutual relations. genres, use different intervals, including divi- and output ports. Any physical stimulus alter- syntax and vocabulary – i.e. they have a set Therefore, not every combination of sounds sion of octave into 4, 5, 7, 34 (to name only a ing the internal dynamics can be considered of elements (words or notes) and a set of rules should be considered as music. This indicates few possibilities), or even 96 equal steps, lead- as a carrier of information. The output in turn (grammar or harmony and counterpoint) that that music (like hardcore pornography) may ing to the whole musical tuning continuum.9 monitors the internal state of a part of the res- govern the appropriate combination of these be considered as a kind of an emotional com- ervoir and is the only trainable (in the sense elements. Some kinds of music, like Europe- munication of the « I know it when I see it » These very strict structural rules and mathemat- of machine learning) element of the whole an tonal music, have strict syntax, some oth- type.6 Despite that, specific fractal signatures ical relations are naturally embedded in musi- device. Whereas the construction of a reser- ers (like dodecaphonic music) may be strictly derived from compositions can be assigned to cal structures.10 Current progress in computer voir computer following the description given

30 31 This example illustrates the close relationship 21st Century,” Computer Music Journal 31, 2007, of contemporary music with unconventional 15-32; E. Blackwood, The Structure of Recognizable computing, especially with the novel compu- Diatonic Tunings, Princeton, Princeton University tational paradigms. It also shows how areas Press, 1985. 10 seemingly unrelated to art can become an in- G. Loy, Musimatics, Cambridge, MIT Press, 2006; L. M. Zbikowski, Foundations of musical grammar, spiration for it and can be better understood Oxford, Oxford University Press, 2017. thanks to it. 11 G. Nierhaus, Algorithmic composition. Paragidms of automated music generation, Wien, Springer, 2009; R. T. Dean, A. McLean, The Oxford Handbook 1 PhD student (physics), guitarist, darbuka player, of Algorithmic Music, Oxford, Oxford University AGH University of Science and Technology, Kraków, Press, 2018. Poland. 12 A. Adamatzky (ed.), Advances in Unconventional 2 Music theorist and composer, instrumentalist, Computing Theory, Springer International Publish- Academy of Music in Kraków, Poland. ing, 2017; A. Adamatzky (ed.), Advances in Uncon- 3 Professor of chemistry, philatelist, AGH University ventional Computing. Prototypes, Models and Algo- of Science and Technology, Kraków, Poland. rithms, Springer International Publishing, 2017; A. 4 G. Mazzola, M. Mannone, Y. Pang, M. O’Brien, N. Adamatzky, S. G. Akl, G. C. Sirakoulis, From Parallel Torunski, All about music. The complete Ontology: to Emergent Computing, Boca Raton, CRC Press, Realities, Semiotics, Communication and Embodi- 2019. ment, Cham, Springer Nature, 2016. 13 E. R. Miranda (ed.), Guide to unconventional com- 5 J. G. Roederer, The physics and psychophysics of puting for music, Cham, Springer Nature, 2017. music, New York, Springer Science+Business, 2008. 14 V. Athanasiou, Z. Konkoli, “On mathematics of 6 P. Gewirtz, “On ‘I Know It When I See It’,” Yale Law universal computation with generic dynamical sys- Fig. 8. Spectrograms calculated from the audio path of the Resevoir Study No. 1 world premiere recording. Journal 105, 1996 1023-1047; “Jacobellis vs State tems,” in A. Adamatzky, S.G. Akl, G.C. Sirakoulis of Ohio,” United States Supreme Court 378, 1964, (eds.), From Parallel to emergent computing, CRC 184, available at https://openjurist.org/378/us/184. Press, London, 2019. above may pose significant difficulties, a sim- The Reservoir Study opens with a short im- 7 P. Cooper, Perspectives in Music Theory: An His- 15 D. Przyczyna, P. Zawal, T. Mazur, M. Strzelecki, plified scheme based on a single nonlinear provisation of keyboard (Fig. 8a), that can be torical-Analytical Approach, New York, Dodd, Mead P.L. Gentili, K. Szaciłowski, “In-materio neuromimet- node equipped with a delayed feedback loop understood as an input for computation. These and Co., 1973. ic devices: dynamics, information processing and may be equally efficient from computational improvisations are followed by a slowly evolv- 8 R. Chuckrow, Historical Tuning: Theory and Prac- pattern recognition,” Japanese Journal of Applied point of view, however much easier to build ing tune, each bar is repeated four times and tice, Briarcliff Manor, Rising Mist Publications, 2006. Physics 59(5), 2020, 050504. and operate. In such systems, the input signal subsequently bars introduce subtle harmonic 9 A. Milne, W. Sethares, J. Plamondon, “Dynamic To- (stream of data) circulates in a feedback loop and timbral changes, as a very suggestive illus- nality: Extending the framework of tonality into the and undergoes gradual changes (Fig. 7). The tration of a revolution of signal in a feedback evolution of this signal serves as the reservoir loop (Fig. 8b). In the middle part, this regular state and is used for the generation of the out- pace is suddenly broken and followed by an- put. This computational scheme has inspired other improvisation loaded with glissandi and us to compose and perform a piece of music irregular rhythmic patterns. Then the reservoir inspired by the concept of reservoir computer. has reached the chaotic state (Fig. 8c)! Musi- cal chaos slowly calms down and the regular The Reservoir Study No. 1 (Marcin Strzelecki, pattern is reborn – the reservoir has reached 2019) scored for two electric guitars, cello, the final state, which is the end of computation piano four hands and electronics is a com- (Fig. 8d). Final chords represent the output lay- position in repetitive minimalism style. It is er generating the result of computation. World based on 555 ms delay feedback loop, which premiere performance of this piece was giv- repeats and transforms music being played by en by The Nano Consort (Konrad Szaciłowski a consort of musicians. These repetitions and – cello, Dawid Przyczyna, Kacper Pilarczyk – transformations result in harmonic and tim- guitars, Marcin Strzelecki – keyboard, Domini- bral fluctuations of particular aesthetic quality. ka Peszko, Piotr Zieliński – piano) in Krakow Numerous repetitions (both in the score and Opera House, September 16th, 2019. Original also added by the feedback) reflect dynamic recording is available as a supplementary ma- changes inside the reservoir computer. terial to our recent paper.15

32 33 Unconventional sensing: doing it unusual way in unusual settings Zoran Konkoli1

The standard way of sensing implies a linear flow of information, from the object we wish to analyse towards the observer. The object of interest will be referred to as “the environment.” The environment can be many things, a temperature in a room or the amount of cracks in the material. The usual sensor is like a factory line where the flow of information is well understood and every step is carefully engineered. Normally, a sensing instance is a one-time event. It can be, and often is, repeated, leaving the impression of continuity. We know exactly how every part of the sensor is supposed to behave. But it is a one-time event Fig. 1. The traditional sensing setup. The flow of information is linear. nevertheless and the execution of every sensing event is always nearly the same. But there are other ways of doing sensing, and over the course of the last few years we have explored paramount importance, the SWEET sensing reservoir)5 is an environment sensitive dynam- a novel, somewhat unconventional way of sensing, to be referred to as the SWEET sensing setup.2 The SWEET sensing setup is an algo- ical system. It is affected by the environment, approach. SWEET is more a template than it is an approach. The SWEET is an algorithmic rithmic template. The most important compo- but the details of the proxy interacts with the template for building intelligent sensing substrates. The user is supposed to engineer differ- nents are depicted in the figure below.Though environment are not important from an engi- ent instances of it depending on the situation. The typical SWEET sensing process is very the SWEET sensing setup has been developed neering point of view. It might appear that this flexible, and is essentially a dynamic process, where the single time instance is irrelevant, with a particular application in mind, the anal- interaction is a one-way information channel but rather the behaviour over an extended time interval is of paramount importance. It is ysis of time series data, it is very likely that the where the information propagates from the a sort of indirect sensing which happens through a proxy. There is an ongoing dialogue setup could be used to solve problems featur- environment into the proxy. To some extent between the observer and the proxy, in which the observer accumulates small clues proxy ing in other disciplines, but more on that later. this is true, as the proxy is not supposed to in- provides about the system of interest. In turns, the proxy also accumulates information The details will of course differ depending on fluence the environment. However, the proxy 3 through a dialogue. This article summarizes how such an unconventional sensing setup the implementation context. Our own work updates its state recurrently, where the state of covered some problems related to ionic sens- the proxy at a particular time instance depends can be realized and what its essential ingredients are. The main objective is to present the ing with ion sensitive electronic components, on its previous state and the information it has material in a pedagogical way so that colleagues from other disciplines can understand the such as an organic transistor and a memristor. received from the environment. method and use it to solve their problems. The SWEET sensing process is very flexible, Through the dialogue with an environment and is essentially a dynamic process, where (cf. fig. 2, dialogue 1) the proxy is pushed to- the single time instance is irrelevant, but rather wards a certain state, and the state of the proxy The standard way of sensing implies a linear gather information obtained from the sensor, the behaviour over an extended time interval encodes all previous instances of environ- flow of information, from the object we wish and further process it. The typical time to ex- is of paramount importance. It is a sort of in- ment-proxy interaction. Perhaps, one could to analyse, the environment, towards the ob- ecute the sensing event is much smaller than direct sensing which happens through proxy think of it as a one-way dialogue, in the same server. In sensing applications the “environ- the times that separate these events. Sensing and it happens in a dialogue form. A similar way as a psychotherapist gets to know his pa- ment” can be many things, a temperature in instances can occur at an equally spaced in- indirect sensing idea has been suggested in tient. Through this dialogue, the proxy accu- the room, the amount of cracks in the mate- tervals, or when triggered by a control mech- 20064 but, surprisingly, has not been pursued mulates small clues about the environment of rial, or the amount of rare molecules in a unit anism. Regardless of the engineering details, rigorously. The authors have shown that by interest, which a traditional setup might simply volume of solvent. The usual sensor works ac- we are talking about a one-time event since monitoring the changes in the structure of the miss. Again, it is important to realize that this cording to well-understood principles which the execution of the sensing event is always feedback apparatus that controls the robot it would be impossible without a memory of the are carefully engineered. There are no surpris- nearly the same, and we know exactly how is possible to infer about the environment that past, the system used as a proxy would “for- es. The flow of information is linear. Further, every part of the sensor is supposed to behave. the robot resides in. get” every bit of information it has collected. a traditional sensing instance is a one-time In fact failing to do so is considered to be a The SWEET approach is an algorithmic tem- There is a second dialogue going on, the one event. Events like these are often repeated in malfunction. The typical sensing setup is show plate for realizing the indirect sensing idea in between the observer and the proxy (indicated time, which might give an impression of con- in the figure below. However, there are other the context of time-series data analysis where by dialogue 2 in fig. 2). This second dialogue tinuous sensing, even some sort of intelligence ways of doing sensing. the notion of time and remembering history is happens through two mechanisms: (a) the perhaps, but in reality such sensing events Over the course of the last few years we have treated as an opportunity rather than a prob- fixed instructions in the form of a drive signal, are discrete separate events. To gain a time explored a novel, somewhat unconventional lem. The notion of time is extremely important and (b) through a feedback. In many instances, perspective on the observed data, one needs way of sensing where irregularity and tem- as there is an ongoing dialogue between the this feedback can greatly improve the perfor- to engineer an external intelligence that can poral aspects of the sensor’s dynamics are of environment and the proxy. The proxy (sensing mance of a device. The feedback mechanism

34 35 specific question. The way we can interact follow up questions would be needed to with the proxy is critical. For example, if determine this. we can assume that we can observe the - The feedback mechanism: In this par- person, we could try to see if the person ticular instance a useful feedback mech- carries a wet umbrella. A wet umbrella anism would be to ask some provocative would imply that very likely there is a rain questions. For example, if the person is outside. But one cannot be sure. It could happy, we might try to provoke the per- have rained few hours earlier but we can- son into angry response and from that not be certain. Even a dry umbrella might judge the original “degree of happiness” imply a bad weather. For example, it could that the person had before he/she entered be that it is cloudy outside. Clearly, if we the room. Likewise, if the person appears are not allowed to ask a direct question, calm, we could ask provocative questions the dialogue is the best option. Through a to see if there is some discontent lurking dialogue we can acquire information. For behind the surface. All this would indicate example, we can ask the person how she/ that we are likely dealing with the case of he feels like. If the person appears grumpy, the bad weather. then it might have to do with the bad weather, but there could be other reasons. In fact, the sensing solutions we envision re- Fig. 2. The SWEET sensing setup. Dialogue 1: There is an ongoing dialogue between the environment and the proxy. For example the person might have lost a semble a thought experiment discussed above. During this dialogue the proxy accumulates the information about the environment. Dialogue 2: The user interacts The SWEET setup mimics the way of how hu- with the proxy in a simple way to infer what the environment looks like. shoe, and that could be inferred from follow up questions. If the person appears mans communicate experiences and process happy, very likely the weather is nice. exchanged information, rather than how a has the tendency to make the system “sharper” - The proxy: A person comes into the room But, again, we cannot be sure. The per- machine would perform similar tasks. This ar- or simply more “intelligent,” especially if it is and we are allowed to interact with the son could have won the lottery, and more ticle explores the ways of realizing the human provided with a delay in time. This improve- person to figure out what the weather is ment is a well-known fact,6 and is nothing like. This is our only chance to infer about specificity to the SWEET setup. The delay can the weather. be explicitly engineered, but it can be also an - The interaction with the proxy: By as- intrinsic part of a dynamical system since such sumptions, we are not allowed to ask di- systems clearly exhibit some sort of “memory rect questions like “What is the weather behaviour”. The state of a dynamical system like outside?” This constraint is very com- depends on everything that the system expe- mon in practical applications that are close rienced in the past. Furthermore, dynamical to engineering. We cannot interact with systems might have the ability to “propagate” the proxy in any way we please. There are behaviour through the system to different lo- likely going to be constraints imposed on cations, which could bounce around, causing how we can interact with any system. For a natural delay. All very exciting possibilities. example, we cannot easily measure the Perhaps the simplest way of explaining the positions of all atoms in a gas. We could SWEET sensing concept is through the follow- try to measure their average velocity, which ing thought experiment (cf. fig. 3): gives us an idea about the temperature of - The sensing problem (the environment): the gas. Thus to illustrate that aspect of the Imagine that we are sitting in a room with- problem, in our thought experiment we are out windows and that we are interested restricting the way we can interact with our in the weather outside. Thus the object of human proxy. Naturally, the more direct our interest is the weather. However, we questions one can ask the better. However, are not allowed to open the window and the main idea is to “interview” the person Fig. 3. An example of implementing the SWEET sensing setup. peek out to see what the weather is like. about the weather. Ask small questions Likewise, we are not allowed to use the and try to assess what they imply. Here the phone or any other means of communica- emphasis is on the full set of answers we tion with the external world. are getting, not on a particular answer to a

36 37 way of understanding and analysing environ- implementing. One might think of it as a “re- 20(13), 2020, 6782-6791; V. Athanasiou & Z. Kon- 5 Z. Konkoli, “On developing theory of reservoir comment in the engineering context. This is the ligious text” in which the principles are given koli, “On Improving The Computing Capacity of puting for sensing applications: the state weaving en- main point behind the SWEET sensing setup. but the followers are supposed to interpret it Dynamical Systems,” Scientific Reports 10(1), 2020, vironment echo tracker (SWEET) algorithm,” op. cit. 6 Instead of a human one uses a generic dynam- and apply it in everyday life. Because of that, 9191; V. Athanasiou & Z. Konkoli, “Memristor Models L. Appeltant et al., “Information processing using a for Early Detection of Sepsis in ICU Patients,” Com- single dynamical node as complex system,” Nature ical system as a proxy. In pretty much the same our sensing ideas could be of relevance for puting in Cardiology (CinC), 2019; Z. Konkoli et al., Communications 2, 2011, 468/1-6. See Vasseleu’s way as the mental state of mind of a human is other areas of human endeavour, including “Reservoir computing with computational matter,” poignant discussion of “fantasies of disembodied mas- influenced by weather, so is the state of the humanistic sciences. in M. Amos, S. Rasmussen, and S. Stepney (eds.), Com- tery” in C. Vasseleu, “Virtual Bodies/Virtual Worlds,” dynamical system influenced by the environ- Naturally, one might even have to modify the putational Matter, Cham, Springer, 2018; V. Athana- Australian Feminist Studies 19, 1994, 155-169. For a ment. The existence of this interaction is the setup depending on the problem but the core siou & Z. Konkoli, “On using reservoir computing for critical discussion of “contemporary technoscientific minimal requirement for the SWEET setup to idea of a two-fold dialogue will likely survive sensing applications: exploring environment-sensi- corporealizations of the ‘almost human,’” see C. Cas- work. However, the trademark of our sensing if the setup is applied in other areas: tive memristor networks,” International Journal of Par- taneda, L. Suchman, “Robot visions,” Social Studies of setup is that it is extremely flexible. allel, Emergent and Distributed Systems, 2017. Science 44(3), 2014, 315-341. We have investigated numerous options 4 Why should one bother with such unconven- F. Iida & R. Pfeifer, “Sensing through body dynam- ourselves. All the sensing problems we ics,” Robotics and Autonomous Systems 54(8), 2006, tional sensing setups? There are several rea- have investigated hatched from vastly dif- 631-640. sons, ranging from pure engineering/practical ferent application contexts: monitoring towards more profound: ionic solution for rare ions that are hard To begin with, there are many instances in the to detect, monitoring ECG (electrocardio- information processing engineering where the gram) signals using simple hardware, pre- goal is to collect and analyze information in dicting chance for the occurrence of sepsis situ. For example, in the traditional setup, re- for intensive care patients. These might be mote sensors might collect information and considered as standard engineering prob- channel it to a huge data center where this in- lems, very typical for natural sciences. formation is stored and processed. However, We gave a serious thought of applying the disadvantage with such a setup is that one the SWEET sensing setup to tackle a range might need to both store large amounts of data, of completely unrelated problems to the and most importantly, perhaps, arrive at simple ones we published on. We have thought conclusions, after all the fuss. It is much better about other much more “crazy” ideas such to make such conclusions locally, and simply as helping spine-cord injuries to heal, we send the results of the analysis. For example, have explored some innovative informa- a bridge operator only needs to know one bit tion processing options in the IoT (Inter- of information, whether the bridge is stable or net of Things) context related to creating about to collapse or in somewhat simplified a gigantic intelligent sensing substrate to language “everything under control” versus realize distributed sensing, and believe it “trouble.” It is much simpler to send this infor- or not envisioned the setup to enhance mation instead of constantly streaming sensor human learning, and finally tried to think data from dozens of sensors. about ways of enhancing the outcome of a The more subtle reason is as follows. The psychotherapy session. whole SWEET setup is powered by a very simple idea discussed above, and because of that These rather bold aspirations listed above it is extremely flexible. Since SWEET is a tem- ought to justify the title. plate, an engineer only needs to implement its key mathematical abstractions (essentially the various forms of the dialogues introduced 1 Professor at Chalmers University of Technology, earlier). Of course, this is a bit of oversimplifi- Goteborg, Sweden. 2 Z. Konkoli, “On developing theory of reservoir com- cation (if it were that easy), but in the nutshell puting for sensing applications: the state weaving this is what needs to happen. Regardless of the environment echo tracker (SWEET) algorithm,” Inter- practical difficulties the implementation strat- national Journal of Parallel, Emergent and Distributed egy is very clear. One can think of the SWEET Systems, 2016, 121-143. setup as a very generic user manual, where the 3 V. Athanasiou et al., “On Sensing Principles Using user can exercise a great deal of flexibility in Temporally Extended Bar Codes,” IEEE Sensors Journal

38 39 Interestingly, the progress in computer science First, scientist learn something about results of Induction versus Deduction in Science, Computing, Literature and Art and mathematics was achieved by going other scientists in their area. Mark Burgin1 from the models of computation based on Second (this step is sometimes skipped), deduction, such as Turing machines, to the scientists conduct some experiments and Induction and deduction are important cognitive processes, which exist in all spheres of hu- models of computation based on empirical collect experimental data. man culture. These processes are analyzed, formalized and utilized in logic and mathematics. (scientific) induction, such as inductive Turing Third, scientists elaborate a hypothesis L often machines. formulating it in mathematical terms. However, to better understand their essence, we examine these processes using theoretical Let us consider these models. Fourth, scientists conduct new experiments and tools of computer science and describing their role in science, computing, literature and art. In his pioneering paper published in 1936, check the hypothesis L. Turing clearly explains that his a-machine, Fifth, if a sufficient number of experiments As a cognitive mechanism, deduction is a type statement induced (the conclusion). However, later called Turing machine, mathematically support their hypothesis, scientists call L a law of logical inference of knowledge performed if the evidence is not complete, the conclusion models the work of a human computer. We of nature. by application of specific deduction rules may be incorrect. For instance, Aristotle saw can also add that it models the work of an Note that experiments are not only physical but having, in general, the form that all of the swans in the places he lived were accountant. In both cases, the goal of the also mental. Mental experiments are especially A → B white, so he induced that all swans are white in process is computation of values of functions popular in mathematics. or general. However, much later, Europeans came according to exact (mechanical) rules and As the time goes, the following situations are A B to Australia and discovered black swans. This ⊢ stopping when the result is obtained. possible. where A is called the assumption of the rule, B shows that in contrast to deduction, induction does not always give correct results because it is called the conclusion of the rule, and both of “The idea behind digital computers may be (a) Whenever all further experiments works with incomplete information, while the them consist of a finite number of expressions, explained by saying that these machines are related to the law L support L, this law L is number of initial cases usually is not bounded formulas or statements. intended to carry out any operations which accepted forever as a law of nature. and the researcher does not know for sure when could be done by a human computer. (b) A new experiment contradicts L. In this to stop. However, the whole science is actually The human computer is supposed to be For instance, taking the expression “X is equal case, either it is declared that L is not a built on induction because scientific laws have following fixed rules; he has no authority to Y“ with variables X and Y, we can build the law of nature or it is assumed that L is not to be in agreement with nature for natural to deviate from them in any detail. We formal deduction rule valid in the initial domain. In both cases, sciences and with social systems for social may suppose that these rules are supplied “U is equal to V“& “V is equal to L is rejected as a law of nature (either sciences, while it is possible to make only a in a book, which is altered whenever he W“ ⊢ “U is equal to W“ is put on to a new job. He has also an completely or for the initial domain) and finite number of experiments. It means unlimited supply of paper on which he scientists start searching for the new law, does his calculations. He may also do his which more correctly than L describes the If U is equal to V and V is equal to Naturally, there is also inductive learning, multiplications and additions on a ‘desk experimental data. 5 W, then U is equal to W. which involves making uncertain inferences machine’, but this is not important.” We can see that this process exactly reflects how that go beyond direct experience and are based 7 Recursive algorithms and the majority of on intuition and insight. The work of a scientist or mathematician is an inductive Turing machine is functioning. logical systems formalize deduction, which However, this is only one kind of induction essentially different because in essence, it is Note that if inductive Turing machines obtain became the basic inference tool in logic – empirical induction, correct application of exploration, which can include calculation their results, they do this in finite time, i.e., and mathematics.2 In mathematics, the term which demands highly developed intuition and but cannot be reduced to it. This situation is making only a finite number of steps. They deduction is often used as a synonym of the can be invalidated by some new observations reflected in the status of scientific theories and mathematically describe and formalize empirical term proof. or experiments. There is also mathematical laws in general and the theories and laws of induction, that is, inductive reasoning prevalent At the same time, mathematical and scientific induction. physics, in particular. For instance, Stephen in science and mathematics. Note that induction practice shows that deduction is used not Mathematicians, being largely dissatisfied by Hawking writes: used in science is not mathematical induction, which reduces induction to deduction. so much for knowledge production as for absence of absolute reliability in empirical “Any physical theory is always provisional, knowledge justification because, as Aristotle induction used by physicists and other scientists, in the sense that it is only a hypothesis: you Thus, we come to the following conclusion: can never prove it. No matter how many observed, scientific discovery by deduction elaborated mathematical induction, which, in Turing machine formalizes the work of an times the results of experiments agree with is impossible, except one knows the “first” essence, reduces induction to deduction by the accountant or a human computer. some theory, you can never be sure that primary premises, and it is necessary to obtain axiom of induction, which is very popular in Inductive Turing machine formalizes the work of a the next time the result will not contradict these premises by induction.3 mathematics and has several forms. scientist and functioning of science. the theory.”6 As a cognitive mechanism, induction is a form of While mathematical induction eliminates logical inference that allows inferring a general necessity of intuition in making the conclusion, That is why, in science, e.g., in physics or Creative work of scientists, which includes statement from a sufficient number of particular acceptance of the axiom of induction and its biology, we can observe the following process scientific induction, belongs to a higher level cases, which provide evidence for the general application still demand intuition.4 of research. in the hierarchy of intellectual activity in Interestingly, the progress in computer science First, scientists learn something about results 40 41 comparison with the reproductive work of machines18 and periodic Turing machines19 – Hence, texts regularly need to be interpreted and 8 M. Burgin, “Intellectual activity in creative work,” accountants.8 were constructed. reinterpreted while interpretation is an inductive in Forms of knowledge representation and creative Hence, it is natural that inductive Turing In addition to the individual level of a scientist, process by its very nature. thinking, Novosibirsk, 1989, 53-56 (in Russian). 9 M. Burgin, “Nonlinear Phenomena in Spaces of machines can do much more than Turing induction is prevalent in science as a whole. It Algorithms,” op. cit.; M. Burgin, Super-recursive machines and this feature of inductive Turing is possible to find a methodological analysis of As it was already exhibited, even creation Algorithms, op. cit. machines is mathematically proved.9 In inductive processes in Kuhn’s and Prigogine & of insightful works in art and literature 10 K. Gödel, Collected Works, Vol. II, Publications particular, inductive Turing machines can Stengers’ works.20 involves inductive processes. For instance, La 1938-1974, Oxford, Oxford University Press, 1990. 11 solve problems that cannot be solved by any However, inductive processes are not bounded Rochefoucauld had difficulties arranging his M. Burgin, “On the power of oracles in the context of hierarchical intelligence,” Journal of Artificial Turing machine. by the domain of science – they exist in many maxims. He issued no fewer than five editions Intelligence Research & Advances 3(2), 2016, As a supportive evidence (not a proof) for other areas, including art and literature. in his lifetime, all with significant alterations, 6-17; M. Burgin, “Inductive Turing Machines,” in the above statement, it is possible to take For instance, writing about discourse, Paul deletions, and addenda. In the fifth edition A. Adamatzky (ed.), Unconventional Computing, what Kurt Gödel wrote in a note entitled “A Ricoeur stresses that there is always a surplus of 1678, his publisher apologetically notes, A volume in the Encyclopedia of Complexity and philosophical error in Turing’s work”: of meaning that goes beyond what objective “As for the order of these reflections, you will Systems Science, Berlin/Heidelberg, Springer, 21 2018, 675-688. techniques seek to explain. There is a surplus easily appreciate that it was difficult to arrange 12 “Turing gives an argument which is A. Sloman, “The Irrelevance of Turing machines of meaning because we apply objective them in any order, because all of them deal supposed to show that mental procedures to AI,” in M. Scheutz (ed.), Computationalism: New 22 Directions, Cambridge, MIT Press, 2002, 87-127 cannot go beyond mechanical procedures. techniques to things we already understand with different subjects.” (http://www.cs.bham.ac.uk/~axs/). However, this argument is inconclusive. as having a possible meaning without fully Even more explicitly this trait was expressed 13 M. Burgin, Super-recursive Algorithms, op. cit. What Turing disregards completely is the exhausting that meaning. The meaning of acts when in his conversations with the Russian 14 M. Burgin, “Nonlinear Phenomena in Spaces of fact that mind, in its use, is not static, but of discourse is moreover always open to new Music Professor Aleksandr Borisovich Algorithms,” op. cit. constantly developing, i.e., we understand interpretations, particularly as time passes and Goldenveizer, Leo Tolstoy characterized the 15 M. Burgin, “The Notion of Algorithm and the abstract terms more and more precisely the very context in which interpretation takes creative work of an artist saying: Church-Turing Thesis,” VIII International Congress as we go on using them... though at each place changes. Consequently, we once more on logic, methodology and philosophy of science, “I can’t understand how anyone can write stage the number and precision of the come to inductive processes. Moscow, 1987, v. 5, pt. 1, 138-140; M. Burgin, abstract terms at our disposal may be finite, without rewriting everything over and over “How We Know What Technology Can Do,” both... may converge toward infinity…”10 again. I scarcely ever re-read my published Communications of the ACM 44(11), 2001, 82-88. The same is true for the true creations of art writings, but if by chance I come across a 16 T. S. Kuhn, The Structure of Scientific Revolutions, Implementing both empirical induction and and literature. For instance, Leonardo da Vinci page, it always strikes me: All this must be Chicago, University of Chicago Press, 1962. deduction, inductive Turing machines provide wrote “Art is never finished, only abandoned.” rewritten; this is how I should have written 17 M. Burgin, “Inductive Cellular Automata,” more efficient tools for artificial intelligence In a similar vein, Pablo Picasso asserted: it.” International Journal of Data Structures and Algorithms 1(1), 2015, 1-9. (AI) in comparison with Turing machines or 18 This distinctly demonstrates that for Tolstoy M. Burgin & E. Eberbach, “Evolutionary Automata: 11 “To finish a work? To finish a picture? What other recursive algorithms. This is important nonsense! To finish it means to be through writing was an inductive process. Expressiveness and Convergence of Evolutionary because researchers explain that recursive with it, to kill it, to rid it of its soul, to give Thus, we can see that inductive processes Computation,” Computer Journal 55(9), 2012, algorithms are not adequate tools for AI.12 it its final blow the coup de grace for the 1023-1029. pervade in all kinds of creative human activities 19 M. Burgin, “Periodic Turing Machines,” Journal of Indeed, inductive Turing machines are much painter as well as for the picture.” while mathematically they are modeled by 13 Computer Technology & Applications (JoCTA) 5(3), more powerful than Turing machines. While inductive Turing machines. 2014, 6-18. Turing machines generate only two lowest This naturally implies that, at least, for some 20 T. S. Kuhn, The Structure of Scientific Revolutions, levels of the infinite arithmetical hierarchy artists the process of creation follows inductive op. cit.; I. Prigogine & I. Stengers, Order out of Chaos, Toronto/New York/London, Bantam Books, used as measurement tool of the power of footsteps. 1 UCLA, Los Angeles, CA 90095, USA. 1984. automata and computing machines, inductive Besides, comprehension and understanding 2 M. Burgin, Super-recursive Algorithms, New York, 21 P. Ricoeur, Hermeneutics and the Human Sciences: Springer, 2005; D. Deutch, The beginning of infinity, Turing machines of higher orders can generate of artistic creations is a kind of discourse Essays on Language, Action and Interpretation, ed. 14 London, Penguin Books Ltd, 2011. the whole arithmetical hierarchy. and creations of art and literature, especially & trans. J. B. Thompson, Cambridge, Cambridge 3 Aristotle, The Complete Work of Aristotle, ed. J. Invention of inductive Turing machines profound ones, are always open to new University Press, 1981. Barnes, Princeton, Princeton University Press, 1984. 22 Cf. A. Hui, A Theory of the Aphorism: From changed the concept of algorithm essentially interpretations. Culture is changing. Knowledge 4 H. Poincaré, La valeur de la science, Paris, Confucius to Twitter, Princeton/Oxford, Princeton extending its scope and power.15 It was a of people is changing. It brings necessity in new Flammarion, 1905. University Press, 2019. transformation of the computing paradigm in and new interpretations and commentaries. 5 A. Turing, “On Computable Numbers with an the sense of Kuhn,16 symbolizing emergence Consequently, we once more come to inductive Application to the Entscheidungs-problem,” Proc. Lond. Math. Soc. Ser.2 42, 1936, 230-265. and proliferation of a new type of algorithms processes. 6 S. W. Hawking, A Brief History of Time, Toronto/ called super-recursive algorithms. In addition, natural languages and especially New York/London, Bantam Books, 1988. Later, other classes of abstract automata that languages of art convey more than a single 7 M. Burgin, “Nonlinear Phenomena in Spaces of also perform inductive computations – inductive meaning. Thus, text in these languages can Algorithms,” International Journal of Computer cellular automata,17 inductive evolutionary always be understood in more than one way. Mathematics 80(12), 2003, 1449-1476.

42 43 an essential component of the spiritual cere- stalks of sporangia. Basidiomycetes are less Fungal Grey Matter monies, rituals, community building events, susceptible to infections, when cultured in- Andrew Adamatzky1 and Irina Petrova2 healing, mind opening inspirational trips and doors, especially commercially available mental healings. No one will ever forget their species, they are larger in size and more con- first trip with Psilocybin mushrooms and will venient to manipulate than slime mould, and Fungi are creatures with remarkably pronounced protocognition abilities. They control always be grateful to shrooms for showing un- they could be easily found and experimented seeable. Here we discuss how electro-physi- with outdoors. This makes the fungi an ideal ‘thinking’ of trees. They open minds of humans. They help us to live in the world and to ological properties of fungi can be used in object for developing future living computing see the invisible. Recently we discovered that the electrical activity of fungi is similar to sensing and information, in unconventional devices. Availability and scalability of fungi is neurons. Fungi communicate with trains of spikes of electrical potential. Fungi respond to computing. yet another advantage. The fungi is a largest, stimulation by changing their electrical properties and patterns of their electrical activity. A vibrant field of unconventional computing widely distributed and the oldest group of liv- Here, we briefly overview our discoveries on sensing and computing with fungi. aims to employ space-time dynamics of phys- ing organisms. Smallest fungi are microscopic ical, chemical and biological media to design single cells. The largest fungi, Armillaria bulbo- novel computational techniques, architectures sa, occupies 15 hectares and weighs 10 tons, and working prototypes of embedded comput- and the largest fruit body belongs to Fomitipo- ing substrates and devices. Interaction-based ria ellipsoidea which at 20 years old is 11 m computing devices is one of the most diverse long, 80 cm wide, 5 cm thick and has estimat- and promising families of the unconventional ed weight of nearly half-a-ton. computing structures.3 They are based on interactions of fluid streams, signals propagating along conductors or excitation wave-fronts. Typically, logical gates and their cascade implemented in an excitable medium are ‘hand- crafted’ to address exact timing and type of interactions between colliding wave-fronts. The artificial design of logical circuits might be suitable when chemical media or functional materials are used. However, the approach might be not feasible when embedding computation in living systems, where the architecture of conductive pathways may be difficult to alter or control. During the last decade we produced nearly forty prototypes of sensing and computing devices from the slime mould Physarum polycephalum, including shortest path finders, computational geometry processors, hybrid electronic devices.4 We found that the slime mould is a convenient substrate for unconventional computing however geometry of the slime mould’s protoplasmic networks is continuously changing, thus preventing fabrication of long-living devices, and the slime Fig. 1. Irina Petrova, Deep Down the Rabbit Hole. Installation with Macrolepiota procera fungi, 2020. mould computing devices are confined to experimental laboratory setups. Fungi Basidio- Fungi are the first creatures which arrived on message from one tree to another fungi do ac- mycetes are now taxonomically distinct from our planet. They are creatures of magic. They tually alter the meaning of the messages thus the slime mould, however their development populate a thin layer of soil, just under the sur- controlling ‘thinking’ of trees and ultimately and behaviour are phenomenologically simi- Fig. 2. Fungi P. ostreatus explores space while geometrically constrained. face and implement chemical, and possibly governing a Mind of the Forest. To some degree lar: mycelium networks are analogous to the electrical communication between trees and fungi also shaped a Mind of Noosphere. From slime mould’s protoplasmic networks, and the plants. There is a chance that when sending a the beginning of civilisations fungi have been fruit bodies are analogous to the slime mould’s

44 45 Spiking fungi Fungal electronics Not only neurons spike. Action potential-like observed two types of spikes: high-frequency Fungi are memristors. The memristor is a de- mycelium can be used as part of a capacitors spikes of electrical potential have been discov- spikes, duration nearly 3~min, and low-fre- vice whose resistance changes depending on array. A fungal electronic circuit could have ered using intracellular recording of mycelium quency spikes, duration nearly 14~min. The the polarity and magnitude of a voltage ap- chemical, mechanical or optical inputs. of Neurospora crassa5 and further confirmed spikes are observed in trains of 10-30 spikes. plied to the device’s terminals. A memristor is A range of fungal responses to stimulation have in intra-cellular recordings of action potential The depolarisation and repolarisation rates of a material logical implication. Therefore any been discovered in our experiments13 with in hypha of Pleurotus ostreatus and Armillar- both types of spikes are the same. Refractory logical circuits can be made purely from the fungal skin14 – a thin flexible sheet of a living ia bulbosa6 and in extracellular recordings of period of a high-frequency spike is one sixth memristors. We have examined the conduct- homogeneous mycelium made by a filamen- fruit bodies and of substrates colonized by of the spike’s period, and of a low-frequen- ed current for a given voltage applied as a tous fungus. We demonstrated that a thin sheet mycelium of Pleurotus ostreatus.7 While the cy spike one third of the spike’s period. We function of the previous voltage to fungi fruit- of homogeneous living mycelium of Ganoder- exact nature of the travelling spikes remains showed that fruit bodies respond with spikes ing bodies and substrates colonised by fungi, ma resinaceum shows pronounced electrical uncertain we can speculate, by drawing anal- of electrical potential in response to physical, and showed that the fungi exhibit remarkable responses to mechanical and optical stimula- ogies with oscillations of electrical potential chemical and thermal stimulation; not only a memristive properties.11 Indeed, demonstrat- tion. It is possible to differentiate between the of slime mould,8 that the spikes in fungi are simulated body responds with a spike but oth- ing that a fruit body or a substrate colonised fungal skin’s response to mechanical and op- triggered by calcium waves, reversing of cy- er fruit bodies of the cluster respond as well. by fungi exhibit memristive properties is a just tical stimulation. The fungal skin responds to toplasmic flow, translocation of nutrients and We believe the spikes of electrical potential tiny step forward: cascading fungal memristors mechanical stimulation with a 15 min spike of metabolites. Studies of electrical activity of travelling in mycelium networks play the same into function circuits will be the challenging electrical potential, which diminishes even if higher plants can bring us even more clues.9 roles of information carriers as action potential task. the applied pressure on the skin remains. The Thus, the plants use the electrical spikes for a travelling along neural pathways in e.g. human long-distance communication aimed to coor- brains. Thus it would be advantageous to dis- dinate an activity of their bodies. The spikes of cover what types of information processing electrical potential in plants relate to a motor devices we could make from fungi. To make activity, responses to changes in temperature, information processing devices from fungi osmotic environment and mechanical stimula- we can either use fungi as electronic compo- tion. In experiments with Pleurotus ostreatus10 nents of analog computers or employ internal we demonstrated that fruit bodies of oyster dynamics of excitation in fungi directly. Both fungi exhibit trains of action-like spike of ex- options are illustrated below. tracellularly recorded electrical potential. We

Fig. 4. Responsive fungal skin. Left, pairs of differential electodes inserted in the fungal skin of G. resinaceum. Right, response of the fungal skin to pressure and illumination.

Despite being logically universal, memristors skin responds to optical stimulation by raising might not be enough to build fully functional its electrical potential and keeping it raised till computing circuits. We might need to store the light is switched off. We can even differ- energy, implement digital memory, do signal entiate the responses to loading and removal coupling and decoupling, make high-pass of the weight. Whilst amplitudes of ‘loading’ and low-pass filters, suppress noise. All these and ‘removal’ spikes are the same (0.4 mV in can be done with capacitors. Fungi are capac- average) the fungal skin average reaction time itors, albeit rapidly discharging. In laboratory to removal of the weight is 2.4 times short- experiments we showed that the capacitance er than the reaction to loading of the weight of mycelium is in the order of hundreds of pi- (385 sec versus 911 sec). Also ‘loading’ spikes co-Farads and the charge density of the myce- are 1.6 times wider than ‘removal’ spikes lium decays rapidly with increasing distance (1261 sec versus 774 sec). from the source probes.12 Nevertheless, the Fig. 3. Example of electrical spiking activity recorded from a hemp substrate colonised by mycelium of P. ostreatus. 46 47 enhance the stimulated tube and encourages environmental sensor networks in ecological abandonment of other tubes. research to assess not just soil quality but an over health of the ecosystems. Interaction of Application domain: distributed networks voltage spikes, travelling along mycelium of ecological sensors strands, at the junctions between strands is a Likely application domains of the fungal de- key mechanism of the fungal computation. vices could be large-scale networks of myce- We can see each junction as an elementa- lium which collect and analyse information ry processor of a distributed multiprocessor about the environment of soil and, possibly, computing network. We assume a number of air, and execute some decision making pro- junctions is proportional to a number of hy- cedures. Fungi sense light, chemicals, gases, phal tips. There are estimated 10-20 tips per gravity and electric fields. Fungi show a pro- 1.5-3 mm3 of a substrate. Without knowing nounced response to changes in a substrate the depth of the mycelial network we go for pH, demonstrate mechanosensing; they sense a safest lower margin of 2D estimation: 50 toxic metals, CO and direction of fluid flow. tips/mm2. Considering that the largest known Fig. 5. Computing with travelling spikes in mycelium networks. Left, a snapshot of an excitation waves propagating 2 in the network. Right, encoding of the spiking response to Boolean gates. Fungi exhibit thigmotactic and thigmomor- fungus Armillaria bulbosa populates over phogenetic responses, which might be reflect- 15 hectares we could assume that there could ed in dynamic patterns of their electrical activ- be 75·1017 branching points, that is nearly a ity. Fungi are also capable of sensing chemical trillion of elementary processing units. With with message propagation speed 0.5 mm/sec. Fungal computing cues, especially stress hormones, from other regards to a speed of computation by fungal Diameter of the colony, which experimental Mycelium networks are disorganized and dif- species, thus they might be used as reporters computers, electrical activity in fungi could be laboratory images have been used to run the ficult to program at a fine-grained level. Thus of health and well-being of other inhabitants used for communication with message propa- model, is c. 1.7 mm. Thus, it takes the excita- direct design of computing circuits might be of the forest. Thus, fungal computers can be gation speed 0.5 mm/sec (this is several orders tion waves initiated at a boundary of the colo- impossible. In such situations an opportunistic made an essential part of distributed large-scale slower than speed of a typical action potential approach to outsourcing computation can be ny up to 3-4 sec to span the whole mycelium adopted. The system is perturbed via two or network (this time is equivalent to c. 70K iter- more input loci and its dynamics if recorded at ations of the numerical integration model). In one or more output loci. A spike appearing at 3-4 sec the mycelium network can compute one of the output loci is interpreted as logical up to a hundred logical gates. This gives us the Truth or ‘1’ and absence of the spike as logical rate of a gate per 0.03 sec, or, in terms of fre- False or ‘0’. Thus a system with relatively un- quency, this will be c. 30 Hz. known structure implements a mapping {0, 1} n→{0, 1}m, where n is a number of input loci Programmability and m is a number of output loci, n, m>0. Us- To program fungal computers we must control ing numerical modelling of excitation wave- the geometry of mycelium network. The ge- fronts propagating on images of real colony of ometry of mycelium network can be modified Aspergillus niger we have demonstrated how by varying nutritional conditions and temper- sets of logical gates can be implemented in ature, especially a degree of branching is pro- single colony mycelium networks via initiation portional to concentration of nutrients, and a of electrical impulses.15 The impulses travel in wide range of chemical and physical stimuli. the network, interact with each other (anni- Also, we can geometrically constrain it. A fea- hilate, reflect, change their phase). Thus for sibility of shaping similar networks has been different combinations of input impulses and demonstrated by us previously: high ampli- record different combinations of output im- tude high frequency voltage applied between pulses, which in some cases can be interpreted two electrodes in a network of protoplasmic as representing two-inputs-one-output func- tubes of slime mould P. polycephalum leads to tions. To estimate a speed of computation we abandonment of the stimulated protoplasmic refer to Olsson and Hansson’s original study,16 without affecting the non stimulated tubes, in which they proposed that electrical activi- and low amplitude low frequency voltage ap- ty in fungi could be used for communication plied between two electrodes in the network Fig. 6. Irina Perova, The X-Files. Ecological Disaster in an Industrial Wonderland. Installation with Macrolepiota procera fungi, 2020.

48 49 in plants: from 0.005 m/sec to 0.2 m/sec). Thus 8 A. Adamatzky (ed.), Advances in Physarum Ma- it would take about half-an-hour for a signal in chines, op. cit. Le vignoble cosmique 9 the fungal computer to propagate one meter. J. Fromm & S. Lautner, “Electrical signals and their Alessandro Chiolerio1 The low speed of signal propagation is not a physiological significance in plants,” Plant, cell & environment 30(3), 2007, 249-257. critical disadvantage of potential fungal com- 10 A. Adamatzky, “On spiking behaviour of oyster puters, because they never meant to compete fungi Pleurotus djamor,” op. cit. with conventional silicon devices. The myceli- 11 A. E. Beasley, A. L. Powell and A. Adamatzky, um network computing can not compete with “Memristive properties of mushrooms,” arXiv pre- existing silicon architecture however its appli- print arXiv:2002.06413 (2020). cation domain can be a unique of living bio- 12 Ibid. sensors (a distribution of gates realised might 13 A. Adamatzky, G. Gandia and A. Chiolerio, “Fun- be affected by environmental conditions) and gal sensing skin,” arXiv preprint arXiv:2008.09814 computation embedded into structural ele- (2020). 14 J. Mitchell, G. Gandia, J. Sabu and A. Bismarck, ments where fungal materials are used18 and 19 “Leather-like material biofabrication using fungi,” fungal wearables. Nature Sustainability, 2020, 1-8. 15 A. Adamatzky, M. Tegelaar, H. A. Wosten, A. L. Powell, A. E. Beasley, and R. Mayne, “On Boolean 1 Professor in Unconventional Computing and Di- gates in fungal colony,” Biosystems, 2020, 104138. rector of the Unconventional Computing, Lab, 16 S. Olsson & B. S. Hansson, “Action potential-like UWE, Bristol, UK. activity found in fungal mycelia is sensitive to stim- 2 Affiliated artist in the Unconventional Computing, ulation,” op. cit. Gianni Verna, « Digradano su noi pendici / di basse vigne », gravure sur bois, 1360x480 mm, 1991. Lab, UWE, Bristol, UK. 17 A. E. Beasley, A. L. Powell and A. Adamatzky, “Ca- 3 A. Adamatzky (ed.), Advances in Unconventional pacitive storage in mycelium substrate,” arXiv pre- Computing, Cham, Springer, 2016. print arXiv:2003.07816 (2020). 4 Tout est si ouvert, même à la pluie poussée par le vent et aux rayons clairs du soleil, tout est A. Adamatzky (ed.), Advances in Physarum Ma- 18 A. Adamatzky, P. Ayres, G. Belotti and H. A. aussi silencieux que le regard du spectateur, seul un spectateur patient pourrait voir un outil chines, Cham, Springer, 2016. Wösten, “Fungal Architecture Position Paper,” Inter- 5 C. L. Slayman, W. S. Long and D. Gradmann, “’Ac- national Journal of Unconventional Computing 14, poussiéreux, un reste de guerre très bruyant, ou un tracteur moderne brillant, une créature tion potentials’ in Neurospora crassa, a mycelial 2019. technologique parcourir les rangs. fungus,” Biochimica et Biophysica Acta (BBA)-Bi- 19 A. Adamatzky, A. Nikolaidou, A. Gandia, A. Chi- Pourtant, cette même technologie pourrait nous aider à voir une colline d’une manière dif- omembranes 426(4), 1976, 732-744. olerio, and M. M. Dehshib, “Reactive fungal weara- 6 férente, le vignoble reposant harmonieusement dessus, la plantation ordonnée des vignes, S. Olsson & B. S. Hansson, “Action potential-like ble,” arXiv preprint arXiv:2009.05670 (2020). activity found in fungal mycelia is sensitive to stim- leur production de sucre obstinée, enfin savamment transformée en or rouge liquide. Le ulation,” Naturwissenschaften 82(1), 1995, 30-31. vignoble étant constamment soumis aux champs électromagnétiques naturels, aux signaux 7 A. Adamatzky, “On spiking behaviour of oyster fun- radio que les étoiles nous envoient. Ce chuchotement électrique polarise nos vignes, se gi Pleurotus djamor,” Scientific reports 8(1), 2018, disperse dans une symphonie d’impulsions, détermine leur métabolisme, peut-être leur 1-7. humeur. Et qu’affinons-nous sinon leur humeur, à l’aide d’enzymes et de bactéries, pour en faire du vin ? Le vin est le résultat de ce calcul de proportions cosmiques et holistiques, qui finit par nous envahir et nous enivrer d’étincelles d’étoiles.

La complexité d’une vigne Sardaigne4 (Fig. 1). La production de vin était La vigne se développe au fil des saisons, par la si importante que lorsque l’épidémie de phyl- fatigue et le travail du paysan. Mais on cache loxéra a détruit la plupart des vignobles euro- beaucoup de secrets invisibles. La vigne a péens, on a appris à créer des chimères avec une histoire fascinante, qui accompagne l’his- les vignes américaines les plus résistantes. Et toire de l’homme et de ses migrations depuis une partie de cette histoire reste à écrire, car des millénaires. Des découvertes récentes de nouveaux hybrides résistants aux maladies montrent que la production de vin est docu- sont en cours de développement pour assurer mentée à partir du VIe millénaire avant J.-C. un avenir durable à nos vignerons5. dans des endroits très éloignés les uns des Un vignoble est un système extrêmement autres, comme le Caucase2, la Sicile3 et la complexe dans lequel les principales espèces

50 51 Fig. 1. a : La bouteille de vin de Speyer, datée d’environ 325-359 après J.-C., trouvée lors des fouilles d’une villa patricienne romaine et conservée au Musée historique du Palatinat, en Allemagne (pho- to d’Emmanuel Giel) ; c’est le plus ancien échantil- lon de vin qui nous soit parvenu. b: bocaux B1 et B2 trouvés dans le tunnel Bellitti à Monte Kronio, Sciacca (Sicile), contenant des traces d’acide tar- trique et de tartrate de sodium ; ils remontent au début de l’âge du cuivre, environ 4000 avant J.-C. c: graines de raisins domestiques, Vitis vinifera subsp. Vinifera et pédicelles, trouvés dans un puits de Villanovan près de Bologne, environ 900 avant JC.

Fig. 3. a : Exemple de pic de potentiel bioélectrique enregistré pendant les heures de nuit par une vigne Lattuario à Turin, en 2020. b : Interplanetary Scintillation Array (ISA) à l’Observatoire de ra- dioastronomie Mullard, archives photographiques du Département de physique, Université de Cam- bridge (1967). c: couverture de l’album Unknown Pleasures de Joy Division (1979). Bien qu’il fasse désormais partie de l’imaginaire collectif, peu savent qu’il ne s’agit pas de traces sonores, mais du radiogramme original enregistré par Jocelyn Bell Burnell et Antony Hewish, deux astronomes du Mullard, qui en cherchant des traces de quasars ont découvert le premier signal pulsar, l’appelant LGM-1 (Little Green Man-1, aujourd’hui il s’appelle CP1919), représenté par Harold Craft, un étu- diant de l’Université Cornell et pionnier de la visualisation de données numériques.

peuvent vivre des dizaines voire des centaines Influx qui vient des étoiles d’années, les racines s’étendant jusqu’à cinq Un vignoble est naturellement exposé à l’en- mètres à l’horizontal et à un mètre à la verti- vironnement extérieur et en tant que tel, il cale, créant une symbiose au fil des ans avec absorbe les radiations électromagnétiques, le de nombreuses espèces de bactéries et de flux de particules chargées, les neutrinos, les champignons, collaborant avec des herbes au rayons cosmiques, qui interagissent faiblement développement de la chimie des sols (Fig. 2). avec la matière ordinaire. Cette interaction Un nombre incalculable d’espèces animales est aussi sporadique que cruciale pour l’éco- coexistent alors avec les vignes, la plupart sont logie de notre planète. Un exemple frappant Fig. 2. a : Association de Orchis purpurea et Ranunculus acris avec Vitis vinifera. b : Association de Taraxacum offi- des insectes et des arachnides, qui entrelacent est représenté par les processus qui régissent cinale avec Vitis vinifera. c : Association de Muscari neglectum avec Vitis vinifera. d : Association de Viola odorata avec Vitis vinifera. Les vignobles sur les photos sont situés sur le territoire de la commune de Vigliano d’Asti. leur vie et leur mort à l’enchevêtrement de tis- la condensation d’un nuage. Les noyaux de sus de soie, de fils de fer et de feuilles de vigne condensation porteurs d’une charge électrique séchées. subissent en effet une croissance spontanée

52 53 pour former les gouttelettes d’eau qui consti- et de télécommunication devenus désormais 1 Istituto Italiano di Tecnologia, Center for Sustai- Candido, E. De Luca, A. Khafizova, et E. Sartori, « Le tuent un nuage. Et il n’y a aucun doute que les fondamentaux, notamment suite au dévelop- nable Future Technologies, Via Livorno 30, 10144 varietà resistenti alle malattie », Quaderni tecnici e rayons cosmiques y jouent un rôle fondamen- pement de la pandémie. Comment cet instru- Turin, Italie ; University of West of England, Uncon- VCR, 18 (3 édition), 2018. 6 tal6. Un organisme vivant, qu’il soit végétal ment est-il fabriqué ? À tous égards semblable ventional Computing Lab, Coldharbour Lane, BS16 J. Kirkby et alii, « Role of sulphuric acid, ammonia 1QY Bristol, Royaume-Uni. and galactic cosmic rays in atmospheric aerosol nu- ou animal, est sensible à toutes les conditions à un vignoble (Fig. 3), constitué de longs fils 2 D. Lordkipanidze, « Le antichissime origini della cléation », Nature 476, 2011, 429. extérieures auxquelles il est soumis ; il est pos- métalliques conducteurs, et éventuellement 7 viticoltura in Georgia », in G. Di Pasquale (éd.), Vi- Ş. Petrescu, R. Mustăţea, I. Nicorici, « The influence sible d’extrapoler des informations à son sujet, de nombreuses rangées placées dans des po- num Nostrum, arte, scienza e miti del vino nelle ci- of music on seed germination of Beta vulgaris l. var. par exemple en surveillant le potentiel bioé- sitions à différentes longueurs10, pouvant car- viltà del Mediterraneo antico. Catalogo della mostra Cicla l. », Journal of Young Scientist V, 2017, 67-72. lectrique de cet organisme. L’étude et l’analyse tographier le ciel alors qu’il coule devant leurs (Firenze 20 juillet 2010 - 30 avril 2011), Florence, 8 V. Zappalà, Vini dell’altro mondo, Il mio libro, numérique des potentiels d’action pourraient, yeux pour intégrer les fluctuations locales de Giunti, 2010, 32-33. 2012. entre autres, permettre de surveiller la santé la densité ionosphérique au fil du temps et les 3 D. Tanasi, E. Greco, V. Di Tullio, D. Capitani, D. Gu- 9 J. A. González-Esparza, A. Carrillo, E. Andrade, R. d’une culture, ce qui est essentiel pour préve- annuler. Quel meilleur outil qu’un vignoble ? llì, E. Ciliberto, « H-1H NMR 2D-TOCSY, ATR FT-IR Pérez Enríquez et S. Kurtz, « The MEXART interpla- nir l’apparition et la propagation d’agents pa- Le radiotélescope fonctionnerait à des fré- and SEM-EDX for the identification of organic resi- netary scintillation array in Mexico », Geofìsica In- dues on Sicilian prehistoric pottery », Micromecha- ternational 43(1), 2004, 61-73. thogènes contre lesquels les vignerons luttent quences comprises entre 50 et 500 MHz, en nical Journal 135, 2017, 140-147. 10 M. Tokumaru, M. Kojima, K. Fujiki, K. Maruyama, perpétuellement pour sauvegarder la produc- fonction de ses caractéristiques de construc- 4 M. Rubino, « Sardo, rosso, di 3mila anni fa: Y. Maruyama, H. Ito, et T. Iju, « A newly developed tion agricole, comme le mildiou et l’oïdium. tion : la longueur des fils de réception déter- identikit del vino più antico del Mediterraneo », UHF radiotelescope for interplanetary scintillation De plus, en « écoutant » la pensée des vignes, mine uniquement la tonalité sur laquelle vous La Repubblica online, https://www.repubblica.it/ observations: Solar Wind Imaging Facility », Radio nous avons pu collecter suffisamment de don- syntonisez. Et il ne serait pas affecté par les sapori/2016/12/19/news/sardegna_primo_vino_ Science 46, 2011, RSoFo2. nées pour déterminer leur bien-être émotion- signaux bioélectriques des vignes, qui suivent millenario-154444878/. nel, et mettre en œuvre des actions visant à les des processus physiologiques beaucoup plus 5 R. Testolin, E. Peterlunger, S. Collovini, S. Castella- faire se sentir mieux, afin que la qualité des lents et plus proches du Courant Continu. rin, G. Di Gaspero, F. Anaclerio, M. Colautti, M. De raisins, et par conséquent du vin, soit affectée En substance, la construction d’une usine ex- positivement. Par exemple par l’expérimenta- périmentale permettrait aux agriculteurs de tion musicale et sonore7. Et peut-être décou- disposer d’un nouvel outil d’analyse de l’état vrira-t-on qu’ils se comportent comme un or- de bien-être du vignoble, aux scientifiques ganisme collectif8 ! d’un nouvel outil de mesure de la scintillation interplanétaire, et aux consommateurs Le vent solaire mis en bouteille de boire un vin tracé, où les techniques mo- La scintillation interplanétaire est la variation dernes de la blockchain et de l’IoT converge- de l’intensité d’une source radio cosmique, raient pour compiler un passeport numérique caractérisée par un très petit diamètre d’émis- contenant les notes de la symphonie cos- sion, induite par des fluctuations de l’indice de mique qui a secoué le vignoble pendant toute réfraction du milieu interplanétaire turbulent. une année. En effet, grâce à la blockchain, il Les perturbations de la phase du front d’onde, est possible de stocker des informations par qui peuvent être supposées parallèles à la sur- ordre chronologique concernant la période de face de la Terre, proviennent de la diffraction temps pendant laquelle les transformations du qui produit de petites inhomogénéités dans vin ont eu lieu, du champ à la bouteille. Les la densité électronique du milieu, qui sont systèmes IoT, d’autre part, peuvent être utili- finalement directement proportionnelles à la sés pour collecter sur le terrain les paramètres densité du vent solaire. Cette diffraction peut climatologiques environnementaux tels que la à son tour être corrélée à des changements pression, la température, l’humidité relative, brusques de la vitesse du vent solaire, ou à des l’humidité du sol, la vitesse et la direction du événements particulièrement énergétiques tels vent, le degré d’ensoleillement, l’humidité des que l’éjection de masse coronale du Soleil. feuilles, etc., et transmettre ces informations Un instrument capable de mesurer la scintil- via des canaux sans fil à un système capable lation interplanétaire pendant 24 heures est de les mémoriser. Toutes ces données contri- donc un analyseur de l’héliosphère interne, bueraient donc à la formation du passeport qui fournit des informations très utiles relatives numérique du vin en question. à la météorologie spatiale9, à même de nous aider à préserver nos systèmes électroniques

54 55 Novel reversible logic elements for unconventional computing Kenichi Morita1

Logic elements used in conventional computers are mostly logic gates such as AND, OR, NOT, NAND, etc. Their history is quite long, since logical operations of AND, OR and NOT were already known more than two-thousand years ago.2 They were obtained by analyzing human thinking and reasoning, and thus it is easy for us to understand them. However, when we investigate future computing systems, we should not be tied to the old traditions. Reversible computing3 is a paradigm of computing that reflects physical reversibility, one of the fundamental microscopic physical laws of nature. It searches for novel and unconventional methodologies that are directly related to reversible microscopic phenomena. We consider here a reversible logic element with 1-bit memory (RLEM), and examine its possibilities as a novel logical device. Though its physical realizability in the nano-level is not known at present, it gives new vistas on unconventional computing devices. We shall see that it has very different features that cannot be seen in conventional logic gates. In Fig. 2. An example of a reversible Turing machine composed of rotary elements. particular, reversible computing systems such as reversible Turing machines can be constructed out of RLEMs in a very unique way. We also see that an RLEM can be implemented in reversible environments such as a billiard ball model of computation, and a very simple reversible cellular automaton. In the following, these features are explained using many illustrations without giving technical details.

Reversible logic element with 1-bit memory on the direction of the bar (i.e., horizontal or Fig. 3. (a) Two states of RLEM 3-7. (b) The case where the state does not change. (c) The case where the state changes. A reversible logic element with 1-bit memory vertical). If a signal comes from the direction (RLEM) is a kind of reversible finite automaton. parallel to the bar, it goes straight ahead and Fig. 1 shows a typical example of an RLEM the state does not change. If a signal comes with four input ports and four output ports from the direction orthogonal to the bar, it Composing reversible computers out of ro- Universal RLEMs called a rotary element (RE).4 Conceptually, it turns rightward and the state changes. It is re- has a rotatable bar that controls the move di- versible in the following sense: From the state tary elements There are infinitely many RLEMs if we do not rection of an incoming signal (or a particle). It at t+1 and the output, the state at t and the A reversible Turing machine is an abstract restrict the number of input/output ports. Fig. 3 takes one of the two states H and V depending input are uniquely determined. model of a reversible computer where every shows RLEM No. 3-7, where “3” stands for 3-in- computational state has at most one predeces- put and 3-output, and “7” is its serial number. sor. Hence, we can trace back its computing Two boxes in Fig. 3(a) indicate its two states. The process uniquely. It is known that any (irre- dotted and solid lines give input-output relation versible) Turing machine can be simulated by in each state. If an input signal goes through a reversible one without leaving garbage infor- dotted line, the state does not change (Fig. 3(b)). mation on the tape, and thus reversible Turing If it goes through a solid line, the state changes machines are computationally universal.5 We (Fig. 3(c)). Note that RE can also be represented can construct any reversible Turing machine by such a figure, but we employ Fig. 1 for ease in out of rotary elements. Fig. 2 shows a circuit understanding. An RLEM is called universal if it that simulates a simple reversible Turing ma- can simulate any other RLEM. Remarkably, it has chine that checks if a unary number given on been proved that every RLEM (except degenerate its tape is even.6 In this figure, a finite-state ones) is universal if it has three or more input/ control of the reversible Turing machine is in output ports.7 Therefore, RLEM 3-7 and RE are of the left part, and a tape unit is in the right part. course universal. Figure 4 shows how to simulate Fig. 1. Rotary element (RE) and its operations. (a) The parallel case, and (b) the orthogonal case. If a particle is given to the Begin port, it starts an RE by RLEM 3-7. Replacing each occurrence to compute. of REs in Fig. 2 by the circuit of Fig. 4, we obtain

56 57 a circuit made of RLEM 3-7 that simulates the elementary triangular partitioned cellular au- Fig. 4. Simulating a rotary reversible Turing machine. tomaton (ETPCA) since it is very simple. Each element by a circuit com- cell of ETPCA is triangular, and it is further di- posed of RLEM 3-7. Simulating a rotary element using billiard vided into three parts (Fig. 6). Each part has balls two states 0 and 1, which are indicated by a The billiard ball model (BBM) of computation blank and a dot. Here, we consider a particu- was proposed by Edward Fredkin and Tom- lar local transition function defined by the four maso Toffoli8 to show that the Fredkin gate, a local transition rules shown in Fig. 7, which is universal reversible logic gate, is realizable in identified by the number 0347.10 We assume the BBM. It is a kind of reversible mechanical that these rules are rotation-symmetric, i.e., for system consisting of ideal elastic balls and re- each rule in Fig. 7 there exist rules obtained flectors. We can see that an RE is also realized by rotating both sides of it by a multiple of 60 in the BBM as shown in Fig. 5, where small degrees. As seen from Fig. 7, the next state of rectangles are reflectors.9 Here, two kinds of a cell is determined by the three parts of its balls, i.e., a state ball and a signal ball, are neighboring cells. used. One of the key points of the construction is that the state ball (yellow) is put stationarily Consider the configuration given at time t=0 at the position H or V in a resting mode. Fig. in Fig. 8. Applying the local function to all 5 shows the cases where the directions of the the cells in parallel, we have a configuration bar and the incoming signal are orthogonal as at t=1. Configurations at t=2,3,... are obtained Fig. 5. A rotary element realized in Fig. 1(b). Consider the case that the state in the billiard ball model, an likewise. Note that, the dot patterns at t=0 and idealized mechanical compu- ball is put at the position H, and the signal ball t=6 are the same except that the latter is shifted ting model. (green) comes from the input port s. The signal rightward. Hence, it is a space-moving pattern ball collides with the state ball at the position called a glider, which can be used as a signal. H. Then, the state ball and the signal ball move The local transition function defined by the

along the paths p0 and p1, respectively. When rules in Fig. 7 is injective, since there is no pair the state ball comes to the position V, these of distinct rules whose right-hand sides are the balls collide again. Then, the state ball stops same. By this, for each configuration we can at V, while the signal ball moves eastward and find a previous configuration uniquely. Such goes out from the output port e’. By this the an ETPCA is called reversible. operation of Fig. 1(b) is realized. The case that the state ball is at the position V, and the signal The moving direction of a glider is controlled ball comes from s is trivial. In this case, the sig- by a stable pattern called a block. Figure 9 Fig. 6. Cellular space of an ele- nal ball simply moves northward without in- shows the process of the backward turn by mentary triangular partitioned teracting with the state ball and the reflectors, a single block. At t=0 a glider (left) is about cellular automaton (ETPCA). and thus Fig. 1(a) is realized. In this way, the to collide a block (right). At t=38 the glider is whole circuit that simulates a reversible Turing split into a rotator (left) and a fin (right). The fin machine given in Fig. 2 is also embeddable in moves around the block. At t=97 the rotator the BBM. and the fin meet, and a glider is reconstructed. Then the resulting glider moves leftward. Ap- Realizing RLEMs in a simple reversible propriately placing several blocks, we can also cellular space realize the right turn by 120 degrees, the left There is yet another spatiotemporal model of turn by 120 degrees, and the U-turn of a glider. a reversible environment called a reversible cellular automaton. A cellular automaton (CA) Combining several useful phenomena found consists of an infinite number of finite autom- in the reversible cellular space of ETPCA ata called cells that are placed and connected 0347, we can construct a pattern that simu- Fig. 7. Local transition rules of ETPCA 0347. uniformly in a space. A cell changes its state lates RLEM 3-7 (Fig. 3) as shown in Fig. 10. A depending on the states of its neighboring glider is given to one of the three input ports cells. We use a special type of a CA called an as a signal. After changing the state, the glider

58 59 comes out from one of the output ports. The Computations, and Universality) 2001, LNCS 2055, pattern contains many backward turn, right Berlin, Heidelberg, Springer, 2001, 102-113. 5 turn, and U-turn modules. To keep the state of C. H. Bennett, “Logical reversibility of computa- Fig. 8. A space-moving pattern RLEM 3-7, a fin is put around the center of the tion,” IBM J. Res. Dev. 17, 1973, 525-532. 6 K. Morita, “Constructing reversible Turing ma- called a glider in ETPCA 0347. pattern. A fin is a periodic pattern of period 6 chines by reversible logic element with memory,” consisting of three dots. Two small circles in in A. Adamatzky (ed.), Automata, Universality, Com- the figure show possible positions of a fin. If putation, Cham, Springer, 2015, 127-138. Hiroshi- a fin is at the lower (upper, respectively) posi- ma University Institutional Repository, http://ir.lib. tion, then we consider the state is 0 (1). Testing hiroshima-u.ac.jp/00029224 (2010). whether the fin is at the position 0 or 1, and 7 K. Morita, T. Ogiro, A. Alhazov, and T. Tanizawa, shifting it between these two positions are per- “Non-degenerate 2-state reversible logic elements formed by collisions of the glider. In this way, with three or more symbols are all universal,” Jour- RLEM 3-7 is simulated in the cellular space of nal of Multiple-Valued Logic and Soft Computing 18, 2010, 37-54. ETPCA 0347 having an extremely simple local 8 E. Fredkin & T. Toffoli, “Conservative logic,” In- function. Since a rotary element can be com- ternational Journal of Theoretical Physics 21, 1982, posed of RLEM 3-7, circuits that simulate re- 219-253. versible Turing machines like the one in Fig. 2 9 K. Morita, Theory of Reversible Computing, op. are also simulated in this cellular space. An cit. emulator for ETPCA 0347 has been given,11 10 K. Morita, “A universal non-conservative revers- which works on the general purpose cellular ible elementary triangular partitioned cellular au- automaton simulator Golly.12 There, comput- tomaton that shows complex behavior,” Natural ing processes of reversible Turing machines Computing 18(3), 2019, 413-428. 11 K. Morita, “Reversible world: Data set for simu- composed of RLEM 4-31 can be seen. Fig. 9. Backward turn of a glider is realized by a collision with a block. lating a reversible elementary triangular partitioned cellular automaton on Golly,” Hiroshima University Institutional Repository, http://ir.lib.hiroshima-u.ac. 1 Profressor Emeritus, Hiroshima University, Higashi-Hi- jp/00042655 (2017). roshima, Japan. 12 A. Trevorrow, T. Rokicki, T. Hutton et al, “Golly: 2 J. M. Bochenski, Ancient Formal Logic, Amsterdam, an open source, cross-platform application for ex- North-Holland, 1951. ploring Conway’s Game of Life and other cellular 3 K. Morita, Theory of Reversible Computing, Tokyo, automata,” http://golly.sourceforge.net/ (2005). Springer, 2017. 4 K. Morita, “A simple reversible logic element and cellular automata for reversible computing,” in M. Margenstern & Y. Rogozhin (eds), Proceedings of MCU (International Conference on Machines,

Fig. 10. RLEM 3-7 implemented in the reversible cellular space of ETPCA 0347.

60 61 novel. Intelligent responses, in contrast, are told that he is welcome to eat it but, if he can An Unconventional Look at AI: Why Today’s Machine Learning Systems local strategies that individuals develop in re- sit patiently for X minutes without tasting the sponse to new, locally experienced, situations. marshmallow, he will receive another marshmallow in addition to the first. He will receive are not Intelligent one marshmallow if it is eaten right away and 1 Intelligent Action is not Continual Nancy Salay Notice that having a capacity for intelligent two marshmallows if he waits until the experi- action does not entail that one uses this capac- menter returns. Young children find it very dif- Machine learning systems (MLS) that model low-level processes are the cornerstones of ity all the time. That it does was the working ficult to resist the sensory draw of the marsh- current AI systems. These ‘indirect’ learners are good at classifying kinds that are distin- assumption in the early days of AI — ‘Good- mallow and generally give in and eat it before Old-Fashioned-AI’ (GOFAI). On those com- the experimenter returns. As children mature, guished solely by their manifest physical properties. But the more a kind is a function of pletely top-down models, every action (lim- however, they are increasingly able to wait spatio-temporally extended properties — words, situation-types, social norms — the less ited to simple screen outputs in most cases for the arrival of the second marshmallow. likely an MLS will be able to track it. Systems that can interact with objects at the individ- since GOFAI systems were not equipped with They are capable of suffering through short ual level, on the other hand, and that can sustain this interaction, can learn responses to bodies) was the product of a line of ‘reason- term deprivation — not tasting the marsh- increasingly abstract properties, including representational ones. This representational ca- ing,’ a decision. Today, thanks to the insights mallow that is present — for the sake of in- pacity, arguably the mark of intelligence, then, is not available to current MLS’s. of Embodied Cognitive Science and, more creased future gain — two marshmallows. To broadly, Phenomenology, we understand that repeatedly not succumb to the marshmallow even intelligent individuals mostly act in au- temptation, to what is sensorily present, chil- Introduction do next, provide us with paradigmatic intel- tomatic or unconsciously directed ways. Such dren must behave now in a way that takes into The current rhetoric has it that AI is here, or, ligent behaviour. Think here of the battery of actions might be skillful, as when someone account factors that are not spatio-temporally at least, around the corner. But if this claim researchers currently working on the problem plays an instrument or adeptly traverses a nar- present, namely that there is a potential for fu- is false, then treating systems as such, that is, of developing a Covid-19 vaccine. The task row cliff-side path, but such behaviour unfolds ture gain. Younger children, perhaps because relying on them to make judgements, could draws on much background knowledge, to be according to learned responses to the occur- they have not developed the relevant linguistic have grave consequences. Autonomous vehi- sure, but it also requires a capacity for solving rent features of an ongoing situation. When representational skills, are capable only of re- cles are just one example of the many new AI new kinds of problems. If we were not confi- an obstacle looms, the body swivels to avoid sponding to the occurrent, sensory factors of technologies poised to enter the public space. dent that these scientists were capable of such it; when a note is played, the next note in the the situation. Being thus completely in the mo- Since stemming this technological tide seems ‘out-of-the-box’ thinking, we’d have no reason learned sequence is anticipated. In intelligent ment, they gobble up the sweet-smelling treat. futile, the academy has a responsibility to raise for hope. behaviour, in contrast, factors beyond the oc- Another version of the marshmallow exper- the public’s understanding around what con- But we need to be careful — a novel response current features of the ongoing situation in- iment,3 this time a reverse contingency test stitutes intelligence. Here I begin this effort by is not always an indicator of an intelligent re- fluence our behaviour: a note is played, but with chimpanzee subjects, demonstrates the arguing that we should stop thinking about sponse. Many animals are capable of adapt- now the anticipated next note is not played. critical role of representations in intelligent current machine learning systems (MLS’s) as ing to changing situations in what seem like My musical execution of Beethoven’s Emperor behaviour even more clearly. A chimpanzee is ‘intelligences’ since they do not model the ‘pre-programmed’ ways: viruses mutate when Concerto might be skillful, but when I inter- presented with two plates of treats, one hav- learning necessary for intelligent behaviour. hosts become resistant; cockroaches change sperse it with the melodic line for Happy Birth- ing visibly more than the other, and is invited food sources during resource scarcity; and, day, because I know that today is yours, I have to choose one of them. A second chimp sits What is Intelligent Behaviour? primates shift their group dynamics when acted intelligently as well. That it is your birth- by, observing. The plate chosen is given to the The very first question we might ask, then, territories diminish. We call the capacity for day is not a physical fact in the occurrent situ- second chimp and the chooser is awarded the is “What is it to act intelligently?” Examples this sort of behavioural change ‘adaptability.’ ation in which we are participating and yet, as one not selected. Similarly to young children, help orient our thinking so let us begin with a While there is a relationship between adapt- intelligent beings, it is something to which we though they understand the terms of the offer few here. A robot that has been programmed ability and intelligence — they are both ca- are both capable of responding. perfectly well, chimpanzees are incapable of to perform basic household chores, but which pacities for learning new responses to new resisting the overwhelming sensory draw of the freezes when confronted with an unfamiliar situations — the former is on an evolutionary Representation makes Intelligent Behaviour treats — their smell, touch, appearance — and task or situation, is not behaving intelligently: time-scale, one that extends across individuals Possible they invariably choose the plate with the great- it can do only what it has been programmed to species, and the latter is on a developmental How do we become responsive to such ‘of- est amount. Repeatedly they watch, furiously, to do. Similarly, any machine that does only time-scale, one that extends across an individ- fline’ factors? We represent them to ourselves as the larger pile of candies goes to the lucky what the limits of its design permit and no ual over its own lifetime. From the perspec- and one another. A classic demonstration of bystander. But when a slightly altered version more — calculators, toasters, cranes — does tive of the individual, adaptive responses are the dramatic behavioural effect this capacity of the experiment was run with a chimpan- so without what we would call intelligence. canned responses, backup strategies that kick for representation can have is the infamous zee — Sheba — who already knew some ru- In contrast, beings who make novel responses in when first pass responses fail; only from the marshmallow test.2 A subject, usually a child, dimentary mathematical symbols, the results to novel situations, who ‘figure out’ what to perspective of the species are such responses is presented with a single marshmallow. He is were very different. Instead of being asked to

62 63 choose between two plates with visible piles ink patterns on the page, representing nothing. artificial intelligence research. If intentionality action at the object-level corresponds to thou- of candies, Sheba was offered two plates with Physical objects become symbols only in the is not exhaustively accounted for by sub-per- sands of low-level processing steps. Relative to lids labelled with the number of treats under- context of a larger system within which in- sonal activity, then AI systems that only model the object-level, processing occurs at speeds neath. Since numbers have no sensory draw dividuals respond to them in ways that point sub-personal activity, which is precisely what that do not register as activity at all; while, whatever, Sheba was now able to consistently beyond themselves. Such individuals are current MLS’s do, will not be intelligent. Here I relative to the processing level, object-level make the self-maximising choice of the plate themselves intentional beings since they can will try, in broad brush strokes, to explain how change occurs so slowly that, again, it does with fewer candies. By using the numbers, rep- respond to a symbol’s representational proper- and why low-level processes cannot constitute not register as change at all during a single, resenting the possibility of future treats, Sheba ties as well as its physical ones. Intentionality, intentional behaviour. low-level time-step. The two levels of gran- was able to take into consideration factors that then, is a key aspect of intelligence. ularity are thus spatio-temporally distinct. were not spatio-temporally present and there- To build an intentional machine, namely one Low-Level Processing is not Intentional Since MLS’s cannot interact directly with me- by make the intelligent choice. that can use representations to guide its behav- MLS’s model, albeit simplistically, the low-lev- dium-sized objects, but only indirectly over iour, is one of the central tasks of AI. The foun- el neural processes that underwrite organism many low-level time-steps and by way of reg- Representations have Unusual Properties dational assumption that continues to drive learning. Today’s MLS’s have achieved much ular, low-level features, the object ‘learning’ A word needs to be said here about representa- research in the field, and which has spawned success in classification, in ‘learning’ to dis- they achieve will always be brittle. Change tions themselves since they are peculiar things. the current zeitgeist of mainstream cognitive tinguish between different kinds of objects, one lower-level feature of an object that the A representation — for example, a sentence science more generally, is this: intentionality is pictures of cats and dogs, for example. I call MLS has not had training on, and it breaks. For utterance, a physical token such as a game (exhaustively) reducible to low-level process- this ‘learning’ in scare quotes because the rel- this reason, no matter how robust the low-lev- playing piece, or an occurrent thought — has, es. If we want to understand the intentional evant classifying behaviour is achieved only el training is, MLS’s will always be subject to in addition to the usual physical properties that capacity of human beings, we need to look indirectly, by way of the pixel-level features adversarial attack. But, more saliently with all physical things have, representational prop- inside human beings, at their neural circuitry that consistently corelate with object-level respect to the question of intelligence, such erties that extend beyond these. My arm is a mostly, to see which aspects of it are responsi- kinds such as dogs and cats. That there real- systems could never learn to respond to an configuration of cells and impulses, and this is ble for intentional behaviour. In other words, ly are natural kinds in the world — individu- object’s representational properties. More on all that it is, nothing more than these physical the capacity to respond to a symbol’s rep- als that share a statistically significant sub-set this momentarily. The only sense in which a properties. But the sentence token, “My arm resentational properties (and not just its physi- of features with other individuals — is what cat/dog classifier represents a distinction be- is a configuration of cells and impulses,” has cal ones) is nothing more than a (possibly very makes this kind of indirect learning useful. tween the concepts CAT and DOG is from our the physical properties constituted by the ink complex) combination of the low-level pro- If the world were not regular in this way, if spatio-temporally extended vantage point rel- on this page, the molecules in the paper, and cesses that constitute the response behaviour. there were no natural kinds, such an approach ative to the network, namely the vantage point so on, as well as the property of being about The problem with this idea, however, is that would be useless. Imagine a world in which of the personal-level, from which we can see my arm. It represents the world, with respect it is wrong: low-level processes and person- low-level patterns did not correspond to an- that the ongoing activity of the network corre- to my arm at least, as being a certain way. The al-level intentional behaviour are not compa- ything useful at the personal level, where a sponds to a distinction between cats and dogs. technical term for this property of representa- rable, and hence not identifiable, activities. low-level sequence meant CAT one day and From the classifier’s vantage point, however, tion is ‘intentionality:’ anything that is about Yes, of course, the sub-personal processes of then DOG the next! This is an important fac- there are only ever pixels and responses to something beyond itself in this way is an in- Fred taken together are necessary for Fred to tor to keep in mind: the learning success of them; there are no cats and dogs at all. tentional thing. All signs,4 then – words and learn a new language, but, they are not suf- indirect classifiers is partly determined by the To help clarify what it is for an individual to sentences, numbers, icons – are intentional ficient: factors that are external to Fred, e.g. high-level homogeneity of environmental con- interact and learn about an object directly, let objects. And if we think that thoughts are in- the way that symbols are used in his linguis- ditions. us first consider another personal-level activi- ternal representations of the way the world is tic community, determine whether and how But given that our world is populated by de- ty: locomotion. A cat jumps from the ground or could be, then they are intentional objects Fred’s learned responses are about anything pendable, statistical regularities, isn’t this in- to a branch by virtue of a multitude of ongo- as well. at all, which is to say, whether they are inten- direct learning good enough? For simple ap- ing, low-level processes that constitute its per- Unlike physical properties, however, rep- tional at all. Furthermore, a model of just the plications, in the context of web searches for sonal-level activity, but none of the low-level resentational properties are not intrinsic to sub-personal learning part of Fred’s linguistic example, it might be. As a model of person- processes are themselves locomotions. Loco- things. A stop sign is a symbol in the context of skill, placed in the appropriate environment, al-level behaviour, however, it falls short: there motion is something that organism wholes do. road traffic systems, but outside of these con- will not yield the appropriate intentional be- is a critical granularity gap between low-lev- A single locomotive step, so to speak, spans a texts, to a squirrel for example, the stop sign haviour. Without coordinated, personal-level el processing and object-level action. At the multitude of low-level processes and a single, is merely a physical thing in the world, rep- activity, Fred’s neural activity is just a series low-level, interaction is with sensory bits — in low-level process does not map to anything resenting nothing. Likewise, the sentence “My of low-level processes, not linguistic at all. In the case of our example MLS these are pix- at all that would count as a step at the per- arm is a configuration of cells and impulses,” other words, intentional behaviour is a person- els — not with medium-sized objects such sonal-level. Some machines locomote as well. to someone who does not speak English or to al-level activity, not a low-level one. This is not as cats and dogs. One low-level processing When a car moves down the road, it is the car- something not capable of speaking at all is just a distinction that is often made in cognitive time-step does not register at the object-level whole that is moving, not its parts. The parts, the physical thing that it is, the letter-shaped science, but it is a critical one in the context of of granularity at all and, conversely, a single working together, make the car locomotion

64 65 possible, but there is no part or set of sub-parts As we move along the sign abstraction contin- possibility for tracking even a simple type of perhaps out of a complex configuration of these that is doing the locomoting. uum, however, representational and physical situation such as game playing by tracking the networks? No. But a potential AI will need a Perception, which is the method by which organ- properties increasingly diverge. The physical low-level properties of the objects that might capacity analogous to basic perception, name- isms interact with their environment, is likewise properties of the utterance ‘Fire!’ for example, figure in them seems very small. What chance, ly, a capacity for direct interaction with the ob- a personal-level activity. As with locomotion, are entirely distinct from its representational then, is there for indirectly tracking complex, jects in its environment. In the case of humans myriad low-level (sensory) processes under- properties. Learning the latter requires not only language-learning situations? this is sentience, sometimes called ‘pre-re- write perceptual activity, but perception itself is a series of learning situation experiences in Systems such as MLS’s, then, that are capa- flective consciousness:’ our basic capacity to a personal-level interaction with the objects in which different utterances are associated with ble only of indirect object tracking by way of experience our world, not simply infer it. But an individual’s environment. For humans these different fire situations, but it also requires an low-level properties could learn responses to we still need a better understanding of what are mostly medium-sized objects such as cats, entire system of symbol use within which ut- natural signs but will not be capable of more this is before we can start building systems that dogs, tables, computers, and the like. Of course, terances evoke appropriate fire responses. It abstract symbolic responses. And it is argua- exhibit it. organisms that are capable of perception do not requires a community wide practice of linguis- ble that since the symbolic properties of such always and only navigate their environment with tic use. Because these representational prop- natural signs trade completely on their physi- 1 Associate Professor at the Department of Philoso- perception; rather, there is an ongoing, dynam- erties extend to the features of the situations cal ones, individuals that are capable only of phy, Queen’s University, Canada. 2 ic shifting between unconscious/indirect senso- within which sign vehicles and objects occur learning to respond to them, and not to more W. Mischel & E. B. Ebbesen, “Attention in delay of ry tracking and conscious/direct perception, so — a child learns the word ‘ball’ as a result of abstract symbols, are not intentional agents. gratification,” Journal of Personality and Social Psy- rapid that most perceiving individuals are them- myriad and various BALL situations — learn- Most new cars today are outfitted with an array chology 16 (2), 1970, 329-337. 3 selves completely unaware of the oscillation ing a response to them requires sustained in- of sensors that track the objects in a car’s im- S. T. Boysen, G. Bernston, M. Hannan, and J. Ca- between modes of interaction. The frequency of teraction with the relevant sign objects, long mediate surround. When my car is in reverse, cioppo, “Quantity-based inference and symbolic representation in chimpanzees (Pan troglodytes),” this oscillation, however, is a critical factor in an enough for the situation to unfold. And there’s for example, it will emit different sequences Journal of Experimental Psychology: Animal Behav- individual’s capacity to learn to respond to the the rub. MLS’s track objects only indirectly, of ‘beeps’ according to how close a potential ior Processes 22, 1996, 76-86. representational properties of objects since the they never interact with them at all; conse- obstacle is to the rear fender. In one sense, 4 ‘Sign’ is a technical term for a unit of meaning. 5 degree to which an individual is capable of sus- quently, they will not be able to sustain inter- this seems like an intentional action since it J. Chen, K. Li, Q. Deng, K. Li, S. Y. Philip, “Dis- taining perception — of maintaining ongoing di- action with objects, at least not across the sorts looks like the car is responding to what things tributed deep learning model for intelligent video rect interaction with an object — will determine of complex, varied situations in which humans in the environment signify — potential obsta- surveillance systems with edge computing,” IEEE the degree to which that object can become a learn. Remember that from the vantage point cle — rather than to them directly as physical Transactions on Industrial Informatics, 2019, 1-8. 6 symbol for an individual. Before we can see how of the cat/dog classifier, there are no cats and objects. But, of course, the car is not beeping L. Wittgenstein, Philosophical Investigations., trans. and why this is the case, a few words need to be dogs, only pixels. And the more abstract a sign because it perceives a potential obstacle; rath- G. E. Anscombe, Oxford, Blackwell, 1967, §83. said about symbols themselves. is, the more its representational properties will er, the triggering of one set of sensors triggers trade on spatio-temporally diverse situational another set that in turn triggers the beep mech- Symbol Abstractness is an Indicator of features rather than on a sign vehicle’s physical anism. The car has been designed so that its Intentionality ones. parts work in concert with one another in such As we have seen, a sign is anything that repre- In theory, of course, MLS’s could be trained to a way that the car signals precisely when a po- sents something to an agent. The more removed indirectly track situations, just as they do ob- tential obstacle is present. This is clever design a sign’s representational properties are from its jects. Newer deep learning models attempt to to be sure, but the car itself is behaving in the physical ones, the more symbolic it is, while the just that.5 But success will be elusive: the prop- sort of unintelligent, pre-programmed way we less distinct a sign’s representational properties erties of situations exponentially out-number began this discussion with. At best we can say are from its physical ones, the more natural a those of objects, even supposing that there are that it has been designed to respond to a nat- sign is. Natural signs and human language lie at statistically reliable patterns that underwrite ural sign. opposite ends of this abstractness continuum. them. In most cases there are not. As Ludwig Smoke, for example, is a physical by-product Wittgenstein famously observed,6 even seem- Conclusion of fire, serving as a natural sign of fire to any ingly regular situation-types such as games are Because they cannot interact directly at the individual capable of tracking it. Many animals impossible to pin down: some games such as object-level, current MLS-based systems are that already have an avoidance response to fire baseball and soccer involve many players, oth- not capable of the sustained interaction with learn, through association, to exhibit the same ers such as chess and tennis just two, and some objects required for developing responses to avoidance response to smoke. Because smoke such as solitaire only one; some games have abstract symbols. As they are fundamentally is sensorily more dispersed than fire, and so can win/lose conditions, while others — many non-intentional entities, then, we should not be perceived more quickly, it is a useful natural new board games for example — are coop- treat them as intelligent systems, no matter sign. erative; some have fixed rules; others — e.g. how clever their design. Does this mean that ‘playing house’ — do not, and so on. Thus, the there is no possibility of creating an AI system,

66 67 Bioinspiration is based on basic functional made possible to generate and evaluate The benefits of being wrong: bonding epistemic and cognitive incompleteness properties of living systems, taken not as a huge sets of data, something that allowed whole but according to specific problem-solv- the statistical approach to mathematical ing scenarios. Such bioinspiration extracts fea- proofs: 4CT, Kepler’s Theorem, etc. As a for natural and artificial intelligent systems tures related to the biochemistry (hormones, consequence, computer assisted proofs 1 Jordi Vallverdú molecular nature, genetic machinery, etc.), the opened a new debate about epistemic neural interactions, social cooperation, or sen- opacity, black boxes, and paradoxes in sorimotor actions (hand grips, touch, smelling, comprehensive argumentation. walk, etc.) of living systems. But in no case, Such scenario, and we have in mind a pos- it is related to epistemic or high cognitive as- sible future superintelligence or AGI, cre- pects of living systems (some of them social, ates a tense framework: a perfect reason- and with culture). I define the biomechanistic ing machine, even having more computer or functional approach as the First Wave of Bi- power and data access than any single oinspired AI, although the second is the most mind or networked set of minds, will clash promising one: the Second Wave of Bioin- with the logical serious limits of the formal spired AI. And the reasons are compelling. The tools, as well as with the problem of eval- most important ones are related, first, to the uating and verifying the quality of data. At notion of formal coherence and, second, with a meta-level, the internal paradoxes and meaning. Let me explain both in some detail: contextual limitations force any cognitive system to deal with approximate, and re- (1) Formal coherence: the holy grail of visable sets of knowledges. Western Thoughts has been the accom- plishment of a perfect logico-mathemati- (2) Meaning: this second aspect, which af- cal description of the world. With a perfect fects rational entities, is surely the most un- set of tools, a complete analysis of reality explored but fundamental of all approach- should be possible, they thought. From Ar- es to AI. And we are talking about how the istotelian syllogistics, to the mathesis uni- AI will generate its own meaning. And the versalis of Leibniz, to the new logical frame- ways are similar to those displayed by nat- work of Frege or Boole this was the main ural cognitive systems: due to embodied Made by Azhmodai Artist ( for commercial items available at https://www.redbubble. aim. When, finally, Russell and Whitehead and/or socio-cultural reasons. How do we com/i/tote-bag/Entropy-by-Azhmodai/26493277.PJQVX) wrote their Principia Mathematica (1910- evaluate the true meaning of things? Evalu- 1913), trying to demonstrate how logics ating them from our embodied experience could explain and justify the foundations of positive or noxious events, that is, from Currently, the main intense debates about the next steps of AI advancements are related of mathematics, appeared a devastating or emotional experience. Meaning is also to two concepts: the singularity, and AGI (Artificial General Intelligence). By one side, the figure: Kurt Gödel. With his incomplete- related to the functionality, including into crucial moment in which AI will reach and surpass human brain (and collective brain coop- ness theorem about mathematics, Gödel this category wishes, aspirations, neces- eration) power and, by the other, the birth of a conscious and creatively intelligent artificial demonstrated the inherent limitations of sities (food, mating, survival…), among a intelligence. In most of philosophical fiction studies, both events led to the same apocalyptic every formal axiomatic system capable of long list. Even at an epistemological lev- scenario: the destruction of humanity. modeling basic arithmetic. While Hilbert el, the common-sense about reality, or the But with the evidences obtained by cognitive sciences and epistemological studies provided was trying to create the mathematics for description about reality itself, is biased to us in the last decades (following, in fact, ancient philosophical interests originated plenty the new century, Gödel put on the table by such conditions. Water looks like a sta- of centuries ago), the real scenario is a completely different one: AI is still fighting for under- the more deep fact that nobody can have ble thing when it can adopt three general standing how to do the most simplest things, according to the human standards. While it is both completeness and consistency. After states, as well as the bonds in the liquid it, new kids of logic (fuzzy, paraconsist- form being broken constantly every few true that AI can play chess or Go and bet the best of all human players, it cannot achieve ent, etc.) appeared, trying to deal with nanoseconds. From the perspective of a the simpler visual, linguistic or sensorimotor skills of any (even average) human. Therefore, more specific and creative approaches neutrino we are basically empty. Time the most recent trends in AI are reinforcing not pure power based on statistical data analysis to symbolic processing. After Gödel, the lapses are relevant or not according to (although they are very promising, thanks to the re-birth of Neuronal Networks under Ma- second fracture into the realm of reason- the lifespan on an entity. Such meaning chine and Deep Learning techniques). Instead, approximate computing and bioinspiration ing perfection was related with the infor- constraints are also the framework upon are opening new paths into the inexorable computational revolution. mational turn: new computational tools which cognitive systems are built. In that

68 69 sense the map of cognitive biases of hu- the perfection of things with imperfections. man beings express not only the mental That is, wabi-sabi is the notion about the value Collapsing the wave function on postquantum unconventional computing skills but the adaptive requirements made of imperfections for the reality of an entity as Richard Mayne1 for such bodies during millions of years. such. In that sense, what explains the success of As a consequence, these elicitors of mean- (some) humans is not their perfection, but a list ing explain how we understand existence, of peculiarities that mixed together help to de- Unconventional computing is the field that drives innovation and progress in computer aims, the evaluation of death, or the aes- fine innovative patterns of thinking and action. science. One of its sub-fields, quantum computing, is a potentially breakthrough, disrup- thetics of reality. Possible embodiments of Nevertheless, such patterns are not intrinsical- tive technology in which there has been gradual but encouraging progress in recent years. next AI systems will define the semantic ly good (stubbornness, obsession, idealization, If developed sufficiently, it is predicted that quantum computing will revolutionise a great possibilities of such entities, at a complete magic thinking,…) but help to create rich diver- many fields of human enquiry through laying bare cryptosystems, accelerating research in different level from those available for hu- sities of agencies. It is the blending of heuristics, the natural sciences and providing enormous speed and efficiency increases in machine man beings, but biased (or situated) too! not its coherence or hierarchized coherence, learning, to name but a few applications. This article examines what quantum computing is, that makes possible such extraordinary beings. why we need to be aware of it and whether there is a role for unconventional computing in Taking into consideration both aspects, coher- Taking into account that life is not a game with a postquantum world. ence and meaning, we can foresee a plausi- clear rules and from which we do not have all ble scenario for the next generation of AI sys- the necessary information, an imperfect way to tems. First of all, the beginning of a new era deal with it is surely the best solution for ad- of exploration of the benefits on integrating vancing into the path of knowledge. Certainly, Is quantum computing ‘unconventional’? number. The creativity evident in the design of new bioinspired models, which, by defect, a biased approach is a better way to increase the Unconventional computing is the search for these devices speaks of the close interrelations must include biases and lack of accuracy (at complexity and adaptability of AI. What, then,… new materials, methods and applications for between the arts and sciences, with uncon- expenses of another benefit); second, the on- Wabisabi AI? computing technologies. This doesn’t neces- ventional computing at their nexus; manifold tological horizon to which such systems will sarily imply making smaller, faster or more studies in modern art,6 architecture and wear- be faced. One of the most childish aspects efficient general purpose computers, as is able fashion,7 etc., both inspire and emerge of techno-fetish followers (under the form of 1 ICREA Acadèmia Researcher at Universitat commonly considered: many research foci from the field. transhumanism), is to consider that the way of Autònoma de Barcelona. concern making new types of computers that Under this definition of unconventional com- escaping from death involved a technological do things which classical, silicon-based archi- puting, the emerging field of quantum com- transfer or enhancement, from natural bodies tectures can’t do, or otherwise use inspiration puting would doubtlessly find a home. In spite to new forms of embodiment. But it is only a from nature to program classical systems in of this, quantum computing is generally con- small patch in relation to the physical time in novel ways. sidered to be its own field, as happens to the this universe: entropy is the final destiny of this This is an extremely wide remit for a field of more successful offspring of the original parent universe. There is no way of escaping from ab- enquiry and accordingly, advances therein field –– artificial intelligence being arguably solute informational destruction: big crush, big are typically highly multidisciplinary, melding the most significant other example. Quantum rip, big freeze… this is the absolute truth in the expertise of the natural sciences, applied computing’s proponents argue that it offers our universe. Perhaps some humans can feel mathematics and philosophy into this branch routes towards enormous speed increases in happy thinking of small time postponements, of computer science. This past decade has computation of certain tasks, with database but for a really intelligent system the reality seen functional unconventional computing searches and factorization of prime products is there: it doesn’t matter the kind of strategy devices arising such as slime moulds tackling being amongst the most intensively researched you wish to follow, because everything in this problems of graph optimization (with better upon applications in the field to date. Some go universe will be destroyed. How a real intel- success rates than undergraduate mathematics further to suggest that quantum computers will ligent AI will react to this statement? Surely, students),2 soldier crab logic gates,3 neuromor- also reach the stage of general-purpose com- adopting a personal neo-phenomenological phic ‘liquid marble’ ballistic-reaction-diffu- putation, although all purported future appli- attitude towards reality. Under such concep- sion circuits4 and progress towards using intra- cations are the topic of much speculation and tual horizons, the refugee of existence is the cellular protein networks used as nano-scale debate. acceptance and practice of the things we’ve data buses5 (Fig. 1). The applications of these This raises an important question: if quantum been calling as biases, or local embodiments rich and varied prototypes clearly do not sup- computers are developed sufficiently that they as producers of meaning. To assume the funda- port general purpose computation, but rather will revolutionise computing and, by exten- mental value of the impurity (bodily and cog- suggest new routes to understanding the sci- sion, every field of human endeavour, what nitive) for the existence, a new way to embrace ences, such as ‘reprogramming’ of live cells for will be the purpose of unconventional com- what Zen monks described as wabisabi 侘寂 biomedical benefits or realizing true massively puting? (わびさび). This rich concept tries to capture Free picture from pixabay: https://pixabay.com/ photos/home-lost-alone-cosmos-robot-2305431/ parallel processing to the scale of Avogadro’s

70 71 quantum computers and underly the claims contemporary quantum computer prototypes that these architectures will achieve enormous as anything other than the domain of the un- increases in efficiency over classical machines, conventional, as may be observed in the dis- at least at some tasks. tinctly alien device shown in Fig. 2. True to the ethos of general unconventional Quantum computing concepts were first de- computing, quantum computers seek exploit vised in the 1970’s, but there was arguably the natural transfers of state and energy by in- little commercial justification for their devel- terpreting them as information processing. For opment until the mid-1990’s, when two algo- example, the aforementioned probabilistic in- rithms were described. Firstly, Shor’s algorithm terpretation of a qubit’s state arises from a pro- described a method by which a quantum com- cess of overlying the wave functions of quan- puter may factorise prime numbers efficiently,8 tum information (as quantum matter assumes something which is not possible on conven- the properties of both particles and waves), ob- tional computers: as several cryptosystems are serving and thresholding patterns of construc- based on the intractability of prime factorisa- tive and destructive interference therein. One tion, this algorithm understandably generated would struggle to describe the appearance of significant interest in academia, industry and Fig. 1. Examples of unconventional computing devices. Left: A slime mould (Physarum polycephalum) navi- gates its way between distributed nutrient sources, optimising its morphology in a manner that may be exploited to plan transport networks. Above: A ‘neuromorphic’ liquid marble containing carbon nanotubes whose electrical resistance ‘remembers’ past electrical activity in a manner similar to human neurons. Scale bar = 10 mm.

The purpose of this article is to briefly delin- quantum matter, is stored as ‘qubits’, which eate what quantum computers are, evaluate may assume a ‘1’, a ‘0’, or a linear combination whether they are likely to achieve such lofty of both of these (superposition). This article’s goals and discuss what role unconventional title alludes to a concept in quantum science computing will play in a postquantum world. which states that when a qubit is observed, its manifold states will appear to collapse, at How does/will quantum computing work? which point the qubit will resolve probabilis- Let us consider some fundamental information tically as a binary bit. Whilst it would be tech- theoretical concepts relevant to classical com- nically inaccurate to say that superposition puter systems. Data exist as electrical charge enables a greater informational density in a distributed across silicon circuit components, qubit than a conventional bit, there are tools to where the presence of charge is a binaric bit allow for multiple calculations to be resolved representing ‘1’ and its absence is a ‘0’. We on a single qubit. It should be noted that quan- may observe these bits and store them: doing tum computers are deterministic under most something to a bit won’t alter anything else in interpretations of quantum mechanics, but our the system and the process is generally lossy, inference of their output may not be. i.e. one cannot deduce the input pattern from Another strange property of quantum matter is observing its output with no prior knowledge. called entanglement, which is where changes None of these facts are true for quantum com- in the state of one qubit will have simultane- puting, or indeed many other unconventional ous effects on another qubit, even if they are computing paradigms. separated by great distances. Coupled with su- Fig. 2. Photograph of the IBM Q 53 qubit quantum computer. Image courtesy of IBM.9 Quantum information, which may be rep- perposition, these are the primary two physical resented by any of a variety of properties of principles that are exploited in the design of

72 73 government cybersecurity divisions. Second 2001. Similarly, Shor’s algorithm is purported the course of inquiry in all fields where data Quantum matter is extremely difficult to ma- was Grover’s algorithm, which described to be a route towards breaking RSA encryption science is applied, which is to say, practical- nipulate due to its sensitivity to even minor methods to achieve quadratic increases in schemes, thereby laying bare all internet-based ly ever field of contemporary research. Most environmental changes: a phenomenon called search efficiency over classical systems.10 communications and transactions. From the popular machine learning methods now have ‘decoherence’ stalks every advance in the paucity of published progress, we must con- their own quantum implementations ready- field, which introduces error into calculations There have been a significant number of inter- cede that these applications are a long way and-waiting for the architectures that can run once qubits experience the changes in entro- esting developments in the field since these al- away; furthermore, in the author’s opinion, them, including fully scalable neural networks. py that are unavoidable during computation, gorithms emerged (e.g. quantum teleportation these tasks are also an inelegant and restrictive Quantum machine learning may also refer to for example resulting from self-examination, as a basis for a new wireless internet),11 but ex- application of such technologies, despite their the use of conventional machine learning to moving data and performing calculations. perimental progress in the physical engineering obvious utility. interpret the output of a quantum computer Quantum computers must be isolated from of quantum computers has not yet caught up. To reiterate a theme expounded upon in the which is, unfortunately, currently very noisy. all forms of radiation, vibration, temperature, Whilst both Shor’s and Grover’s algorithm have previous section, unconventional computing There is an elegant self-perpetuation here in etc. For these reasons, it’s difficult to imagine both been experimentally realised, both have concerns doing things that classical computers the use of unconventional computing to accel- miniaturised, affordable quantum chips being been done so on systems with extremely lim- cannot, as opposed to competing with them. erate the progress of unconventional comput- available during this century, although they ited capabilities: only the numbers 15 and 21 One intuitive application for quantum coming research. may reach academic institutions and large have been successfully factorised by true quan- puters is, therefore, simulation of the quantum The past decade has seen an enormous in- businesses much sooner. Furthermore, several tum systems and Grover’s searches haven’t been world: something which is extremely difficult crease in the use of machine learning concom- cloud computing services are planning to or implemented on systems utilising more than a to do on classical systems as the interaction itant with the emergence of affordable com- have already begun to offer access to quantum handful of qubits. environment needed to represent a quanti- puters capable of having arguments with large compute clusters. In 2019, researchers at Google claimed to have ty of quantum particles must necessarily be quantities of data. The field of data science has A significant number of dissenters argue that, experimentally demonstrated what they called exponentially larger than the number of par- arisen from this and industry is only starting to due to the requirement for quantum comput- ‘quantum supremacy’: using a 54 qubit system ticles contained. This presents a problem as realise the great many incentives that emerge ers to have vastly larger qubit capacities than called ‘sycamore’, they implemented a non-use- quantum physical experiments are notorious- the field including accelerated research, opti- their algorithms require to compensate for ful function in 200 seconds which would have ly complex, time-consuming and expensive. misation, anomaly detection and intuitive in- error correction mechanisms, we will never apparently taken about 10,000 years on a clas- Simulation of these events therefore allows us terpretation of natural languages. It is therefore achieve the aforementioned quantum comput- sical supercomputer, although both these results access to previously unfound tools for unlock- no exaggeration to say that quantum computing goals. These arguments, which are based and the estimations of their significance are con- ing the secrets of the natural world. Recent ing will, through enhancing simulation of the in convincing quantum theory, are difficult to tested. results from IBM’s quantum group, based on natural world and enabling further advances counter, although developments such as quan- The reader should now appreciate that quan- their previous numerical work, have already in artificial intelligence, lead to momentous tum machine learning seek to bridge the cap tum computers utilise unconventional media found uses in the design of next-generation re- progress in every field of human enquiry. by resolving engineering issues through intelli- and algorithms to do certain tasks very well, chargeable batteries.12 The only caveat to these optimistic appraisals gent use of software. but that we are yet to witness the advent of There have also been encouraging results in the is that quantum computers may never reach quantum computing at which it becomes a field of quantum machine learning. Conven- these dizzy heights: therein will lie the answer We are currently at an historic fulcrum be- useful and widespread technology. Before we tional machine learning refers to techniques to our main issue as to what role there is for tween which we must consider the putative evaluate whether quantum computers will which use computers to do classification or the entirety of unconventional computing in future of unconventional computing as both ever become useful and widespread, en route prediction, typically using very large datasets, this process, one way or the other. existing and not existing (no pun intended): towards assessing the postquantum future of where the experiment is repeated many times will quantum computation fall by the wayside unconventional computing, let us briefly ex- with minor variations in run parameters. The The postquantum role of unconventional and leave room for other unconventional sub- amine why we should be excited by the pros- computer keeps a score of what works well, computing strates to fill the gap, or will the future lie with pect of quantum computing, as it is perhaps and ‘learns’ how to adjust itself to achieve It is impossible to predict the scale of invest- quantum and leave us wondering how we may difficult to be enthralled by discussing tedious optimal results, which can then be leveraged ment in quantum computing to date, due to advance the field yet another ‘quantum’ leap. and abstruse mathematical algorithms. on new data. Incidentally, machine learning the nature of hidden business interests and The most salient fact here is that we are al- and its parent field, artificial intelligence, were state involvement in potentially disruptive ready in a quantum era: the sparse experimen- Why should we care about quantum com- once considered unconventional and derive technologies, but the size of government tal advances in the past two or three years have puters? from the biological sciences. grants and magnitude of bespoke laboratories shown that the theoretical benefits of these ar- An obvious application of quick searches is Quantum machine learning in its purest sense, of tech giants (notably, IBM, Google and Mic- chitectures may be achieved on a small scale; the ability of the use of brute force to crack which is using quantum computers and their rosoft) indicate that tens of billions have been it’s unreasonable to assume that we won’t re- encryption schemes; indeed, the emergence inherent mechanisms for doing efficient work spent. Yet, the pace of experimental develop- alise significant improvements on this design. of Grover’s algorithm contributed to the in- on very large quantities of data to do machine ment after 20 years of work and 50 of academ- This cannot be overstated: we are already us- dustry-wide adoption of 256-bit encryption in learning, may potentially greatly accelerate ic interest is unequivocally glacial. ing quantum computers and they are already

74 75 being applied to real problems, albeit on an 1 Unconventional Computing Laboratory, Universi- st extremely limited scale. ty of the West of England, Bristol BS16 1QY, United How to face the Complexity of the 21 Century Challenges? The contribution A key role for unconventional computing re- Kingdom. [email protected] 2 searchers is to recognise and understand the A. Tero, S. Takagaki, T. Saigusa, et al., “Rules for bio- failings of quantum computers, rather than just logically inspired adaptive network design,” Science of Natural Computing 327(5964), 2010, 439-442. 1 their advantages. This article offers no specif- Pier Luigi Gentili 3 Y.-P. Gunji, Y. Nishiyama, A. Adamatzky, “Robust sol- ic mathematical or experimental method by dier crab ball gate,” AIP Conference Proceedings which we can propose to exert control over a 1389(995), 2011, 10.1063/1.3637777. The 21st Century Challenges are Complexity Challenges because they regard Complex Sys- number of error-corrected qubits greater than 4 R. Mayne, T. Draper, N. Phillips, et al., “Neuromor- tems, and hence other types of Complexities, such as Bio-ethical, Computational, and the number of subatomic particles in the ob- phic liquid marbles with aqueous carbon nanotube servable universe and hence enable the cre- cores,” Langmuir 34(40), 2019, 13182-13188. Descriptive Complexities. This article proposes some strategies to tackle the compelling ation of ‘useful’ quantum computers, but we 5 A. Chiolerio, T. Draper, R. Mayne, et al., “On resis- challenges of this century. A promising strategy is the interdisciplinary research line of Nat- have seen how a bioinspired unconventional tance switching and oscillations in tubulin micro- ural Computing that includes Artificial Intelligence. computing tool (machine learning) has already tubule droplets,” Journal of Colloid and Interface been applied to clean the output of true quan- Science 560, 2020, 589-595. 6 tum computers, which goes at least some way A. Adamatzky, The Silence of Slime Mould, Bristol, Luniver, 2019. to bridging this gap. 7 A. Adamatzky (ed.), Slime Mould in Arts and Archi- Quantum computers are noisy, don’t achieve tecture, Gistrup, River, 2020. true parallelism and will demand compara- 8 P. Shor, “Polynomial-time algorithms for prime tively strenuous engineering, but this doesn’t factorization and discrete logarithms on a quantum detract from the magnificent vision with which computer,” SIAM Journal on Scientific Computing they are being developed. 26(5), 1997, 10.1137/S0097539795293172. Regardless of whether the future is quantum, 9 IBM, Newsroom image gallery, available at https:// unconventional computing research fill both newsroom.ibm.com/image-gallery-research. seek to improve its sister field and look for al- 10 L. Grover, “A fast quantum mechanical algorithm ternatives. We will still find enormous use in for database search,” STOC ‘96: Proceedings of the parameterising biological mechanisms that 28th Annual ACM symposium on Theory of Com- puting, 1996, 212-219. afford us control over biomedical systems, de- 11 W. Pfaff, B. Hensen, H. Bernien, et al., “Uncondi- signing chemical systems which realise true tional quantum teleportation between distant sol- massive parallelism and developing natural- id-state quantum bits,” Science 345(6196), 2014, ly-inspired algorithms for use on conventional 532-535. systems that solve open problems on comput- 12 J. Rice, T. Gujarati, T. Takeshita, et al., “Quantum ability, to name but a few, limited examples. chemistry simulations of dominant products in lith- In an ideal world, we would have a different ium-sulfur batteries [preprint],” ArXiv, 2020, avail- The phenomenon of chemical waves generated by the Belousov-Zhabotinsky reaction (on the left) and specialised computing substrate for each task: able at http://arxiv.org/abs/2001.01120. its interpretation according to the theory of Natural Computing that describes the thin film of the solution as a collection of artificial neuron models communicating chemically (on the right). a biological CPU (Central Processing Unit) for neural networks, a quantum computer for database searches and a conventional computer to compose text documents with, and A fundamental role of science is that of solv- planets of our solar system, and engineer liv- so on. Until then, unconventional computing ing practical problems and improve the psy- ing beings. Despite many efforts, there are still research will continue to find new methods, chophysical well-being of humans. Science compelling challenges that must be won. They st materials and applications for novel comput- succeeds in playing this role when it promotes are the so-called 21 Century Challenges in- ing materials. technological development. Mutual positive cluded in the 2030 Agenda composed by the feedback action exists between science and United Nations. Examples of these challenges technology: science sparks technological de- are all those diseases that are still incurable. velopment. At the same time, new technolo- There are challenges that concern about hu- gies allow an always more-in-depth analysis man activities. Our manufacturing processes of natural phenomena. Cutting-edge technol- must become circular, minimizing waste. They ogies let us manipulate materials at the mo- should not perturb the fragile stability of natural lecular and atomic scale, send robots to other ecosystems and contribute to climate change.

76 77 Poverty should be eradicated from the Earth, the exact solution in a reasonable lapse of Therefore, the Uncertainty Principle places type of Complexity, which can be named as and justice should be assured in our societies. time with the available computing machines. concrete limits to the deterministic dream of Bio-Ethical Complexity (BEC). Whenever we tackle one of these challenges, On the other hand, an Exponential Problem, describing the dynamics of the universe, start- From this discussion, it is spontaneous to name we need to deal with Complex Systems, such whose number of computational steps is an ing from the description of its microscopic the challenges of the 21st century as Complexi- as living beings, ecosystems, climate, and exponential function of the problem’s dimen- constituents. We might think of describing ty Challenges. They involve Natural Complex- human societies. When we focus on human sion, is tractable only if it has a small dimen- Complex Systems only from the macroscop- ity (NaC) and Bio-Ethical Complexity (BEC), health, the immune and the nervous systems sion. Exponential Problems with large dimen- ic point of view, neglecting their microscop- which are interlinked with Computational are other examples. Complex Systems appear sions are intractable. In these cases, they are ic “bricks.” However, Complex Systems can Complexity (CoC) and Descriptive Complex- so diverse. Currently, they are investigated transformed into Non-deterministic Polyno- exhibit chaotic dynamics. Chaotic dynamics ity (DeC). How can we think of winning these by distinct disciplines. The burgeoning Com- mial Problems (NP). After fixing an arbitrary are aperiodic and extremely sensitive to the Complexity Challenges? plexity Science is trying to point out the fea- criterion of acceptability, solutions are gen- initial conditions. Since the determination of First of all, we need an interdisciplinary ap- tures shared by all Complex Systems, i.e., the erated through heuristic algorithms, and they the initial conditions is always affected by un- proach. Natural Complexity must be faced characteristics of Natural Complexity (NaC).2 are checked if acceptable or not. Meanwhile, avoidable experimental errors, the chaotic dy- by all the scientific disciplines, including the All Complex Systems can be described as net- some scientists, allured by the amount of mon- namics are unpredictable in the long term by social and economic ones. Philosophers can works with nodes and links. Different Com- ey promised by the Clay Mathematics Institute definition. help to formulate new epistemological mod- plex Systems usually have distinct architec- in Cambridge, are trying to rigorously verify if els and new methodologies. When we tackle tures; the nodes and links are often diverse and the NP problems are reducible to P problems The limited predictive power of science the Bio-Ethical Complexity, the involvement evolve in time. Complex Systems are constant- or this reduction is impossible. makes many ethical issues related to techno- of scientists and philosophers and jurists, art- ly out-of-equilibrium in the thermodynamic The second reason why we find unsurmount- logical development fiercely arguable. The ists, and theologians is appropriate. The artists, sense. The behaviour of inanimate matter is able difficulties in describing Complex Systems unstoppable technological development in- guided by their intuitions, could spark new driven by force fields, whereas that of living is that they show variable patterns. Variable pat- duces humanity to continuously raise a funda- ideas and unconventional ways for interpret- beings is information-based. Furthermore, terns are objects or events whose recognition is mental question: “Is it always fair to do what ing Complexity. The theologians offer an extra Complex Systems exhibit emergent proper- hindered by their multiple features, which vary technology makes doable?” It is a tormenting dimension for giving meaning to our lives. The ties. The integration of the features of nodes and are extremely sensitive to the context. Ex- question that has accompanied humankind Universities worldwide should offer Interdis- and links gives rise to properties that belong amples of variable patterns are: the human fac- since the beginning. Suffice to think about the ciplinary courses on Complex Systems,4 and to the entire network. The whole is more than es, voices, and fingerprints; handwritten cursive Greek myth of Prometheus or the most recent the formation of genuinely interdisciplinary the sum of its parts. Finally, there is another words and numbers; patterns and symptoms in novel Frankenstein written by Mary Shelley research groups should be favoured by public universal attribute: Complex Systems cannot medical diagnosis; patterns in apparently un- in the 19th century. Cutting-edge technologies and private funding. be described exhaustively. In other words, correlated scientific data; aperiodic time series; allow for manipulating and re-engineering The investigation of Complex Systems cannot science finds many difficulties in predicting political and social events. It is necessary to for- life. Therefore, bioethical issues arise. There be performed by relying only on the reduction- the behaviour of Complex Systems, especially mulate algorithms for recognizing every type of are bioethical issues that concern about the ist approach, because Complex Systems exhib- in the long term. These difficulties are due to pattern. The steps of pattern recognition are: ac- beginning of a new life. Examples are: “Is it it emergent phenomena. A systemic approach three principal reasons. quisition of instrumental data; selection of the fair to manipulate human embryonic stem is also needed. Furthermore, when we study features that are considered as representative of cells?” or “Is it safe to originate genetically the behaviour of Complex Systems, we cannot The first reason hasa computational character. the pattern; application of an algorithm for the modified organisms?” Other bioethical issues trust anymore in one of the cornerstones of the Most of the computational problems regarding classification step. Despite many attempts, it is regard suffering and the end of human life. scientific method, which is the reproducibility Complex Systems and their simulation, such still necessary to propose universally valid and Examples are: “Is euthanasia fair?” or “What of the experiments. Experiments on Complex as scheduling, machine learning, financial effective algorithms for recognizing variable can we state about the therapeutic obstina- Systems are usually historical events. The phi- forecasting, solving the Schrödinger equation, patterns. This difficulty generates a third type of cy?” Finally, there are forefront technologies losopher Karl Popper has effectively described and the Traveling Salesman problem are solv- Complexity that it might be named “Descriptive that enhance human intellect and physiology. this state of affairs by declaring5 that, in the able but intractable. According to the theory Complexity” (DeC). “Is it fair to exploit such enhancement’s tech- past, science had been occupied with clocks, of Computational Complexity (CoC),3 all the The third reason why we find difficulties in niques?” It is tough to find shared solutions to i.e., simple, deterministic systems having re- solvable problems can be grouped into two predicting the behaviour of Complex Systems all these queries. They are intrinsically linked producible behaviours. Currently, instead, sets: the set of Polynomial Problems and that derives from the intrinsically limited predictive to the meaning we give to our lives. Further- science has to deal with clouds, i.e., Complex of Exponential Problems. A problem is polyno- power of science. In the description of the mi- more, from both a biological and a physiolog- Systems having unique and hardly replicable mial when the number of computational steps croscopic world, it is necessary to deal with ical point of view, every living being is a Com- behaviours. grows in a polynomial way with respect to the the Heisenberg Uncertainty Principle. Such a plex System, and we have already declared The investigation of Complex Systems requires dimension of the problem. The Polynomial principle asserts the impossibility of determin- the limitations we encounter in predicting the to monitor them continuously because their Problems (P) are problems of recognition. They ing position and momentum of every micro- behaviour of Complex Systems. The bioethi- behaviour is hardly static, but rather highly are tractable because it is possible to achieve scopic particle, simultaneously and accurately. cal issues mentioned above generate another dynamic. Therefore, it is necessary to collect,

78 79 process, and store massive data sets, i.e., the computations. Every physicochemical law de- rigid if made of solid inorganic compounds or 1 Physical Chemistry Professor focused on Complex so-called Big Data. Furthermore, it is becom- scribes a causal event, and any causal event flexible if based on organic films. Alternative- Systems, Department of Chemistry, Biology, and Bio- ing evident that an alternative way of doing ex- can be conceived as a computation. In fact, ly, surrogates of neurons can be implemented technology, Università degli Studi di Perugia, Italy. 2 periments on Complex Systems is to perform the causes are the inputs, the effects are the through solutions of specific non-linear chem- M. Mitchell, Complexity: A Guided Tour, New York, Oxford University Press, 2009; P. Charbonneau, Nat- simulations with computers. To deal with the outputs, and the law governing the transfor- ical systems, in wetware (see the Figure on ural Complexity: A Modeling Handbook, Princeton, huge volume and the fast stream of data, their mation is the computation algorithm. The sec- p. 77). Finally, specific hybrid electrochemical Princeton University Press, 2017; P. L. Gentili, Un- variety, and variability, and to extract insights ond research program of Natural Computing systems can play as surrogates of neurons. In tangling Complex Systems: A Grand Challenge for from them, it is necessary to speed up our mimics the features and performances of the our research group, we are exploiting molec- Science, Boca Raton, CRC Press, Taylor & Francis computational machines, extend their memo- natural information systems that belong to liv- ular, supramolecular, and systems chemistry Group, 2018. ry space, and always contrive more effective ing beings. We might mimic living cells (called to mimic some performances of human intel- 3 O. Goldreich, Computational Complexity: A Con- algorithms. Biomolecular Information Systems), nervous ligence and develop Chemical Artificial Intel- ceptual Perspective, Cambridge, Cambridge Univer- systems (called Neural Information Systems), ligence.7 sity Press, 2008. 4 There are two relevant strategies to succeed. immune systems (called Immune Information Specifically, we are devising modules for fu- P. G. Mahaffy, A. Krief, H. Hopf, G. Mehta, S. A. Matlin, “Reorienting chemistry education through The first strategy consists of improving current Systems), and societies (Social Information turistic chemical robots. A “chemical robot” systems thinking,” Nature Reviews Chemistry 2(4), electronic computers. Electronic computers Systems). All these systems have the peculiar- is thought as a molecular assembly that re- 2018, 0126; S. A. Matlin, G. Mehta, H. Hopf, A. are based on the Von Neumann’s architec- ity of exploiting matter and energy to encode, acts autonomously to its environment through Krief, “One-World Chemistry and Systems Think- ture, wherein the memory, storing both data collect, store, process, and send information. molecular sensors; it makes decisions by its ing,” Nature Chemistry 8(5), 2016, 393-396; P. L. and instructions, is physically separated from intrinsic Artificial Neural Networks, and- per Gentili, “Designing and Teaching a Novel Interdisci- the central processing unit. The pace of com- With human intelligence as its emergent prop- forms actions upon its environment through plinary Course on Complex Systems To Prepare New puters’ improvement has been described by erty, the human nervous system is particularly molecular effectors. The intelligent activities of Generations To Address 21st-Century Challenges,” Moore’s law, stating that the number of transis- attractive when we want to face Complexity. a chemical robot should be sustained energet- Journal of Chemical Education 96(12), 2019, 2704- tors (i.e., the ultimate computing elements that It allows us ically by a metabolic unit. Chemical Robots 2709. 5 K. Popper, “Of clouds and clocks”, in Objective are binary switches) per chip doubles every should be easily miniaturized and implanted Knowledge: An Evolutionary Approach Oxford, Ox- - to handle both accurate and vague information, two years. There is a worldwide competition in living beings to interplay with cells or or- ford University Press, revisited edition, 1972, 206- computing with numbers and words. in devising always faster supercomputers. It ganelles for biomedical applications. They 255. - To reason, speak, and make rational decisions is the TOP500 project. According to the last should become auxiliary elements of the hu- 6 S. J. Russell, P. Norvig, Artificial Intelligence: A in an environment of uncertainty, partiality, list compiled in June 2020, globally, the fast- man immune system and help us to defeat the Modern Approach, Englewood Cliffs, Prentice-Hall. and relativity of truth when the Incompatibility still incurable diseases. 2009; C. Mead, Analog VLSI and Neural Systems, est supercomputer is the Japanese Fugaku that Principle holds: “As the complexity of a system Boston, Addison-Wesley, 1989. reaches the astonishing computational rate of increases, accuracy and significance become Finally, this research line of Chemical Artificial 7 P. L. Gentili, “The Fuzziness of the Molecular World 415.5 PFlops/s. Meanwhile, Chips’ producers almost mutually exclusive characteristics of our Intelligence hopefully will give clues about and Its Perspectives,” Molecules 23(8), 2018, 2074; are investing billions of dollars in contriving statements.” the origin of life on Earth. The appearance of P. L. Gentili, “Small Steps towards the Development computing technologies that can go beyond - To recognize quite easily variable patterns. life on Earth was a phase transition or sudden of Chemical Artificial Intelligent Systems,” RSC Ad- Moore’s law. change in how chemical systems could pro- vances 3, 2013, 25523-25549. The second strategy is the interdisciplinary re- Therefore, it is worthwhile studying human cess and use information. In the beginning, the search line of Natural Computing. Researchers intelligence and trying to reproduce it by de- world was abiotic, and any chemical matter working on Natural Computing draw inspira- veloping Artificial Intelligence. Artificial Intel- was unable to process information. About 4 tions from nature to propose: ligence is revolutionizing our lives and soci- billion years ago, the phase transition from a - new algorithms, eties. It is used in basic and applied science, purely abiotic to the biotic world occurred. - new materials and architectures to compute medicine, well-being, economy, and security. What happened at that time? The answer to and store information, There are two strategies to develop AI.6 One this question might favor a new general theory - new methodologies, new models, and a new strategy consists in writing human-like intelli- on Natural Complexity. theory to interpret Natural Complexity. gent programs running in computers or special-purpose hardware. The other is through It is based on the rationale that any distin- neuromorphic engineering. In neuromorphic guishable physicochemical state of matter and engineering, surrogates of neurons are imple- energy can be used to encode information. mented through non-biological systems either Every natural transformation is a kind of com- for neuro-prosthesis or to design “brain-like” putation. Within Natural Computing, there are computing machines. Surrogates of neurons two important research programs. The first one can be implemented through specific solid exploits the physicochemical laws to make materials, in hardware. Such hardware can be

80 81 What causes otherwise sane, educated, rea- A quantum computer is composed of qubits, The Quantum Computing Delusion sonable (even dull!) people to firmly hold which are like bits in a normal computer ex- Dan V. Nicolau, Jr.1 and publicly extol such extraordinarily firm cept that they can simultaneously be in both views on technologies and discoveries that the 0 and 1 state, as with Schroedinger’s cat they know virtually nothing about and that, in being both alive and dead. So, a quantum many cases, are not even (or not yet) real? computer with, say, 200 qubits (something in Observe that this is different in kind — not just reach of near-future technology) could hold in quantity — from the many irrational beliefs more “computational states” than the number that we all hold because we grew up with of atoms in the known Universe. them. When people believed the Earth was flat What does this mean for computation? Regu- or that God made it in seven days, that was lar computers, while very fast, are sequential irrational and out of touch with basic obser- — one operation at a time. That works very vations about the world around them, but they well for some things, like handling spread- had been told those things all their lives. We sheets, playing chess or finding paths through might find some people’s beliefs of this type cities using GPS: situations where we under- strange, silly or stupid but we do not usually stand the rules of the game, in some sense. But 2 Fig. 1. Lauren Anne Marie Carter, think of them as insane. Holding beliefs about it fails at many of the computational tasks hu- Éblouie par la lumière quantique (Dazzled by the quantum light). the future of a currently non-existent technol- manity cares about, for example the discovery Acrylic on canvas, September ogy in an area of human endeavour that one is of new drugs, understanding the economy and 2020. completely ignorant of feels different. planning under uncertainty and constraint. For Although in common usage, the word ‘delu- these and myriad of other problems, the com- sional’ is used pejoratively, in medicine it has puter is forced, it would seem (though we can’t a very specific meaning. A delusion is an- ir yet formally prove it), to search for the prover- rational belief, firmly maintained in spite of bial needle in the haystack by checking each compelling and voluminous evidence to the strand of hay, one at a time. For a drug “made” contrary and not shared by other members of a — modest, by biochemical standards — of the patient’s culture. The second phrase is 200 molecular parts, each of which could be there precisely to delineate between the two in one of two states, finding the needle might kinds of irrational beliefs described above, to involve looking at a number of hay strands excuse, as it were, irrational beliefs that we greater, once again, than the number of atoms In the days before Christmas last year — it was a dark and rainy London evening, you grow up with or are surrounded by. A lot of in the Universe. know exactly what I mean — I grudgingly accepted an invitation to a house party. After a French people appear, interestingly, to believe few glasses of mulled wine, I started talking to a friend of a friend who works at a tech firm that the French nation is superior to all others, It’s basically for this reason that so much hope and if they look, they’ll find plenty of (most- is placed on quantum computing. In princi- that you’ve heard of. He’s smart, young, educated and previously started and then sold his ly French) people who agree with them, but if ple, since a quantum computer with N qubits own successful startup. He told me about his work, which sounds interesting, and asked you think that you are Napoleon Bonaparte, or can be in all 2N states at the same time, us- me about mine. I took my phone out and showed him a microscopic image, reprinted on even that he is alive, that’s a different situation. ing the drug discovery example above, it the next page, of one of my lab experiments. It shows a handful of white “snakes” — flu- The basic idea of quantum mechanics — that could search through the astronomically large orescent proteins extracted from rabbit muscle, about a millionth of a millimetre across — efforts at quantum computing are built on — is: solution space all in one go, finding the mo- wandering aimlessly on a similarly protein decorated surface. Unseen to the microscopist, to each possible state of a physical system, i.e. lecular configuration or configurations that but highlighted in blue by the image analysis algorithm, are “railway tracks” guiding the every way it could be, we can assign a number successfully kill the pathogen (or whatever nano-snakes’ movements. I explained that the point of the experiment was to see if, by called an amplitude. Amplitudes are concep- the aim of the drug is). Since virtually every specially arranging these tracks, the mindless motor proteins could nonetheless generate tually similar to probabilities, in the sense that area of human endeavour — and even logical simple arithmetic sums (2+5, 2+9, 5+9 and 2+5+9, in this case). We wanted to show, ba- a higher amplitude is associated with a higher reasoning itself — is in some sense founded likelihood of finding the world in that state. on ultimately computational problems of this sically, that biological — but nonetheless lifeless, in the usual sense of the word — matter But they are different from amplitudes in that type, it follows, as I’ve argued before, that such was capable of being harnessed to perform basic mathematical operations. My interlocutor, they can be negative and can even be imagi- number-crunching power would make us in- who was clearly intelligent but a layman in respect of bionanotechnology, mathematics or nary numbers. This means that while probabil- distinguishable from demigods (at least as far the dark depths of theoretical physics, suddenly became animated: “it’s the future of quan- ities can only add up, amplitudes can cancel as intelligence goes). tum computing!” out (“interfere destructively”) as well.

82 83 Of course, for a computer to be actually use- regular computer. In other words, if a garden ful, it mustn’t just compute: we also need to variety computer needs T seconds to do a get the answer out. To do that, we need a way job, the ideal quantum computer, if it existed, to turn the amplitudes of the quantum comput- could do it in √T seconds. er — once it has finished its work — into real probabilities corresponding to the answers of Is that a big deal? For easy computational the original problem. The rules for how am- problems, of the type regular computers can plitudes of a quantum system (not just a com- do quickly, we don’t need quantum computers puter) convert to probabilities are well known (or other alternative computing technologies), and are amongst the most fundamental laws of so the answer is ‘no’. On the other hand, for Fig. 2. Fluorescent proteins extracted physics as we understand them. In the case of the problems we believe to be fundamentally from rabbit muscle, about a millionth a quantum computer that ‘naively’ looked at ‘hard’, requiring unreasonable (exponential) of a millimetre across. all the strands of hay, pulling the probabilities time on a regular computer, the quantum com- out would simply give us a random answer, puter, in its ideal embodiment, would turn an like listening to a bunch of people playing exponential into a slightly smaller exponen- different tunes on different instruments all at tial. The image I have in mind when I think once. Obviously, that would not be useful. about that is of the authorities in Bangalore Of course, we can do better than that. We can in the 1980s, who, faced with exponentially try to exploit how amplitudes interact with one growing traffic, razed the city’s glorious, green another by setting up something like an or- roundabouts to enlarge intersections. It bought chestra: a (hopefully) clever pattern of interfer- them about 6 months. ence, so that most or all of the wrong answers In short, as far as we can tell, for most prob- to the problem cancel out (interfere destruc- lems of interest, quantum computers would tively), while for the right answer or answers, offer only a modest speed-up on their elec- the amplitudes all reinforce each other. tronic counterparts. None of this is controver- Firstly, the zeal of the quantum computing system’s stability — and temperature control. The challenge, naturally, is setting up such an sial. Grover’s result is almost 30 years old and community for breaking Internet passwords is There is also the quite real possibility, point- orchestra that would work for all problems of quantum computing research goes back to the itself suspect. If a bunch of materials engineers ed out by Simon Levin, one of the fathers of interest and, crucially, without knowing what 1980, so we have had plenty of time, brain told you about a cutting edge nanotechnology computational complexity theory, that we may the right answer is in advance, or even if one power and money to think about ways around and, on questioning about its potential uses, not understand the laws of quantum physics as exists! And, ay, there’s the rub. In the tug-of- these limitations. all they could offer was that it could be used well as we think we do, potentially building war between the enormous state-storing pow- Friends of quantum computing point out that to easily smash every window in the world, quantum computers on foundations of theoret- er of the qubits and the limitations necessari- there are important computational problems most people would raise an eyebrow. Less pe- ical sand. ly imposed by any structured orchestration of for which quantum computers could make joratively, the use of factorisation for online But that’s not the point. If there was a rea- their interactions, the quantum computer loses something currently intractable, tractable. In security is largely a historical accident, since sonable expectation that quantum computers some of the “speed-up” conferred on it by its particular, they point to Internet cryptography, factorisation is not believed to be in the class could, in principle, offer exponential speed- ability to store an exponentially large set of much of which is based on the presumed dif- of ‘exponentially hard’ problems. We already up over regular computers for even a few key strands of hay. The question is, how much? ficulty of the problem of factorising numbers have myriad security systems based on the computational problems of practical impor- The answer to this question is not definitely into primes (e.g. finding out that 143 can be purported difficulty of those harder problems, tance, the excitement around the technology known, and of course depends on the difficul- made by multiplying 11 and 13). This is indeed all of which could replace factorisation as the would be more than justified and investment ty of the computational problem we’re trying the case: a quantum computing ‘orchestra’ de rigueur security technology, rendering the in overcoming those engineering problems to solve, but all the theoretical results we have scheme called Shor’s algorithm can rapidly speed advantage of quantum computers essen- would be warranted. Unfortunately, based on point to an answer that goes like: “for most find prime factors. If quantum computers can tially insignificant. what we have learned over the past 40 years, problems, the quantum computer loses most successfully overcome the formidable techno- Note that none of this has to do with questions that is simply not the case. of its power.” Although I’ve smudged a lot of logical challenges they face (but see below), of whether quantum computers can scale in On the other hand, there are excellent reasons technical details in the discussion above, a they may render much of existing Internet se- practice. There are, to be sure, serious engi- to continue to study quantum computers. For specific result, called Grover’s Theorem, says curity systems vulnerable. neering challenges facing their development. one thing, they are likely to lead to insights that — at best — all that quantum computers I can’t resist the temptation of comparing that These include, inter alia, ‘decoherence,’ in- into the laws of quantum physics that we may (as currently conceived) can do when search- to someone defending a delusion of being creasing the density of signalling and wiring be able to reach by other experimental means. ing through a large, disorganised haystack (a constantly followed by the CIA by pointing to — which is hard to do without degrading the And quantum computer-like systems could database) is run squared-times faster than a an occasional black van passing by.

84 85 still find an indispensable role in drug discov- price” makes it clear that this hurdle, wherever ery, for instance by using quantum computers it may lie, was passed long ago. When a large The art of unconventional computing with cellular automata* to simulate quantum molecular processes. number of people come to believe irrational Genaro J. Martínez,1 Andrew Adamatzky,2 Marcin J. Schroeder3 Most excitingly, I think, the effort to build and and probably false things based on hearsay, as scale quantum computers may teach us about I suspect is the case of my friend at the Christ- the limits of computing and even, maybe, sup- mas party, that’s not considered to be a case The exploration of unconventional computing in its diverse forms is not only, and not pri- ply us with a profound new law of physics, of ‘clinical’ delusion by the psychiatric profes- marily a result of the natural human pursuit for innovation but rather a response to chal- which would say that there are some problems sion. Instead, we call it something more like lenges faced by the current information technology. Some of these challenges are not new, for which no computer, of any kind, can find ‘mass hysteria’, which, on my view, is much e.g. the expected end of applicability of Moores Law or the von Neumann bottleneck in answers in practice, in this world. worse, by dint of lacking the originality and the transfer of data between the CPU (central processing unit) and RAM (random-access innocence that tend to characterise personal memory). However, the bottleneck in the past was just a nuisance, but at present the need So, does the hype around quantum comput- delusions. for massive processing of synaptic weights in the network for machine learning which re- ers fit the medical definition of ‘delusion’? Not quires multiple transfer makes this primary tool of AI (artificial intelligence) inefficient and exactly. For one thing, the Diagnostic and Sta- hopeless in the competition with the natural, biological systems of information processing. tistical Manual of Mental Disorders tells us that 1 Mathematician, physician and engineer, Associ- An example of another challenge of a very different “down to the earth” type is the high en- a person cannot be diagnosed as being delu- ate Professor of Computational Mathematics at the ergetic cost of machine learning estimated already as a substantial portion of the energetic sional if the belief in question is one “ordinar- Queensland University of Technology and Visiting needs of the industrial societies which in the near future is expected to become the main ily accepted by other members of the person’s Professor of Experimental Medicine at the Univer- consumer of energy. Thus, the question about the frugality of nature in the energetic budget culture or subculture.” It’s not clear how many sity of Oxford. 2 Lauren Carter is a London-based painter. for the human or animal brain is worth billions or trillions of the future dollars. believers are needed for a delusional belief at the individual level to escape from the “folie à…” diagnostic category, but a cursory In- These and other challenges direct the research dynamics of interaction is computable, but ternet search for “quantum computing stock towards unconventional forms of computing nothing makes this computability unavoid- with the special interest in its natural forms able.6 identified in living organisms on the one hand, The shift of the focus on the dynamic, inter- and in the utilization of new, natural, physical action based forms of information processing phenomena in information processing. can be implemented in the most natural way This brings us to a more general and theoret- in the information processing in cellular au- ical question overarching the interests in nat- tomata where the art of unconventional com- ural forms of information processing about puting begins. Unconventional and natural what constitutes the fundamental distinction computing7 has the capacity to handle infor- between the traditional form of computing mation at an atomic and molecular level, the originating in the theoretical model of a Turing first stage. A diversity of scientific fields study machine, and unconventional, natural com- and research all these ways on continuous puting. One of the possible answers is that the and discrete domains. Lines of research can Turing machine model is based on the princi- be found in Table 1. ple of a one-way, goal-oriented action initiated and controlled by a pre-defined program, while all natural processes are dynamic, i.e. they are based on mutual interactions within the processing system and with its environment.4 It is possible to consider a modification of the In this way, the cellular automata theory con- Turing machine model in which instead of the ceived by von Neumann in the late 1950s one-way action of the head on the tape the years as a tool of super computation.16 Von processing is performed by mutual reading Neumann has been working with primitive and mutual re-writing of the two interacting and indivisible elements and where this theory central components.5 This model of symmet- offers an inherently and massively computation ric inductive machine remains within the in parallel. He had discussed that universal Turing limit of computability as soon as the Turing machines cannot exploit the process in

86 87 nature and the universe. This way, the existence architecture. In the literature of cellular au- of universal constructors becomes essential for tomata theory we can see a diversity of de- the universe.17 An actual problem is how to signs without any particular architecture. This control and design reliable components from way, we can think that these machines are Fig. 3: Three-dimensional projection of a two-di- unreliable organisms.18 Indeed, this issue is adapted for a specific environment. There- mensional cellular automaton Life without Dead, preserved in any unconventional computing fore, we can imagine how these machines rule B3/S012345678. This rule is able to support complex behaviour and logic computability.22 From random initial conditions you can see the emergence of worms and interesting designs when the worms interact with each other. This evolution start with an initial condition defined by a line of eleven alive cells.

Fig. 1. A three-dimensional projection of cellular automata Life-like rule B4/S9. It is a projection of the two-dimensional Life-like rule B2/S7, the Diffusion Rule.20 The rule is a chaotic rule although it supports complex patterns as oscillators, gliders, puffer trains, and an ample diversity of gliders guns. This rule proved logical universal by realisation of computing circuits via collisions between particles. This evolution displays the result of two particles colliding, thus later of 112 steps we can see symmetric complex structures emerging during the evolution, travelling, expanding and interacting with others.

Fig. 4. Metaglider (mesh) designed with the elementary cellular automaton rule 54 syn- chronising multiple collisions evolving in a Fig. 2. Three-dimensional projection of the two-di- ring. It is a three-dimensional projection of 21 mensional Life-like rule B2/S7, the Diffusion Rule. a typical two-dimensional evolution. Rule The rule is classed as chaotic although it supports 54 is a logically universal automaton.23 Logic complex patterns as oscillators, gliders, puffer computation in rule 54 is performed by colli- trains, and a diversity of gliders guns. The rule is sions of particles in its evolution space. proved logical universal via collisions of particles. This evolution displays the result of two particles in vertical position colliding. The reaction produces a replication of particles periodically in thousands of generations. With time a symmetry is lost and the automaton dynamics becomes chaotic. We call it the cellular automata origin. https://youtu.be/ BqTU_uW-zaI

88 89 are working simultaneously in nature or the extended analog computer,” Physica D: Nonlinear universe, each with its own architecture and Phenomena 237(9), 2008, 1235-1256 ; S. B. Coo- environment.19 per, “What Makes A Computation Unconvention- al?,” in G. Dodig-Crnkovic & R. Giovagnoli (eds), Fig. 6: Two-dimensional representa- Cellular automata are adequate mathematical Computing Nature: Turing Centenary Perspective, tion by colours of a Turing machine machines to represent unicelular computers that simulates the behaviour of ECA Berlin/Heidelberg, Springer, 2013, 255-269. rule 110. The history of the Turing because of their architectural properties: ar- 8 I. L. Chuang, “IBMs Test-Tube Quantum Computer machine is represented as a cellular ray of infinite state machines matches arrays Makes History,” IBM Research News, 2001. 25 automaton. The initial condition of these units. Historically cellular automata 9 A. Adamatzky, B. D. L. Costello & T. Asai, Re- starts with the string B∗010B∗ show- theory has been analyzed as supercomput- action-diffusion computers, Amsterdam, Elsevier, ing in two snapshots the evolution to 27 10,000 steps. ers. On the other hand, cellular automata are 2005. explored in an artistic way as was presented 10 G. Paun, G. Rozenberg & A. Salomaa, DNA in the book Designing Beauty: the Art of Cel- computing: new computing paradigms, Berlin, lular Automata.28 Springer, 1998. 11 We can think of unconventional computers as A. Adamatzky, “Hot ice computer,” Physics Letters A 374(2), 2009, 264-271. the physical devices and unconventional com- 12 A. Adamatzky, Physarum machines: computers puting as the logic medium where these de- from slime mould, London, World Scientific, 2010. vices work. This way, we can complement the 13 A. Adamatzky (ed.), Advances in Unconventional Table 1 with some unconventional computing Computing: Volume 1: Theory, Cham, Springer, models listed in the Table 2. 2016. 14 T. Yatagai, “Cellular logic architectures for optical computers,” Applied optics 25(10), 1986, 1571- 1577. 15 T. Hylton, “Thermodynamic Computing: An Intel- lectual and Technological Frontier,” Multidisciplinary Digital Publishing Institute Proceedings 47(1), 2020, Fig. 5: Two-dimensional representa- 23. tion by colours of a Turing machine 16 J. Von Neumann, Theory of Self-reproducing Au- that doubles the number of ones as a 1 tomata, ed. A. W. Burks, Urbana and London, Uni- 24 Escuela Superior de Cómputo, Instituto Politécnico cellular automaton. versity of Illinois Press, 1966. Nacional, México; Unconventional Computing Lab- 17 J. Von Neumann, “Probabilistic logics and the syn- oratory, University of the West of England, Bristol, thesis of reliable organisms from unreliable compo- United Kingdom; [email protected] nents,” Automata studies 34, 1956, 43-98. 2 Unconventional Computing Laboratory, Universi- 18 Ibidem. ty of the West of England, Bristol, United Kingdom; 19 A list of computable cellular automata can be [email protected] found in: Complex Cellular Automata Repository 3 Institute for the Excellence in Higher Education, https://www.comunidad.escom.ipn.mx/genaro/ Tohoku University, Sendai, Japan; schroeder.mar- Complex_CA_repository.html [email protected] 20 S. J. Martínez, I. M. Mendoza, G. J. Martínez, & S. Ninaga- 4 M. J. Schroeder, “From proactive to interactive theory of computation,” The 6th AISB Symposium wa, “Universal One-dimensional Cellular Automata on Computing and Philosophy: The Scandal of Derived from Turing Machines,” International Jour- ComputationWhat is Computation?, 2013, 47- nal of Unconventional Computing 14(2), 2019, Fig. 7: Two-dimensional representation by colours of a Turing 51. 121-138. machine that simulates the behaviour of ECA rule 110. The 21 Ibidem. history of the Turing machine is represented as a cellular au- 5 M. J. Schroeder, “Towards Autonomous Compu- 22 D. Griffeath & C. Moore, “Life without death is tomaton.26 The initial condition start with the string B∗010B∗ tation: Geometric Methods of Computing,” APA showing the evolution to 700 steps. Newsletter on Philosophy and Computation 15(1), P-complete,” Complex Systems 10, 1996, 437-448. 23 2015, 7-9. G. J. Martínez, A. Adamatzky & H. V. McIntosh, “Phe- nomenology of glider collisions in cellular autom- 6 M. Burgin, “Information Processing by Symmetric Inductive Turing Machines,” Multidisciplinary Digi- aton Rule 54 and associated logical gates,” Chaos, tal Publishing Institute Proceedings 47(1), 2020, 28. Solitons & Fractals 28(1), 2006, 100-111. 24 S. J. Martínez, I. M. Mendoza, G. J. Martínez, & S. Ninaga- 7 T. Toffoli, “Non-conventional computers,” Ency- clopedia of Electrical and Electronics Engineering wa, “Universal One-dimensional Cellular Automata Derived from Turing Machines,” op. cit. ; P. Rendell, 14, 1998 455-471; J. W. Mills, “The nature of the

90 91 Turing Machine Universality of the Game of Life, A. Adamatzky (ed.), Collision-based computing, Lon- Cham, Springer, 2016. don, Springer, 2002, 277-297. Living wearables from slime mould and fungi 25 S. J. Martínez, I. M. Mendoza, G. J. Martínez, & S. Ninaga- 38 A. Adamatzky, “Slime mould computing,” Inter- Andrew Adamatzky,1 Anna Nikolaidou,2 Antoni Gandia,3 wa, “Universal One-dimensional Cellular Automata national Journal of General Systems 44(3), 2015, Derived from Turing Machines,” op. cit. 277-278. and Alessandro Chiolerio4 26 Ibidem. 27 N. Margolus, T. Toffoli & G. Vichniac, “Cellu- Smart wearables, augmented with soft and liquid electronics, can display sensing, respon- lar-automata supercomputers for fluid-dynamics modeling,” Physical Review Letters 56(16), 1986, * Free software used to create the simulations sive and adaptive capabilities, but they cannot self-grow or self-repair. Living organisms 1694; S. Wolfram, “Cellular automaton supercom- in this paper. colonising a fabric could be a viable alternative. In the present article we briefly review our puting,” Center for Complex Systems Research, - Ready (Tim Hutton, Robert Munafo, Andrew ideas on implementing living wearables with slime mould and fungi. The living networks of 1987, online: https://content.wolfram.com/uploads/ Trevorrow, Tom Rokicki, slime mould protoplasmic tubes and fungal mycelium networks can act as distributed sen- sites/34/2020/07/cellular-automaton-supercom- https://github.com/gollygang/ready) sorial networks, fuse sensorial inputs from wearers and environment, process information puting.pdf; A. Adamatzky, Computing in nonlinear - CAviewer (José Antonio Jiménez Amador, media and automata collectives, Boca Raton, CRC Genaro J. Martínez, in a massive parallel manner and provide responses in benefit of the consortium human-mi- Press, 2001. https:// www.comunidad.escom.ipn.mx/genaro/ crobe. 28 A. Adamatzky & G. J. Martinez (eds), Designing Papers/Thesis_files/CAviewer. tar.gz) Beauty: the Art of Cellular Automata, Cham, Spring- - CATM (Sergio Eduardo Juárez Martínez, César er, 2016. Iván Manzano Mendoza, https://www.comuni- Most living creatures have plenty of living for instance a colour or shape or form change.8 29 C. H. Bennett, “Logical reversibility of compu- dad.escom.ipn.mx/genaro/Papers/Thesis_files/ wearables: skin, mites, fungal and bacterial Smart materials are often embedded in more tation,” IBM journal of Research and Development maquinaTuring.java.tar.gz) colonies colonising the skin, and critters living conventional materials and applied in a sys- 17(6), 1973, 525-532; K. Morita, “Reversible our hairs. Skin is out living wearable number tem with microelectronic components and computing and cellular automata: A survey,” The- one. The skin senses, transmit information and, miniaturized technologies.9 oretical Computer Science 395(1), 2008, 101- more likely, is capable of distributed decision Smart wearables are devices that are respon- 131. making. Limitations of the skin are that the skin sive to the wearer, they can sense and pro- 30 E. Fredkin & T. Toffoli, “Conservative logic,” In- ternational Journal of theoretical physics 21(3-4), is not disposable, we cannot change our skin cess information from the user’s body and 1982, 219-253; K. Morita, “A simple universal logic as easy as we can change the pants or socks, environment and report results of their anal- element and cellular automata for reversible com- sensorial and computational properties of the ysis as electrical signals.10 In the last decade, puting,” in M. Margenstern, Y. Rogozhin (eds), Inter- skins are not easily tunable, attempts to inte- electronics and textiles (e-textiles) have been a national Conference on Machines, Computations, grate soft and liquid electronics into human fundamental part of smart wearables. Integrat- and Universality, Berlin/Heidelberg, Springer, 2001, skins pose health risks and incompatibility ising electronics into textile products enables 102-113. sues. Also it is not acceptable in many cultures the development of wearable electro-textiles 31 L. O. Chua, “Chuas circuit: An overview ten years to appear in public naked, so a substantial for sensing / monitoring body functions, deliv- later,” Journal of Circuits, Systems, and Computers area of our skin should be covered by fabric ering communication facilities, data transfer, 4(02), 1994, 117-159. and thus renders useless for immediate envi- control of the environment, and many other 32 N. H. Margolus, “Crystalline computation,” in A. ronmental sensing. Traditionally, wearables applications.11 For example, a material sur- Hey (ed.), Feynman and Computation: Exploring the Limits of Computers, Boca Raton, CRC Press, 1998, have acted as covering tools aiming to provide face, such as a common fabric that embeds 267-305. comfort and protection from the elements. a nitinol wire (a smart material), can become 33 T. Sienko, A. Adamatzky & N. Rambidi, Molecular They have also constituted semiotic devices, sensitive and responsive (with visual or kinetic computing, Cambridge, MIT Press, 2003. machines for communication5 and functioned response) according to an external stimulus, 34 B. Gr¨unbaum & G. C. Shephard, Tilings and pat- as social mediators and interfaces between like a rise in temperature. This may happen terns, Mineola, Courier Dover Publications, 1987. our bodies and society.6 With the emergence when you wear it, and the increase in body 35 G. J. Martínez, A. Adamatzky, K. Morita & M. Mar- of novel and smart materials, the functionality temperature causes the expansion of the fab- genstern, “Computation with competing patterns in of wearables has been extended, offering new ric.12 One of the most impacting issues regard- Life-like automaton,” in A. Adamatzky (ed.), Game opportunities. Smart materials can be defined ing both electron devices and nanocomposite of Life Cellular Automata, London, Springer, 2010, as highly engineered materials that respond in- materials is represented by their poor capabili- 547-572. telligently to their environment.7 They are char- ty to self-repair and grow, to self-organize and 36 M. Burgin, “Information Processing by Symmetric acterized by their ability to detect and respond adapt to changing environmental conditions. Inductive Turing Machines,” op. cit. to stimuli from the environment (such as stress, Although smart wearables can display sens- 37 M. H. Jakubowski, K. Steiglitz & R. Squier, “Com- puting with solitons: a review and prospectus,” in temperature, moisture, pH, electric or magnet- ing, responsive and adaptive capabilities, they ic fields), by a specific change of behaviour, as cannot self-grow and self-repair. In addition to

92 93 by illuminating Physarum with red, green, blue response and two for a prolonged response. and white colours and analysing patterns of the Despite the sufficient sensorial abilities, the slime mould’s electrical potential oscillations. slime mould is rather fragile, highly depend- We defined that the slime mould recognises ent on environmental conditions and requires a colour if it reacts to illumination with the particular sources of nutrients. Fungi could, colour by a unique changes in amplitude and however, make a feasible alternative to the periods of oscillatory activity. In laboratory ex- slime mould for the following reasons. Fungal periments we found that the slime mould rec- composite materials, normally in form of solid ognises red and blue colour. The slime mould lignocellulosic substrates colonised with the does not differentiate between green and mycelium of filamentous fungi (e.g. Ganoder- white colours. The slime mould also recognis- ma spp., Pleurotus spp., Trametes spp.), are an es when red colour is switched off. We also emerging type of biomaterial known by being mapped colours to diversity of the oscillations: a robust, reliable and ecologically friendly re- illumination with a white colour increases di- placement for conventional building materials Fig. 3. Imitation of scalp innervation with versity of amplitudes and periods of oscilla- and fabrics.15 Fungi possess almost all the sens- Fig. 1. Live slime mould Physarum Fig. 2. A polyurethane mannequin head colo- Physarum polycephalum. tions, other colours studied increase diversity es used by humans.16 Fungi sense light, chem- polycephalum growing on a doll. Exper- nised by slime mould Physarum polycephalum. iments conducted with A. A.’s daughter, either of amplitude or period. icals, gases, gravity and electric fields. Fungi Adriana Adamatzky, in 2010. show a pronounced response to changes in a As a proof of concept we designed an exper- substrate pH,17 mechanical stimulation,18 toxic 19 20 21 this, the materials usually used to create the diffusion pattern formation mechanism; Physar- imental laboratory implementation of a slime metals, CO2, and stress hormones. Fungi electronic components of the wearables such um may be considered as equivalent to a mem- mould based tactile bristles, where the slime are known to respond to chemical and physi- as metals, plastics and other petroleum-based brane bound sub excitable system (excitation mould responds to repeated deflection of bris- cal stimuli by changing patterns of its electri- 22 23 materials are derived from natural resources, stimuli provided by chemo-attractants and tle by an immediate high-amplitude spike and cal activity and electrical properties. Thus, which are limited and non-renewable. Elec- chemo-repellents); Physarum may be regard- a prolonged increase in amplitude and width wearables made of or incorporating a cellu- tronic waste or e-waste is one of the emerging ed as a highly efficient and living micro-ma- of its oscillation impulses. We demonstrated losic fabric colonised by fungi might act as a problems in developed and developing coun- nipulation and microfluidic transport device; that signal strength of the Physarum tactile bris- large distributed sensorial network. tries worldwide as it comprises a multitude of Physarum is sensitive to illumination and AC tle sensor averages near six for an immediate components with valuable materials, some electric fields and therefore allows for paral- containing toxic substances, that can have an lel and non-destructive input of information; adverse impact on human health and the envi- Physarum represents results of computation ronment.13 Living organisms could be a viable by configuration of its body. In experimental alternative. laboratory studies, we showed that when in- oculated on bare plastic surfaces, Physarum Back in the 2010s we proposed a concept of successfully develops an optimal network of extralligence by growing living slime Physar- protoplasmic tubes spanning sources of at- um polycephalum on models of human bod- tractants while avoiding domains with over ies.14 We designed, and partly implemented threshold concentration of repellents. When in laboratory conditions with slime mould exposed to attractants and repellents, Physar- Physarum polycephalum, an intelligent adap- um changes patterns of its electrical activity. tive living network wearable by humans and We experimentally derived a unique one-to- robots. When grown on 3D bodies (living or one mapping between a range of selected bio- inanimate) the living Physarum network proactive chemicals and patterns of oscillations of vides a highly-distributed sensorial structure the slime mould’s extracellular electrical po- (light-, electro-magnetic, chemical and tactile tential. This direct and rapid change demon- sensitivity) with embedded dynamic architec- strates detection of these chemicals in a similar ture of massive-parallel computing processors manner to a biological contactless chemical based on geometry of proximity graphs. We sensor. We believe results could be used in have chosen an acellular slime mould Physarum future designs of slime mould based chemi- polycephalum as amorphous living substrate be- cal sensors and computers. We also evaluated Fig. 4. Rat whiskers made of living slime mould Physarum polycephalum. cause Physarum is a living, dynamical reaction feasibility of slime-mould based colour sensors

94 95 To evaluate feasibility of the living fungal of electrical potential oscillation in a response wearables, we conducted two sets of labora- to application of chemo-attractants or nutri- tory experiments. ents is consistent with previous studies. The In the first set, to assess the sensing potential increase in amplitude of spiking hours after of fungal wearables, we undertook laboratory the application of malt or dextrose might be experiments on electrical response of a hemp due to the fungus ingesting the nutrients and fabric colonised by oyster fungus Pleurotus transposing them across the wide mycelial ostreatus to mechanical stretching and stimu- network. lation with attractants and repellents.24 A fab- In the second set of experiments25 we experi- ric colonised by the fungus P. ostreatus shows mented with fungal skin. A fungal skin is a thin distinctive sets of responses to chemical and flexible sheet of a living interwoven, homoge- mechanical stimulation. The response to 50 g neous, and continuous mycelium made by a load is in the range of 1.5 min which might filamentous fungus. The skin could be used in indicate that rather purely electro-mechani- future living architectures of adaptive buildings cal events take place than reactions involving and as a sensing living skin for soft self-grow- propagation of calcium waves. The response to ing/adaptive robots. In experimental labora- stimulation with ethanol is in a range of 7 sec. tory studies, we demonstrated that the fungal This would rather indicate physico-chemical skin is capable of recognising mechanical and damages to hyphae walls and corresponding optical stimulation. The skin reacts differently electrical responses. The increase of frequency to loading of a weight, removal of the weight,

Fig. 7. Pairs of differential electrodes inserted in the fungal skin to record electrical response of the fungal skin to mechanical and optical stimulation.

and switching illumination on and off. These clothing that responds to the environment, are the first experimental evidences that fungal self-sustaining and self-healing clothing and materials can be used not only as mechanical parchments grown in situ, exoskins and exo- skeletons in architecture and robotics but also skeletons that symbiotically interact with the as intelligent skins capable of recognition of user, cross-over synergistic interactions be- external stimuli and sensorial fusion. tween biological entities and electronic cir- Living wearables offer a new spectrum of per- cuits or machines (advancements in biorobot- formance possibilities such as reactiveness, ics and biomechanoids). adaptiveness, and sensing capabilities. They are harmless to the environment, biodegrada- ble and they can even nurture the cultivation of new materials in their end of life. The liv- 1 Professor in Unconventional Computing, UWE, ing material provides a unique opportunity for Bristol, UK. the wearables to be programmable by guiding 2 Senior Lecturer in Architecture, UWE, Bristol, UK. the growth, controlling the nutrients and set- 3 Leading Researcher at MOGU, Italy. ting up the conditions in which the wearable 4 Leading Researcher at IIT, Torino, Italy. can be created. Their ability to self-repair and 5 U. Eco, Travels in Hyperreality, New York, Mariner self-grow makes them one of the most prom- Books, 1986. 6 ising. Future studies can be focused on better M. Barnard, Fashion Theory: An Introduction, Lon- understanding of electrical communication don, Routledge, 2014. 7 M. Addington, D. Schodek, Smart Materials and and stimulation in fungi and other microbes Fig. 5. A photo of experimental setup showing a New Technologies. For Architecture and Design Pro- hemp pad colonised with fungi, attached to a T-shirt (advancements in biocomputation), develop- fessions, Oxford, Architectural Press-Elsevier, 2005. with electrodes and recording equipment. Fig. 6. The fungal skin shows animal type wrinkles. ment of biological sensors able to report slight 8 M. Ferrara, M. Bengisu, Materials that Change changes in physico-environmental conditions Color. Smart Materials, Intelligent Design, Cham, and biochemical traces, biological sentient Springer, 2013.

96 97 9 M. Ferrara, “Smart Experience in Fashion Design: 17 I. M. Van Aarle, P. A. Olsson, B. Soderstrom, “Ar- A speculative analysis of smart material systems ap- buscular mycorrhizal fungi respond to the substrate Brain Lego plications,” Arts Basel 8, 2019, 1-11. ph of their extraradical mycelium by altered growth 10 A. Adamatzky, A. Nikolaidou, A. Gandia, A. Chi- and root colonization,” New Phytologist 155, 2002, olerio, and M. M. Dehshibi,“ Reactive fungal weara- 173-182. Toy Computing with Lego Bricks ble,” arXiv preprint arXiv:2009.05670 (2020). 18 C. Kung, “A possible unifying principle for mech- Stefan Höltgen1 11 X. T Tao, Wearable Electronics and Photonics, anosensation,” Nature 436(7051), 2005, 647. Cambridge, Woodhead Publishing Limited and Tex- 19 M. Fomina, K. Ritz, G. M. Gadd, “Negative fungal tile Institute Abington, 2005. chemotropism to toxic metals,” FEMS Microbiology 12 M. Ferrara, M. Bengisu, Materials that Change Letters 193, 2000, 207-211. “HIRNLEGOHIRNLEGOHIRNLEGOLEGOLEGO Color, op. cit. 20 Y.-S. Bahn, F. A. Muhlschlegel, “Co2 sensing in HIRNLEGOLEGOLEHIRNLEGOLEGOLEGO 13 S. Needhidasan, M. Samuel, R. Chidambaram, “Elec- fungi and beyond,” Current opinion in microbiology HIRNLEGOLEGOLEGOHIRNLEGOLEGOLEGO“ tronic waste – an emerging threat to the environment 9, 2006, 572-578. 21 (Einstürzende Neubauten, Hirnlego, 1989) of urban India,” Journal of Environmental Health Sci- K. T. Howitz, D. A. Sinclair, “Xenohormesis: sens- ence and Engineering 12(1), 2014, 36. ing the chemical cues of other species,” Cell 133, 14 A. Adamatzky & T. Schubert, “Slime Extralligence: 2008, 387-391. Developing a Wearable Sensorial and Computing 22 S. Olsson, B. Hansson, “Action potential-like ac- “I have always had a predominantly visual approach to my environment. This is also prob- Network with Physarum polycephalum,” UWE Re- tivity found in fungal mycelia is sensitive to stim- ably why I never pursued music. This perhaps one-sided talent was also evident in the con- search Repository 927012, 2013. ulation,” Naturwissenschaften 82, 1995, 30-31; A. struction of my computer models; here, too, I preferred mechanical and electromechanical 15 F. V. Appels, S. Camere, M. Montalti, E. Karana, K. Adamatzky, “On spiking behaviour of oyster fungi constructions and left the electronics to others who were better qualified.”2 M. Jansen, J. Dijksterhuis, P. Krijgsheld, H. A. Wos- pleurotus djamor,” Scientific reports ,8 2018, 1-7; A. ten, “Fabrication factors influencing mechanical, Adamatzky, A. Gandia, A. Chiolerio, “Fungal sensing In this quote, computer pioneer Konrad Zuse describes his tinkering with construction kits moisture-and water-related properties of myceli- skin,” arXiv preprint arXiv:2008.09814 (2020). he played with as a boy and a teenager from his viewpoint as an engineer. He used those um-based composites,” Materials & Design 161, 23 A. E. Beasley, A. L. Powell, A. Adamatzky, “Fungal kits in the 1920s to build all sorts of things with them: (award winning) models of cranes 2019, 64-71; M. Jones, A. Gandia, S. John, A. Bis- photosensors,” arXiv preprint arXiv:2003.07825 and excavators, spare parts for his bike, and mechanical household aids. Later on, when marck, “Leather-like material biofabrication using (2020). his computers were already working electronically, he used the thought pattern for a new fungi,” Nature Sustainability, 2020. https://doi. 24 A. Adamatzky, A. Nikolaidou, A. Gandia, A. Chi- system of self-reproducing machines.3 org/10.1038/s41893-020-00606-1 olerio, and M. M. Dehshibi, “Reactive fungal wear- 16 Y.-S. Bahn, C. Xue, A. Idnurm, J. C. Rutherford, J. able,” op. cit. 25 Heitman, M. E. Cardenas, “Sensing the environment: Ibidem. This mechanical thinking of computer func- they are often built from construction kits (for lessons from fungi,” Nature Reviews Microbiology tions has a long tradition reaching back into children and youth) or from everyday objects 5 , 2007, 57. the Middle Ages: from Ramon Llullu’s book –– according to the “Baukastenprinzip” (“kit Ars Magna published in 1305 where a the- principle”),5 using heuristic design procedures, ological ‘converter’ for Muslims to become trial and error, and learning by doing. Christians is drafted, to Leibniz’ Machina ar- The invitation to think while tinkering (“think- ithmeticae dyadicae from 1679 (a mechanism ering”)6 seems to be a basic principle of both to calculate with binary numbers) –– both re- logic and kit toying because both make it pos- mained “paper machines” –– through to the sible to comprehend/handle complex phe- mechanical and electromechanical logical nomena. This logic (the two-valued sentential machines of the 19th and 20th centuries,4 cul- logic, inaugurated in the 3rd century B.C. from minating in Claude Shannon’s switching alge- Aristotle) is the timeless and non-spatial basis bra from 1937. All of these drafts were based of all our thinking. It provides the transcen- on the idea to make calculation and computa- dental basic structure of truth-apt propositions tion not only logically but also mechanically which are the foundation of our everyday constructible. thinking, actions, science, playing, … This re- From our present-day perspective, some of ality is formalized in logics: propositions be- these drafts appear more like toys than serious come tokens that can hold a truth value (true/ calculators; toys that merely show the princi- false –– no third option) and can be combined ples of computation but are not very suitable with junctors (and, or, if-then, not, …) to com- for actual usage. This view also has to do with plex sentences. the fact that those prototypes show their ma- A sentence like “Tonight I’ll go to the movies terial and epistemological toy characteristics: or I will read a book” can be formalized as p

98 99 v q where p means “I’ll go to the cinema”, q As early as the 1950s, toys8 were built that means “I’ll read a book”, and the v stands for made logical computer functions comprehen- the logical OR (not either-or since I can read sible/tangible (Fig. 1). The advent of digital my book in the cinema as well). Since each computers in children’s rooms transformed the of these sentences can be true (t) or false (f), didactics into a hands-on comprehension. This their or-combination can also be true or false. was realized by the use of kit systems that al- Ludwig Wittgenstein, following the system of lowed implementing logical values and junc- Chrysippos of Soloi (279-206 B.C.), inaugurat- tors in many different ways: electronic kits9 ed a notation table to show the possible iter- (with newly designed “digital expansions”, fig. ations:7 1, middle) and building bricks that facilitate the construction of mechanism –– like Fis- 10 p v q chertechnik or Lego. “Denken mit Lego” (Thinking with Lego) paved t t t the way for these ‘brick didactics’: a lego kit t t f with a book companion where two mathe- f t t maticians suggested “funny games with logics and set theory”11 to “provide experiences f f f of the cohesion between propositional logics and set theory to children.”12 Lego bricks were The fact that topics of thoughts and deeds can particularly suitable for this and could also be formalized and written down in this man- be used to explain “different bases of number ner fueled the speculation that logic does not systems”13 –– especially of the binary system. always have to be transcendental but can be By playing so-called “goal games” (91) logical transferred from the realm of the symbols into junctors should be ‘passed through’ mental- the real. The mention of the logical machines ly: “Any passway walked through provides a in the beginning proves this to be true: prop- meaningful experience to the pupils”14 –– the ositions can become variables and variables authors note before they show a diagram of can be transformed into versatile rods within a the paths for p v q resp. p ^ q. logical-mechanical design. Using the lego brick to actually convert such With the help of these machines logic, and ‘thinking paths’ into operational mechanisms only logic, can be automatized. To transform only came to the minds of Lego players in the logical machines into computers that can cal- course of the last decade. Initially, they had to culate anything calculable, a third transforma- try the ‘misuse of toy devices’ and convert all tion must happen: propositions must become Fig. 1. Braun Lectron (top center), Dr. NIM (bottom left), “Denken mit Lego” (bottom right). sorts of things15 into computers –– just to see variables again and truth values must become if it was possible. Computers themselves had numbers. This transformation was accom- provoked such hacking –– unfinished gadgets plished by George Boole in the late 19th centu- differences of air or liquid, the presence or ab- be reenacted with macroscopic materials. To that were just waiting to be transformed into ry when he invented an algebra on the basis of sence of a sound (or two different frequencies) get an understanding of the logic behind those usable tools by programming them. The hack- Leibniz’ system of binary numbers. Here, the –– or the locomotion of mechanical parts. computing machines, it would have to be ers had approached them down to their hard- truth values of t became 1, f became 0, and To say “computers do understand only ones made visible again –– by magnification, spa- ware substrates. So, why not shift away this the logical junctors became arithmetic opera- and zeros” means: all of their computation is tialization, and deceleration. This is where a last symbolic historic and spatial border and tors: and as *, or as + and not as -. Only three based on binary switching logic on whatever fundamental review of computer history starts expose their basic functions to the hacker operators were sufficient to build all of the 16 substrate. This primitive foundation is capable that can be considered as didactics: the hand- creativity? Just to explore what computers are possible junctors as the logician Charles Sand- of an enormous complexity which can be de- iness of toys that led to the construction of the made of … ers Peirce proved in 1880. termined in modern computers. They are only first computers nearly one century ago can be This is why so many Lego projects can be found To implement those logical functions into using more, faster, and smaller logical gates used to get an understanding of today’s ances- today that introduce computers as calculat- machines, merely a process of mental reinter- but work on the same regime. tor. That is mainly because their fundamental ing machines,16 as theoretical constructions pretation had to happen where a real state is The incrementation of complexity that leads principles are the same. Even the didactic is (Turing Machines),17 and as logical networks read as a mathematical cipher. The real basis to all the emergent effects of modern comput- not new. –– for replication with bricks. Logical AND, could be different electrical currents, pressure ing is nearly incomprehensible let alone can OR, and NOT gates can be easily assembled

100 101 Fig. 2: Lego Lever Logic: AND, OR, NOT Gates (left), NAND gate (combined from AND and NOT) (right). with only a few Lego bricks. (Only adding Such projects can show how the abstract ideas 1 11 some rubber bands to help the gates return to of digital switching circuits become compre- Humboldt-Universität zu Berlin, Institut für Musik- H. FREUND, P. SORGER, Denken mit LEGO. their default state.) Instructions for “Lego Lever hensible hands-on. There are no boundaries wissenschaft und Medienwissenschaft, Bereich Vergnügliche Denkspiele für Logik und Mengenlehre, Medienwissenschaft, Georgenstraße 47, D-10117 Freiburg/Basel/Wien, Herder. (Quotes translation by Logic”18 gates can be recommended because for the creator’s creativity and the circuit’s Berlin. S. Höltgen.) they are easy to combine with each other to complexity. The mechanical and material 2 12 K. Zuse, The Computer – My Life, Berlin/Heidel- Ibidem. larger structures. point of view of the formal principles of com- berg, Springer, 1993, 9. 13 Ibid. The gate’s switching states can be recognized puting can help to not only comprehend the 3 N. Eibisch, Selbstreproduzierende Maschinen. 14 Ibid. by the length of their levers: a long lever at the fundamentals of actual computer technology Konrad Zuses Montagestraße SRS 72 und ihr Kon- 15 “Dominoes even make for a fun gate imple- input stands for 0, a short lever stands for 1 but also offers new ways of building computer text, Wiesbaden, Springer/Vieweg, 2016, 21. mentation (albeit one that can only be run once).” –– vice versa at the gate’s output. Connecting technology by understanding the metaphor of 4 Cf. M. Gardner, Logic machines and diagrams, J. Seiffertt, Digital Logic for Computing, Cham, the levers of a gate’s output to another gate’s “modular systems”21 literally: “Logic gates can New York/Toronto/London, McGraw-Hill, 1958. Springer, 2017, 76. input enables it to transmit a signal from the be built in many ways. In mechanical comput- 5 N. Eibisch, Selbstreproduzierende Maschinen, op. 16 http://txt3.de/brainlego4 17 first to the second gate. Using some crafting ers they can be constructed by gear systems. cit. http://txt3.de/brainlego5 6 18 skills, a stable construction of Lego gates In molecular computers they can be represent- E. Huhtamo, “Thinkering with Media. On the Art http://txt3.de/brainlego6 of Paul deMarinis,” in I. Beirer, S. Himmelsbach, C. 19 J. Seiffertt, Digital Logic for Computing, op. cit. that is anything but “crude and [...] unwork- ed chemically.”22 These and even more ‘alien’ eiffarth 20 use 19 S (eds), Paul DeMarinis: Buried in Noise, Cf. K. Z , The Computer – My Life, Berlin/Hei- able” can be built that provides complex concepts are discussed within the realm of un- Heidelberg, Kehrer, 2010, 33-46. delberg, Springer, 2007, 35. working ‘digital-mechanic’ arithmetic cir- conventional computing. Toy computing with 7 L. Wittgenstein, Tractatus logico-philosophicus, 21 H. G. Frank, B. S. Meder, Einführung in die kyber- cuits –– like an adder that only utilizes AND, Lego and other construction kits lines up into trans. D. F. Pears & B. F. McGuinness, London/New netische Pädagogik, München, dtv, 1971, 102-107; OR, and NOT gates. Such constructions are this experimental computer science –– and en- York, Routledge, 2002, 38. N. Eibisch, Selbstreproduzierende Maschinen, op. mostly build with the trial-and-error method: ables an epistemological view on its historical 8 http://txt3.de/brainlego1 cit., 36-45. re-thinking and re-plugging bricks again and and material sources.23 9 http://txt3.de/brainlego2 22 J. Seiffertt, Digital Logic for Computing, op. cit. again –– which can be seen as an re-enact- 10 http://txt3.de/brainlego3 23 http://txt3.de/brainlego7 ment of Konrad Zuse’s mechanical working Z1 computer architecture.20

102 103 Intelligent technological tattoos. Science, Art and Technology on and under the skin Catarina Pombo Nabais1

“The most profound in man is the skin.” Paul Valéry

This article explores the most recent kind of tattoos: the intelligent technological tattoos. These tech-tattoos have the capacity of sensing, measuring, analysing and emitting data about the body’s biochemistry through signs and colours inscribed in and on the skin, depending if they are done in the body with conductive ink or if they are worn on the skin. Even if still temporary –– because conductivity is lost through skin’s natural resistance ––, tech-tattoo aims at becoming a daily device. Fig. 1. In the Skin Motion website, there are some recommendations about the Soundwave tattoo: it should be no larger than 6 inches or 150 mm to be fully captured by the camera on the phone, it should What if we could transform our skin into the colours inscribed in and on the skin. Through be done in a flat surface such as the inner-forearm and it should be placed where one can easily hold the 3 most intelligent, smart, interactive technolog- tech-tattoo, skin becomes the body’s biggest phone to play the tattoo back with the Skin Motion app. Image credit: Sarah Tew/CNET. ical device? What if our skin would be able exposure. The enclosed mysterious body is First, an audio clip is uploaded in the website tracking individuals in space, or giving instruc- to exhibit all kinds of internal data about our now transformed in pure transparency as if of Skin Motion company and then a certified tions to the Wi-Fi devices to which the tattooed body’s biochemistry and nervous system? body becomes naked. artist will grave it in the skin as a traditional subject may be connected. Or they may have a What if our skin, our thin and fragile surface, tattoo but with a conductive ink which is con- deeper bio-medical-political dimension when, was the most profound and powerful part of To be or not to be human. That is the question. nected to the Skin Motion app. The way this e.g. they make possible measuring the body’s our body? Nowadays, it is interesting to realize that one app scans the tattoo is similar to some apps temperature, the heart beats, the level of alco- of the most ancient practices of body inscrip- that scan QR codes. It is called the Soundwave hol or the blood pressure, supervising fitness, The skin is the biggest organ of the body. It tion such as tattooing2 becomes a recent area Tattoo™ and it was invented in April 2017, computing sleep patterns, in a word, monitor- is the body’s frontier, its physical limit and of research in science and technology. Many by the tattoo artist Nate Siggard, who shared ing vital, bio-metric data. delimitation, its surface, its border. The skin laboratories have taken tattooing into the his invention in a video on Facebook that im- functions as a membrane-wall of protection world of artificial intelligence. Close to a sci- mediately went viral (over 150 million views There are at least two main methodologies for as well as an opaque boundary concealing ence-fiction scenario, tech-tattoo is now on during the first month). He then created the producing smart tattoos: synthetic biology and the body from the outside. But the skin is also the way of becoming the most intelligent body Skin Motion company, specialized in what he nanotechnology. Synthetic biology operates what exposes the body to the exterior world, device, transforming humans into cyborgs. expresses as “personalized Augmented Reality skin genetic manipulation. It may produce a what opens up the body, connecting it with Made of nanotech electronic components Tattoos.”4 (Fig. 1.) The other kind is a tattoo that cell that gets coloured when it detects bio- the outside. Thus, paradoxically, the skin is at such as electro-conducive ink or fabric tape, is glued over the skin and disappears by wash- chemistry changes in the body, thus rendering the same time what encloses and what opens bio-sensors, curvy wires, thermo-chromic ink, ing like the fake tattoos that some kids use. Ti- the tattoo visible and coloured. Nanotech- up the body. For centuries, the only way to and sometimes also imitation gold leaf metal tled Duo skin, Double Skin or Tech Tat,5 this nology manipulates matter on the nano scale see the interior of the body, underneath the inscribed over the skin, technological tattoo is temporary tech-tattoo belongs to a new gen- (1-100 nano meters). Instead of using solid skin, was by anatomical interventions done exponentially expanding. Even if still tempo- eration of flexible nano materials. The future pigment particles like in standard tattoos, nan- to dead corpses. Only recently, medicine was rary because conductivity is lost through skin’s perspective is that they will become a daily otechnology uses hollow microcapsules which able to overcome the opacity of the skin by natural resistance, tech-tattoo aims at becom- life’s device (Fig. 2). can be filled with diverse materials, depending using technologies such as X-ray, Ultra-sound, ing a permanent bio-smart device. on the tattoo function. Computed tomography (CT) or magnetic res- There are two kinds of tech-tattoos nowadays. Due to the fast-technological evolution and to onance imaging (MRI), among many others. One is inscribed in the skin, as a traditional their cheap and easy process of fabrication, All these technological advances on smart tat- Nowadays, another big step is being done. tattoo but with a special ink that is linked to tech-tattoos are being appropriate for an enor- toos, are used for military purposes by detect- What was available only through medical ex- Wi-Fi devices. A recent yet already famous ex- mous range of concrete purposes having direct ing poisons in the air, by discovering pathogens ams may now be easily shared by technologi- ample is a tattoo which can reproduce a sound impact in daily life. They may have utilitarian in soldiers or by recognizing when soldiers are cal tattoo which emits data through signs and that is previously memorized in the drawing. purposes such as providing a payment system, stressed or hurt. Tech-tattoo has already and

104 105 will have further in the future a great value in medical uses. One example: Harvard Medical School and MIT have been developing a project called “Dermal Abyss.” This project aims at identifying the levels of glucose and sodium in the blood to help in diabetes medical care. In this case, tattoo is made with a smart ink that contains colorimetric and fluorescent biosensors which transforms the skin into a colour sign emitter of biochemical changes in the body. Depending on blood glucose, sodium or Fig. 4. When UV ray light illuminates the skin (on the right), two blue spots appear on the skin (on the left). pH levels, the skin emits various shades of co- Both images are taken from TED talk by Carlson Burns.6 lours. It can become pink or purple depending Fig. 2. Tech-tattoo made with one-atom size, two-dimensional single layer of graphene. Contrary to regular on the pH level, it can go from blue to brown temporary tattoos, graphene tattoo is almost transpar- depending on blood glucose, or even fluores- ent. Image credit: Shideh Kabiri Ameri, Deji Akinwan- providing all this multitude of inner, intimate to the control society. This shift happens with cent under ultraviolet light depending on sodi- de, et al. data, tech-tattoo is in total, instantaneous, and the emergence of a diffuse world-capitalism um level (Fig. 3). permanent connection with the control tech- aligned with digital devices able to control Another example: Carson Burns, a researcher nologies around us. Besides emitting data, individuals in their personal activities and in molecular nanotechnology at the University from international companies allied with re- tech-tattoo is also capable of sensing, measur- consumption habits. In disciplinary societies of Colorado, is developing a tattoo that goes search centres and science laboratories makes ing, and analysing data. Therefore, we may say described by Michel Foucault,8 all activities from invisible to coloured spots when the skin the biopolitical power of tech-tattoo very that “bio-wearable” tech-tattoo turns the body were framed in specific architectonic build- is overexposed to sun light and to UV rays. clear. In a control society as we already live in, into a digital cyborg exempted from privacy ings (schools, hospitals, fabrics, etc.) where Powered by solar energy, this tech-tattoo has tech-tattoo is a big step into the reinforcement and, moreover, it transforms the body into a individuals were fixed in space and time and in its micro particles an UV sensitive colour of individual’s control. With tech-tattos, data bio-tech surface, a smart and quantifiable can- could be controlled by central structures. Time changing dye. Working as an alert, appearing emission on individuals’ lives is done, not just vas. Tech-tattoo is thus a truly control device, and space dictated life, in a transcendent only when the skin is overexposed to UV ra- from the cell phone but from bio-nano-sen- which can be easily used by power structures. mode. Now, in control societies, individuals diation, this tattoo may help in the sunburn or sors of a body artificial device. The cell phone become digital nomads. No matter where and cancer prevention (Fig. 4). –– which is already a smart tool –– is able to In “Post-Scriptum on Control Societies” (1990), when, they are flowing in a global web, sub- spread lots of information about our move- Gilles Deleuze analyses the shift from the dis- jected to an immanent control. To be or not to be surveilled. That is the other ments, GPS location, tastes, social milieus, ciplinary society, which extends from the 18th Deleuze seems to be terribly prescient. In the question. number of daily steps, etc. But the tech-tat- century to the last decades of the 20th century, early 90s, two years before Tom Barnes Lee’s Technological tattoo is incredibly expanding. too with its bio-nano-sensors goes deeply by However, it is important to notice that the in- informing about the diseases, the genetics, vestment being done in this kind of technology the very chemistry of each individual. And in

Fig. 5. Software company Chaotic Moon has developed a tech-tattoo that is implanted into a person’s arm, capable of registering Fig 3. On the left, Dermal Abyss tattoo. On the right, Dermal Abyss colour palette. Both photos are from Nan Jiang, postdoctoral the financial and medical information of the tattooed individual. According to Chaotic Moon’s hardware creative technologist, fellow at the School of Engineering and Applied Sciences at Harvard University, who has been working at Harvard Medical Eric Schneider, “with the tech tattoo you can carry all your information on your skin and when you want your credit card informa- School undertaking research on nano biotechnology and biosensors for the Dermal Abyss project. tion or your ID, you can pull that up automatically through the system.” 7 Image credit: www.emergeinteractive.com.

106 107 creation of the World Wide Web, Deleuze Unlike Jeremy Bentham’s Panopticon, with a stresses that the subject produced by a con- centralized focal point from which the disci- trol society is a navigator (a surfer) in a glob- plined activity of individuals is monitored, al floating world: “The disciplinary man was in control society, a diffuse, widespread, and a discontinuous producer of energy, but the decoded matrix of information controls the subject of control is undulating, in orbit, in a individuals’ body and behaviour all the time continuous network. Everywhere surfing has and everywhere. The “Panopticon” becomes already replaced the old sports.”9 a “Superpanopticon”: more subtle, invisible, Now, the body is no longer an independent close and so intimate that it turns to be al- and autonomous entity, living almost anony- most indifferent. We know that we are being mously, as it used to be in disciplinary soci- watched, but we are not forced to be in a spe- eties. In control societies, the body becomes cific place. On the contrary, we are - encour an entity within the global digital world. It is aged to move and not to worry about being part of an infinite database of power structures watched. This normalization of surveillance which, through digital devices, have a perfect has become immanent to the modern body and total command of the individual’s life, and will become even more internalized with even if only while taking a walk in the street. the spread of tech-tattoo. Modern body has become the locus of con- Fig. 7. Iconic representation of the web. Image credit: https://pixabay.com/ stant social management, a satellite unit or –– precisely by means of tech-tattoo –– even a 1 PhD in Philosophy from the University of Paris 8 control device in itself. (2007), researcher at the Faculdade de Ciencias da Universidade de Lisboa, Departamento de Historia https://www.ted.com/talks/carson_bruns_could_a_ e Filosofia das Ciencias. Integrated member of the tattoo_help_you_stay_healthy/transcript#t-403948. Centro de Filosofia das Ciencias, Universidade de For further information, see J. L. Butterfield, S. P. Lisboa, Campo Grande 1749-016 Lisboa, Portugal. Keyser, K. V. Dikshit, H. Kwon, M. I. Koster, and C. Email: [email protected]. J. Bruns, “Solar Freckles: Long-Term Photochromic This work is financed by national funds through Tattoos for Intradermal Ultraviolet Radiometry,” in FCT – Fundação para ea Ci ncia e a Tecnologia, ACS Nano 14(10), 2020, 13619–13628, https://pubs. I.P., within the scope of the Norma Transitoria – acs.org/doi/10.1021/acsnano.0c05723. DL57/2016/CP1479/CT0067 and the Norma Tran- 7 In https://newyork.cbslocal.com/2016/01/29/tech-tat- sitoria – DL57/2016/CP1479/CT0065. toos-chaotic-moon/. 2 The most ancient tattooed body dates from 5000 8 See M. Foucault, Discipline and Punish. The Birth years ago, but tattoos are known to be practiced of Prison, trans. A. Sheridan, New York, Vintage since the Upper Paleolithic period (10-30 000 years Books, 1995. ago). Cf. C. Taliaferro & M. Odden, “Tattoos and the 9 G. Deleuze, “Post-scriptum sur les sociétés de con- tattooing arts in perspective: an overview and some trôle,” in Pourparlers, Paris, Minuit, 1990, 244. preliminary observations,” in R. Arp (ed.), Tattoos: 10 In J. Bowring (ed.), The Works of Jeremy Bentham, philosophy for everyone: I Ink, Therefore I Am, Ox- Edinburgh, William Tait, 1838-1843, vol. 4, 172. ford, John Wiley & Sons, 2012, 4. For a more detailed analysis of tattoo throughout history and its meanings, see my article “The most profound is the skin – the power of tattoos,” in D. Honorato, A. Gi- annakoulopoulos (eds), Taboo-Transgression-Tran- scendence in Art & Science, Proceedings of the 10th Interdisciplinary Conference and Audiovisual Arts Festival, Department of Audio & Visual Arts – Ionian University of Corfu, Greece, Corfu, Ionian Universi- ty Press, 2017, 128-148. 3 In B. VanGelder, A. Nunes, “Skin Motion app turns my tattoo into sound waves,” https://www.cnet. com/news/skin-motion-app-soundwave-tattoo-i- tried-it/ 4 In Skin Motion. Tattoos brought to life, https://skin- motion.com/soundwave-tattoos/. Fig. 6. Image of the Panopticon elaborated by Jeremy Bentham in 1791 in his work Panopticon; Or, 5 In Chaotic Moon, https://www.youtube.com/watch?v=9i- The Inspection-House.10 FuTaqD4fM&t=29s. 6 See TED talk by Carlson Burns:

108 109 About the authors

Andrew Adamatzky. Professor, Unconventional Computing Laboratory, University of the West of England, Bristol, United Kingdom; [email protected]. Selim G. Akl. School of Computing, Queen’s University, Kingston, Ontario K7L 3N6, Canada, [email protected]. ca. Mark Burgin. UCLA, Los Angeles, CA 90095, USA. Alessandro Chiolerio. Leading Researcher at Istituto Italiano di Tecnologia, Center for Sustainable Future Technologies, Torino, Italy; University of West of England, Unconventional Computing Lab, Bristol, UK. Antoni Gandia. Leading Researcher at MOGU, Italy. Pier Luigi Gentili. Physical Chemistry Professor focused on Complex Systems, Department of Chemistry, Biology, and Biotechnology, Università degli Studi di Perugia, Italy. Stefan Höltgen. Humboldt-Universität zu Berlin, Institut für Musikwissenschaft und Medienwissenschaft, Bereich Medienwissenschaft, Georgenstraße 47, D-10117 Berlin. [email protected] Zoran Konkoli. Professor at Chalmers University of Technology, Goteborg, Sweden. Conception and layout on InDesign Johanna Blayac & Louis-José Lestocart. Olga Kosheleva. University of Texas at El Paso, El Paso, TX 79968, USA, [email protected]. Vladik Kreinovich. University of Texas at El Paso, El Paso, TX 79968, USA, [email protected]. Bruce MacLennan. Associate Professor Emeritus, Department of Electrical Engineering & Computer Science, University of Tennessee. Genaro J. Martínez. Escuela Superior de Cómputo, Instituto Politécnico Nacional, México; Unconventional Computing Laboratory, University of the West of England, Bristol, United Kingdom; genaro.martinez@uwe. ac.uk. Richard Mayne. Unconventional Computing Laboratory, University of the West of England, Bristol BS16 1QY, United Kingdom. [email protected]. Kenichi Morita. Profressor Emeritus, Hiroshima University, Higashi-Hiroshima, Japan. Dan V. Nicolau, Jr. Mathematician, physician and engineer, Associate Professor of Computational Mathe- matics at the Queensland University of Technology and Visiting Professor of Experimental Medicine at the University of Oxford. Anna Nikolaidou. Senior Lecturer in Architecture, UWE, Bristol, UK. Irina Petrova. Affiliated artist in the Unconventional Computing, Lab, UWE, Bristol, UK. Catarina Pombo Nabais. Department of History and Philosophy of Sciences, Faculty of Sciences, University of Lisbon, Portugal and Integrated member of the Centre of Philosophy of Sciences of the University of Lisbon, [email protected]. Dawid Przyczyna. PhD student (physics), guitarist, darbuka player, AGH University of Science and Technol- ogy, Kraków, Poland. Website : LINKs-series.com. (Jacques Urbanska) Nancy Salay. Associate Professor at the Department of Philosophy, Queen’s University, Canada. Marcin J. Schroeder. Institute for the Excellence in Higher Education, Tohoku University, Sendai, Japan; [email protected]. Marcin Strzelecki. Music theorist and composer, instrumentalist, Academy of Music in Kraków, Poland. Konrad Szaciłowski. Professor of chemistry, philatelist, AGH University of Science and Technology, Kraków, Poland. Bernd Ulmann. Professor for business informatics at the “Hochschule für Oekonomie und Management” in Frankfurt/Main, Germany; guest professor and lecturer at the Institute of Medical Systems Biology at Ulm University; [email protected]. Jordi Vallverdú. ICREA Acadèmia Researcher at Universitat Autònoma de Barcelona.

110 111 A three-dimensional projection of cellular automata Life-like rule B4/S9.

LINKs-series est édité avec le soutien de Transcultures Europe, Pépinières de Création (France) et de Transcultures (Belgique) ISSN 2592-6756