Ecological Clues to the Nature of Consciousness

entropy

Concept Paper Ecological Clues to the Nature of Consciousness

Robert E. Ulanowicz 1,2 1 Department of Biology, University of Florida, Gainesville, FL 32611-8525, USA; [email protected]; Tel.: +1-(352)-392-6917 2 Chesapeake Biological Laboratory, University of Maryland Center for Environmental Science, Solomons, MD 20688-0038, USA


Received: 20 April 2020; Accepted: 26 May 2020; Published: 30 May 2020


Abstract: Some dynamics associated with consciousness are shared by other complex macroscopic living systems. For example, autocatalysis, an active agency in ecosystems, imparts to them a centripetality, the ability to attract resources that identifies the system as an agency apart from its surroundings. It is likely that autocatalysis in the central nervous system likewise gives rise to the phenomenon of selfhood, id or ego. Similarly, a coherence domain, as constituted in terms of complex bi-level coordination in ecosystems, stands as an analogy to the simultaneous access the mind has to assorted information available over different channels. The result is the feeling that various features of one’s surroundings are present to the individual all at once. Research on these phenomena in other fields may suggest empirical approaches to the study of consciousness in humans and other higher animals.

Keywords: autocatalysis; centripetality; coherence domain; consciousness; ecosystem dynamics; simultaneity

1. Introduction Panpsychism is the view that all features of the natural world share elements of consciousness or mind. One need not accept this belief in its entirety to acknowledge that behaviors contributing to consciousness might be evident in natural systems seemingly removed from the brain or human mental activity, thereby contributing insights into the nature of consciousness and how it might have arisen. While physics certainly can contribute to understanding many biotic phenomena, it is limited in that its laws can treat only collections of indistinguishable objects [1]. This restriction to homogeneous variables makes it difficult to apply the fundamental laws to behaviors among radically different biological kinds [2,3]. Ecology, in contrast with physics, embraces heterogeneity in its very foundations with its emphasis on the relationships among many differing types. Some even assert that proto-ecosystem behaviors had to precede the appearance of the first organisms—that physical cycling among regions that are dominated by antagonistic reactions (e.g., oxidation/reduction) provided the crucible that fostered the first proto-organisms [4]. It is thus plausible to consider whether some features of ecosystem dynamics might resemble those of the complex phenomenon known as consciousness. There is almost universal agreement that the experience of consciousness is one of the most difficult problems facing science. Theories of consciousness are common [5,6], relying on a host of subsidiary theories and phenomena. The major challenge is to connect consciousness to theories that are amenable to quantification, and empirical investigation [7]. One such endeavor is the Global Workspace Theory, where information is considered to be held in a global workspace and distributed to brain modules associated with specific tasks [8]. Another is Integrated Information Theory [9], which is an attempt to quantify the information that is actually fed back into the neuronal system to change it. The following essay is an attempt simply to highlight two ecosystem repertoires that might contribute to these efforts to illumine the very complex phenomenon of consciousness.

Entropy 2020, 22, 611; doi:10.3390/e22060611 www.mdpi.com/journal/entropy EntropyEntropy2020 2020, 22, 2,2 611, x FOR PEER REVIEW 22 of of 10 10

The first such behavior is autocatalysis, in which major reactants and products catalyze one anotherThe in first a closed such behavior fashion. isSuch autocatalysis, autocatalytic in dynamics which major are reactantscapable of and engendering products catalyzea progressive one anothertendency in to a closeddraw ever fashion. more Such resources autocatalytic into its dynamicsactive orbit. are (See capable example of engendering below.) This a phenomenon progressive tendencywas noted to drawin chemistry ever more decades resources ago intoby Bertrand its active Russell orbit. (See [10] example, who called below.) it “chem This phenomenonical imperialism” was notedand he in pointed chemistry to it decades as the drive ago byr behind Bertrand all Russellof evolution. [10], who Ulanowicz called it [11] “chemical instead imperialism”used Isaac Newton’s and he pointedterm, “centripetality” to it as the driver to describe behind allsuch of accumulation. evolution. Ulanowicz Despite [the11] fact instead that usedthis phenomenon Isaac Newton’s is readily term, “centripetality”visible in all living to describe systems, such it accumulation. appears on no Despite one’s the list fact of the that fundamental this phenomenon properties is readily of life. visible For inexample, all living Varela systems, et al. it [12] appears, in their on nodetailed one’s listpioneering of the fundamental description of properties autopoesis of life.(as engendered For example, by Varelaautocatalysis) et al. [12],, do in their not detailed touch upon pioneering the phenomenon. description ofYet, autopoesis the phenomenon (as engendered implicitly by autocatalysis), defines the dosystem not touch as a self, upon the the focus phenomenon. of its component Yet, the activities. phenomenon implicitly defines the system as a self, the focusThe of its second component property activities. concerns the simultaneity with which various sources of information are accessibleThe second to a virtual property center concerns that may the simultaneity be defined by with centripetality. which various That sources is, at any of information moment, an areindividual’s accessible attention to a virtual may center be focused that may on be a particular defined by thing centripetality. or activity, That but is, that at agent any moment, remains anconscious individual’s of a host attention of other may sources be focused of information on a particular—neuronal, thing visual or activity,, olfactory, but taste that agentor sensory remains—all conscioustranspiring of at a hostthe same of other time sources on the periphery of information—neuronal, of the mind. The theoretical visual, olfactory, origins taste of such or sensory—all simultaneity transpiringmight be traced at the same back time to physics, on the periphery and in particular of the mind. to the The notion theoretical of a origins “coherence of such domain”. simultaneity Such mightcoherence be traced is exhibited back to physics, by persisting and in particular aggregations to the notion of hundreds of a “coherence or more domain”. water molecules Such coherence in the isplasmas exhibited of living by persisting systems aggregations [13]. Below, how of hundreds the same or coherent more water behavior molecules might in be the extrapolated plasmas of to living work systemsin the process [13]. Below, of ecosystem how the development same coherent is behaviordiscussed might [14]. be extrapolated to work in the process of ecosystem development is discussed [14]. 2. Towards a Conception of Self 2. Towards a Conception of Self Autocatalysis is a dynamic that appears in consciousness literature (e.g., [15–17]. Broadly defined,Autocatalysis an autocatalytic is a dynamic set is a that collection appears of in entities, consciousness each of which literature benefits (e.g., [and15– 17is ].benefitted Broadly defined,by other anentities autocatalytic within the set same is a collection set so as ofto entities,maintain each the ofconfiguration which benefits of the and wh isole. benefitted To illumine by other some entities of the withinproperties the same of set autocatalysis, so as to maintain one the may configuration begin by of considering the whole. To simple illumine autocatalytic some of the cycles. properties An ofautocatalytic autocatalysis, cycle one mean may begins any bycycle considering of processes simple for autocatalyticwhich each constituent cycles. An autocatalytic process benefits cycle the means next anyone cyclein the of sequence processes [18] for. whichIn Figure each 1, constituentfor example, process if process benefits A facilitates the next another one in the process, sequence B, and [18 ].B Inbenefit Figures 1C,, forwhich example, in its turn if process augments A facilitates A, then another the activity process, of A B, indirectly and B benefits promotes C, which itself. in The its same turn augmentsgoes, of course, A, then for the B activityand C. of A indirectly promotes itself. The same goes, of course, for B and C.

Figure 1. Schematic of a hypothetical three-component autocatalytic cycle. Figure 1. Schematic of a hypothetical three-component autocatalytic cycle. As an ecological example of autocatalysis, one may consider the aquatic community that develops As an ecological example of autocatalysis, one may consider the aquatic community that around a family of aquatic weeds known as Bladderworts (genus Utricularia)[19]. Scattered along the develops around a family of aquatic weeds known as Bladderworts (genus Utricularia) [19]. Scattered feather-like stems and leaves of these plants are small visible bladders that normally maintain within along the feather-like stems and leaves of these plants are small visible bladders that normally themselves a lower osmotic pressure than their surroundings (Figure2a). At the end of each bladder maintain within themselves a lower osmotic pressure than their surroundings (Figure 2a). At the end are a few hair-like triggers, which, when touched by any tiny suspended animals (such as 0.1 mm water of each bladder are a few hair-like triggers, which, when touched by any tiny suspended animals fleas), will open the end to suck in the animal (Figure2b). It then closes the opening and the entrapped (such as 0.1 mm water fleas), will open the end to suck in the animal (Figure 2b). It then closes the animal becomes food for the plant (akin to what happens with the more familiar Venus fly trap). opening and the entrapped animal becomes food for the plant (akin to what happens with the more familiar Venus fly trap).

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FigureFigureFigure 2.2. 2. ( (aa)) Sketch Sketch of of a a typical typical “leaf”“ “leafleaf”” of of Utricularia Utricularia floridanafloridana floridana,, , withwith with (( b(bb))) detaildetail detail ofof of thethe the interiorinterior interior ofof of ana ann utricleutricle utricle containingcontainingcontaining aa a capturedcaptured captured invertebrate.invertebrate. invertebrate.

InInIn nature, nature, the the surface surface surface of of of Bladderworts Bladderworts Bladderworts always always always hosts hosts hosts the the the growth growth growth of of a a of nutrient nutrient a nutrient-rich--richrich algal algal algal film. film. film.This This Thissurfacesurface surface growthgrowth growth servesserves serves asas readyready as ready foodfood food forfor aa forvarietyvariety a variety ofof microscopicmicroscopic of microscopic animals.animals. animals. TheThe algaealgae The attachedalgaeattached attached toto thethe toleavesleaves the leaves benefitbenefit benefit fromfrom thethe from streamstream the of streamof nutrientsnutrients of nutrients thatthat waterwater that cucu waterrrentsrrents currentsbringbring toto them, bringthem, in toin contrast them,contrast in withwith contrast freefree-- withfloatingfloating free-floating plankton,plankton, plankton, whichwhich quicklyquickly which exhaustexhaust quickly nutrientsnutrients exhaust fromfrom nutrients aa smallsmall from quiescentquiescent a small surroundingsurrounding quiescent surrounding spheresphere [20][20]. . sphereHHence,ence, [20 bladderworts bladderworts]. Hence, bladderworts provideprovide aa surface providesurface upon aupon surface whichwhich upon thethe which algaealgae the cancan algae grow; grow; can thethe grow; algae algae the feedfeed algae thethe feed micromicro the microanimals,animals, animals, which which which clos closee close the the cycle the cycle cycle by by bybecoming becoming becoming food food food for for for the the the Bladderwort Bladderwort Bladderwort ( (Figure(FigureFigure 3 3). 3).). Bladderwort Bladderwort Bladderwort communitiescommunitiescommunities dominate dominatedominate many manymany nutrient-poor nutrientnutrient--poorpoor freshwater freshwaterfreshwater habitats, habitats,habitats, like likelike the thethe innerinner inner reaches reachesreaches of ofof the thethe Florida FloridaFlorida EvergladesEvergladesEverglades grasslands.grasslands. grasslands.

FigureFigureFigure 3.3. 3. SchematicSchematic Schematic ofof of thethe the autocatalyticautocatalytic autocatalytic looploop loop inin in thethe the UtriculariaUtricu Utricularialaria system.system. system. TheThe The UtriculariaUtricularia Utricularia plantplant plant providesprovides provides necessarynecessarynecessary surface surface upon upon which which which periphyton periphyton periphyton (an (an (an algae algae algae film film film designated designated designated by by the the by speckled speckled the speckled area) area) can area)can grow. grow. can grow.ZooplanktonZooplankton Zooplankton consumes consumes consumes periphyton periphyton periphyton and and is is and itself itself is trapped trapped itself trapped in in bladder bladder in bladder and and absorbed absorbed and absorbed in in turn turn in by by turn the the byUtriculariaUtricularia the Utricularia. . .

TheTheThe autocatalyticaut autocatalyticocatalytic dynamicsdynamics dynamics among among among the the theUtricularia Utricularia Utriculariaplant, plant, plant, U, U, U, the the the attached attached attached algae algae algae (periphyton) (periphyton) (periphyton) film, film, film, P, andP,P, andand the the zooplanktonthe zooplanktonzooplankton density, density,density, Z, can Z,Z, be cancan modeled bebe modeledmodeled after Ulanowiczafterafter UlanowiczUlanowicz [19] in [19][19] abbreviated inin abbreviatedabbreviated form (The formform reader (The(The readerreader is is referred referred to to Ulanowicz Ulanowicz [19][19], ,where where the the dynamical dynamical equations equations an andd their their steady steady--statestate solutions solutions

Entropy 2020, 22, 611 4 of 10 is referred to Ulanowicz [19], where the dynamical equations and their steady-state solutions are more completely articulated. Limits, such as nutrient scarcity and periphyton shading, were eliminated here for simplicity, leaving autocatalysis unbounded.) as:

dU = αUN + ϕZU mU (1) dt − dP = γPN ρZP µP (2) dt − − dZ = ρZP + σZΨ ϕZU ξZ (3) dt − − dΨ = ηΨN σZΨ εΨ (4) dt − − where α, γ, ϕ, ρ, σ and η are Lotka–Volterra reaction constants, N is the concentration of dissolved nutrient, Ψ the density of free-floating phytoplankton, and m, µ, ξ and ε are the mortality rates of U, P, Z and Ψ, respectively. If one identifies M = U + P + Z as the total mass of the Utricularia system, then adding the first three equations yields, dM = αUN + γPN + σZΨ mortalities (5) dt − Now, if algae could not anchor to the Utricularia (i.e., P = 0), there would still be a slight subsidy to the Utricularia system via its carnivory in the amount σZΨ. This advantage would be almost negligible, however, because of the nutrient limitation to free-floating phytoplankton mentioned above. By attaching to a leaf surface, however, nutrients are swept close to its surface, significantly accelerating absorption [21]. Thereby, the system, M, accretes by γPN, which in turn increases the rate of zooplankton growth by ρZP, and the assist to Utricularia, ϕZU inflates accordingly. Ulanowicz [19] did not numerically integrate this set of equations. Rather, he set all derivatives to zero and solved for the steady-state values of U, P and Z. After obtaining realistic estimates for all parameters, it was concluded that the feedback, ϕZU adds roughly 33% to intrinsic Utricularia growth, αUN allowing it to outcompete other systems when nutrients are low. While autocatalysis among simple, invariant chemicals remains strictly mechanical, whenever the reactants are malleable to an extent, or when contingencies occur in, or impinge upon, elements of the cycle, endogenous (within system) selection can occur. For example, in the Utricularia system, if there happens to be some contingent change in the surface algae that either allows more algae to grow on the same surface of Bladderwort (e.g., by becoming more transparent), then the effect of the increased algal activity induced by that contingent event will be rewarded two steps later by more Bladderwort surface. The activities of all the members of the triad will be increased. Conversely, if the change either decreases the possible algal density or makes the algae less palatable to the microanimals, then the rates of all three processes will be attenuated. Simply put, contingencies that facilitate any component process will be reinforced, whereas those that interfere with facilitation anywhere will be decremented. The net result is the facilitation (selection) of features of participating members and pathways over and above non-participating entities. Evidence of such selection in the Utricularia system include the plant morphology of hair-like leaves that provide a maximal surface to biomass ratio to enable it to host more periphyton. Additionally, some subspecies exude mucilage to help the algae adhere to its surface, while others, in low-pH waters, host more transparent periphyton. Having established how autocatalysis can select for changes that contribute to greater autocatalysis, it is a minor step to broaden the narrative to encompass exchanges with the rest of the world. Processes A, B and C cannot occur without inputs of energy or resources from elsewhere. So if a contingency in B happens to enable it to import more needed resources into itself, that change will be reinforced. If the change decreases the ability of B to import resources, autocatalysis will regress, thereby decrementing the change. Now, the same dynamic applies not only to B, but to all members of the cycle. Hence, Entropy 2020, 22, x FOR PEER REVIEW 5 of 10 Entropy 2020, 22, 611 5 of 10 will be reinforced. If the change decreases the ability of B to import resources, autocatalysis will regress, thereby decrementing the change. Now, the same dynamic applies not only to B, but to all membersover time, of the the interaction cycle. Hence, of autocatalysis over time, with the interaction contingent changesof autocatalysis induces withthe system contingent to import changes ever indugreaterces amountsthe system of necessaryto import ever resources greater over amounts all possible of necessary inputs to resources the system. over Such all possible “centripetality” inputs to is theillustrated system. schematicallySuch “centripetality” in Figure is4 .illustrated schematically in Figure 4.

FigureFigure 4. 4. CentripetalCentripetal action action as as engendered engendered by by autocatalysis. autocatalysis.

ItIt is is not not possible to completely mathematize the the action of centripetality beyond beyond the the simple simple representationrepresentation of of positive positive feedback, feedback, as as was was carried out above for the Utricularia system. One One notes notes thatthat the the extent extent of of the the autocatalytic autocatalytic system, system, MM,, isis inflated inflated by by 훾푃푁γPN++ 𝜎푍훹σZΨ,, ther therebyeby extracting extracting nutrients nutrients fromfrom the the stores stores of ofN Nand and competing competing phytoplankton, phytoplankton,Ψ. More훹. More generally, generally, however, however, centripetality centripetality arises arisesthrough through the boundary the boundary conditions, conditions, which are which dominated are dominated by contingencies. by contingencies. Kauffman [ 21 Kauffman] characterizes [21] characterizesthose boundary those constraints boundary and constraints events as and the “adjacentevents as the possible” “adjacent and possible” argues how and such argues contingencies how such contingenciescannot even be cannot categorized even be in advance.categorized His in simple advance. example His simple is to challenge example anyone is to challenge to list all anyone the uses to of lista screwdriver. all the uses Oneof a screwdriver. begins by drawing One begins up a listby drawing of the most upobvious a list of the alternative most obvious uses, but alternative discovers uses that, buteach discovers new use suggeststhat each further new use variations, suggests progressively further variations, lengthening progressively the list ad-infinitum. lengthening He the concludes list ad- infinitum.generally, therefore,He concludes that generally, boundary therefore, conditions that remain boundary “unprestatable”. conditions remain “unprestatable”. TheThe centripetal system inin FigureFigure4 4 is is capable capable of of exerting exerting agency agency upon upon the the external external world—it world— actsit acts as asan an entity entity upon upon its surroundingsits surroundings so as so to aggrandizeas to aggrandize itself. Initself. fact, In if twofact, autocatalyticif two autocatalytic systems inhabitsystems a inhabitregion with a region finite with resources, finite competition resources, competition will inevitably will ensue. inevitably Heuristic ensue. evidence Heuristic of centripetality evidence of centripetalityexerted by Utricularia exerted bysystems Utricularia lies in systems the observations lies in the that observationsUtricularia thatusually Utricularia forms uniform usually standsforms uniformin relatively stands clear in water relatively by sequestering clear water resources by sequestering to the exclusion resources of toother the competitors, exclusion of such other as competitors,phytoplankton. such Hence, as phytoplankton. competition as aH processence, competition is always secondary as a process and subsidiary is alwaysto the seco morendary primary and subsidiarymutual beneficence to the more at the primary next level mutual down. beneficence The inward at radial the directions next level of down. inputs The in Figure inward4 imply radial a directionsvirtual center of inputstowards in whichFigure action 4 imply is directed. a virtual Within center thetowards brain which and body action of ais higher directed. organism, Within such the braindirectionality and body engendered of a higher organism by autocatalytically, such directionality related sets engendered of neurons by can autocatalytically support the notion related of sets self, ofid or neurons ego—central can support players the in the notion phenomenon of self, of id consciousness. or ego—central players in the phenomenon of consciousness. Hypothesis 1. Autocatalysis among the processes of the brain works to produce an image of the self as the focus Hypothesisof all mental activities.1. Autocatalysis among the processes of the brain works to produce an image of the self as the focus of all mental activities. 3. Bringing the Outside World Within 3. BringingThe foregoing the Outside description World ofW centripitalityithin tends to gloss over considerations of the rates of signal transmissionThe foregoing and phasedescription relationships of centripitality among tends them. to Forgloss example, over considerations the material of in the each rates link of signal in an transmissionecosystem trophic and phase web may relationships take days, amongweeks or them. years For to travel example, from the one material element in to eachthe next, link yet in the an ecosystemresponse of trophic the system web sometimesmay take days, must weeks take place or years on a to much travel shorter from one timescale. element How to the is thisnext, possible? yet the responseA key of observationthe system sometimes in this regard must was take made place by on physicists a much shorter studying timescale. interstitial How water is this in biologicalpossible? plasmasA key [13 observation]. It appears in that this collections regard was of made many by water physicists molecules studying persist interstitial as quasi-stable water aggregationsin biological plasmaswithin living [13]. It systems. appears Thesethat collections “coherence of domains”many water were molecules capable persist of catalyzing as quasi necessary-stable aggregations molecular withinbiological living processes, systems. suchThese as “coherence photosynthesis. domains” Now, were this capable phenomenon of catalyzing was strange,necessary because molecular the biologicalelectromagnetic processes, (EM) suchforces as among photosynthesis. the molecules Now, are capable, this phenomenon at biotic temperatures, was strange, of because maintaining the

Entropy 2020, 22, 611 6 of 10 coherence only over a distance of a few molecules. How does the aggregation persist in the face of molecular perturbations? Physicists theorized that the phase correlations within the larger coherent ensemble were maintained not by their EM fields directly (which travel near the speed of light), but by their potentials that can travel across the quantum vacuum at a phase velocity that can exceed the speed of light [22]. Quantum esoterica aside, for a coherence domain to persist, simultaneous activities at two separate hierarchical levels are required: slower and stronger forces govern the movements of the water atoms themselves, but weaker and faster communication keeps those movements in coherent cadence at longer distances. This complex dynamic bears analogy to the movement of an Olympic rowing scull. The scull is propelled by the exertions of eight strong rowers, who are kept in synchrony by a diminutive coxswain, who calls out the cadence. At the macroscopic scales of an ecosystem, bulk mass and energy flows are maintained among species over pathways that are relatively slow. The coordination and phasing of autocatalytic activities are maintained by much faster communication routes, such as visual cues (speed of light), sound, olfactory signals and pressure waves (in water). Such biosemiotic cues co-evolve with autocatalytic trophic activities that constitute the bulk flows to create what has been called “biosemiotic scaffolding” [23], which maintains the flow network in existence. That is, the complex of rapid biosemiotic signals develop so as to coordinate and support the slower trophic transfers in autocatalytic, self-re-enforcing fashion [24]. Such bi-level, parallel patterns of coordination likely arise in other domains of ordered phenomena, such as neuronal activities in the brain (ibid.). As is well-known, synaptic firings are relatively slow, taking on the order of 0.1 s to transpire. Brain activities, however, do not appear to be dominated by transmission along concatenated neuronal pathways, but instead as spatio-temporal patterns of neuronal bulk firings. It would appear plausible that these larger patterns of firings might be coordinated by faint electromagnetic emissions emanating almost at the speed of light from other bulk firings. That is, the stronger, slower firings are being coordinated by weaker but much faster EM pulses that serve as a biosemiotic scaffold. The extreme speed with which the weak EM pulses travel means that information received at disparate regions of the central nervous system could immediately be sensed over all the approximately 20 cm domain of the brain. This could likely give rise to the sensation of simultaneity, whereby one has the feeling that information of various sorts is accessible all at once, allowing one to direct attention to the source of greatest immediate import. The dynamic is similar in effect to the Global Workspace Theory, except the workspace here is physically distributed, rather than central (although with respect to the configuration of processes, all incoming signals point towards a virtual center [i.e., the “self”, as in Figure4]).

Hypothesis 2. The sensation in consciousness that various sources of information are simultaneously available is a manifestation of a coherence domain existing among all sensory regions of the brain.

4. Centripetality and Simultaneity as Concerns Empirical Projects Although centripetality and simultaneity are, at best, cryptic in the two leading theories (the Global Workspace Theory and the Integrated Information Theory), their expositions here suggest possible new pathways for studying and quantifying these phenomena. Tononi [25], for example, quantifies his integrated information using the Kullback–Leibler Divergence formula to quantify change in before and after probability distributions. This is a legitimate way of reckoning information, but it only measures differences in marginal probabilities. The brain and its mental activities are more fully conceived as networks of relationships among entities or events [26]. If one can identify and quantify the connections that embody these relationships, one can array them in matrix form, which reveals both the topology of the interactions and the relative magnitudes of Entropy 2020, 22, 611 7 of 10 each one (Figure5). As is preliminary to the derivation of the Kullback–Leibler Divergence, one first identifies the diversity among those flows as, Entropy 2020, 22, x FOR PEER REVIEW ! 7 of 10 X   X Tij Tij H = pijlog pij = log (6) − i.j − i,j 푇T.. 푇T.. 퐻 = − ∑ 푝 푙표푔(푝 ) = − ∑ 푖푗 푙표푔 ( 푖푗) (6) 푖.푗 푖푗 푖푗 푖,푗 푇.. 푇.. where pij is the joint probability of the flow from i to j, Tij is the actual value of the ijth relationship where 푝푖푗 is the joint probability of the flow from i to j, 푇푖푗 is the actual value of the ijth relationship and aand dot a indot place in place of anof an index index indicates indicates summation summation over that that index. index. Therefore Therefore 푇. Tis. isthe the sum sum of all of all systemsystem flows. flows.

FigureFigure 5. ( a 5.) ( Aa) hypothetical A hypothetical four-node four-node weighted weighted network. network. (b (b) ) Network Network (a) ( a arrayed) arrayed as aas matrix. a matrix. T = ) (Example:(Example:23 푇2360= .60).

H isH conventionally is conventionally and mistakenly and mistakenly referred referred to as the to “entropy” as the “entropy” of the distribution of the distribution of relationships, of whenrelationships, in fact it can when be decomposed in fact it can be into decomposed two complementary into two complementary non-negative non components,-negative components,

2 푇푖푗 푇푖푗푇..! 푇푖푗 푇푖푗 2  퐻 X= + ∑T푖,푗 푙표푔T( T.. ) −X∑푖,푗 T푙표푔 (  T),  (7) ij푇.. ij푇푖.푇.푗 푇.. ij 푇푖.푇.푗 ij  H = + log log , (7) i,j T.. Ti.T.j − i,j T.. Ti.T.j  or or HA H = A + Φ In information theory, the first term is called the “average mutual information”, A (≥0) and it quantifiesIn information the degree theory, of constraintsthe first term that is bind called the the relationships “average mutual into a whole information”, system, whereasA ( 0) the and it second term is called the “conditional entropy”, Φ (≥0), which measures the apophatic ≥ lack of quantifies the degree of constraints that bind the relationships into a whole system, whereas the second constraint, or freedom remaining among the relations [27]. Thus, one sees that, more generally, H term is called the “conditional entropy”, Φ ( 0), which measures the apophatic lack of constraint, represents not just entropy (unconnectedness≥ or freedom), but information on binding as well [28]. or freedom remaining among the relations [27]. Thus, one sees that, more generally, H represents not (It should be mentioned in passing that autocatalysis tends to contribute to greater and more efficient just entropystreamlining (unconnectedness of the network [higher or freedom), A]). but information on binding as well [28]. (It should be mentionedUlanowicz in passing [27] that applied autocatalysis this analysis tends to of contribute conditional to probabilities greater and more to networks efficient of streamlining trophic of theexchanges network in [higher ecosystems, A]). which in principle can be assessed directly. The relative values of A and Φ associatedUlanowicz with [27] any applied particular this analysis ecosystem of conditional indicate how probabilities streamlined to (organized) networks of or trophic how branched exchanges in ecosystems,(indeterminate) which its innetwork principle is, canrespectively. be assessed The directly.compilation The of relative ecosystem values networks of A and fromΦ variousassociated withhabi anytats particular and conditions ecosystem reveal indicate a surprisingly how streamlined narrow grouping (organized) of the orrelative how branchedvalues of A (indeterminate) and Φ [29], its networkclustering is, around respectively. a value of TheA/H compilation≈ 0.40. This observation of ecosystem inferred networks that ecosystems from various do not perform habitats at and conditionsmaximum reveal (streamlined) a surprisingly efficiency, narrow but groupingrather retain of a the lar relativege degree values of indeterminacy of A and Φ that[29 can], clustering serve as a wellspring for new configurations capable of resisting or accommodating novel threats.

Entropy 2020, 22, 611 8 of 10 around a value of A/H 0.40. This observation inferred that ecosystems do not perform at maximum ≈ (streamlined) efficiency, but rather retain a large degree of indeterminacy that can serve as a wellspring for new configurations capable of resisting or accommodating novel threats. It is well accepted that brain activity, likewise, is neither very rigid (organized) nor too chaotic [30]. A question of great interest might be whether networks of neural activities exhibit clustering similar to that of ecosystems and where along the spectrum of organization might such cluster lie. One experiment that immediately presents itself is whether there is any significant change in the relative values of A and Φ between conscious and unconscious brain activity. The system-level information indices are also useful in ecosystems to identify which links are most important or limiting [31]. Such knowledge might also be useful for assessing what is important for consciousness by comparing the differences in limiting transfers between states of consciousness and unconsciousness. Other tools from network analysis could also be applied to neuronal networks. The autocatalysis present in networks often is associated with (pathway) cycles in the activity network. Provided the network is of manageable dimension, all simple cycles can be identified and abstracted from the starting network [32]. Comparing these patterns of cycles in conscious and unconscious states could identify those loops most important in autocatalytic and centripetal phenomena. The list of other possible methods that can be borrowed from ecological network analysis is wider still and involves various measures of indirect effects, pathway distances of causal chains (akin to trophic analysis in ecology) and the propagation of positive and negative influences [33].

5. Coherence Phenomena The empirical investigation of coherence phenomena in the brain is confounded by the method used to measure brain activity. That is, brain activities are usually mapped by sensing the EM emissions of synaptical firings. The method of measurement thus coincides with the very phenomenon hypothesized to maintain coherence. How to deconvolute the neuronal firings from the phenomenon that both signals the existence of a firing and coheres multiple firings with one another seems to be a problem almost as complex as observing consciousness itself. Nevertheless, enterprising and brilliant electrical engineers could possibly observe coherence signaling using something akin to “stereoscopic” sensors of separate brain scanners. There then remains the problem of how an EM signal could trigger a firing and how different EM signals emanating from different locations in the brain could be distinguished one from another. There remains yet two other possibilities. The coherence signal might possibly be other than EM emissions from firing neurons. Mae-Wan Ho [34], for example, wrote about how living tissue is close to chemical equilibrium and that disequilibria can propagate through the system at a very rapid rate. That rate need only be fast in comparison with neuronal firings, but could remain slower than the almost-as-fast-as-light EM signals. The technical problem would remain how to detect and measure the development of such intercellular communications. Finally, Stuart Kauffman [17] hypothesized that neuronal activities might be synchronized via quantum entanglement.

6. Conclusions The conscious experience of identity is likely a neuronal phenomenon analogous to the centripetality, or inward-directedness, that is engendered by autocatalytic cycles of processes, such as the characterization of dynamics in ecosystems and numerous other ensemble entities. If neuronal activity can be characterized in terms of networks among portions of the nervous system, then autocatalytic activity can likely be tracked using information metrics such as average mutual information to quantify differences between conscious and unconscious brain activities. The apparent simultaneous access to different sorts of information in the mind is very likely related to coherence phenomena within the brain. The slower propagation of serial neuronal firings is likely coordinated by faster but weaker modes of communication facilitated by EM emissions Entropy 2020, 22, 611 9 of 10 from the synaptic firings themselves, by quantum entanglement or by metabolic waves that can race through tissues. The fact that both aspects of consciousness exhibit dynamics similar to those in macroscopic systems, like ecological communities, shows promise that the recondite problem of consciousness may soon be partially resolved through the study of large-scale systems.

Funding: This research received no external funding. Acknowledgments: The author is indebted to Heide Kloosa for her incisive critique of the first draft of this essay. Joseph Brenner, Malcolm Dean and Robert Prentner later contributed useful comments for the final revision. Contribution No. 5865, University of Maryland Center for Environmental Science. Conflicts of Interest: The author declares no conflict of interest.

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