Comments on the Functional Forms of the Life Game

 

Peter Putnam

 

Vol. XXIII No. 4 Summer, 1968
Union Seminary Quarterly Review

Author's Note: The following are summary notes on leading themes of Philosophy of Religion 387 as given at Union since 1965. They are intended to be suggestive rather than self-contained, merely the starting point of an ongoing investigation to which many persons have contributed, especially Professor Robert Fuller of The Battelle Institute in Seattle. 

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What is it all about? Life is a pursuit of inclusion in love which is al­so being. But such old words, at first so full of pain or (later perhaps) of heroic qualities that joy demands, rapidly fade into a sawdust of triviality. To try to "explain" or revive them in a way at all adequate to the needs of our time, we must return to bare beginnings and relearn what an explanation is about. What is an explanation? Roughly speak­ing, it is a bringing of (ever) more particular forms of the universal un­der (ever) more general forms of the universal. More concretely (the word being the most concrete of elements), an explanation is a kind of mechanical substitution game. A mathematical system can be viewed as made up of three parts. There are rules for the identification of prop­er symbols—the allowed types of building blocks. There are rules for well-formed sentences—the allowed linear sequences or strings of these blocks. Then there are the rules of substitutions which enumerate the strings from which you are allowed to start and the ways in which given strings may be enlarged or reduced, as by substitution, etc.

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Such a mechanical scaffolding relates to human or felt categories when we can associate goals with certain incomplete system-forms to be filled in via the allowed substitution procedures of the game. The relevant (and allowed) substitution procedures then have the character of a symbolic field of random search, and the incomplete form has the character of a (sub-) goal function which, when satisfied, stops the random search. The perception of a common element in the two classes of strings (the one defined as reachable by substitution, the oth­er defined as completing the form or satisfying the goal function) is the form under which the formal mathematical concept of identity relates most simply to its subjective counterpart. All perception is ulti­mately a perception of identity which can be interpreted in these gen­eral ways.

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The Real and the Life Game

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The forms under which we make our jump from syntactic to subjec­tive categories determine what we sense as real. The structure felt is not a structure "out there, " independent of the will, but rather has the logical status of abstraction from the decision process itself. Modern research has been rapidly undercutting all self-evident forms of such linkage. (Neither the meeting of parallel lines, nor even the forms of logic have any self-evident or elemental justifying subjective counter­parts. ) Only via forms of a causal efficacy in effecting decisions or generating the emitted ordering can syntactic and subjective categories be linked. But how is it possible that any grouping of causal categories can have natural subjective correspondence, unless subjective differ­ences just "happen" to be already mathematical and the very categories under which causal law is made objective to us? (A most unlikely coincidence! )

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The theory of games provides a framework within which to de­velop the rather specialized mathematics of subjective forms in such a way that their at once (or paradoxically) causal and yet theoretic nature may be formally reconciled. For this purpose, the world may be viewed as built up of words plus their individuating and linking or generating universals or world conditions. A word, in this sense, is not a subjective category. It is "merely" a carrier of position in ab­stract linear ordering. Different word types mutually exclude and stand in well-defined before-after relations.

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The word in this sense has both an existential and a symbolic status. It may be viewed as a unit of the balancing point of the world, as words "may" be emitted in any which order. This potential arbitrari­ness of the order of emission of any finite sequence of words might be one way of interpreting the concept of freedom. Its recognition is not incompatible with a causal explanation of the correlations actually manifest in the verbal order. It is easy to build a word-emitting ma­chine with a random component which "might" emit ten words "any which" way yet exhibit much systematic correlation in its over-all emission, both aspects of which can be causally systematized.

Meaning is closely related to ordering phenomena, being (as clari­fied) organized in discrete either/or units. (Even the meaning of the continuous is a type of discreteness. ) To this degree, the word already exhibits an embryo of meaning. As a unit of separation, it also has a group status of a primitive character, enforced by the powerful effect of imitative couplings between people. Thus, it also possesses, as a type of mutually excluding unit, another basic property of meaning: person independence.

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The felt world is treated as built up of the universal operators gen­erating the verbal order. Or rather, the generating operators of the verbal order can be abstracted into compounding person-independent or denotable elements, which can themselves be systematized under the form "objective world. "

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The word exhibits the symbolic properties that game moves possess —mutual exclusion and ordering. We may, therefore, try to treat life as a one-person game and write down (in theory) an exponentially opening "tree" of possible moves to represent all possible life games. But to complete the functional forms of game theory, one needs a goal function. What is the goal function of the life game?

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The goal function is a sort of metaphysical tour de force. It is the search for the "self-repeating" paths in the exponentially opening tree of possible moves. The concept "self-repeating" can be further clarified by identifying it with the concept "institutional element, " the so-called concrete isolate of cultural anthropology. To clarify the form of the given repetition is to clarify its place in the life cycle called culture.

This goal function links mechanical and conceptual. The self­-emergence of self-repeating patterns is not only a weak transcendental form, or characteristic, of causal law, but also the form under which our own will is made objective to us.

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Heuristics and Questions

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Since the full tree of the life game is even less subject to explicit inves­tigation than a chess tree, we must make use of heuristics of the life goal function as choice functions to guide the finding of a way through the exponentially opening field of possible moves. Similarly, in chess we must use heuristics of the chess goal function—checkmate the opponent's king—such as "avoid pins" and "get control of the center," because the full tree (of about 10^32 branches) cannot be explicitly investigated. Associated with each such heuristic in chess, as in life, is a corresponding sub-goal function. The subjective uni­versals, or "eternal objects, " are ultimately treated as abstracted com­ponents of heuristics of this common goal function. The world itself is then viewed as made up of such heuristics, which form a spectral or all-inclusive form of decomposition of world conditions, and together fill time or define a policy for all possible occasions or tree positions.

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Various occasions serve to activate or engage different heuristics. One only experiences a sensory distinction to the extent that it is heuristically significant in distinguishing the self-repeating paths. Feeling involves purpose already. Our believed or implied theories or heuristics of the self-repeating paths are the actionable forms that de­fine the multiple sub-goals, as "get control of the center" defines a sub­goal in chess. We only feel a difference to the extent that it is heuris­tically significant in guiding the ordering of emission of behavior.

The brain may be usefully viewed as a computer for predicting the order of emission of our behaviors. The phenomena of a center of at­tention may then be further interpreted as associated with collision or contradiction among competitive heuristics of the common goal function. The collision of heuristics defines a mathematical problem to be solved (by introducing into them needed qualifying variables) pre­cisely because they are heuristics of a common goal function.

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The identification of the latent mathematical character of subjective categories involves placing them in such a problem-solving frame­work. More especially, the general character of random search factors and of stop random search factors discussed above is further specified by recognizing this form of their embedding in the theory of games. To bring the "felt" under mathematical categories involves building a type of mathematical framework within which latent colliding heuris­tics can be exhibited as of a common goal function.

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The identification of the goal function within a formulated mathe­matical system involves its further concretization as a set of recon­ciled sub-goals which are systematized within the physics framework or technical level of the day. These goal functions, or incomplete forms, have the logical status of commands, generating the ordering of emission.

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Discovering what is the question or problem is the main life task. Answering questions is easy once the questions are asked; one has only to toss them to "scientists." This has its aspect as the struggle to define or bring colliding heuristics within a common mathematical system. The abstracted theoretic or person-independent components of the generating heuristics are further isolated and clarified or reconciled by art itself. In so doing, art makes the heuristic reconciliation po­litically possessive.

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The Word and Contradiction

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The idealistic position is committed to treating the world as made up of words. This position is saved from seeming paradox by developing indirect techniques to bring the verbal ordering itself under causal categories. The word is thus treated as both an existential and denota­tive unit. The denotation function closes back upon the word, how­ever, because that which is denoted is treated as person-independent components of the decision or word-ordering process itself.

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Error is treated as purely verbal. "Subjectivity is truth. " We blame what must change—and that is the word—not "feelings, " which later "merely" open or become progressively demythologized in jumps, their status as generators of the verbal order ever further clarified. This treatment of error as verbal (and so subjectivity as truth) is a hall­mark of the idealistic position which views the world as a great in­formation-processing computer with its more digital parts in the brain and its more analogue parts (engaged upon command) forming the environment.

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In this context, the three levels of interpretation of the concept of a contradiction serve as a Rosetta Stone to tie together three disjoined bodies of discourse (whose separation undermines the idealistic posi­tion, which is in effect committed to a common syntax view).

A contradiction is first syntactic: the statements "B is true" and "B is not true" both asserted at once. Implicit in the denotative side of such statement is a behavior counterpart consisting of multiple incon­sistent predictions of the order of emission of our behaviour. Via these implicit predictions, we go about deciding over or clarifying the incon­sistent denotations insofar as the denotations are not "self-evident" enough and cause trouble.

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Underlying both aspects of the contradiction is a clash in feelings. That such felt specific clash can be gotten at and resolved via the reso­lution of verbal and behavioral counterparts provides a key falsifiable content of the "dominance of the intellect" side of the idealistic posi­tion. These three aspects of a contradiction also serve to help orient or tie in the practical application of basic functional models of the operation of the nervous system.

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The Nervous System

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All meaning depends on correlation. The basic unit of nervous sys­tem operation is but a mechanical reflection of this bare minimum of all meaning. The conditioned reflex principle which underlies brain operation is not so much a "machine" as an open functional form into which any two machines can be fitted.

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Thought can be viewed as a set of interacting conditioned reflexes whose positions (as synapse in the jungle that forms a brain) can be functionally determined by their effect on the ordering of emission of behavior. The nervous system is organized about the motor path­ways. (Thinking is "dancing inside your head, " and sensory cues are only felt or linked by way of the motor pathways which they ex­cite or take into higher transference.) These pathways are further or­ganized in patterns of reciprocal enervation (tensing flexors relaxes extensors, etc.). The basic synapses underlying the texture of thought may be viewed as those serving to tie together past motor sequences.

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The basic operation of the nervous system is one of establish­ing a stable choice or relative dominance among competitive motor possibilities which have been engaged by our past history. What de­termines the stable choice function is what will "repeat" in the given situation. The class of previously competitive behaviors which the repeating sequence eliminates can be viewed (from hindsight) as forming part of a random search for this repeating combination. The repeating form stops the associated random search.

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These competitive equivalent factors that past history ties together as random searches or drive factors may also be viewed as sets of over-general—and so competitive—heuristics of the common goal function which the isolation of a repeating path further qualifies. Conceptual contradiction between a set of competitive over-general­ized heuristics has its mechanical counterpart as random search. The conceptual search for repeating paths—the goal function as subjec­tively apprehended—has its mechanical counterpart as a physical stability condition associated with repetition or with what stops an associated random search.

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Thinking, in its conceptual side, is closely related to material stability conditions or conditions of expected repetition. All think­ing has its aspects as self-prediction or self-model building. Inter­nally established relative dominances or choice functions allow us to predict acts which will follow after certain choices of acts. These internally self-predicted followers of a given act may be called the series elaboration of that act.

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When the series elaboration of a given act undercuts that act before it can be emitted, then one has an internal random search and the embryo of what is called thought. External random search tests the environment and brings in new data. Internal random search helps reconcile data already internalized; it is a dynamic way to effect or encode internal integration of data.

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No Debunking

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The above is a very rough sketch of a type of reasoning that enters into emerging theories of brain functioning. Thought (in its terms) is ultimately a property of the environment or class of correlations fed into the brain, not of the brain itself. Were there not these latent harmonies in the data, the brain's organization would rapidly fall apart. (Such disorganization is in fact seen when bodies are subject to "sensory deprivation, " i.e., put in constant temperature baths, eyes covered, ears blocked, and not even allowed to touch them­selves.)

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A mechanical explanation of the brain's function is no more a debunking of man than is a mechanical explanation of a typewriter a debunking of the poem the poet writes on it. Man, as apart from God, or the whole, is but a meaningless machine. But this recogni­tion is an ancient religious one—not something new.

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This point has various technical counterparts. Causal law (so the best evidence suggests) can never be fully known. The more we learn about it, the more we discover our own ignorance and open up new areas for investigation. Matter itself is a transcendental category. Every new layer of structure in matter, when opened, gives rise to a theory, by which we can isolate a whole new technology (hidden off before in the field of possibles like the combination to a safe in the field of numbers). This new technology not only allows us to open new layers of matter, but also transforms the social order and even forces a differentiation of the accepted concepts of the self—and the design of brains.

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The transcendental character of matter thus puts us in a very dif­ferent relation to causal law than would be the case if it were fully "knowable." Nor can emotionally significant major human issues ever be predicted—in the sense in which electron tube response, or even a dog's response, can. The reason for this is, as above mentioned, that the center of attention is a function of the inconsistencies in our best available self-models, and so cannot be predicted by these self-models.

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Further discovery of causal law, or God's law, is indirectly im­plicit in the systematization of a wider body of conflicting heuristics of the common goal function. Thought is only a negation, only a set of choice functions. We have only a "negative image of God. " The process of building such an image is also the process of drawing order out of chaos. Induction is creation. Catching the resolving un­iversal in the particular thickens our felt experience of the world, and so "creates" nature insofar as nature is "felt. " (And who cares about it as unfelt?)

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Society and the Individual

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The link to society is established by means of imitative coupling. This also forces upon the basic elements themselves a certain univer­sal or person-independent character, so that even what is felt as per­sonal is a construct of impersonal factors.

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Actionable heuristics derive from the group. The character-form­ing contradictions that distinguish people and orient life pattern derive from the latent inconsistencies in this group consensus which "success" or new conditions bring to the surface. Because of the one-way nature of the conditioned reflex principle, these basic in­consistencies and. associated alternations (rather than "degree" of reinforcement, etc. ) determine involvement. When an "expecta­tion" is frustrated, the old conditioned reflex connection is not elim­inated but rather overridden by the new one. A return to the old, similarly, does not eliminate the over-riding of the new, but merely overrides the overriding. In this way, alternation can quickly create a breakdown level of involvement (hence, all we can use) at any point of contradiction.

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Our world models are first classificational of all the correlations that enter into the decision process, and then classificational of the various decision functions that use these correlations. The process of reconciling these decision functions as they come into contradiction forces the development of better verbal self-models and defines new tasks. New tasks are formed as a by-product of the systematization or mathematicalization of areas of latent conflict that leisure draws forth. It is precisely the entering of system, and so the re-defining of the former contradiction as problem (removing the contradic­tion), that makes the associated group-change or task possessive.

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This mathematicalization has, ever implicit in it, added causal in­sight. Problem solving has, in its forms, an impressive degree of computer independence. The design of chess-playing machines uses mechanical decision procedures that closely parallel those in the ver­bal rationalizations of human chess moves. To systematize or re­concile a wide class of heuristics economically can only be done via techniques of reconciliation that have implicit in them a causal un­derstanding of the situation. If models "can" send us the wrong way, they will.

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This reconciliation process involves a breaking up of the gen­erating universals as felt into person-independent components or denotable components which turn out to be of a "theoretic" character. Social reconciliation of denoted factors as felt cannot be achieved short of this. It is through such considerations that the personal and social dynamics link and force up the causal insight. Only God is or is beautiful, and only in God do we love or know each other.

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Role and Conflict

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The social dynamics is oriented by the routine re-creation of the past. In this routine, there are many programmed conflicts for which there are stable forms of resolution. These serve to organize assign­ment of role and the build-up of the sort of specialized involvement that each role needs. Such routine conflicts need to be carefully dis­tinguished from the deeper, character-forming types.

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A culture is a set of negations for breaking conflicts. These are made actionable in the group through the sensitive roles of poli­ticians operating as consensus pumps on the maxim structures of the family unit, blowing them large so as to squeeze out the last drop of their latent implications through the state. (Basic self-model as­sumptions are few compared with the cascade of their latent elabora­tions. Compare, for example, the books on number theory and the one-half page needed for its assumptions.)

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Character-defining conflict is not simple conflict (which is easily taken care of), but rather derives from inconsistencies latent in the set of negations used to resolve conflicts. (The "frantic" elaboration of a heuristic which takes place once it becomes "official" quickly draws out its latent exaggerations!) Latent inconsistencies are blown large by consensus pumps and appear as wars, etc.

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The resolution of these character-forming contradictions is in effect programmed by the device of splitting up its branches into distinct people (or nations, or types, etc.). Each of these pushes his one-sided commitment until it gathers in enough data to lead to a specific well-defined collision with its inducing complement(s) that cannot be resolved by mere separation into mutually inducing types. This is, as it were, God's trick for getting through a contradiction which is not yet ripe enough to be faced into directly. Various "back­ground" roles of routine re-creation of the past split apart to rep­resent competitive branches of the latent contradictions in the old consensus.

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Where people and roles are self-divided in this way, there is a forced generation of a social arbitrary to regulate the fight between roles until such time as a synthesis based on belief can be re-created. Thereby, an outer game is defined among these competitive branches for possession of group emission time (symbolized roughly by mon­ey). The outer games are generated by the over-elaboration of the old and appear to involve an "arbitrary excess" authority in central organs, an excess which is created by the self-paralysis of the in­dividual or worker—their inability to reach or form a local consensus.

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These outer games may also be viewed as forms of investigation of the inconsistencies in the old consensus, as a way of clarifying which branch wins when by letting them fight it out for emission time and seeing. Actually, a "win" is impossible because the game rules are psychologically upheld only by the conflicts defined in their terms. But as a win emerges, the outer principles involved are internalized to define an inner reformation. The forms, actionable when completed, are the forms predicting the repeating paths, and with an adequate theory of who wins when the character structure of the players, or rules of the game, become themselves reformed. (The novel creates new personalities rather than—or as well as— describes them.)

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The "excessive" blind role of the consensus pump is then taken up as renewed forms of self-command based on causal conviction, or God's laws. These renewed command forms have implicit in them added causal self-model insight. Most changes only excite their opposite and disappear; they have no lasting institutional character. Only causal self-model insight has such a character. This recogni­tion is the key to distinguishing the institutional control variable, or control variables of lasting social change, from those merely as­sociated with incidental changes. The search for the general func­tional form of institutional control variables is at the heart of the theory of social change, as well as of religious tradition.

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The Implied God Concept

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Obedience is basic, de facto. Assertion derives from obedience, from the will sexually posited on us by the group, or others. Each "other" stands for the heuristics which animate him, and which his exist­ence couples imitatively upon ourselves, as a demand of obedience.

The self is born of seeming inconsistencies in demands for obe­dience. These seeming inconsistencies force the use of personal ne­gations, or personal selection functions among the imitatively cou­pled demands, in order to reach emission at all. These personal ne­gation functions, or rejections of obedience, are the essence of "evil", through whose acting out (a clarification of who wins when) a rela­tive negation of personal negation or death of self is reached, and a larger model found that reconciles the conflicting obediences. The attack on others is resolved as a joyously opening (problem solving) attack on ourselves, within which we realize that beneath the seem­ingly competitive demands of others is a consistent mathematical scheme, previously obscured by a failure adequately to verbalize the felt.

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Only the word can be wrong. The felt is always right. The strug­gle of empathy to link the felt beneath conflictingly articulated de­mands, or impulses, involves an acceptance of evil, a jazz-like acting out of the self-assertive selection functions to joy in another's joy through which inner self-clarification is achieved, rationalizing lust.

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But through evil, or evil's own self-transcendence, the hidden family or unity in others, which lies at the root of the will, is re­vealed. God is not abstract, but precisely another for us. The wor­ship of God is precisely the worship of the others we know, the struggle to obey them. Another for us is more—as well as less—than he is for himself, since for us he represents the reconciliation of his maxims with our own: hence; an enlarged self-model, drawing in the new (whereas for himself he is only what he is). It is precisely through this "more" that he becomes God to us. Synthesis involves loving those we hate. It is to those we hate that we owe the most. The Russians owe their liberalization to us, and we owe ours to them! It is this love which brings the aesthetic to a standstill, real­izing artistic sensibilities.

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The experience of the many competitive demands as problems to be solved reveals the many as one and God, and turns us into self-attack. It involves the revelation of the latently mathematical and ideal in the felt and related problem-like nature of conflict. It brings the past to repetition in the present under ever new conditions, further differentiating that past which exists only as an aspect of the eternal present.

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The gap between ourselves and God becomes revealed as the gap between our words and our feelings, as the distant grammatically implied "many" emerge as a present One. God loves us all equally. Hate too is a mask of love, a needed probing to bring in the fact of who wins where, which added information makes love's synthesis possible. No phase in problem solving is "better" as such. Things as they are are already ideal, so that union with God is basically funny. It is "merely" the verbal realization—relative to presently existential issues or questions—of what we have always been. Obe­dience of those rejected, which is one and not a matter of degrees (despite the "chaos" this entails), is protected by humor. It is that for which we search and the foundation of all else.

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[Note: This is an abbreviated version of a more extensive class handout. This version is taken verbatim from sections of that longer paper.]