LECTURE 6

6.1) THE INDEFINITE HIERARCHY OF AGENTS.

i. The emergence of higher order Autonomous Agents is possible in the Abstract and in Actuality.

ii. Grammar models, as defined above. Post systems: A "Grammar Table" consisting in a finite set of pairs of symbol strings, showing for each pair, that the "right" member of the pair is to be substituted for instantiations of the "left" member of the pair.

iii. Requires precedence rules, and rules to avoid infinite loops when a substitution creates a "site" where the same substitution can again be inserted.

iv. Extension of Grammar model to allow symbol strings to act as "enzymes" able to act on symbol strings according to the Grammar Table to create new symbol strings. For example, a symbol string that bit matches a "right" symbol string "site" on some symbol string, X, might carry out the "reaction" that substitutes the correct "left" symbol string at that site in X.

v. Given Grammar Table, one then has a "pot of symbol strings" constituting the World. The set of symbol strings then operate on one another.

-- Consider grammar models as "as if" models of chemical transformations, or a models of goods and services in an economy, hence as "as if" models of technological complementarities and substitutabilities. Thus, grammar models are finitely specifiable models for the emergence of functionally organized systems. --

6.1.2) Similarity to Fontana's Algorithmic Chemistry, where there is a pot of symbol strings that can act on one another, but the pot acts as a chemostat, maintaining the total number of symbol strings at, say, 10,000. Thus, this selection pressure selects for symbol strings that are often produced.

His results include:

0) Initially, a "flight" of ever novel symbol strings are produced. After a while, more and more of the symbol strings in the system have been produced before. So the "soup" starts to show recurring symbol strings.

1) Emergence of 0 order "organizations" - i.e. copiers able to copy themselves and anything else.

2) Emergence of 1st order "organizations," namely collectively autocatalytic sets in which no symbol string copies itself, but a last step in the formation of each is catalyzed by some symbol string in the set. Here one gets a stable core "metabolism" of the collectively autocatalytic set, and flares of novel strings which are produced, but not sustained by the chemostat pot system.

3) Emergence of "2nd order" organizations when two first order organizations exchange symbol strings. The exchange in Fontana's system creates symbol strings that are in neither first order organization, but act as a "glue" of interactions generated by the commerce between the two first order organizations.

NB, first order organizations, collectively autocatalytic sets, become my Autonomous Agents as soon as inclusion of work cycles is instantiated.

6.1.3) Higher order collectively autocatalytic sets, work to construct constraints on energy release, thus propagating work and tasks, task closures, and niches.

Consider "Machines" as ordered sets of symbol strings. Think of a Machine as an "assembly line" of symbol strings, able to act on "input bundles" comprised of ordered sets of symbol strings, to create "output bundles" that are, again, ordered sets of symbol strings.

i. Molecular examples of Machines include multienzyme complexes where a single substrate enters and is "processed" down the assembly line of enzymes without release of intermediate products. The retention of intermediates speeds assembly of the final product compared to release of intermediate products, their free diffusion in cell, and rebinding to the next enzyme.

Note that such supramolecular complexes constitute work done to create low energy structures which create constraints on the release of energy to abet flow down a coordinated sequence of reactions along one of many branching pathways, thus this work of construction is an example of work done to create the constrained release of energy along restricted pathways that constitutes work done and task accomplished.

ii. In origin of life as a phase transition, we showed that a phase transition between subcritical and supracritical behavior in chemical systems occurs because, as the diversity of organic molecules increases, the ratio of reactions to molecules itself increases. Thus, for any fixed probability that each molecule can act as a catalyst for each reaction, ultimately, the catalyzed reaction subgraph forms a giant connected component and collectively autocatalytic sets emerge.

iii. The same emergence of HIGHER ORDER autocatalytic sets will emerge in a world of Machines, Input Bundles, and Output Bundles.

(The set of possible Machines, Input Bundles and Output Bundles is the Power-Set of a set of symbol strings. Thus, suppose we consider a finite set of symbol strings bounded by the twin facts that: i. The number of symbol strings is finite. ii. The length of any symbol string, say in binary form, is finite. Then the set of possible input bundles is just all possible subsets of the set of symbol strings, i.e. the power set. The set of machines is the same power set. And the set of output bundles is also the set of all possible subsets of symbol strings, hence the same power set. In its most general form, the set of possible "grammars" is the set of possible mappings from input bundles and machines to output bundles.

For almost any grammar, say with a maximum bound on the number of symbol strings that may be in an input bundle, a machine, and an output bundle, the number of transformations among input bundles via machines increases vastly faster than the mere diversity of input bundles and machines, for a given input bundle may be acted upon by many machines and transformed into many output bundles. Conversely, a given output bundle may be generated by a multiplicity of machines acting on a multiplicity of input bundles.

-- This mirrors the same property of simple polymer chemistry where the reaction transformations among these combinatorial chemical objects increases faster than the diversity of the chemical objects themselves. --)

Symbol strings are combinatorial objects made out of symbols -- hence the theory above about a phase transition to autocatalytic sets of symbol strings as the diversity of symbol strings increases and the ratio of transformations to symbol strings increases even faster.

But Machines, input bundles and output bundles are themselves also combinatorial objects made out of symbol strings.

Therefore:

As the diversity of symbol strings within an input bundle, machine, and output bundle increases, the ratio of potential transformations among the input bundles and output bundles to the number of bundles increases. As the diversity of transformations increases over the diversity of Input Bundles and Output Bundles, collectively autocatalytic sets of Machines, Input Bundles and Output Bundles will arise.

Thus, higher order Agents will emerge, able to achieve closure in a functional task space and work cycles. That is, if the objects in question are real physical systems, the increasing ratio of transformations to input bundles and output bundles with diversity also means that work done to construct constraints on energy release that constitutes propagating work and simultaneously self-consistently achieves "propagating work task closure "becomes easier. Thus, with diversity, invasion of the adjacent possible becomes easier.

6.1.4) Higher order Agents and Darwinian functional explanations.

The combinatorial features of machines, input bundles and output bundles and the fact that the ratio of transformations among these combinatorial objects to the number of kinds of objects increases with diversity of the combinatorial objects is central to the occurrence of higher order functionally coherent Agents linking autocatalytic closure in a space of tasks to function to work cycles to propagating functionally whole agents - work-record-know-how:

i. Consider first the standard Darwinian account of function in biology. The function of a part, say the lactose operon in E. coli, is that causal consequence of the part, or subsystem, that fulfills a task required by the cell as part of making its living. Thus, the lactose operon encodes and controls the synthesis of Beta galactosidase and a permease related to the metabolic use of exogenous lactose as a food source and activated only in the presence of that food source.

But the Darwinian account of function via natural selection is two-fold:

First, the function of a part is that subset of causal consequences of the part for virtue of which it has been selected. The heart has been selected to pump blood, not to make sounds. Thus, the functional account via natural selection picks out those causal consequences of the part for which the part has been selected.

Second, the Darwinian account is an ontological explanation for the persistent existence of the part. Thus, the part exists because it has been of functional use, conferred a selective advantage on the "whole," therefore has been persistently maintained in the propagating organization called the cell and its progeny.

The Darwinian account is also an ontological account of the coming into existence of the part. In general the explanation is phased in terms of exaptations and gradual modifications. An exaptation occurs when a causal consequence of an existing part comes to have selective significance in a "new environment.

If we now phrase the Darwinian account in terms of Autonomous Agents, we see that the functional explanation tells us how and why a given part or work process has come into existence in the actual Universe. Lactose operons and hearts exist as organizations of matter and energy because each has come to carry out one or more selectively useful functional tasks and self-consistent constraint construction and propagating work in the Agents of which each is a part.

So the Darwinian account explains the actual existence of complex parts in functional wholes as part of the existing furniture of the Universe, as opposed to the vastly many complex things that will never come to exist.

Getting to "exist" at all is a triumph in a Universe where most "things" will never come into existence. I return to this below for this is a signature of the non-ergodic behavior of the Universe.

6.1.5) Higher order Agents and Higher Order Niches.

Returning the grammar models, consider the set of transformations among the input bundles mapping to output bundles via the actions of machines.

These transformations constitute "POTENTIAL "TASKS" carried out by specific machines. The potential tasks will become real tasks when instantiated within functionally whole Agents and the Communities the Agents create.

i. As the diversity of input bundles and output bundles increases, for most grammars, the diversity of possible transformations, hence potential tasks, increases.

ii. Consider the emergence of a collectively autocatalytic set of input bundles, machines, and output bundles. Once such a functionally "whole" autocatalytic system carrying out work cycles is in place, a new Agent has emerged. The Darwinian categories now arise, and the functionality of the input bundles, machines, and output bundles for the autocatalytic functional closure of the Agent is present and statable.

iii. The new functionalities within and between Agents constitute the new niches whereby the new Agents can make a living in their world. The new functionalities are context dependent.

iv. The autonomous agents comprised of input bundles machines and output bundles can themselves form into still higher order autonomous agents. A multicelled organism or a colonial organism are examples.

Thus, the combinatorial explosion of input bundles, machines and output bundles in most grammar models exhibits the fact that functional diversity and the possibilities of novel Agents, Niches, and Natural Games, can expand into ever greater potential diversity as the combinatorial complexity of the entities in question increase.

6.1.6) Hypercycles: A simple example of a higher order Agent.

i. Eigen and Schuster consider a set of N pairs of +/- single stranded RNA sequences. Each +/- of Watson Crick complements is assumed to be capable of replication WITHOUT any enzymes. Hence each +/- pair is a tiny replicating "cycle," and is a replicator.

(*It is not yet an Autonomous Agent in that the replicator does not yet explicitly carry out thermodynamic work cycles of coupled exergonic and endergonic reactions.)

A hypercycle is a cyclic coupling among the N pairs of +/- strands such that each of the N helps one "successor" around a cycle of help. Pair 1 helps pair 2, pair 2 helps 3, ...pair N helps pair 1. Help consists in helping the replication of the next sequence pair. This cyclic connection pattern among individual cyclic +/- RNA pairs creates a "hypercycle."

Note that the hypercycle is a higher order replicating system comprised of lower order replicating systems. If we add coupling of exergonic and endergonic reactions within each of the lower order replicating systems, each of them becomes an Autonomous Agent, and the Higher Order Hypercycle becomes a Higher Order Autonomous Agent comprised of lower order Autonomous Agents.

Note that nothing precludes an indefinite hierarchy of such autonomous agents, each comprised of lower order autonomous agents.

ix. An Ambiguity: Is a Hypercycle a Higher Order Autonomous Agent or a Mutualistic Society (Economy) of Lower Order Agents?

a) Hypercycles confront us with the Levels of Selection issue, and ambiguity. From one point of view, the hypercycle is nothing but a mutualism among the lower order +/- RNA strand replicating pairs. Indeed, if each pair helped all N - 1 other pairs, the resulting system would still be a hypercycle in which each pair has advantages of trade. So from this point of view, the system is merely a mutualistic society governed by Adam Smith's kind of Invisible Hand. Yet, if Hypercycles can compete with one another as reproducing organizations, then hypercycles act as "individuals" under Darwinian selection. Here hypercycles function as higher order Autonomous Agents. And here the levels of selection issue arises, since a lower order agent might "defect" from the hypercycle. Or another might "cheat" as a free-rider, accepting help but giving none to the hypercycle in return.

x. The "ecology - economy" perspective.

a) The hypercycle can be seen as an economy -ecology among a society of N lower order +/- replicators.

b) In general, ecologies and economies seem to allow higher order Agents to emerge. Multicelled Organisms, Social Insect Colonies, Firms, Nation States.

xi. Infinite "sink" of ordered complexity "upwards" can "absorb" order generated in Universe, perhaps indefinitely.

a) The hierarchy of potential Autonomous Agents and the Ecologies and Economies of coupled exergonic-endergonic process, propagating Work-Cum-Record, that these combinatorial entities create and link together seems to be of indefinite "upward" potential. Thus, Autonomous Agents made of Machines that are themselves Autonomous Agents can propagate upward in complexity.

6.2) FUNCTIONS TROUVE' AND EMERGENCE.

i. Evolution is replete with emergence of Novel Functions called "exaptations."

a. Darwin taught us that natural selection for some traits might, nevertheless, "pull along" correlated traits that were themselves not positively selected. For example, presumably the heart has been selected for its capacity to pump blood, thereby conferring selective advantage on organisms where diffusion alone cannot solve transport problems. But the heart beats, setting up vibrations. A vibrating chamber such as the heart is capable of responding by resonant vibration to vibrations appropriate to its resonant frequency. It is conceivable that an environment might exist in which the capacity of the cardiac system to exhibit such resonant vibrations would allow its bearer to detect an environmental danger or opportunity, hence the capacity of the heart for sympathetic vibrations would thereby become a new useful function, selected for and grafted into the organisms in the ongoing process of evolution.

b. Such "carried along" traits used to be called "preadaptations" but, to avoid the apparent teleology suggested, are now called "Exaptations."

c. Standard Darwinian account of the "Function" of a Trait. "The heart's function is to pump blood" means that the heart is present in organisms in the historically contingent process of evolution by virtue of the fact that the heart's capacity to pump blood conferred, and still confers a selective advantage on its bearer.

That is, the function of a part is the property (the causal consequences) in virtue of which it has been selected.

d. Any part of any system, organism or artifact, has causal consequences that are broader than but inclusive of those causal consequences that comprise the function of the part. The heart vibrates. So does the motor of a car. The vibration of each might become a novel function, a function trouve'.

1) ENGINE block of tractors is so massive that, one day, tractor designers decided to STOP MOUNTING the engine block on a STURDY CHASSIS, AND INSTEAD, USE THE ENGINE BLOCK ITSELF AS THE CHASSIS! Here is a novel function trouve' based on a new use of a causal consequence of a part - the rigidity of the chassis.

2) Reported flock of birds in Australia, crows, that discovered the utility of dropping nuts in car traffic so wheels would crack nuts! Functions trouve'. Does this imply the coevolution of crows and Volvos?

3) It is immaterial to the crow story that they happened to pick Volvos to crack their nuts. They might have learned to drop nuts under stampeding Buffalo, whence the thundering hooves of the Buffalo would have acquired a coevolutionarily definable role in the Niche of the Nut and Crow.

Note again that the functional explanation in the Darwinian framework, is both functional and ontological. Were crows to coevolve with buffalo and nut, the pattern of causal interactions such that a sustainable ecosystem is created and propagated is both a statement of which causal consequences are functions and carry out tasks, and why those features exist at all.

6.3) HIERARCHICAL PHYSICAL AND ALGORITHMIC AGENTS AND THE FURNITURE OF THE UNIVERSE.

i. Let me first draw a tentative distinction between Algorithms, "Physically embedded algorithms," and Physical systems that are not algorithms. An algorithm is an effective procedure guaranteed to produce some result such as finding the square of a number. That abstract algorithm might be embedded in a special purpose computer comprised by a set of connected water tumblers whose pouring patterns from an initial set of filled tumblers led to the square of that number have a finite amount of water poured into each.

The embedded tumbler system, however, is itself not algorithmic. Thus, the algorithm might "hang" might suffer the halting problem, etc. Yet the physically embedded system is still a "causal" system and will do something. Among these are causal consequences that have nothing to do with the algorithm, perhaps collecting beads of moisture outside each tumbler.

In general, a physical system behaving "causally" is not, thereby, carrying out an algorithm.

ii. With these caveats, let us use the fact that richer mathematical systems can behave in ways that less rich systems cannot. A classical example is given by Gödel's theorem which shows that, for rich enough mathematical systems, a set of axioms generally is not complete - that is, formally undecidable statements exist which cannot be proved or disproved from the axioms by the rules of inference of the formal system. Yet if further statements are added to the axiom set, the formally undecidable statement(s) may become decidable, but new ones will emerge that are no longer decidable.

Obviously, in analogy, were such formal systems embedded into causal physical systems, the less rich system would be capable of fewer formally decidable causal behaviors than the richer system.

iii. Based on this, we may ask if there are kinds of emergent functionality in evolution such that the "richer" Autonomous Agents can exhibit behaviors simply inaccessible to simpler systems. But if so, then these new behaviors imply that the Universe unfolds in a different way; and perhaps in a way that cannot be "reduced" to the behaviors and the categories appropriate to the less rich systems of Agents.

iv. Dennett, in "Darwin's Dangerous Idea," defines a hierarchy of behavioral phenotypes:

* Darwinian Agents, hard wired, evolving by natural selection.

* Skinnerian Agents have wired in "reinforcers" that happen to favor "smart moves," actions that were better for their agents. These agents generate a variety of actions until they find and then reinforce useful ones. This is conditional plasticity and operant condition, as in aplysia.

* Popperian Agents have capacity to preselect among many possible behaviors or actions, weeding out the truly stupid options before risking them in the harsh world. (As Popper said, this design enhancement "permits our hypotheses to die in our stead"). To carry this out, Popperian Agents must have some sort of Inner Environment structured so that the surrogate actions it favors are more often than not the very actions the real world would also bless. Thus, the inner environment contains a lot of information about the outer environment and its regularities.

* Gregorian Agents - agents whose inner environments include the Designed portions of their outer environments these include human tool users. A well defined artifact, knife, embodies design intelligence, and confers intelligence in abetting the capacity to make smart moves creating new useful tools in the Adjacent Technological Possible.

a. Note first that this hierarchy of behavioral types has emerged in evolution. Presumably this is emergence is due to a sequence of exaptations which came to be selected.

b. Focus on all that emerges when Popperian creatures emerge: All the problems that economists discuss about rationality, bounded rationality, forward planning horizons, convergence of first period plans as a function of planning horizon, arise. Skinnerian critters cannot care. Popperian critters, an enriched type of Autonomous Agent, can now run internal "as if" models and plans about what would happen "if," the conditional tense enters the Universe with forward planning. So does lying about one's plans.

c. But plans and forward planning horizons now become part of the real furniture of the universe.

Once Popperian Autonomous Agents arise, their novel forward planning capacities alters the unfolding of the biosphere, hence the Universe.

And notice that we Gregorian agents have created legal systems that enable contracts that enable legal individuals such as firms to exist, cooperate, compete and flourish. These too are now part of the real furniture of the universe, and alter the way the universe behaves. --For example, due to the Cold war, the United States beat the Soviet Union to the moon and left material on the moon, thereby changing the dynamics of the solar system.--

There are strong connections between these points and J. Crutchfield's efforts to find a computational framework in which to characterize when computational systems "move up" the Chomsky hierarchy. Such moves in an evolutionary system can be viewed as kinds of exaptations to a new level of functionality that is not reducible to lower levels, for the new "machine" has computational capacities not present in lower level machines.

Yet Crutchfield's work, so far, does not involve concepts of matter, work cycles, and the actual creation of things in the world.

6.4) DOWNWARD CAUSATION.

i. There are lots of cow proteins and no trilobite proteins around today. You can have lobster or crab, but not trilobites for dinner.

ii. Why?

iii. The trilobites went extinct many millions of years ago. But when the trilobites went extinct, they carried their unique proteins and small molecules with them. The future unfolding of the biosphere at the molecular level was changed.

iv. Yet trilobites went extinct as whole Autonomous Agents, not as aggregates of proteins. Some last trilobites dodged the wrong way when some archaic starfish were hunting for dinner because, as Popperian creatures; their plans went somewhat awry.

v. This is genuine, and entirely non-mysterious downward causation. The behaviors of Autonomous Agents in their society, winning and losing the Darwinian race run as whole organisms, governs the molecular unfolding of the biosphere.

vi. The same is true in the technosphere. Hubcaps outnumber wagon wheels. The Ford displaced the Connestoga.

vii. And humans can rocket to the moon, leave a hunk of metal there, and thereby alter the orbits of the moon, earth, and members of the solar system. Here too is non-mysterious downward causation.

viii. Thus, in a non-mysterious way, the emergence of a hierarchy of behaviors among coevolving Autonomous Agents, Darwinian to Popperian to Gregorian, alters the furniture of the Universe, and is coupled to legitimate downward causation changing how the universe unfolds.

ix. A complete theory would incorporate this emergence and downward causation with upward causation into some seamless web embracing the knowledge and plans and "intentions" of coevolving agents as parts of the total unfolding of the Universe.

x. Failure of physicists' potential Theory of Everything to incorporate the knowledge of agents in coevolutionarily constructable systems of autonomous Agents suggests that such a theory is foredoomed. if it is to be a real theory of everything. It will not be able to account for many aspects of how the Universe behaves.

xi. In Lecture 7 I suggest attempting to endogenize coarse graining in a thermodynamics that includes the Agent as coevolving knower-constructor of its world.

6.5) DIFFICULTIES WITH REDUCING ALL FUNCTIONS TO A "BASIS SET" OF FUNCTIONS. ARE ALL THE CONTEXT DEPENDENT CAUSAL CONSEQUENCES OF PARTS FROM WHICH EXAPTATIONS CAN ARISE AND COME TO EXIST IN THE UNIVERSE FINITELY SPECIFIABLE IN ADVANCE? IF NOT, WHAT ARE THE IMPLICATIONS?

i. It might be the case that all functions that shall ever arise among the indefinite potential hierarchy of agents can be "prestated" in some BASIS SET of functions, somewhat as all continuous single valued functions can be redescribed by Fourier Analysis into a weighted sum of the infinite Basis Set of sin and cosine functions.

ii. Yet this hope seems doubtful based on some well known failures in similar attempts in philosophy.

a. Classical hope to "reduce" statements about the external world to logical combinations of statements about "sense data" - the Logical Atomism of Russell.

But this effort failed. Why? Success was said to require that the statement: "There is a chair in the room" could be set logically equivalent to a set of necessary and sufficient conditions stated only in terms of sense data statements conjoined as logical atoms.

An example of such a reduction would be: "Chair in room" == "I will have the following set of sense data:...."

But the difficulty arose. What if the observer were not in the room, were color blind, ....It turned out that no finite list of necessary and sufficient conditions could be listed.

b. Second classical case: "England declared war on Germany." The hope was to reduce this statement about the actions of nations to the actions of individuals. Again, the effort fails, for no finite list of necessary and sufficient conditions about the actions of individuals can be proposed. Thus, the Brits might declare war on Germany because the Prime Minister obtains the vote in Parliament, because the Queen mutters: "After them" at a Leeds football game against Munich, or because large numbers of gentlemen farmers hoist hoes and head for the east bank of the Rhine with murder in their eyes.

Consider Wittgensteinian language games - for example the legal description of an event, a description in terms of human actions but without the concepts of law, evidence, guilt, responsibility, etc. And a description in terms of the positions and momenta of particles. One cannot translate between these descriptions without loss of meaning. In each language game, the concepts are internally defined and cannot be replaced by a necessary and sufficient set of expressions in the other language games.

c. Now consider the emergence of Popperian Autonomous Agents. Suddenly forward planning horizons, rationality, bounded rationality, convergence of plans, become part of the Universe.

It is simply not obvious at all that this new furniture of the universe can be reduced, or stated, in terms of the properties and categories which apply to mere Darwinian or Skinnerian creatures. That is, it would seem that entirely new functionalities have emerged that are not reducible to those of Skinnerian or Darwinian agents. The Popperian Agents can behave in ways that, like a richer arithmetic system, cannot be derived from the impoverished one.

Thus, I suggest, we will not be able to reduce the behavior of Popperian Agents to a finite list of necessary and sufficient conditions about the behaviors of Skinnerian Agents. Forward planning horizons are new stuffs when they arise. Yet, no mystery, they emerge as exaptations. No mystery here;self reproducing molecular systems can also have "crystallized" as phase transitions from sufficiently complex chemical reaction systems.

6.5.1) Are the Context Dependent Causal Consequences of Physical Systems Finitely Specifiable in Advance?

Consider a physical object such as a table. What are its properties? What are its causal consequences? Are either finitely specifiable. Thus, it is a well known bit of philosophy that the properties of the table are not finitely specifiable, because "property" is systematically vague. Among the properties of the table are its height, material, age, exact dimensions, possession of cracks, and indefinite list of relations between such properties. For example, there is the distance between a given crack on the surface and each of the edges of the table, the of the crack to the floor, the distance from the crack to an ordered set of edges, other cracks and the floor. Again there is the presence of the crack today, and its relation in distance to the edges as these change over time due to eat expansion and cooling, moisture, carpenter ants, and so forth. Thus, "all" the properties of the table, do not appear to be finitely specifiable.

On the other hand, most properties, once noticed by an agent and specified, can be assessed.

Thus, "all the properties" of the table are not finitely specifiable "beforehand."

Yet all these properties may become, in a context dependent way, requisite to a "Rube Goldberg" function trouve' for the table. For example, to hold my lap-top computer such that I, an agent, can run the power line via the crack to a floor socket with enough slack that I can move the lap-top and use it easily.

But it is just such context dependent properties that are the sources of functions trouve' in exaptations in evolution, let alone in human ingenuity in concocting odd jury rigged Rube Goldberg machines that propagate work and functional task closures.

If the "physical system" simply by existing, is not thereby carrying out an algorithm, and if its properties and a forteori, all its potential casual consequences cannot be prespecified, then the process of exaptation in evolution and discovery of functions trouve' does not appear to be algorithmic.

For an autonomous agent, existing and propagating as a coherent closure of work and task and reproduction of matter and energy flows, the failure to "search" algorithmically into the adjacent possible is not a hindrance at all. Precisely because each part has context dependent properties and causal consequences, if a novel useful function is found and integrated because the Agent is "fitter," that exaptation will be incorporated. The Agent just does make the "discovery," then pulled out by Darwinian selection.

In Carl Simm's fine work creating a simulation of a physical world in which agents compete to place maximal surface area on a box, one agent "discovers" that it can simultaneously "knock away" its opponent while moving its "wings" to the box. The audience of humans laugh with delight, as this "behavior" is henceforth selected in the agent. But was this context dependent function finitely prespecifiable? I do not think so.

If this failure of complete finite prespecification is correct and general, then the process of evolution of Agents into the Adjacent possible cannot be prespecified, but can often be made sense of in hindsight - after the function trouve' has arisen in its context, then this seems to imply that the evolutionary pathway into the Adjacent possible is not, in general, predictable.

But the problem seems to run deeper. Newton taught us to do science by defining the appropriate abstract variables for the question at hand, then create a state space, initial and boundary conditions, and a dynamical flow in that state space. The flow trajectory, as Robert Rosen points out in "Life Itself," captures causality. For a pendulum, the relevant variables for its oscillatory motion are length, mass, and center of mass, friction and displacement from vertical in a gravitational field. Its color, material, make, and filigrees of artful decoration are not of interest.

In contrast, with respect to "all its properties," hence functions trouve' and, hence for evolving Agents, the actual coming into existence in this particular non-equilibrium Universe of hearts, hair, and hazelnuts, just these other "properties" can turn out to be essential in the proper context.

We seem to confront a need to learn to do science in a deeply new way! It is just the non-finitely prespecifiable set of properties that allows exaptations whereby the biosphere constructs its wondrous linked webs of propagating work and co-construction entities. This is local evidence of how the Universe actually is creative. And the creativity appears to be non-algorithmic, not prespecifiable. The novelty is genuinely "emergent."

How do we do science in addition to telling the "story" of this unfolding. That is, the emergent unfolding of evolution invites a narrative stance - even a first person narrative stance from each Agent. Can we still seek laws?

I hope so. I suspect that such a law relates to the way Autonomous Agents coevolve and invade the Adjacent Possible.

6.6) THE ACTUAL AND THE ADJACENT POSSIBLE

I return now to what appears to be a centrally important issue: The Universe is expanding from the Actual into the Adjacent Possible. I state this first at the level of complex molecules, then hierarchical Agents, then explore the concept more generally based on grammar models. In turn, this leads me to wonder about the definition of entropy in expanding phase spaces, and to raise the issue of a separate concept of propagating Organization, uniting matter-energy-and record-information via coevolving autonomous agents. In the final part of this lecture, I broach as tentative working hypothesis for an attractor achieved by such coevolving systems of Agents.

6.6.1) i. Recall from above the behavior of a supracritical chemical reaction system. At any moment in its explosion of diversity some set of molecular species actually exists in the system. At that moment, define the Actual as that set of molecular species. Define the Adjacent Possible as all those molecules that are Not present in the Actual, but are derivable from it by a single reaction step involving molecules in the Actual as substrates (and catalysts). Then the Adjacent Possible is, in principle, perfectly definable, given full knowledge of quantum chemistry.

ii. Recall that the equilibrium constant of any reaction across the boundary between the Actual and Adjacent Possible depends on thermodynamic factors such as the enthalpy of the reaction, definable in the limit of zero concentrations, and the entropy of the reaction. On the other hand, the displacement from equilibrium depends upon the ratio of substrates to products. The displacement determines the direction of the reaction.

iii. Since the concentration of substrates in the actual is finite, while the number of copies, hence concentration of novel products in the Adjacent Possible is strictly zero, the reaction system is shifted to the left of equilibrium.

Therefore, a real chemical potential exists across the frontier of the Actual to the Adjacent Possible, for each reaction coupling of Actual substrates to Adjacent Possible products.

iv. The total potential is presumably given by some function of the potentials of all the reaction couples across the frontier.

v. While the chemical potential is real and favors synthesis of Adjacent Possible products, the kinetics of that synthesis might be arbitrarily slow. In part, the kinetics may be slow because the Actual substrates are in very low concentrations, are isolated from one another, because the activation barrier is high, etc.

vi. Nevertheless, the real chemical potential implies at least a tendency to transgress the frontier from the Actual to the Adjacent Possible.

6.6.2 The indefinite extension from the actual into the molecular Adjacent Possible.

i. The supracritical behavior of the formal reaction graph, obtained by writing down substrates, writing down all possible transformations, shown as reactions via reaction nodes, then all possible (including novel) products, can extend indefinitely. This behavior reflects the fact that molecules are combinatorial objects made of atoms, and that we have placed no limit on the number of atoms per molecule.

ii. The actual behavior of a real chemical system can be supracritical as well. Recall the expected behavior of a supracritical chemical reaction system using antibodies as candidate catalysts in Random Chemistry.

In principle, this extension can proceed for periods that are long with respect to the lifetime of the universe. In Lecture 7 I discuss this possibility with respect to quasi-closed thermodynamic systems such as an isolated spiral galaxy. In meantime, our own biosphere, part of such a galaxy, appears to be supracritical.

iii. The biosphere itself is a concrete example of such a supracritical system.

a. Presumably, 4 billion years ago, the molecular diversity of the proto-planet was much lower than the molecular diversity of the current Earth. The burgeoning diversity reflects, in large part, the behavior of Life in Darwin's Tangled Bank of coevolving ecosystems. Hence coevolving Autonomous Agents have achieved exploding molecular diversity.

b. Thus, a feature of coevolving societies of molecular Maxwell Demons, namely Autonomous Agents called cells, is that the total system expands from the molecular Actual into the Molecular Adjacent Possible.

c. The tangled bank of this global ecosystem expands into the Adjacent Possible in large part because each Autonomous Agent links exergonic and endergonic reactions, thereby synthesizing some molecules to concentrations far in excess of that expected at chemical equilibrium. These unexpected high concentration molecules can then interact with one another as one or more substrates (and catalysts) to generate novel molecules in the Adjacent Possible.

d) The fact that we have defined Autonomous Agents as Autocatalytic systems that carry out work cycles - e.g. linking exergonic and endergonic reactions - (unlike the case of a simple trimer-hexamer autocatalytic reaction) implies that ecosystems CAN AND DO create linked webs of metabolic reactions where the propagating Work-Cum-Record embodied Know-how of the coevolving Agents does actually, via high above equilibrium concentrations of many molecules, step progressively into the adjacent possible.

e. If the estimated protein diversity of the biosphere is something like 10 to the 14th molecules, and small molecule diversity is tens of millions or more, and if the diversity of species of organisms is increasing, as appears to be the case, then there is no reason to think that this expansion will soon halt.

6.6.3) The expansion from the actual into the molecular Adjacent Possible cannot have reached equilibrium in the history of the universe.

i. Typical biological proteins are 200 amino acids or longer.

ii. The number of possible proteins length 200 is 20 raised to the 200th or 10 raised to the 260th.

iii. All these proteins are chemically perfectly possible. Indeed any one of them could be synthesized rather easily. Indeed, since peptide bonds are of similar energy regardless of the flanking amino acids, all of these 200 amino acid polymers are more or less isoenergetic.

iv. Now consider the number of proteins that might, maximally, have been synthesized since the big Bang assumed to be 14 billion years ago.

a. Assume there are about 10 to the 60th atoms in the known Universe.

b. Assume that bimolecular reactions could occur on a femtosecond time scale (this is vastly too fast).

c. Then the number of reactions in which two atoms could have interacted in the 10 to the 33 femtoseconds since the big Bang is "only" 10 to the (60 + 60 + 33) = 153.

d. Of course, 10 to the 153 is enormous. But it is enormously less than the number of possible proteins length 200.

e. To stress the obvious: The Universe, since the Big Bang, can only have sampled a tiny fraction of the possible proteins length 200.

f. Thus, obviously, the Universe cannot have remotely reached any kind of equilibrium with respect to the possible proteins.

g. Thus, the Universe is kinetically trapped in a tiny subspace of the space of possible proteins length 200.

h. Furthermore, as witnessed on this Earth, the exploration of protein space is not a random sampling of possible 200 long amino acid sequences, rather it is a biased exploration from the actual to the adjacent possible.

i. The biased expansion from the Actual to the Adjacent Possible means that this exploration is a movement from an historically contingent subspace of protein space into adjacent possible region.

v. Now generalize from the space of possible proteins length 200 to the set of all organic molecules with 10,000 or fewer atoms of CHNOPS - carbon, hydrogen, nitrogen, oxygen phosphorous, and sulfur.

a In the history of the Universe, it is not possible to have explored the space of all possible organic molecules of lengths up to a few thousand atoms per molecule.

b. Yet the Biosphere is carrying out one such exploration from the Actual to the Adjacent Possible.

6.6.4) Consider the entire universe as a "Closed System."

The Universe is Kinetically Trapped in a subregion of this space, expanding into the Adjacent Possible. History enters when the space of the possible is vastly larger than the actual.

i. Since the Universe as a whole cannot have created all possible organic molecules of masses up to a few thousand atoms per molecules, the Universe as a whole has not equilibrated with respect to this process.

ii. Since the Universe has not equilibrated, the standard assumptions of equilibrium statistical mechanics do not apply. In particular, we cannot apply the ergodic hypothesis to achieve insights about the Kinetic behavior along dynamical trajectories from the phase volume averages of microstates and corresponding macrostates.

iii. Thus, any theory of the unfolding of the universe must be a non-ergodic theory which seeks laws, if any, about properties of trajectories. In particular, a candidate 4th law suggests that such trajectories maximize the increase in the effective dimensionality of the unfolding system, as described below.

6.6.5) Hierarchically complex combinatorial objects - Autonomous Coevolving Agents -- also invade the Adjacent Possible.

i. Molecules are only one level of combinatorial objects where the Universe cannot have equilibrated hence invade the adjacent possible.

ii. Consider Agents themselves as integrated self-reproducing systems of molecules carrying out work cycles. The diversity of potential agents, presumably, cannot have equilibrated, hence invade the adjacent possible.

iii. Consider the potential different ecosystems of first order Agents -- say like bacteria. This cannot have equilibrated. Hence new types of ecosystems keep emerging, thereby invading the adjacent possible.

iv. Consider higher order Agents comprised of lower order Agents, from Eigen-Schuster hypercycles on up. These cannot have equilibrated.

v. Consider Darwinian, Skinnerian, Popperian, and Gregorian Agents. The exaptations creating each new level begets novel possible behaviors - planning horizons etc. not present at nor reducible to lower levels, creating new furniture of the Universe, hence New Kinds of Adjacent Possibles. It is not obvious that we can finitely state the conceivable hierarchy of Adjacent Possibles that can emerge and higher order entities emerge. Furthermore, at each level, novel "species" emerge, invading the adjacent possible.

vi. Consider legal systems, as invented by us Gregorian agents, that enable the creation of contracts, hence corporate individuals, firms, which may also be coevolving Autonomous Agents, consider nation states. Legal systems are creations of Gregorian Agents, and presumably not reducible to acts of mere Popperian Agents. Meanwhile, the firms enabled by the law invade the adjacent possible in terms of goods and services, novel modes of organization, and so forth.

6.6.6) The Indefinite Hierarchy Upwards in Complexity is a "Sink" where the burgeoning Order of the Universe coconstructed by such agents can be "dumped." And that Indefinite Hierarchy does invade from Actual ever into the Adjacent Possible.

i. Consider the well known example that a gas expanding in an even more rapidly expanding volume of 3 space experiences an increase in order since the expanding gas lags the expansion of the 3 dimensional volume.

ii. This is typically used to say that the literal expansion of the Universe can induce a similar order as degrees of freedom escape into the expanding universe.

iii. Yet it appears that the universe also has available to it a direction towards increased complexity into which it can place degrees of freedom. There seems to be a sense in which this indefinitely expanding complexity is a "sink" into which degrees of freedom can "escape." I try next to formalize that which is expanding:

6.6.7) Formalization of the concept of the Adjacent Possible

i. Consider a closed thermodynamic system of classical particles - e.g. atoms.

As a case in point, consider an isolated spiral galaxy.

ii. Define the standard 6N dimensional phase space for this system. (Ignore gravity for the moment).

iii. Partition the 6N dimensional phase space into microstates as usual. Then each microstate is a tiny "box" in the 6N phase space.

iv. Consider the set of classical trajectories within one box and passing across its boundaries.

v. These trajectories flow from the current box to some set of neighboring boxes.

vi. Draw a single arrow from the current box to each of the neighboring boxes accessible by one or more trajectory from the initial box.

vii. The set of accessible neighboring boxes is the Adjacent Possible from the present box.

viii. Thus, each box can carry a number denoting how many boxes are in its Adjacent Possible.

ix. The actual flow of the system therefore is associated with a change of the Adjacent Possible from box to box.

x. Therefore, we can define the derivative of the Adjacent Possible. The derivative of the Adjacent Possible is just how rapidly the Adjacent Possible is increasing or decreasing.

xi. But notice that the Adjacent Possible is precisely the available phase space for the "next" moment in the evolution of the 6N dimensional system.

xii. Thus, given the coarse graining into "boxes" we can think of the Adjacent Possible as the "dimensionality of the current work space" --i.e. the number of "boxes" -- now available to the 6N dimensional system.

Let me refer to the Adjacent Possible as also the Dimensionality of the Available Work Space.

Then the derivative of the Adjacent Possible is just the way that the dimensionality of the available work space expands or contracts, given a coarse graining into "boxes"

And, since we wish to think of Autonomous Agents as setting their own functionally relevant coarse graining in terms of their capacities to categorize and act without trembling hands in the worlds they mutually create, we will need to investigate how the coarse graining self consistently fits with the way the Adjacent Possible changes over time in an ecosystem, a biosphere, or beyond. I return to this in Lecture 7.

6.7) SINCE THE UNIVERSE IS KINETICALLY TRAPPED WITH RESPECT AT LEAST TO HIERARCHICALLY COMPLEX ENTITIES, WE CAN ASK WHETHER SOME GENERAL LAW MIGHT GOVERN HOW THE NON-ERGODIC FLOW OCCURS.

A first intuition might be that flow is organized such that the Adjacent Possible expands as fast as possible. Such a guess has the virtue that it picks a maximal path from any initial configuration. Probably that path is typically unique.

But, in its most general form, this could not be true. Consider again the Noah' Vessel experiment. Were two members of each of the 50 million or so species of the biosphere placed in a vessel and ground up, breaking all membranes by which organic molecules and enzymes are separated from one another, a vast supracritical explosion of molecular diversity would presumably occur. This explosion would "burst" into and expand the "Adjacent Possible" -- the kinds of molecules in the biosphere. But any functional organization within the complex chemistry in the soup would almost immediately be destroyed. The destruction would drastically lower the further flow into the molecular Adjacent Possible.

Why?

Because life has learned NOT TO DO LOTS OF THINGS. That is part of what it means for cells to be subcritical. By not doing most of the possible "things," cells prevent the uncontrolled accumulation of novelty that would disrupt functional organization.

More generally, coevolution must be a balancing process between the rate of generation of novelty and the molecular and higher functional levels, and the capacity of natural selection or its analogues to constrain, harness, and make use of that novelty. I suggest next that this may lead to a self-organized critical expansion into the Adjacent Possible.

6.7.1) Self-Organized Critical Expansion of the Adjacent Possible: The Possibility that Propagating Communities of Autonomous Agents as the Union of Work-cum-Record Expand the Adjacent Possible in Power-Law Bursts.

i. We have noted above that the biosphere may be organized such that microbial communities are poised on the subcritical-supracritical boundary such that the mean rate of discovery and incorporation of "useful" new molecules may occur in power-law bursts.

Were the community subcritical, discovery could be faster. Were it supracritical, the novelty would be lethal and kill off types of members of the community, slowing discovery of novel useful molecules.

ii. There is, here, a deep analogy to the Eigen-Schuster "Error Catastrophe." In this case one considers a fitness landscape over which replicating RNA molecules are evolving. Given a mutation rate per nucleotide, then for short enough RNA sequences, and if rate of replication "superiority" of the fittest molecule in the population is sufficiently greater than any other RNA molecule, then selection will sustain the RNA population of that "master sequence" and a mutant spectrum "quasi-species" around it. But as RNA sequences become longer for a fixed mutation rate per nucleotide, a phase transition arises at which the mutation rate overwhelms selection and the population of RNA molecules "diffuses" all over RNA sequence space. All accumulation of "information" in the population is lost.

iii. The analogy of a microbial community at the subcritical-supracritical boundary with the Eigen-Schuster error catastrophe is that, in both cases, the evolving system must control the rate of entry of novelty into the system. If the novelty arises too fast, selection cannot maintain functional organization in the face of a diffusive process into the Adjacent Possible that disrupts organization.

The flow of a population on a fitness landscape is largely convergent. That is, selection tends to pull populations toward ridges and peaks from the surrounding volume of the landscape. In the Eigen-Schuster sense, it is this convergence that reflects the build up of "information" in the population.

Now consider simultaneously the convergent flow of a population of autonomous agents on a fitness landscape with the gradual increase in the dimensionality of that landscape or "space of possibilities"

Then selection tends to yield convergent flow in the space of possibilities, while the space of possibilities is itself expanding.

An intuitive hypothesis is that, on average, the convergence induced by selective processes must just slightly exceed the rate of expansion of the space of possibilities. Otherwise the organizational capacities of the coevolving Autonomous Agents would be lost.

iv. These considerations suggest that communities of Autonomous Agents will organize themselves so that the flow into the Adjacent Possible is nearly "parallel" or, in some sense, Self-Organized Critical. Causally local Communities should create and absorb novelty - the Adjacent Possible - with a branching probability of 1.0. Each community should experience a power-law distribution of such bursts.

v. If so, and if communities can be treated as causally independent, then the total rate of entry into the Adjacent Possible should be, approximately, the sum of the bursts of the causally independent local communities

vi. It is far more likely that there will be some form of propagation of novelty between nearby communities linking their global behavior. A model would be the microbial community on the Earth 2 billion years ago. An intuitive bet is that communities will arrange connections among themselves by migration, and otherwise such that novelty at one point in one community spreads in small and large avalanches to generate novelty in other communities. The coupling among communities, as within communities, must be such that the system, on average, is able to sustain embodied propagating know-how-work-record.

vii. This again suggests that the biosphere may be organized so as to propagate into the Adjacent Possible as rapidly, in this sustainable sense, as it can.

6.8) "WORK SPACE" THE DIMENSIONALITY OF THE ADJACENT POSSIBLE IS JUST THE DIMENSIONALITY AVAILABLE TO THE CURRENT SYSTEM'S NON-ERGODIC DYNAMICAL BEHAVIOR, I.E. ITS "WORK SPACE."

i. This suggests that the biosphere may be expanding the dimensionality of its "work space" in a self-organized critical fashion.

ii. Hence a new tentative statement of a candidate fourth law for self constructing non-equilibrium systems of coevolving autonomous agents:

THE AVAILABLE DIMENSIONALITY OF THE COEVOLVING SYSTEM'S TOTAL "WORK SPACE" TENDS TO EXPAND IN A SELF-ORGANIZED CRITICAL WAY IN POWER-LAW BURSTS.

6.8.1) A Corollary: Expansion of the Adjacent Possible From Any "Box" in 6N phase space, implies finer grained partitioning of that box into subvolumes flowing to different adjacent Boxes. In turn, this implies symmetry breaking within the initial box.

If 6N phase space is partitioned into equal sized boxes, and if one arrow be drawn from each box to each of the boxes next reachable along trajectories from anywhere within that box, such that these arrows denote the adjacent possible boxes from this box, then clearly, if along non-ergodic trajectories from box to box, the adjacent possible expands, so more arrows exit successive boxes, then it must be the case that the phase space inside successive boxes is becoming progressively subdivided into subvolumes each of which has states flowing to exactly one of the successor adjacent boxes. In short, more symmetries within the system represented by successive boxes are being broken.

Indeed, this breaking of symmetries must be strongly associated with the exaptations that allow work to be done creating novel constraints that control the release of energy in new ways performing new bits of work and tasks by which Agents coevolve.

In turn, this suggests that Agents construct ever more finely tuned internal "thresholds" by which they govern flow down different pathways of categorization and action within their worlds. But this must be related to optimal ways this coordinated categorization and action can occur, as discussed nest.

But this fine tuning of internal "thresholds" must ultimately be bounded by the Heisenberg Uncertainty Principle. Thus, the hypothesis that Agents drive to enlarge their work space, the adjacent possible, seems to imply that Agents are driven to have aspects of quantum systems deep in their core. It is therefore fascinating that all free living cells are at molecular scales and harbor so much internal organization that they hover at the boundary between obviously quantum behavior - including mutations in DNA, and classical behavior - a protein in liquid water presumably interacts with such a complex aqueous environment that its behavior is soon classical ( See next lecture and emergence of classicity.

(Is there here a whiff of a necessary link between quantum and classical driven by expansion of the adjacent possible? Does a bacterium "making up its mind" to swim for dinner rather than flee a Paramecium, thereby convert quantum to classical behavior? Is this a whiff of consciousness as "experienced" in the first person by the bacterium? How else does it "navigate"? Phil Anderson intuited that Agents are the locus of free will...........)

6.9) THE CANDIDATE 3-PART LAWS GOVERNING COEVOLVING COMMUNITIES OF AUTONOMOUS AGENTS SHOULD APPLY TO HIGHER ORDER AGENTS AND THEIR COMMUNITIES AS WELL.

In lecture 5, I formulated a tentative 3-part law governing the behavior of communities of coevolving autonomous agents. In the present lecture we have seen that higher order autonomous agents emerge and coevolve.

Both the biosphere and econosphere are comprised of hierarchically complex coevolving autonomous Agents. Our candidate laws should apply to higher order agents and the communities they construct as well as to molecular agents at the lowest level.

Thus, higher order agents that are parallel processing dynamical systems should:

i. Coevolve such that each is within the ordered regime while the community is near the dynamical edge of chaos.

ii. Coevolve to a self-organized critical state with respect to coupled landscapes, the rate of deformation of landscapes, and a power-law distribution of speciation and extinction events.

iii. Evolve to a generalized analogue of the subcritical-supracritical boundary.

a. At higher levels, organisms and firms can only incorporate novelty so fast. The rush to the adjacent possible is driven by opportunity for "growth." (New niches for species, new markets and the increasing returns of going up learning curves for firms in the econosphere.)

* "Future shock" for firms is the analogue of supracritical behavior at the metabolic level. Here, the rate of technological change is so great that firms cannot cope and are overwhelmed.

But a self-governing process will balance the rate of entry into the technological adjacent possible such that future shock does not overwhelm the econosphere:

Firms will only create novel technologies if they believe that they can make a profit.

On average, the rate of technological innovation -- future shock -- will be balanced such that firms can enter these new technologies and the growth opportunities in terms of new markets and learning curves and make a profit.

Future shock only would actually arise if entry into the Adjacent Possible were faster than firms can absorb.

But then firms would not be able to enter the Adjacent Possible, so "future shock" is automatically "titrated" by the coevolving system of firms expanding into the Adjacent Possible.

Coevolving firms in the econosphere will tend to invade the Adjacent Possible so as to maximize growth for the invaders, but this will lead to extinction of old technologies.

Thus, firms will invade and expand the adjacent possible as fast as they can make a local profit - hence as fast as they "can."

6.9.1) Some lines of evidence for the attractor with respect to higher level Agents such as whole multicelled organisms, firms, and technologies:

THE "ATTRACTOR" IS SUPPOSED TO HAVE COEVOLVING AUTONOMOUS AGENTS SIMULTANEOUSLY: 1) INTERNALLY AND COLLECTIVELY IN DYNAMICAL ORDERED REGIME NEAR EDGE OF CHAOS, 2) COEVOLVE TO SELF-ORGANIZED CRITICAL STATE. 3) TEND TO INVADE ADJACENT POSSIBLE IN SELF-ORGANIZED CRITICAL BURSTS, HENCE AS FAST AS SUSTAINABLY POSSIBLE.

6.9.1.1) The dynamical "edge of chaos" in communities of higher order agents:

* There is modestly good evidence that some social insect colonies, for example, ant nests, operate at the edge of chaos in terms of the movement of ants and the patterns with which they interact with one another. These patterns of joint activities are clearly examples of parallel processing in a higher level organization than the genetic regulatory networks within each cell within each ant.

As noted above, the genetic regulatory networks within eukaryotic cells also appear to operate near the dynamical edge of chaos.

* The "patch" theory noted in lecture 1 suggests that firms may be able to optimize hard combinatorial optimization problems by partitioning into patches which separately, selfishly, and in parallel each seek to optimize a local figure of merit. The optimal patching lies in the vicinity of a phase transition between order and chaos. This suggests that real firms and other organizations may evolve to an analogue of an order-disorder transition in order to optimize their capacities as adaptive organizations.

6.9.1.2) The self-organized critical poised coevolutionary behavior of higher order agents:

* Evidence of a near power-law distribution of extinction events -- current best fit to data according to Raup -- supports the hypothesis of coevolution to a self-organized critical state at level of species, genera, and families.

* Schumpeterian gales of creative destruction in technological coevolutionary systems may support a self-organized critical attractor for Firms in industries as coevolving Agents.

* Life time distributions of genera, and firms fit predictions of poised coevolutionary attractor for the biosphere and econosphere.

* Organisms do appear to control the number of other species in ecosystem with which each species interacts.

6.9.1.3) A subcritical-supracritical boundary for higher order agents:

i. Higher order agents, organisms and firms can only incorporate novelty so fast. The rush to the adjacent possible is driven by opportunity for "growth." (New niches for species, new markets and the increasing returns of going up learning curves for firms in the econosphere.) .

* "Future shock" for firms is the analogue of supracritical behavior at the metabolic level. Here, the rate of technological change is so great that firms cannot cope and are overwhelmed.

But a self-governing process will balance the rate of entry into the technological adjacent possible such that future shock does not overwhelm the econosphere:

Firms will only create novel technologies if they believe that they can make a profit.

On average, the rate of technological innovation -- future shock -- will be balanced such that firms can enter these new technologies and the growth opportunities in terms of new markets and learning curves and make a profit.

Future shock only would actually arise if entry into the Adjacent Possible were faster than firms can absorb.

But then firms would not be able to enter the Adjacent Possible, so "future shock" is automatically "titrated" by the coevolving system of firms expanding into the Adjacent Possible.

Coevolving firms in the econosphere will tend to invade the Adjacent Possible so as to maximize growth for the invaders, but this will lead to extinction of old technologies.

Thus, firms will invade and expand the adjacent possible as fast as they can make a local profit - hence as fast as they "can."

This should show up as Schumpeterian gales of creative destruction ushering in new technological sectors, and ushering old ones out. If the theory is correct and applies to higher order agents such as firms in an economy, the advance into the adjacent possible should occur in power-law bursts in "causally local" linked sectors of the economy.

6.9.1.4) Invasion of the Adjacent Possible from molecular and higher levels.

i. Biosphere molecular diversity has exploded over past 4 billion years.

ii. Species diversity has exploded over past 4 billion years. Hence:

iii. Niche diversity has exploded over past 4 billion years.

vi. Diversity of goods and services and technologies has exploded over past 100,000 years.

v. Ways of "making a living" among humans has exploded over past 100,000 years.

vi. Cultural diversity and perhaps linguistic diversity has exploded over past 100,000 years.

6.9.1.5) Maximization of the biosphere's "work space."

A particularly interesting line of possible evidence deriving from discussion with Harold Morowitz: The biosphere may have tuned global albedo daisy-world-like, such that the resident energy in biosphere maximizes the ratio of chain extending to chain terminating bonds in organic molecules, hence maximizing organic chemical complexity.

In turn, this would indicate that the biosphere has maximized is molecular "work space."

i. Consider bonds among organic molecules. Some, such as C=O or O-H are chain terminating. Others are chain extending, e.g., C - O, N - O.

ii. Harold calculated two global measures. Consider a box with a large number of atoms of CHNOPS in it, and consider different total energies of this system in contact with infinite thermal reservoir, but pumped by photons of all wavelengths. Because different bonds have different energies above some ground state, a function of the total energy in the system the equilibrium distribution of bond types will differ.

iii. Harold calculated from a low energy to a high energy, the latter corresponding to a plasma: 1) The maximum entropy distribution of types of bonds. 2) The ratio of chain extending (CE) to total bonds. The ratio is unimodal, low for low energies where only CO2 and H20 are around, and low for high energy plasma.

iv. The CE to total ratio reaches a maximum at about 5Kcal/gram.

v. Astonishingly, this is just about the average calorimetric energy of the biosphere.

vi. But if CE to total bonds is highest at 5Kcal/gram, this is also the value of the ratio where the greatest diversity of complex organic molecules is highest.

vii. For any ambient temperature and calorimetric energy of the biosphere, there will be some equilibrium distribution of CE to total bonds. But if the ratio were strongly displaced from the maximum it would be difficult for the biosphere to maintain complex organic molecules at a non-equilibrium CE to total bond ratio.

viii. Thus, perhaps the biosphere, Gaia-like, has regulated total retained energy. A possibility is by regulating the global albedo, a la daisy world. To this end we noted that life has only evolved a few chromophores, notably chlorophyll, to absorb photons. Leaves are "green," not "black."

ix. If Harold's calculations are roughly right, and if the biosphere calorimetric energy is near the value that maximizes CE to total bonds, and given that the earth's atmosphere is further from equilibrium than other members of the solar system, we must entertain the possibility of a mechanism that regulates the resident energy such that organic molecular diversity is maximized. This would be consistent with maximizing the "work space" of the biosphere.

x. In addition to the above, Phil Anderson recently noted to me the work by John Hopfield some years ago. There John noted a kind of "exchange" principle": Represent the energy of a molecule as F = U - TdS. John pointed out that at room temperature for a wide variety of organic molecules, all have about the same total energy. In short, changing from one to another organic molecule leaves total energy, F, constant. This too suggests that room temperature maximizes the diversity of organic molecules the biosphere can create without required too much sustained work to drive the system from equilibrium. Again, this is consistent with maximizing the "work space" of the biosphere.