Int. J. General Systems © Gordon and Breach Science Publishers Ltd. 1977, Vol. 4. pp. 13-28 Printed in Great Britain

SELF-ORGANIZATION OF LIVING SYSTEMS: A FORMAL MODEL OF AUTOPOIESIS

MILAN ZELENY

Graduate School of Business, Columbia University, New York, New York, U.S.A.

(Received August 9, 1976; in final form November15, 1976)

A formalization, computerization and extension of the original Varela-Maturana-Uribe model of autopoiesis is presented. Autopoietic systems are driven by sets of simple "rules" which guide the behavior of components in a given milieu . These rules are capable of producing systemic structures that are far more complex than we could ever achieve by a direct arrangement of components, i.e., by a method of systems analysis and design. The study of autopoietic systems indicates that the traditional emphasis on internal qualities of system's components has been misplaced. It is the organization of components, rather than the components themselves (or their structural manifestations), that provides the necessary and sufficient conditions of autopoiesis and thus of life itself. The dynamic autonomy of autopoietic systems contrasts significantly with the non-autonomous, allopoietic mechanistic systems.

INDEX TERMS Autopoiesis, allopoiesis, autogenesis, biological clock, social autopoiesis, human systems management, production, disintegration, bonding, catalytic neighborhood, APL-autopoiesis.

INTRODUCTION renewing its defining organs, a social group "pro­ duces" group-maintaining individuals, etc. Such In 1974 three Chilean scientists, F. G . Varela, H. R. autopoietic systems are organizationally closed and 7 8 Maturana and R. B. Uribe, published a seminal structurally state-determined, · with no apparent article, 1 entitled "Autopoiesis: The Organization of inputs and outputs. Living Systems, Its Characterization and A Model," In contrast, the product of an allopoietic organi­ providing a new direction as well as a new hope in zation is different from the organization itself, it does contemporary theory of living systems. Their work not produce the components and processes which could represent the first significant advance toward would realize it as a distinct unity. Thus, allopoietic the general theory of organizations since the systems are not perceived as "living" and are usually advents of Trentowski's Cybernetyka,2 Bogdanov's referred to as mechanistic or contrived systems. Tectology, 3 Leduc's Synthetic Biology,4 Smuts' Their organization is open, i.e., with apparent inputs Holism5 and von Hayek's Spontaneous Social and outputs. For example, spatially determined Orders.6 structures, like crystals or macromolecular chains, In this article we deal with organic systems, i.e., machines, formal hierarchies, etc., are allopoietic. both biological and social organizations displaying It is important to distinguish between organi­ the fuzzily defined quality called "life." They are zation and structure of an organic system in this characterized by their self-renewal, self­ context. We shall paraphrase the original thoughts 10 maintenance and stability in a given environmental advanced by Maturana and Varela. 9 • domain. The process of a continuous self-renewal of A given system, observed as a distinct unity in its a systemic whole is called autopoiesis, i.e., self­ environmental domain, can be viewed as a whole of production. interrelated and further unspecified components. Autopoietic organization is realized as an auto­ A network of interactions between · the com­ nomous and self-maintaining unity through an ponents, renewing the system as a distinct unity, independent network of component-producing pro­ constitutes the organization of the system. The cesses such that the components, through their actual spatial arrangement of components and their interaction, generate recursively the same network relations, integrating the system temporarily in a of processes which produced them. given physical milieu, constitutes its structure. The product of an autopoietic organization is The unity and holism of systemic organization thus not different from the organization itself. A cell and structure represents what is -commonly referred produces cell-forming molecules, an organism keeps to as a system. 13 14 M. ZELENY

Thus, two distinct systems may have the same singly bonded link (B) ~ - organization but different structures. Structural fully bonded link (B) - EB- changes do not reflect changes in the system as a catalyst (C) * unity as long as its organization remains invariant. The original Varela-Maturana-Uribe model 1 was A system and its organization cannot be explained based on the following organization of components: by simply reproducing its structure. The structure of a system determines the way its components interact between themselves, with their environment 2.1 Production and with the observer. Organizationally closed systems are not struc­ turally separated from their environment; they are A catalyst and two units of substrate produce interacting and coupled with it. Although they do a free link and a hole, while the catalyst is not have inputs or outputs, they can be externally assumed to be essentially unaffected by this perturbed and undergo structural adaptations. Any operation. Production can take place when a autopoietic system can be perceived as being pair of substrate is in the predetermined allopoietic by specifying its input/output surfaces, neighborhood of the catalyst. Catalytic i.e., by disconnecting its organizational closure, "reach" or the strength of* and its dynamics either experimentally or mentally. can be effectively simulated. Allopoietic systems are organizationally open, they produce something different than themselves. Their boundaries are observer-dependent, their 2.2 Disintegration input and output surfaces connect them mechani­ cally with their environment. Their purpose, as an D +(space)--->20 interpretation of their input/output relation, lies - ~ +(space)--->20 solely in the domain of the observer. Further discussions along the above lines can be - EB- + (space)--->20 11 14 found in a variety of related works. - Any link, free or bonded, can disintegrate into two units of substrate. Additional unit of substrate will occupy an available hole which 2 AUTOPOIETIC MODEL OF A CELL must be in the neighborhood of a disintegrat­ ing component. One of the simplest autopoietic systems exhibiting the minimum organization of components ne­ cessary for autopoiesis, is a model of a biological 2.3 Bonding cell. There is a catalytic nucleus capable of interaction with the medium of substrate so that the D-EB-... - D+D---> 0-EB-... -EB- ~ membrane-forming components can be continually A free link can bond with a chain of bonded produced. The resulting structure displays a memb­ links; two chains of bonded links can be raneous boundary that defines the system as a bonded into one, or re-bonded after their separate and autonomous unity in the space of its connecting link has disintegrated; two free components. links can be bonded together to start a chain In accordance with this basic organization of a formation. cell, the simplest model of its autopoiesis must consist of a medium of substrate, a catalyst capable Observe that disintegration and bonding are of producing more complex components-links, operations that do not require catalyst; they are which are in turn capable of bonding, ultimately "self-catalytic." That does not mean that the catalyst concatenating into a membrane surrounding the has no influence over those operations. For exam­ catalyst. ple, bonding can take place only beyond a prede­ We shall designate the basic components of the termined catalytic neighborhood while disinteg­ model by the following symbols: ration can appear anywhere in the space. hole (H) (space) More detailed rules, guiding the movement of all substrate (S) 0 components and specifying the necessary conditions free link (L) D for the three interactive rules above, are discussed in FORMAL MODEL OF AUTOPOIESIS 15

the next section. Spontaneous encounters, bonding An Abelian-group cellular automaton r IS an and disintegration of components is partially ordered quintuple: guided by chance. We shall only briefly summarize 1 13 15 some additional properties. · • • l6 Each component (and its corresponding neigh­ borhood) is allowed to move over the space where according to predetermined rules. A set of dom­ (i) Q is a set of states inance relations must be established in order to 0 (ii) M = { M 1> ... , M is a generator set of a prevent different components claiming the same m} finite-generated Abelian group having group oper­ space during the same unit time-interval. Any ation"+", i.e., vector addition. component can claim a hole, a link can displace a substrate, and a catalyst can displace both sub­ (iii) f is the local transition function, a set of strates and links. Thus*> 0 > 0 >(space) estab­ rules, a mapping from Q (t) to Q ( t + 1 ). lishes this partial dominance. We do not allow any (iv) His the quiescent state, such thatf(H, ... , H) movement of bonded links. =H. Each link can have at most two bonds: it can be The neighborhood of any position k in G is either free, 0, single bonded,- C], or fully bonded, defined as the set · I - E3-. Additional bonds, - lffil -, are of course I N(k)= {k, k+M1, k+M2, .. ., k+Mm}· possible, but they induce frequent branching of chains, creating thus catalyst-free enclosures. Mul­ The meaning of J, then, is that an assignment of tiple bonds are indispensable for modeling in a three states to N ( k) helps to determine the next state of k. dimensional space. A form F is an assignment of states to all positions Unbranched chains of bonded links will ul­ of an automaton. A finite form is one in which all but timately form a membrane around the catalyst, a finit~ number of positions are assigned the creating the enclosure impenetrable for both * and quiescent state H. The operation of r is assumed to

o. These two components are thus effectively proceed in unit time-intervals, t0 , t 1 = t0 + 1, t 2 = t 1 "trapped" and forced to function for the benefit of + 1, ... , the local transition function being applied the autopoietic unity. Substrate units, O, can pass simultaneously to all positions of G during each freely through the membrane and thus keep the time-interval, thus generating a sequence of forms catalyst supplied for the production of additional F 0 , F 1, F 2 , ...• o. Any disintegrated links, causing ruptures in the Example. Conway's "Life" cellular automaton, membrane, and thus be readily and effectively recently popularized by Gardner, 36 can be de­ repaired by the ongoing production. The unity of the system is recursively maintained through a series scribed as follows:Q=(O, 1), H=O, and G is the Abelian group generated by of minor structural adaptations. In Figure 1, we present a sample of APL printouts providing typical "snapshots" from the "history" of 0 M = {( 1, 0 ), (0, 1 ), (1, 1 ), ( -1, 0), an autopoietic unity. (0, -1),(-1, -1),(1, -1),(-1,1)}

3 A FORMAL MODEL OF AUTOPOIESIS under the operation of vector addition. Each position has exactly eight neighboring positions, the 3.1 Introductory Concepts Moore neighborhood N(k) for a given k, determined 0 Let us define a two-dimensional (Cartesian) tesse­ by M . Letfbe defined as follows: lation grid: a space of an autopoietic automaton. 1) If at time t the state of k is 0 and there are The grid consists of a countably infinite set of G exactly three positions in state 1 in N(k), then at positions, each position referred to by a unique pair time t + 1 the state of k will become 1. of integers (i,j), positive or negative. For practical purposes _we shall consider that the underlying 2) If at time t the state of k is 1 and there are network of positions forms an n-dimensional Car­ exactly two or three positions in state 1 inN ( k ), then tesian grid, i.e., it has the nature of an Abelian at time t + 1 the state of k will remain 1. group. 17 3) If at time t position k and its N(k) do not E FORMAL MODEL OF AUTOPOIESIS 15

the next section. Spontaneous encounters, bonding An Abelian-group cellular automaton 1 is an and disintegration of components is partially ordered quintuple: guided by chance. We shall only briefly summarize 1 13 15 16 some additional properties. · · • Each component (and its corresponding neigh­ borhood) is allowed to move over the space where according to predetermined rules. A set of dom­ (i) Q is a set of states inance relations must be established in order to 0 (ii) M ={M , ... , Mm} is a generator set of a prevent different components claiming the same 1 finite-generated Abelian group having group oper­ space during the same unit time-interval. Any ation"+", i.e., vector addition. component can claim a hole, a link can displace a substrate, and a catalyst can displace both sub­ (iii) f is the local transition function, a set of strates and links. Thus*> D > 0 >(space) estab­ rules, a mapping from Q(t) to Q(t+ 1). lishes this partial dominance. We do not allow any (iv) His the quiescent state, such thatf(H, ..., H) movement of bonded links. =H. Each link can have at most two bonds: it can be The neighborhood of any position k in G is either free, 0, single bonded,- C], or fully bonded, defined as the set - I -B-. Additional bonds, - lffil -, are of course I N(k)= {k, k+Mt, k+M2, .. ., k+ Mm}- possible, but they induce frequent branching of chains, creating thus catalyst-free enclosures. Mul­ The meaning off, then, is that an assignment of tiple bonds are indispensable for modeling in a three states toN ( k) helps to determine the next state of k. dimensional space. A form F is an assignment of states to all positions Unbranched chains of bonded links will ul­ of an automaton. A finite form is one in which all but timately form a membrane around the catalyst, a finit~ number of positions are assigned the creating the enclosure impenetrable for both * and quiescent state H. The operation of r is assumed to

D. These two components are thus effectively proceed in unit time-intervals, t0 , t1 =t0 + 1, t2 =t1 "trapped" and forced to function for the benefit of + 1, ... , the local transition function being applied the autopoietic unity. Substrate units, O, can pass simultaneously to all positions of G during each freely through the membrane and thus keep the time-interval, thus generating a sequence of forms catalyst supplied for the production of additional F0 ,Ft> F 2 , •... D- Any disintegrated links, causing ruptures in the membrane, and thus be readily and effectively Example. Conway's "Life" cellular automaton, recently popularized by Gardner,36 can be de­ repaired by the ongoing production. The unity of the system is recursively maintained through a series scribed as follows:Q=(0,1), H=O, and G is the Abelian group generated by of minor structural adaptations. In Figure 1, we present a sample of APL printouts providing typical "snapshots" from the "history" of M 0 ={(1,0), (0, 1), (1, 1), ( -1,0), an autopoietic unity. (0, -1),(-1, -1),(1, -1),(-1,1)}

3 A FORMAL MODEL OF AUTOPOIESIS under the operation of vector addition. Each position has exactly eight neighboring positions, the 3.1 Introductory Concepts Moore neighborhood N ( k) for a given k, determined 0 Let us define a two-dimensional (Cartesian) tesse­ by M . Letfbe defined as follows: lation grid: a space of an autopoietic automaton. 1) If at time t the state of k is 0 and there are The grid G consists of a countably infinite set of exactly three positions in state 1 in N(k), then at positions, each position referred to by a unique pair time t + 1 the state of k will become 1. of integers (i,j), positive or negative. For practical purposes _we shall consider that the underlying 2) If at time t the state of k is 1 and there are network of positions forms an n-dimensional Car­ exactly two or three positions in state 1 inN ( k ), then tesian grid, i.e., it has the nature of an Abelian at time t + 1 the state of k will remain 1. group. 17 3) If at time t position k and its N(k) do not

E FORMAL MODEL OF AUTOPOIESIS 17 satisfy either condition 1 or 2, then at time t + 1 3 lj. 5 6 7 position k will be in state 0. X 1 2 These three conditions adequately define f and 1 enable us, given any configuration at time t, effectively determine the configuration at timet+ 1. 2 0

3 s 3.2 A Mode! of Autopoiesis ' ' We shall allow the neighborhood of a position to lj. 0 s (i,j) 0 "wander" throughout a constant Abelian space. ' That is, a state is distinct from a position ofthe space 5 s s and is identified with a shifting set of "in­ terdependent positions" in the space. ' 6 Each position is identifiable as (i,j), iJ = 1, ... , n. 0 We define a complete general neighborhood of k =(i,j),N(k), as follows: 7

N(k) = {k +A,M, I r= 1, ... , 8}, FIGURE 2 Complete neighborhood of any position (i,j) where M, indicates one of the eight possible reachable by one or two rectangular moves. The Moore directions over a Cartesian grid and A, represents neighborhood is indicated by the eight marked elements. the number of steps taken. Thus, the Moore neighborhood is characterized by all A,= 1, the von (i,j) +2M I = (i- 2,j) Neumann neighborhood has A,= 0 for all "diagonal" (i,j)+ M 2 + M 3 = (i+ l,j + 1),etc. directions and A,= 1 for the rectangular ones, etc. By varying Jc,'s from 0 to n we can generate a large The set of all possible states, Q, is defined as variety of neighborhoods, depending on a given follows: Q = {H, S, L, B, C}, where context. We shall turn our attention to a very simple and H(i,j)=H(k): hole (a quiescent state) specific neighborhood, depicted in Figure 2. We S(i,j)= S(k) :substrate assume that any movement can proceed in a rectangular fashion only and the complete neigh­ L(i,j)=L(k) : (free)link borhood consists of all positions reachable through B(i,j)=:B(k) :bondedlink either one or two moves, i.e., Jc, = 1 or 2 for all rectangular movements. Thus, C(i,j)=C(k) :catalyst

0 In general, k=(i,j) and E(k)=E(i,j) denotes a M = { M, I M 1 = (- 1, 0 ), M 2 = (0, 1 ), position k being in state E, i.e., any element of Q. M 3 =(1,0),M4 =(0, -1)}. In Figure 2 observe that for n :;=; 3, i, j :;=; 2, i, j~n-1, only incomplete neighborhoods can be In Figure 2 observe that M 1 through M 4 defined. We shall state simple boundary conditions: correspond to four basic directions: North, East, South and West. To establish a circular relation E(i, 2)+ M 1 =E(i, 2) between operators M,, we shall define E(2,j)+M2 =E(2,j)

E ( i, n- 1) + M 3 = E ( i, n- 1)

We can demonstrate the usage of basic movement E(n -l,j) + M 4 =E(n -1,j). operators as follows: Since all movements over N(k) are carried with k, (i,j)+M = (i-1,j) respect to we can further simplify our notation by 1 not repeating k every time. Thus, we useE instead of (i-1,j)+ M 3 = (i,j) E(k ),E(M,) instead of E(k + M,), etc. For example, 18 M. ZELENY for k =(i,j) and M, =M 1, instead of E(k + M 1 procedure," at least partially. It is necessary to +Md we use E(2Md to designate that position (i preserve some randomness because a real-world - 2,j) is in state E. environment has no known, complete, finite de­ There are two essential ways of moving over scription or prediction. Let R, indicate an element N(k): M, randomly selected from M 0 and let RE indicate an element ME of DE, also chosen at random. i) select a direction M, and a number of steps;.,, Now we are ready to define our transition and then identify the state of(k+).,M,). function/, a set of rules similar to those of Conway's ii) select a state E and then identify all positions "game of life." We shall use an arrow,->, to denote a of N ( k) being in that state as well as the directions to transition operator, i.e., a->b means "a is to be reach them from k. replaced by b." Similarly, a, b->c, d would read "a is to be replaced by c and b is to be replaced by d," etc. With respect to (ii ), for example, ME indicates that 0 ( k +ME) position, ME E M , is in state E. In other words 3.2.1 Motion 1

Let Yf = {H ( k) I coordinate set of all holes} and for 0 Let each hole let R, be randomly chosen from M . Units of substrate, links and catalysts can move into their adjacent holes. Substrate can even pass through a bonded link segment while neither free link nor designate a subset of M 0 such that k +ME) position catalyst can do so. Both bonded links and holes are is in state E. subject to no motion at all. Often we use a series of operators to identify a given position: it is always the last operator which H, H (R,)-> H, H (M,) identifies the state. For example, H, S(R,)->S,H(M,) E means that k is in state E H, L(R,)->L, H(M,) E(M,) means that (k+M,) ism any state E 0 because M, E M H, B(R,), S(2M,)->S,B(M,),H(2M,) E(M,+ME) means that (k+M,+ME) is in a H, C(R,)->C,H(M,) particular state E because ME E DE. After Motion 1 any moved links are bonded, if Nate. ME identifies a position only in a complete possible, according to the rules of Bonding. N ( k ). I.e. only two operators in succession are subject to the above interpretations. We can however use any number of operators to explore the situation 3.2.2 Motion 2 beyond a given N(k). For example, E(M,+2ME) means that (k+M,+ME) is in a particular state E Let Sf = {L ( k) I coordinate set of all free links} and 0 but we are identifying the position adjacent in for each link choose R, at random from M . If direction ME> i.e. (k+M,+ME+ME), which could position ( k + R,) contains another link, bonded link be in any state E. It is therefore possible to write, for or catalyst, then no movement of free links ensues. example, H.(M,+2M8 ) but not H(M,+M8 ); that That is, could only be written as either H(M,+M,), or

H(M8 +M,), or B(M,+M8 ). Similarly, E(M,+M1 L,L(R,)->L,L(M,) +2ME) means that position (k+ M, + M, +2M E) is in state E but ME direction has been determined L, B(R,)->L, B(M,) independently. That is, there is some E(M,+ME) L, C(R, )--> L, C(M,) and we use the corresponding direction ME for exploring beyond the N(k) after both M, and M, On the other hand, a free link can displace units of have been selected. We can write, for example, H (M, substrate into adjacent holes or exchange positions

+ M,+2M8 ) or even B(M, + M 1 +2M8 ). with them. It can also push a substrate into a hole Because we deal with an evolutionary system, we through a bonded link. If the adjacent position is a would like to make use of a "blind generation hole then the link simply moves in. Assume that RH FORMAL MODEL OF AUTOPOIESIS 19

and R8 have been randomly selected from DH and C, L(Rr), B(2Mr)--+L, C(Mr), B(2Mr) DB respectively. If position (k + Rr) contains a substrate, we write as follows: C, L(Rr), L(2Mr)--+L, C(Mr), L(2Mr) C, L(Rr), C(2Mr)--+L, C(Mr), C(2Mr) L, S(RrJ, H(Mr + RH )--+H,L(Mr), S(Mr+ MH) L, S(Rr), B(Mr +RB),H(Mr +2MB)-+ and also H,L(Mr),B(Mr+ MB), S(Mr+2MB) L, S(Rr)--+S,L(Mr) Then bond any displaced links, if possible, L, H(Rr)--+H, L(Mr) according to the rules of Bonding. Again, we bond any displaced links, if possible, according to the rules of Bonding. 3.2.4 Production

3.2.3 Motion 3 Whenever two adjacent positions of a catalyst are occupied by substrate units, a link can be produced. Let'(}= {C ( k) I coordinate set of all catalysts} and Each such production leaves a new hole in the space. 0 We allow only one link to form at each step, per each for each catalyst choose Rr at random from M . There is no movement if the adjacent position catalyst, although such rate of production can be contains either a bonded link or another catalyst. varied. The choice of a link-producing pair of That is, substrate is made at random. Thus, for a given C(k) we must list all adjacent C, B(Rr)--+C, B(Mr) positions containing a substrate the adjacent pos­ ition of which is another substrate. We shall define C, C(Rr)--+C, C(Mr)

If the adjacent position contains a free link, dis placeable according to Motion 2, then the as a set of basic movement operators from M 0 catalyst will displace it: leading to a substrate in the Moore (i.e., rec­ C, L(Rr), S(2Mr), H(2Mr + RH )--+ tangular) neighborhood of C(k). Then for

H, C(Mr), L(2Mr), S(2Mr+MH) E(Ms+Ms+ 1 ), C, L(Rr), S(2Mr), B(2Mr + RB), H(2Mr +2MB)-+ we define H, C(Mr), L(2Mr), B(2Mr + MB), S(2Mr if E=S +2MB) always C, L(Rr), H(2Mr)--+H, C(Mr), L(2Mr)

Thus, Xs E W8 = {Xs I S(X8 )}, where W8 is the set If the adjacent position contains a substrate, of all operators and their combinations leading to displaceable according to Motion 2, then it will be the positions containing substrate in the Moore moved as follows: neighborhood. Let us form the Cartesian product of W8 with C, S(Rr), H(Mr + RH)--+1-1, C(Mr), S(Mr + MH) itself, i.e., C, S(Rr), B(Mr + RB), H(Mr +2MB)-+ Ws x Ws= {Xs IXs= (XsJ,Xs2)}, 1-1, C(Mr), B(Mr + MB), S(Mr +2MB) i.:..e., the set of all pairs of operators X , designated by C, S(Rr)--+S, C(Mr) 8 X s· Then we define If the adjacent position contains a free link which cannot be moved according to the rules of Motion 2, then the catalyst will exchange its position with it: as the set of pairs of operators leading to adjacent

F 20 M. ZELENY

there is a hole in the neighborhood into which the 'N. 1 2 3 4- I 5 6 7 additional substrate could sink. To identify the suitable holes we shall define the following sets of 1 movement operators:

2

3 s 8 c and 4- 0 * 0 5 s s I S2+1 J} 6 n L=}i-l B(M52 + M;)nH(M52 +2M;)

7 Observe that these two sets identify neighboring holes into which a substrate can be pushed either directly or through a bonded link, thus making a FIGURE 3 An example illustrating identification of the pairs of substrate (marked) available for production of links. room for disintegration. Let N ={nInE (0, 1)} and RN be a uniform random number selected from N. If, say, RN ~K, pairs of substrates. As an example, consider the where K is predetermined and adjustable para­ situation in Figure 3, where meter, then the chosen link disintegrates. Again, the actual rate of disintegration can be controlled and harmonized with the rate of production. Let E(k) represent either L(k) or B(k) and let us select, and randomly, RH, Rn, Rn, and Rn. Then the following set of rules guides Disintegration: W5 ={M1,M1 +M2 ,M2 +M3 ,M3 ,M4 }. We obtain E,H(RH)-+S, S(MH) E, S(Rn ), H(M n + RH )-+S, S(M n ), S(M n + MH) P= {(M1 , M 1 +M2 ), (M2 + M 3 , M 3 )} E, S(Rn ), B(M n + Rn), H(M n +2Mn) as the set of positions where a link can be produced. Let P f- ~ for a given C. Let R5 indicate a -+S, S(Mn), B(Mn +Mn), S(Mn +2Mn)) randomly selected pair from P. Obviously, Rs = (R 51 , R52 ) and we can write the production rule as follows: As a next step we attempt tore-bond according to the rules of Re-bonding. Then proceed to explore the next L(k) or B(k). C, S(R51 ), S(R52 )-+C, L(X51 ), H(X52 ) Note that one substrate is replaced by a free link while the other substrate is "removed." Recall that 3.2.6 Bonding two substrates are used to produce a link. Try to bond any newly produced link according to the Every free link is a candidate to be bonded with rules of Bonding. another free link or with a singly bonded link. A bonded link, B, is always a component of a chain of bonded links. We shall designate a bonded link in 3.2.5 Disintegration the ath chain by B" ( k ). For a given L(k) we locate all neighboring Each free or bonded link, L ( k) or B ( k ), can positions containing free links, namely I L disintegrate into two units of substrate, providing ={MLjL(ML)}. Similarly, we locate all singly FORMAL MODEL OF AUTOPOIESIS 21

bonded links in the neighborhood, say K 8 :

Let us form a set of all possible pairs of eligible is the set of all "bondable" singly bonded links. We singly bonded links by forming the Cartesian form a list of pairs of such links: product of K 8 with itself: YB x YB= {XB IXB = (XBbXBz)}

K =K8 xK8 = {1\?n I JWn = (Mn1' Mnz)}. Z~ = {XB IXBl -XB2 = Mr} If K +p we perform the following transformation z~ =Z~n ~ {XB I W(XB1)nBii(XB2)}, for r~.

where z~ determines pairs of singly bonded links L, W(R81 ), Bli(R8 z)->B", B"(Mnt ), W(M8 z) which can be bonded. Let us define the following

IfK = p but K 8 +p, then there is exactly one singly set: bonded link and we can form the bond as follows:

L, B"(M8 )-> B", B"(M8 ) where X Bi and X Bj are particular pairs of Z~. For Let us defineKr. analogously withK . Then ifKr. 8 each such X e, form the set e ={XBi, X li.i}. L~t Reb~ a = p, exit. Otherwise, select one free link and form the pair selected at random from e, i.e., Re=XBi or XBj bond as follows: and

Test KL =0 again; if Yes, exit. Otherwise, select one free link and form the corresponding bond:

L,L(Rr.)->W, W(Mr.) Then for each X BE Z B we have the following rule of re-bonding: Next, perform the following operation (symbol ~stands for logical negation): B"(XB1 ), Bfi(X B2)->B"(X B1 ), B"(X B2)

Ir. ->Ir.n ~ {Mr.} since E(Mr.), E "f.L. Define YBn ~ {XB IXB EXB EZB}· Then

If I L 0, repeat the K L = 0 test and perform + YB->[YBn ~ {XB}]u{Xr.}. W,L(Rr.)->Ba,W(Mr.) where XL is derived as follows: again. Then exit. Vr. ={Mr. I L(:AJr.)uL(Mr. + Mu 1 )}

3.2.7 Re-Bonding and for E(Mr. +Mr.+ 1 ): if E=L In place of each disintegrated link, free or bonded, we attempt to re-bond a disconnected chain of always. bonded segments. To that purpose, for any position Next, use the new YB to construct new Z~ and ZB k, we have to determine all neighborhood positions and apply the rule of re-bonding again. Then exit. occupied by singly bonded links. First,

V8 = {M8 I B(M8 )u B(M8 +Mn+ 1 )}. 4 EXPERIMENTS IN SELF­ Then, for E(MB + MB+ 1 ), we determine ORGANIZATION

if E=B Our formalization of a parallel process is very always flexible. Catalytic neighborhoods can change their 22 M. ZELENY sizes and shapes, as well as the neighborhoods of Autopoiesis of a cell can be affected by a other components. The rates of production and particular structural adaptation, its functions of disintegration can vary over time or in dependency production, disintegration and bonding affected to on their previous values. Multiple catalysts can be their extremes. An allopoietic structure, a crystal, introduced, stationary or in flux with respect to each might ultimately form. It can neither disintegrate other. The influence of chance can be further nor expand or move. Either a weak catalytic reach amplified or totally removed (by extending the set of or a high inflow of substrate could lead to such movement rules). The amount of matter in the "allopoietization." On the other hand, an increased system can be kept either constant or external outflow of available substrate, creating dispropor­ inflows and outflows of substrate introduced. The tionately many holes, would cause the catalyst to system can be induced to disintegrate totally or to move rapidly over the space and the turbulence of "freeze" into a stable allopoietic structure. Systems its neighborhood would prevent orderly bonding­ with turbulent behavior or only partially delineated no membrane may eve r form. membranes can be observed as well as the systems One can simulate a growth in system's size quite whose membranes are ever-expanding. Systems simply by establishing a state-dependent change with broad or narrow membranes, substrate­ regime in the size of the catalytic neighborhood. seeking "amoebas" floating through the space, and Also, very complex shapes and patterns can be hundreds of other varieties can be evolved by simulated as arising from structural adaptations of adjusting and harmonizing a few parameters or the autopoietic system. In Figure 5 observe an rules. example of an autopoietic cell acquiring the shape of We can even provide a connection between a a cross. Theoretically, any complex shape can be particular structural adaptation and the change in induced to emerge through induced structural the organization itself. The interacting rules, which adaptations. are otherwise invariant, can be thus allowed to change according to appropriate meta-rules. Such self-affecting systems are then capable of self­ 4.2 Biological Clock reproduction and therefore evolution. We shall introduce a few simple experiments 13 All living systems ex hibit a variety of biorhythms performed with the APL-AUTOPOIESIS model. and cyclical adaptations. The most prominent is the aging phenomenon, a clearly observable "life cycle" of growth, plateau and decline. Organizational 4.1 Function and Form stability and permanence of an autopoietic system is We already discussed the distinction between the permanence and stability of its structural systemic organization and structure. The same history, not of its existence. All known autopoietic autopoietic organization is realizable through dif­ organizations have "built-in death." They either ferent structural forms although its basic unity of crystallize into allopoietic debris or disintegrate function and its identity as a unique system stay back into their components. unchanged. Structural adaptations are triggered by No autopoietic cell can escape death. Observe specific perturbing changes in its environment. that it is unreasonable to assume that the catalyst is Maturana talks about structural coupling, 7 i.e., "the unaffected by its participation in the production of effective spatia-temporal correspondence of chan­ links. Each single act of production diminishes its ges of state of the organism with the recurrent catalytic power. Initially, when there is a lot of free changes of state of the medium while the organism substrate, the number of produced links is naturally remains autopoietic." This structural rapport of the very high. At the same time, the number of holes system and its environment allows us to simulate necessary for disintegration is still very low. As a complex structural histories, in a controlled and result there is a large initial build-up in the amount predictable way, without changing system's organi­ of organized matter (links, free or bonded). As the zation. amount of free substrate decreases and the number For example, such structural variables as size and of holes increases, the two rates, production and shape can be simply studied. Changes in the disintegration, achieve a balance which is character­ catalytic neighborhood could elicit a large variety of istical for a relatively stable period of self-repairing structural r-esponses, see some typical "snapshot" membraneous enclosure. But the production must printouts in Figure 4. go on, although at much slower rate, and the more FORMAL MODEL OF AUTOPOIESIS 23

TME: 20 TIME: 34 HOLES: 6 HOLES: 41 RATIO OF HOLES TO SUBSTRATE: 0.0521 RATIO OF HOLES TO SUBSTRATE: 0.2867 FREE LINKS: 1 FREE LINKS: 14 ALL LINKS: 6 ALL LINKS: 40 CUMULATIVE PRODUCTIONS: 58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PRODUCTIONS THIS CYCLE: 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 o m-m o o o o o o o o o 0 0 0 0 0 0 0 0 0 0 I I 0 0 0 0 m* mo o o o o o o o o 0 0 0 0 0 ffi-00-00-~-00 0 0 0 0 \ I I \ 0 0 0 ffi 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 I I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 I I 0 0 0 0 00 0 0 * 0 00 0 0 0 I \ TIME: 35 o o o o 00 ~ 0 0 0 00 o o HOLES: 4 I I I RATIO OF HOLES TO SUBSTRATE: 0.0336 o o ~-m o o o FREE LINKS: 0 m o oo ALL LINKS: 4 I I o o o o o m-~ oo-m-m-m-m o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 TIME: 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 HOLES: 33 RATIO OF HOLES TO SUBSTRATE: 0.183333 0 0 0 0 0 0 0 0 0 0 0 0 u 0 0 FREE LINKS: 14 ALL LINKS: 33 o o o o o m o o o o o o a o o u 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I \ o o o m* mo o o o o o o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \ I 0 0 0 0 0 0 0 0 0 0 1!1 0 0 0 0 0 0 0 o o o o o mo o o o o o o o o I 0 0 0 0 0 0 0 1!1 o o mo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I I 0 0 1!1-1!1 0 0 Iii-Iii 0 0 D Iii-Iii 0 0 0 0 I \ 0 0 0 1!1 0 0 0 0 0 1!1 0 0 0 0 0

0 0 0 0 0 .. 0 0 0 0 0 0 0

0 0 0 0 o D D 0 0 0 0 0 0 0 o o o o o D o 0 0 1!1-1!1 o o 0 o o o I o o o o o o mo o o o o o o o I 0 0 0 0 0 0 ~ 0 0 1!1-i-1!1 0 0 0 0 0 0

0 0 0 0 (l 0 0 (l 0 0 0 0 0 0 0 0

FIGURE 4 Illustrations of narrow, broad and shattered membranes. Both "crystallization" and "structural turbulence" are extreme manifestations of autopoietic adaptation.

G 24 M. ZELENY

TIME: 30 TIME: 32 HOLES: 48 HOLES: 47 RATIO OF HOLES TO SUBSTRATE: 0.32 R A TIO OF HOLES TO SUBSTR AT£: 0.309210 FREE LINKS: 19 FREE LINKS: 20 ALL LINKS: 48 ALL LINKS: 47

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

() 0 0 0 0 0 0 0 00000 000 0 0 0 0 0 0 0 0 0 0 0

I) 0 0 0 0 0 IB-IB-IB-IlHB o 0 0 0 0 0 0 0 0 0 0 IB-IlHiH:B-IiJ 0 0 0 0 I I I I 0 0 0 0 0 IB 0 0 0 ffi 0 0 0 0 0 0 0 0 ffi 0 Iii 0 0 0 0 I I I I 0 0 0 0 (iJ-ffi 0 @-~ 0 0 0 0 0 0 0 0 0 o o Iii-HI () 0 0 liJ-IiJ 0 0 0 I I \ 0 0 0 1B o 0 0 0 0 0 0 0 0 0 0 0 0 Ill 0 0 0 0 ffi 0 0 0 0 I I 0 0 0 0 IB 0 0 * 0 1!1 0 0 0 0 o 1B 0 o 0 * 0 0 0 HI o 0 0 0 0 'I I I I 0 0 0 0 li:l 0 0 0 0 0 lil 0 0 0 0 0 0 0 0 0 0 Ill 0 0 0 £B 0 0 0 0 I I I I 0 0 0 0 0 liH!I 1!1 o 0 !B-Ill 0 0 0 0 0 0 0 o liHiJ 0 o lli-IB 0 0 0 I I \ I 0 0 0 0 0 Ill(!] 0 li:l 0 0 0 0 0 0 0 0 0 0 0 0 til 0 0 ffi 0 0 0 0 I \ I \ I 0 0 0 0 o !!1 o liHB-IiHB 0 0 0 0 0 0 0 0 0 0 0 0 o llHii-GHll 0 0 0 0 0 0

0 () 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

FIGURE 5 Shape of a cross - induced structural form of a membrane.

productions are performed the weaker the catalyst of holes is up. That allows more links to disintegrate, becomes. Thus, we experience the fastest "aging" of creating more substrate and few er holes again . the catalyst in the initial stages of the most vigorous It would be a gross fallacy to interpret such production activity. Although this "aging rate" structural rapport between the system and its becomes progressively slower, the production rate is environment as being due to some kind of a ultimately exceeded by the disintegration rate and feedback mechanism. There is none. No infor­ the total amount of organized matter starts to mation is transferred , none is coded. It only appears decline. Because the holes become fewer again and as such to an observer. there is more substrate available, the aging and loss of catalytic power speeds up at this later stage in a burst of activity before total catalytic exhaustion. Multiple Catalysts The disintegration rate is already low before the Obviously there can by any number of catalysts death itself and becomes only a slow decay functioning in a given space. When they are distant afterwards. 13 enough they can enclose themsel ves quite inde­ There is a large variety of other emergent rhythms pendently and function without mutual in­ that can be identified in the behavior of this terference. A group of autopoietic cells can be autopoietic cell. For example, there is a natural observed, each and all in a dynamic equilibrium cycle observed in the ratio of holes to substrate even wi th their environment. when the rates of production and disintegration are The most interesting case arises if we assume that kept stable. More substrate leads to more links and at a certain stage the catalyst is allowed to divide higher incidence of bonding. Consequently, the itself into two identical replicas. For example, the actual amount of substrate is less while the number first total closure of a membrane provides the trigger FORMAL MODEL OF AUTOPOIESIS 25 which causes such catalytic replication. The new 13) CJ-EB-···-CJ+O----*CJ-EB-···-EB-CJ catalyst then occupies any immediately adjacent 14) 0----*0+0 hole. Their respective neighborhoods overlap to a 15) -CJ----*0+0 large extent. Note that a large portion ofthe original 16) -EB----*0+0 membrane will disintegrate because no re-bonding 17) 0 +*----** is possible in the area of the overlap. Because a 18) fil+ •----**+* catalyst cannot pass through bonded segments, it 19) *----**+0 will ultimately float out of this new opening. The two catalysts of equal power will float apart and Observe that ultimately the density of substrate gradually enclose themselves by two separate particles 0 increases as it might be necessary for a membranes. The larger is the overlap of their cell to emerge. At the same time both the stable, - respective neighborhoods, the stronger is this initial and the unstable, ...1. , + , compounds are being "pulling apart." Gradually they disconnect them­ effectively trapped within the locality of disequilib­ selves, almost gently. 13 See Figure 6. rium. The chance of ...t. + ..f. ----**is being steadily Apparently a self-reproduction has occurred. increased. When * emerges, one or more, the cell There are two identical and independent auto­ can be produced according to the rules we already poietic cells as a result of a simple mechanical studied. We can imagine that there are dormant and division of a cell. A fairly close replica of the initial cell active layers of rules that are being brought to their is obtained without the benefit of any copying, action by the emergence of the necessary particles, coding or information processing artifacts. molecules or compounds. Finally, the last three rules allow for "self-regeneration" of the catalyst and its replication. That triggers the autopoietic 4.4 Autogenesis of Life: A Simple Scenario division of the cell and induces self-reproduction. Note that our fundamental particles, •, define We shall consider a uniformly distributed environ­ space through their relationship and interaction. ment of basic particles of matter, •, devoid of any Thus space is only derived and an observer­ information and structure. Such universe is initially dependent concept. It consists of a finite number of in a thermodynamic equilibrium. Let us assume that points in any of its neighborhoods and thus it is there is a separate locality where the local values of finite and discrete. Dirac suggested that space is the mean density and temperature can differ from filled with a sea of electrons occupying all energy the equilibrium conditions. Only the particles • can levels up to the "Fermi level." The electrons which penetrate the boundaries of such locality, both we observe have risen above the Fermi level, leaving ways. All other structurally higher combinations of behind a "hole," which is observed as a positively the basic particles are trapped inside the boun­ charged twin of the electron. The elementary daries. particles of contemporary physics are continually The following set of rules (one of many possible) emerging from and being reabsorbed into the would induce a self·organization of an autopoietic "vacuum" of the Fermi sea. They are products of the unity (like a living cell) independently of particular underlying autopoiesis in the domain of fundamen­ chemical and structural properties of the basic tal substrate-particles. components: 5 SOCIAL AUTOPOIESIS 1) •+•----*•-• 2) •-•+•----*J. The range of applications of autopoiesis is extend­ 3) ·-· + •-•----* + ing from atoms and molecules, organisms and 4) ·-· + .1.----*0 nervous systems, language and communication, to 5) 0+•----*0 social behavior, human societies, planning and 6) + + •-•----*0 management. At the same time the implications of 7) J..+ + ----** autopoiesis are profound and often upsetting. The 8) ..1.+ •----* ·-· + ·-· literature dealing with or related to autopoiesis is 9) + + ·----*.1.+ ·-· growing rapidly. We list some of the more impor­ 18 35 10) *+0+0----*0+* tant works in the References. - 11) 0+0----*CJ-CJ We conclude with some thoughts on social 12) CJ- CJ + 0----* CJ- E8- CJ autopoiesis. Human societies, and any other soci- M. ZELENY 26

PHASE 2 PHASE 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 o o o o o o o w-~ o o o o 0 I I 0 0 0 0 0 0 0 0 ~~~ ~-ffi ~ 0 0 0 0 0 0 11-01-18-83-19 I \ o o o o mo o o o o mo o o o 0 0 0 0 0 I I o o o o m o o o o m 0 0 0 0 0 0 ~ 0 0 0 0 0 ~ 0 0 0 I I I I o o o o mo o * o m 0 0 0 0 0 0 fil 0 0 * 0 0 [i] 0 0 0 0 I \ I \ 0 0 0 fj] ~ 0 0 0 0 0 W~OO* fil ~ 0 0 0 0 I I I I I 0 0 0 0 o o o ~ o mo o o o mo o o 0 0 ~ 0 £i1 0 0 I I I 0 0 0 0 0 0 0 0 0 0 m-~ m-m-m-m-m m-m-oo ~-~ I I 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0

PHASE 4 PHASE 3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 0 0 0 0 1!1 I I 0 0 0 0 0 0 0 ~-~-m-m-m 1!1-m o o 0 0 0 o m-m-oo-1!1 m-m-m o I I I o 0 1!l 0 1!1-m o o 0 0 0 0 o o o mo I!J 0 0 0 Ill 0 0 o m I I I I I \ 0 0 0 0 [i] 0 0 0 0 0 0 o mo 0 0 1!1 E!.l 0 0 0 l!l 0 0 !!I Gl I \ I \ I o 0 0 o m 0 0 0 mo 0 • 0 Iii 0 0 0 0 0 o mo 0 * o m I I I I I lil 0 0 0 0 0 1!l 0 0 0 I!J 0 0 0 0 0 0 1!1 0 0 l!l \ 0 0 0 0 [!) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * o o o o m-oo-m-m-1!1 o * o o o o o m-oo-ro-m-1!1 o o o o o o I I 0 0 0 1!1 0 0 0 0 1!1-ffi-ffi-1!1 0 0 0 0 0 1!1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

FIGURE 6 Multiple catalysts and the emergence of two distinct autopoietic unities. FORMAL MODEL OF AUTOPOIESIS 27 eties of autopoietic components, can maintain their is being evolved-Human Systems Management. It cohesiveness and unity through the "rules of is based on the following set of observations: conduct" that are spontaneously generated by the 1) Human systems are to be managed rather than autopoiesis of the components. F. A. Hayek21 analyzed or designed. HSM is not systems analysis emphasized that the order of social events, though it or design. is the result of human action, has not been entirely created by men deliberately arranging the elements 2) Management of human systems is a process of in a preconceived pattern. If the forces or rules that catalytic reinforcement of dynamic organization bring about such spontaneous orders are under­ and bonding of individuals. HSM does not design a stood, then such knowledge could be used to hierarchy of control and command. produce orders that are far more complex than 3) The components of human systems are those attempted by deliberately arranging all the humans. HSM is not general systems theory but a activities of a complex society. This is not an general theory of human organizations. argument against planning but rather against the 4) The integral complexity of human systems can simplistic tinkering and interfering with orders that be lost through the process of mathematical are much too complex to be viewed as mechanical 29 simplification. They can be studied through a contrivances. S. Beer also reiterates the fact that if relatively simple set of semantic rules, governing the a social institution is autopoietic then it is ne­ self-organization of their complexity. HSM is not cessarily "alive," i.e., it maintains its identity in a operations research, econometrics or applied biological sense. mathematics. Human systems, since they are not simple machines, should not be designed or analyzed. They 5) The interactions between individuals are not should be managed. Manager is a catalyst of those of electronic circuitry, communication chan­ spontaneous social forces. Crystals are not produced nels, or feedback loop mechanisms. HSM is not cybernetics or information theory of com­ by directly arranging the individual molecules, but by creating the conditions under which they form munication. themselves. Plants or animals are not put together by 6) The order of human organizations is main­ designers. They are managed by inducing the tained through their structural adaptations under conditions favorable to their growth. The task of the conditions of environmental disequilibrium. human management is to stimulate a growth of HSM is not the theory of general equilibrium. network of decision processes, systems, programs 7) The concepts of optimization and optimal and rules, i.e., an organization, which would be control are not meaningful in a general theory of effective in attaining institutional objectives. Such human systems. Human aspirations and goals are growth process of an autopoietic unity evolves its dynamic, multiple and in continuous conflict. Such own rules of change. These rules, in turn, d~termine conflict is the very source of their catalysis. HSM is the kinds of structural adaptations which could not optimal control theory or theory of conflict emerge. resolution. Humans live their livesthrough human systems, 8) The inquiry into human systems is transdiscip­ shape them through their individual aspirations, linary by definition. Human systems encompass the goals, norms and actions, creating a set of systemic whole hierarchy of natural systems: physical, aspirations, goals, norms and actions, which could biological, social and spiritual. HSM is not in­ be quite different and independent of the individual terdisciplinary or multidisciplinary, it does not ones. Humans are in turn continuously being shaped by such self-organized entities, their spatial attempt to unify scientific disciplines, it transcends them. and temporal arrangement evolving through a succession of state determined structures. Human It is appropriate to conclude by quoting S. actions and interaction with their emerging organi­ Beer:29 zation is irreducible to behavior, as it is so forcefully 30 " ... the way an autopoietic system will respond to a gross stated by E. Jantsch. environmental challenge is highly predictable-once the nature of its autopoiesis is understood. Clever politicians intuit those adaptations; and they can be helped by good scientists using 5.1 Human Systems Management system-theoretic models. Stupid politicians do not understand why social institutions do not lose their identities overnight when A new mode of inquiry into complex human systems they are presented with perfectly logical reasons why they should; H 28 M. ZELENY and these are helped by bad scientists who devote their effort to 16. M. Zeleny and N. A. Pierre, "Simulation of Self-renewing developing that irrelevant logic." Systems." In: Evolution and Consciousness. Edited by E. Jantsch and C. H. Waddington, Addison-Wesley, Reading, Mass., 1976. ACKNOWLEDGMENT 17. P. C. Jackson, Jr., Introduction to Artificial Intelligence. I am grateful to Norbert Pierre for his valuable programming and Petrocelli Books, New York, 1974. computational assistance and to George Klir for his continuing 18. M. Eigen, "Self-Organization of Matter and the Organi­ encouragement and editorial support. Personal communications zation of Biological Macromolecules." N aturwissenschaf ten, with Stafford Beer, Heinz von Foerster, Friedrich von Hayek, 10, 1971, 466. Erich Jantsch, Gordon Pask, Ricardo Uribe, Hugo Uyttenhove 19. G. Pask, Conversation, Cognition and Learning. Elsevier, and Francisco Varela were extremely stimulating and influential. New York, 1975. This project was partially supported through the Faculty 20. G. Spencer-Brown, Laws of Form. The Julian Press, New Research Grant of the Graduate School of Business at Columbia York, 1972. University. 21. F. A. Hayek, Kinds of Order in Society. Studies in Social Theory, No. 5, Institute for Humane Studies, Menlo Park, California. 1975. REFERENCES 22. F. G. Varela, "A Calculus for Self-Reference." International Journal of General Systems, 2, 5, 1975. I. F. G. Varela, H. R. Maturana and R. B. Uribe, "Autopoiesis: 23. H. H. Pattee, "Physical Problems of the Origin of Natural the organization of living systems, its characterization and a Controls." In: Biogenesis-Evolution-Homeostasis. Edited by model." Biosystems, 5, 4, 1974, 187-196. A. Locker, Springer-Verlag, New York, 1973,41-49. 2. B. Trentowski, Stosunekfilozofii do Cybernetyki czyli sztuki 24. G. Pask, "Minds and Media in Education and Entertain­ rzadzenia narodom. J. K. :Zupanski, Poznan, 1843. ment: Some Theoretical Comments Illustrated by the Design 3. A. A. Bogdanov, Tektologiia: vseobschaia organizatsionnaia and Operation of a System for Exteriorising and Manipulat­ nauka. Z. I. Grschebin Verlag, Berlin, 1922. ing Individual Theses." Proceedings of the Third European 4. S. Leduc, The Mechanism of Life. Rebman Ltd., London, Meeting on Cybernetics and Systems Research, Vienna, April 1911. 1976. To appear. 5. J. Ch. Smuts, Holism and Evolution. Greenwood Press, 25. G. Pask, Conversation Theory: Applications in Education Westport, Conn., 1973. and Epistemology. Elsevier, New York, 1976. 6. F. A. Hayek, Law, Legislation and Liberty. The University of 26. G. Pask, "Interaction Between Individuals, Its Stability and Chicago Press, Chicago, 1973. Style." Mathematical Biosciences, 11, 1971,59- 84. 7. H. R. Maturana, "The Organization of the Living : a Theory 27. B. K. Rome and S.C. Rome, Organizational Growth Through of the Living Organization." International Journal of Man­ Decision-Making. American Elsevier, New York, 1971. Machine Studies, 7, 1975,313-332. 28. H. von Foerster, "Molecular Ethology." In: Molecular 8. F. G. Varela, "The Arithmetics of Closure." In: Proceedings Mechanisms of Memory and Learning. Edited by C. Ungar, of the Third European Meeting on Cybernetics and Systems Plenum Press, New York, 1971. Research, Vienna, April 1976. To appear. 29. S. Beer, "Preface to Autopoietic Systems." In: H. R. 9. H. R. Maturana and F. G. Varela, Autopoietic Systems. Maturana, F. G. Varela, Autopoietic Systems. BCL Report . Biological Computer Laboratory, BCL Report No. 9.4, No. 9.4, University of Illinois, Urbana, Ill., 1975, 1- 16. Department of Electrical Engineering, University of Illinois, 30. E. Jantsch, Design for Evolution, George Braziller, New Urbana, Illinois, September 1975. York, 1975. 10. H. R. Maturana and F. G. Varela, De Maquinas y Seros 31. S. Beer and J. Casti, "Investment Against Disaster in Large Vivos. Editorial Universitaria, Santiago, Chile, 1973. Organizations." llASA Research Memorandum, RM-75-16, 11. H. von Foerster, An Epistemology for Living Things. April1975. Biological Computer Laboratory, BCL Report No. 9.3, 32. S. Beer, Platform for Change. John Wiley & Sons, New York, Department of Electrical Engineering, University of Illinois, 1975. Urbana, Illinois, 1972. 33. C. Menger, Untersuchungen iiber die methode der Sozial­ 12. H. R. Maturana, "Neurophysiology of Cognition." In: wissenschaften und der Politischen Okonomie insbesondere, Cognition: A Multiple View. Edited by P. Garvin, Spartan Duncker & H umblot, Leipzig, 1883. Books, New York, 1970, 3-23. 34. A. Locker, "Systemogenesis as a Paradigm for Biogenesis." 13. M. Zeleny, "APL-AUTOPOIESIS: Experiments in Self­ In: Biogenesis-Evolution-Homeostasis. Edited by A. Locker, Organization of Complexity." In: Proceedings of the Third Springer-Verlag, New York, 1973, 1- 7. European Meeting on Cybernetics and Systems Research, 35. A. Gierer, "Hydra as a Model for the Development of Vienna, April, 1976. To appear. Biological Form." Scientific American, December 1974, 44- 14. H. von Foerster, "Computing in the Semantic Domain." 54. Annals of the New York Academy of Sciencies, 184, June 36. M. Gardner, "On Cellular Automata, Self-reproduction, The 1971 , 239-241. Garden of Eden, and the Game of Life." Scientific American, 15. M. Zeleny and N. A. Pierre, "Simulation Models of 224, 2, 1971. Autopoietic Systems." In: Proceedings of the 1975 Summer Computer Simulation Coriference, Simulations Council, La For biography and photograph ofthe author. please seep. 74 ofthis Jolla, California, 1975, 831-842. issue. MILAN ZELE~Y is Associate Professor of Business at the Graduate School of Business at Columbia Universit; in ~C\\ York City. Born in Prague. he received his lng. degree in political economy and quantitative analysis from Prague School of Economics. After 4 years at the Economic Institute of the Czechoslovak Academy of Sciences he came to the L .S.A. where he earned M.S. in systems analysis and Ph.D. in operations research at the University of Rochester. He is the author of Linear .'v!ultiohjcctire Programming. editor and contributor to Multiple Criteria Decision Jfuking and .\fultiple Crileria Decision Jfa~ing: Kyoto 1975. He also contributed '"Simulation of Self-Renewing Systems"' to Emlution and Consciousness. edited by E. Jantsch and C. II. Waddington. He senes on editorial hoards on Computers and Operations Research, Human Srstems :'v!anagcment and Fuc2l" Se1s and Systems. He has published oYer seventy articles. books and essays on CPM and PERT, MCDM. multiobjective and multiparamctric LP. multipayoff games, simulation of autopoietic systems, distribution-free portfolio analysis, and many other topics in such journals as :\1 wwgcmcm Science. Theory and Decision, Joumal o( :'vluthenwtical Analysis and Appliculions, Compt!ler.l and Operations Re.learch.lmcmalional Joumal o(Gwne Theorr. etc. He is completing Jfultiplc Criteria Decision :\laking: .4 Cm11fJI111ion Te:\1 for McGra\\-l-lill.