Chaotic Logic -- Copyright Plenum Press 1994

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Chapter Eleven

MIND AND REALITY

    Now, finally, with the cognitive equation and the theory of belief systems under our belt, we are ready to return to the "crucial connections" of Chapter Six -- to the intimate relationship between language, thought, reality, self and consciousness. In this chapter I will present several different views of the relationship between psychology and the external world.

    In Section 1, using the ideas of the past two chapters, I will present the radical but necessary idea that self and reality are belief systems. Then, in Section 2, I will place this concept in the context of the theory of hypersets and situation semantics, giving for the first time a formal model of the universe in which mind and reality reciprocally contain one another. This "universal network" model extends the concept of the dual network, and explains how the cognitive equation might actually be considered as a universal equation.

    Finally, in Sections 3-5, I will put forth a few speculative suggestions regarding how one might reconcile this idea with our contemporary understanding of the physical world. I will confront the well-known paradoxes of quantum mechanics, and argue that the resolution of these paradoxes may lie in the idea that the world is made of pattern. If this idea is correct, it will provide a basis for integrating the idea that reality is a belief system with modern physical science.

11.1. LANGUAGE, BELIEF AND REALITY

    Nietzsche and Whorf, despite their fundamental theoretical differences, shared the following radical view: external and internal reality are belief systems. Further, they both maintained that one of the main roles of consciousness and language is to maintain these belief systems. Beings without consciousness and language, according to this perspective, do not perceive a split between external and inner reality.

    Let us explore this proposition in detail. I have said that a language consists of a syntactic system appropriately coordinated with a semantic system. But this characterization says nothing about the possibility that the semantic system of a given written/spoken language may also serve other purposes. Perhaps this semantic system is also connected with various belief systems.

    A belief system is itself a special kind of linguistic system. Each belief has a certain meaning, and the meanings, in order to be psychologically useful, must change roughly continuously with the syntactic construction of the beliefs.

On this rarefied level, the Nietszchean/Whorfian insight is simply that different abstract "languages" may intersect one another semantically, while being quite different syntactically. One of the languages is ordinary spoken language, and the others are belief systems, including the one which we call by the name "external reality."

    In terms of efficiency, the sharing of a common semantic system by two different syntactic systems makes a lot of sense. Semantic systems are space-intensive -- they require the storage of a vast number of patterns/processes and the connections between them. Syntactic systems, on the other hand, are more time-intensive: they, like the slightly more general transformation systems discussed in Chapter Two, require the repetitive application of simple rules. Having two syntactic systems share the same semantic system conserves space, allowing the mind to pack a greater number of linguistic systems into the same space.

11.1.1. Reality as a Belief System

    The belief system which we call external reality is a collection of processes for constructing three-dimensional space, linear time and coherent objects out of noise- and chaos-infused sense-data. Neurobiologists are just beginning to probe the most primitive levels of this belief system; the more sophisticated levels are completely out of reach. If the mind had to applyconscious and/or deductive reasoning to every batch of sense-data it received, it would be paralyzed. How long would it take to thoughtfully, logically determine the best interpretation of a given series of photons on the retina? For efficiency reasons, the mind instead applies certain common sense beliefs about the way the world is structured, and automatically or semi-automatically processes sense-data in terms of these beliefs.

    The classic optical illusion experiments show that these common sense beliefs can be misleading. For instance, in the Ames experiment one looks through a peephole into a room with oddly angled walls, and one misjudges the relative positions of objects. But this is because one is applying irrelevant beliefs. Given enough exposure, the "external reality" belief system can use continuous compositionality (analogical structure) to adjust itself to minor changes of this sort. It can create new high-level beliefs to match the situation, by piecing together the same low-level beliefs that are pieced together to judge the relative positions of objects in an ordinary room.

11.1.2. Self as a Belief System

    At first glance, "self" might seem to be a far simpler belief system than "reality." After all, what beliefs are involved in selfhood, beyond the simple faith that "I exist, and I act"? But a more careful investigation reveals that the sense of self is every bit as intricate as the sense of external reality. One's inner world is subtly guided by one's body-concept.

    This point was emphasized repeatedly by Hubert Dreyfus in his What Computers Can't Do (1978). This book, which purports to be a disproof of the possibility of artificial intelligence, fails at its intended goal. But it is devastatingly effective as a diatribe against computer programs which attempt to simulate self in a disembodied way. Human intelligence, Dreyfus points out, is indivisible from the sense which we humans have of presence in a body. When we reason, we relate different ideas in a way that draws analogically on 1) the felt interrelations of parts of our body, and 2) the relation of our body with various external objects.

    For example, the "detached" feeling of logical reasoning is not unrelated to the feeling of a separation between self and world. By learning to distinguish oneself from the external world, one learns moregenerally how to divide a continuum of patterns into actor and acted-upon. Thus I would predict that those who feel themselves more "at one" with the world will also be less likely to enjoy reasoning in a detached, "objective" way. This prediction is validated by the work on "boundaries" to be discussed a little later.

    To see more vividly the reality of body-self interdependence, consider the phenomenon of the "phantom limb," discussed for example in Israel Rosenfield's recent book Strange, Familiar and Forgotten (1992). When a person loses her arm, she may instinctively feel the arm to be there for months or even years afterwards. This means that her sense of the existence of her arm is not tied to the physical sensations being sent from the arm, but rather persists "in itself."

    From the point of view of classical psychological theories or modern cognitive science, this is rather difficult to explain; it requires complex theoretical contrivances. But from the cognitive equation perspective, it is virtually obvious. Since the self is a successful belief system, it must be an attractor for the cognitive equation. But if it is an attractor for the cognitive equation, then each one of its component beliefs must be producible by the others. The belief in the existence of one's right arm can be produced by the other beliefs in the self belief-system.

    To put it less abstractly, we not only have processes for receiving data from our arms, we have processes for analyzing and transforming this data, and requesting more data. The theory of belief systems suggests that this network of processes is capable of producing the belief that the arm exists. And this is exactly what is observed in the phenomenon of the "phantom limb."

11.1.3. Intersections

    Perhaps the most impressive example of intersection between the semantic system of spoken language and the semantic system of self/reality is the imaginary subject, discussed earlier in the context of Nietzsche's thought. Who can dispute the fact that, when we understand the world or self, we assume objects where there may not be any? The interpolation of imaginary subjects is a universal method for finding meaning. It ties linguistic constructions such as "I" and "flash" together with biological constructions like the phantom limb, and thefilled-in blind spot directly in front of every human being's nose.

    But other examples are not lacking. For instance, in one of his most interesting papers, Whorf compares the Indo-European and Hopi concepts of time. The Hopi language, he claims, groups future and imaginary into one category, and past and present into another category. Correspondingly, he claims, their subjective "external worlds" are structured differently. Whereas we perceive a rift between the present and the past, they feel none. And whereas we tend to see the future as something definite, largely pre-determined, they tend to perceive it as nebulous and conjectural.

    Whorf tends to imply that linguistic structure causes the structure of reality. But I don't see the point of introducing a Newtonian concept of causality. If one has two syntactic systems using the same semantic system, then both of them will influence the semantic system every time they access it. Each reference to a structurally associative memory has the potential to affect that memory's notion of association -- and thus its fundamental structure. Therefore, two linguistic systems that share the same memory network will influence one another quite directly -- each one will affect the structure of the common memory, which in turn will affect the direction of deduction in both systems.

    It is possible that one of the two systems will have a greater effect on the common semantic system. But Whorf gives us no reason to believe that this is the fact of the matter in the case of spoken language and external reality. Evolutionarily and socially, these two systems must have originated together. Developmentally, in the mind of a child, the two arise together. And, finally, in day-to-day thought, the two operate symbiotically. Each time a person speaks, her semantic system is reinforced in ways that follow the demands of language; but each time a person perceives or reasons about reality, her semantic system is reinforced in ways that follow the structure of the belief system that is external reality.

11.1.4. Language, Conspiracy and Reality

    If one accepts the idea that spoken language and external reality are interconnected linguistic systems, then one has the question of why these systems survive. Recall the idea that belief systems use three differentstrategies to maintain themselves: 1) effectiveness at protecting high-level processes from problems, 2) internal conspiracy. It seems quite plain that external reality excels in not only in the first category, but also in the second -- that the belief system which we call external reality is a structural conspiracy which relies strongly on internal conspiracy for its survival.

    In other words, I suspect that is is common for belief in one aspect of external reality to reinforce or create belief in another aspect of external reality, and vice versa, even when those aspects of external reality have little or no support outside the belief system of external reality. The Sapir-Whorf hypothesis suggests that language is a key accomplice in this conspiracy.

    This is a very deep and very radical hypothesis. And its complementary hypothesis is equally striking: that the belief system which we call self also has the formal structure of internal conspiracy. Whorf focused on outer reality more than on inner reality, but Nietzsche understood both to be constructs of language and consciousness. As already noted, he saw the "little word I" and the experience of "free will" as the most egregious possible instances of imaginary-subject postulation.

    And, taking the whole process one level higher, these two internally conspiratorial belief systems combine to form a larger conspiracy. Belief in the self and free will encourages belief in an external reality. Belief in an external reality encourages belief in self and free will. The concepts "inner world" and "outer world" are each meaningless in isolation; they gain their meaning from one another. And the two systems involve many similar beliefs -- the postulation of imaginary subjects is one example, and the assumption of a linear time axis is another.

    To make this a little clearer, consider the case of a person in doubt about the reality of the world around her. Two beliefs may pop into her mind: the belief that the wall in front of her is real, and the belief that the floor below her is real. Internal conspiracy suggests that these two beliefs will reinforce one another, increasing one another's strength just like two complementary antibody classes in the immune system.

    Next, suppose that our heroine is also confused about her own reality -- about the effectiveness and substantiality of the mental process called her "self." Suppose, in order to test this hypothesis, she picks up a rock and throws it at the wall. Then two beliefs may occur to her: the belief that "she" is really in control of something, and the belief that the rock is really there. Internal conspiracy suggests that these two beliefs increase one another's strength: the more she believes she is in control, the more she is likely to believe the rock is real; and the more she believes the rock is real, the more she is likely to believe she is in control of something.

    Next, structural conspiracy suggests that, as well as reinforcing one another, these basic beliefs are able to create one another. For instance, belief in the reality of the wall could be created by the belief in the reality of the floor, the ceiling, the lamp hanging on the wall, etc. And it could also be created in a different way, by reference to beliefs from the self system: for instance, belief in the controlling nature of the hand that punches the wall, the fingernail that scrapes the wall, or the voice that echoes off the wall.

11.1.5. Godfrey Vesey on Inner and Outer

    It is interesting to contrast the Nietszchean/Whorfian view of self and reality with that of the contemporary philosopher Godfrey Vesey. In the Introduction to his insightful book Inner and Outer (1991), Vesey writes

The essays in this collection are on a philosophical myth. I call it 'the myth of inner and outer.' It is behind what Gilbert Ryle calls 'the myth of the ghost in the machine.' But it is also behind what might be called 'the myth of a machine with a ghost in it', or, more generally, 'the myth of the world as external'. In brief, the myth divides what, to the philosophically unindoctrinated (and even to the indoctrinated in their non-philosophical moments) is undivided, into two distinct things -- one inner ('mental') and one outer ('physical').

    The myth manifests itself in philosophical theories of voluntary action, perception and communication. In regard to voluntary action, the myth finds expression in the theory that my raising my arm is really two distinct things, one of them inner (my performing a mental act ofwilling, a 'volition') and one of them outer (my arm rising).... In the case of communication, there is what Jonathan Bennett called 'the translation view of language': my saying something involves my translating inner things (ideas or thoughts) into outer things (audible sounds), and my understanding what someone has to say involves my translating outer things (audible sounds) into inner things (ideas or thoughts).

I cannot accept Vesey's classification of the rift between inner and outer as "a philosophical myth," unknown to the "unindoctrinated." Surely the concepts of internal and external reality are more than erroneous theoretical constructs of some philosophers!

    Look at Vesey's two examples: the idea that raising one's arm involves both an inner and an outer act, and the idea that language involve translating sound waves into ideas. Both of these examples represent the standard scientific perspective. We actually know which parts of the cerebellum must be activated in order to cause an arm to be lifted up. And we know which parts of the brain are stimulated by audible sounds, and which parts of the brain process those audible sounds that carry recognizable language. These examples are not philosophical myths, they are elementary neuroscience!

    And, in addition to being good biology, they are also good common sense. We can have the thought of going to the freezer to get some ice cream, followed by the action of going to the freezer to get some ice cream -- these are two different things, and the first in some sense seems to cause the other. It is by analogy to this sort of situation that we analyze arm-raising in terms of a thought followed by an action. This is similar to (and related to) the postulation of an imaginary subject ... it is the postulation of an at least partially imaginary "cause and effect."

    Similarly, when we speak, we often have the experience of first consciously formulating a sentence, then saying it. Although the process is not always so deliberate, even when it is not, we still tend to make the assumption that all speech consists of thought followed by action. This is a commonplace analogy, absolutely natural and inevitable in the functioning of the mental network.

    In sum, what Vesey disparages as "a philosophical myth" is in fact absolutely essential both to everydaylife and to biological science. The concepts of inner and outer reality cannot just be dismissed out of hand. I agree with Vesey that they are not "correct" in any absolute sense. But I contend that they are justified belief systems in the sense of Chapter Ten, as well as being internally conspiratorial belief systems. They are impressively, incredibly dialogical -- the amount of new pattern which they create is far beyond our conscious comprehension.

    It would be of great interest to study the structure of these belief systems in detail, with an eye toward understanding their dialogicality, their internal conspiratoriality, and their relationship with the deep structure of language. To a certain extent this quest is self-referential, since our tools for studying things are largely based on the concepts of internal and external reality. But, as I have repeatedly emphasized, self-reference is not necessarily a problem; it can be part of a solution. It is hard to imagine a research programme of greater importance or interest than this one.

11.1.6. Boundaries

    All this talk of self and reality may seem overly abstract; disconnected from the actual business of thought. In Chapter Twelve, invoking the notion of dissociation, I will present a forceful argument that this is not the case. But dissociation is not the only connection between the self/reality system and ordinary, everyday behavior. In fact, the particular structure of a persons's self/reality system affects everything she thinks and does.

    For example, we have seen that all thought, even the most "rational" and "logical," depends essentially on belief systems. But how, then, does a child's mind learn to develop belief systems? Nietszche was the first to arrive at the correct answer: by analogy to, or direct use of, the self/reality belief system.

    For example, Nietzsche observed that the "little word I" is a paradigm case for reification in all its aspects. Language developed for speaking about the self involves postulation of an imaginary subject. This language is then used for thinking about all sorts of issues, and thus the tool of imaginary subjects spreads throughout all the belief systems of the mind.

    Similarly, I propose, every major aspect of more specialized belief systems may be found to have itscounterpart in the one big belief system -- the self/reality system. One example of this involves the notion of boundaries, as developed by Ernest Hartmann in his intriguing book Boundaries in the Mind. Hartmann has developed a questionnaire designed to distinguish "thick-boundaried" people from "thin-boundaried" people. And through a comprehensive statistical analysis, augmented with numerous personal interviews, he has concluded that these two categories represent genuine personality types. Thick-boundaried people tend to place a large "distance" between themselves and the world -- they tend not to remember their dreams, they tend to be rigid in their beliefs and habits, not to be free in expressing their emotions. Thin-boundaried people, on the other hand, seem to live partially in a dream-world, to be permissive and "liberal" in their beliefs, to express their feelings freely, and to be very sensitive to the emotions of others.     

    These results indicate that the thickness of the "boundary" which a person places between their self and their reality is a quantitative parameter which carries over into all aspects of life. Once someone's self/reality system erects a thin boundary, then that person's subsequent belief systems will tend to be of the "thin-boundary" type, making few rigid distinctions and permitting entities to blur into their opposites. On the other hand, once someone's self/reality system erects a thick boundary, then that person's subsequent belief systems will tend to place things into strict categories, to distinguish X and not-X most strenuously -- to be, in short, "thick-boundaried." This is a very strong piece of evidence that the self/reality belief system is used as a model for all subsequent instances of belief-system formation.

    This example, as you may have guessed, was not selected arbitrarily. It is of paramount importance in the theory of the dual network. Recall that consciousness, in the dual network model, has to do with the iterative strengthening of barriers or boundaries. But the dual network model certainly does not imply that everyone's barrier-strengthening procedures are equally powerful. These procedures, like all others, evolve over the course of a lifetime. For one reason or another, in the course of developing an internal concept of reality, some infants evolve stronger boundary-strengthening processes than others. This psychological trait then carries through to their adult lives, influencing theirpersonalities and their methods of perceiving and categorizing the world.

11.2. COLLECTIVE REALITY

    Hyperset theory shows that there is no logical problem with the philosophically attractive idea of reality as a belief system. Mind can belong to reality, while reality belongs to mind. Mental patterns in the brain can give rise to processes which themselves make up the brain. The contradiction is only apparent.

    But what's the meat of the concept? If reality is a belief system, then what sort of belief system is it? One interesting answer to this question is provided by the situation semanticists, and their intriguing hyperset-based approach to the puzzle of common knowledge.

11.2.1. Reality as a Regress

    I will begin obliquely, with an example that is not at all philosophically loaded. Consider two people staring into one another's eyes. Intuitively, one might say that each one of the two starers recognizes the following sequence:

I look at her look at me

I look at her look at me look at her

I look at her look at me look at her look at me

I look at her look at me look at her look at me look at...

Or, alternately, one might represent the situation by the circular formula

X = I look at her look at X,

(where I use the expression a = b to denote that a and b are equivalent set-theoretic entities, rather than merely that a is to be assigned the value b.)

    What does this have to do with reality? Let us for the moment exclude phenomena such as mysticism, catatonia, extreme retardation, and schizophrenia -- let us consider a society in which everyone recognizes and thinks about essentially the same common externalreality. Then it is only reasonable to conclude that each member of society recognizes the following sequence:

Everyone recognizes the same phenomena

Everyone recognizes that everyone recognizes the same phenomena

Everyone recognizes that everyone recognizes that everyone

            recognizes the same phenomena

Everyone recognizes that ...

Given this regress, it is tempting to sum the situation up by the hyperset formula

X = Everyone recognizes that X.

And if "everyone" is too strong, if one wishes to restrict consideration to some group such as the set of sane individuals, one may construct a similar regress leading up to the hyperset formula

    X = Every sane person recognizes that X

    There is one obvious complaint against this kind of analysis. The infinite regresses I have constructed are logically sensible but psychologically absurd, in the sense that the human mind has only limited recognition abilities. Biologically, at some point the sentences "Everyone recognizes that everyone recognizes that ... everyone recognizes the same reality" will become so long as to exceed the memory capacity of the human brain. So, if the regress is inevitably cut off after some finite point, then what good are the hyperset formulas, which are equivalent only to the actually infinite regresses?

    However, this objection is far from fatal. To resolve the matter, one need only return to the definition of mind as patterns in brain. Suppose someone's brain contains the first twenty iterations of the regress

Everyone recognizes the same phenomena

Everyone recognizes that everyone recognizes the same phenomena...

This collection of twenty patterns is not at all unordered; there are significant patterns in it, relating to its obviously repetitive structure. And if hyperset patterns are permitted, then one of these patterns is clearly of the form "Take the first 20 iterations of the formula X = everyone recognizes that X, from the initial condition 'everyone recognizes the same phenomena'." This is a nice compact formula which allows one to quickly compute the collection in question.

    The limiting hyperset form is part of a pattern in the first few iterations of the regress. So, even if the regress of recognitions is never explicitly completed, the hyperset formula that encapsulates the infinite regress may still be part of the mind. It all depends on whether, in the definition of mind, one interprets the word "pattern" to include "hyperset pattern" instead of just "computable pattern."

11.2.2. Common Knowledge

    To make this line of thought a little more concrete, let us next turn to the Conway paradox. In their charming little book The Liar, Jon Barwise and John Etchemendy have expressed this conundrum in a particularly simple way:

Suppose you have two poker players, Claire and Max, and each is dealt some cards. Suppose, in particular, that each of them gets an ace. Thus, each of them knows that the following is a fact:

            s = either Claire or Max has an ace

Now suppose Dana were to come along and ask them both whether they knew whether the other one had an ace. They would answer "no," of course. And if Dana asked again (and again...), they would still answer "no."

    But now suppose Dana said to them, "Look, at least one of you has an ace. Now do you know whether the other has an ace?" They would again both answer "no." But now something happens. Upon hearing Max answer "no" Claire would reason as follows: "If Max does not know I have an ace, having heard that one of us does, then it can only be because he has an ace." Max would reason in the same way. So they both figure out that the other has an ace.

There is a big difference between the first situation Barwise describes, and the second. Intuitively, Dana's statement gave each of them some essential information. But yet, in a sense, Dana told them something that each of them already knew. This is the "paradox."

    The intuitive solution of the paradox is that, prior to Dana's statement "at least one of you has an ace," the fact s was known to both of them, but it was not common knowledge. The puzzle which this "solution" raises is: what is common knowledge?

    One approach is to declare that, by saying that s is common knowledge, one means

Max knows Claire knows s

Claire knows Max knows s

Max knows Claire knows Max knows s

Claire knows Max knows Claire knows Max knows s

...

Clearly, if one gives the name "G" to the group consisting of Claire and Max, then this is substantially the same as

Everyone in group G recognizes s

Everyone in group G recognizes that everyone in group G

    recognizes s

Everyone in group G recognizes that everyone in group G

    recognizes that everyone in group G recognizes s

...

    This regress encapsulates, in a sense, the fact that s is common knowledge in the group G. But it is an unwieldy way of representing this fact. Much nicer to say, following Barwise,

    X = Everyone in group G knows both X and s

This approach allows us to give a purely "sociological" definition of reality. One may say that a certain thing s is in the reality of a group of people if the hyperset

    X = Everyone in the group recognizes both X and s

is a pattern in this group over some period of time.

    As in the discussion at the end of the previous section, this does not imply that the minds involved must be capable of infinitely complex perception and memory. It just means that they carry out a long enough segment of the regress to make the limiting hyperset formula a pattern in this segment.

    This is a subjective, rather than objective, definition of reality. What it means is that, when we look at a chair, instead of simply seeing a chair, what we see is first of all a regress of the form

Every sane person sees this as a chair

Every sane person knows that every sane person sees this as a chair, and also sees     this as a chair

Every sane person knows that every sane person knows that every sane person sees     this as a chair, and also sees this as a chair

and secondly a hyperset pattern in this regress:

    X = every sane person knows that X, and also sees this as a chair

    So far as I know, this is the first ever precise characterization of external reality as a subjective phenomenon. We have not yet arrived at a comprehensive model of mind and reality, but the idea of collective reality is a significant step along the way. It shows how a group of intelligent entities can generate a reality that is fundamentally, emergently their own.

11.2.3. The Universal Network

    Now, finally, it is time to address the question of the fundamental relationship between mind and reality, from within this hyperset perspective. Let me introduce the word universe, to refer to the set containing both mind and physical reality. I suggest that the universe may be understood as a collection of dual networks, linked at the bottom via certain "connector processes".

    This is a very natural idea -- after all, the lowest levels of the dual network deal with immediate physical stimuli. So if a collection of dual networks are connected at the bottom, this means that there are processes interrelating the physical stimuli received by one network with the physical stimuli received by the other. These "connector processes" are the only physical reality there is.

    And what form do these "connector processes" take? The arguments of the previous section imply that they must take the form

        X = Everyone in the group G recognizes both X and s

In other words, these lowest-level connector processes which underly the collection of dual networks, themselves refer to the collection of dual networks. They contain the collection of dual networks. In this sense, one may say that reality contains mind, while mind contains reality.

    What is the difference between simply "seeing a chair" and seeing a hyperset pattern of the form

    X = every sane person knows that X, and also sees this as a chair    ?

The main practical difference is, I suggest, one of solidity. Patterns of the form

    X = every sane person knows X and s

should logically receive a great deal of protection from reorganization. This gets back to the mind's all-important grouping/scene-making/solidifying processes, which I have said to be intimately involved in consciousness.

11.2.3.1. Reorganization and Reality

    But how exactly do these "scene-making" processes work? How do they determine what sort of coherent wholes to form out of the chaotic fragments of perception with which they are presented? They cannot go on internal clues alone -- they must rely largely on memory, on historical information regarding what is really there, or in other words what is common knowledge. Patterns which are of the "common knowledge" form are much more likely to emerge from their solidifying mechanisms.

    Each mind learns to solidify those subnetworks which other minds have solidified. Thus there emerges a common core of "reality," by a kind of feedback relation: the more common knowledge there is, the greater incentive minds will have to reinforce common knowledge, and the more new common knowledge will be created.

    So, reality is a self-referential, self-supporting system: each person believes in it because the other ones do. It is a belief system which transcends the boundaries of any one mind, and is supported only by the synergetic actions of many minds. One cannot refute the solipsistic proposition that there is only one mind, and all others are illusions. What is necessary for the maintenance of reality, however, is that these illusory minds must act as though they were living in a cooperatively created world. In other words, where reality is concerned, patterns of behavior are more fundamental than so-called "fundamental existence."

11.3. PHYSICAL REALITY AS A MENTAL CONSTRUCTION

    Up till now, this book has been concerned with solving puzzles regarding the nature of mind. In this section and the two which follow it, however, I will take a break from proposing new solutions and present instead a new problem. This represents a bit of a digression from the main thread of the book, and the impatient reader may wish to skip ahead to Chapter Twelve, dipping back into this material later when time permits.

    I do have some ideas regarding the solution of this new problem, but they are frankly speculative and not well developed. My main goal here is to draw attention to the problem itself, for it is a problem that, given its tremendous importance, has not received nearly the attention it deserves.

    The problem is as follows: how are physical structures built from mental structures? Or, more pointedly: if reality is nothing more than a belief system, then why does this belief system obey beautiful, abstract principles like the Schrodinger equation and Einstein's gravitational field equation?    

    This question is an inversion of the point of view taken by systems theorists like Ilya Prigogine, Erich Jantsch and Hermann Haken (1984). For instance, in his classic treatise The Self-Organizing Universe, Eric Jantsch (1980) applies ideas from systems theory to analyze everything from microscopic particles to molecular soups to brains, societies, evolving ecosystems and galaxies. His philosophy is universalist: self-organization, he argues, is a phenomenon underlying all levels of structure and dynamics, perhaps the vital force of the cosmos. But his actual methodology is to takeideas developed for studying physical systems and "extrapolate them upward" toward the mental and social realms.

    To a certain extent, it may well be possible to study mind and brain using physical ideas. What I am suggesting here, however, is that it may also be possible to do exactly the opposite: to "build down" from the complex to the simple, and somehow derive the laws of physics from the laws of psychology.

    How, then, are physical structures built from mental structures? As already warned, I do not have a solution. It seems to me, however, that the most likely source for a solution is quantum physics, and more specifically the quantum theory of measurement. In the remainder of this chpater, therefore, after a few general philosophical comments, I will briefly review some of the discoveries of this odd branch of physics, and then explore their relationship with the pattern-theoretic psychology that was developed in the body of the book. This discussion will serve to make the basic question more concrete. And it will also lead us to some surprising discoveries -- such as the very close relationship between quantum measurement, pattern philosophy, and the cognitive equation.

    This is admittedly a radical programme. But if one is serious about the idea that reality is a belief system, then one cannot avoid the question: where do these elegant mathematical properties of reality come from? Today the phrase "Foundations of Physics" refers to a technical subfield of theoretical physics. I venture the prediction that, in a hundred years time, it will refer to a branch of mathematical psychology.

    So, let's get started. One way to conceptualize the huge gap between physics and psychology is to think about the two most basic aspects of physical reality: the three dimensions of space and the one dimension of time.

11.3.1. Euclidean Space

    The ideas of Chapter Ten imply that three-dimensional Euclidean space is an element of a very very useful belief system. In the mental hierarchy of an individual conscious system, it lies well below consciousness, but well above the lowest "raw perception" levels. The postulate of three-dimensional space allows the organization of a vast amount of pattern in a remarkably convenient and productive way.

    From this point of view, if the question "why three dimensions" has any answer at all, it should have an system-theoretic answer. There should be some reason why three dimensional space leads to a more productive belief system than two or four dimensional space. Maybe, as has been suggested, this has to do with the fact that three dimensional space is the only Euclidean space in which one can tie knots. Or perhaps it has to do with the fact that in three dimensions, but not in two, any finite graph can be drawn without the crossing of edges.

    It may be, of course, that the question has no answer; that the three-dimensionality of our existence is a fluke, with no special meaning. The three-dimensional belief system is ingrained in our minds, brains and culture, but perhaps there are other organisms with mind/brains that naturally organize things in seven dimensions. My suspicion is that there is something special about three dimensions -- but this could be a case of bias, of "dimension-centrism"!

    So Euclidean space is not fundamental. There is a sense in which space is fundamental, but space in this sense means nothing more than separation. It means that the mind can consistently perceive two different things without perceiving the patterns emergent between them, even though these emergent patterns are present in its memory, and not hard to find. The existence of space, in this sense, says simply that two things will often enter different "parts" of the lower levels of its dual network. It means that the lowest "perceptual" levels of the dual network can receive a variety of different input. This sort of space is essential to the universal dual network. But it comes with no inherent dimensional structure.

11.3.2. Linear Time

    Next, what about time? Without pretending to have arrived at a definitive judgement on the matter, let us recall that, according to the cognitive equation, time may be equated with the passage from substance to structure. In other words, time is the process by which a collection of processes is replaced by those processes which are 1) produced by the actions of elements of A upon elements of A, and 2) patterns in the collection of entities formed by actions of elements of A on elements of A.

    The cognitive law of motion therefore contains within it the assumption of one-dimensional time. A cognitive law of motion for two-dimensional time would involve replacing each collection of processes with two mutually noninteracting collections of processes, rather than just one. At the next time step, each of these two would then give rise to two new collections. This is not a completely fanciful idea; one could simulate a two-time-dimensional mind on a computer.

    This would of course be subjective time, only indirectly connected with clock time. Clock time is a complex construct; it comes about as a consequence of the particular structure of space and it enters into the mind only as an outgrowth of other high-level concepts. We all know from personal experience how uncorrelated subjective time and clock time can be.

11.3.3. Conclusion

    Both with space and with time, the gap between physics and psychology is apparent. The dual network model suggests an abstract notion of space, and the cognitive equation suggests an abstract notion of time. But one cannot equate psychological space and time with physical space and time. The movement from one to the other is vastly complex and apparently beyond the reach of contemporary science.

11.4. THE QUANTUM MIND

    The psychological sense of building physical structures from mental structures is easy to see. To understand the physical sense of this point of view, we must begin with the commonplace observation that in quantum physics measuring a phenomenon is equivalent to altering that phenomenon. One cannot determine the position and momentum of an electron simultaneously, not with perfect accuracy -- because the position-determining measurement changes the particle's momentum, and the momentum-determining measurement changes the particle's position. This is the paradox of quantum measurement.

    When no one is looking, quantum systems cannot be assumed to possess definite states; they exist in superpositions of physical states. An electron can spin either right or left, but when no one is looking, it isnot spinning either direction -- it is waiting. And the moment someone looks, it somehow decides which way to go.

    This technical paradox gives rise to numerous conceptual troubles. For instance, there is the paradox of Schrodinger's Cat. Put a cat in a box together with a gun rigged to fire only if a certain electron turns out to be spinning left. Now until you look, the electron is spinning neither right nor left; it is in a state of suspension or superposition. But as soon as as you look, the electron assumes a definite state. So when is the cat shot? At the moment you look? What if your friend walks into the room a minute later -- from her view, the definite state should be assumed at the moment she looks.

    One way of resolving this problem is to simply define consciousness as the reduction of quantum superposed states to definite states. This is the course proposed by John von Neumann, and taken up in SI. It is an attractive idea, although it does have certain puzzling implications. For instance, suppose, for the sake of argument, that a mouse is a conscious system. Then according to the quantum theory, the mouse's thoughts and perceptions play a role in shaping the universe. Einstein could not digest this; he said something like "I cannot believe that, when a mouse looks at the world, it is altered." He rejected Nietzsche's idea that

    A thing would be defined once all creatures had asked "what is that?" and had answered their questions. Supposing one single creature, with its own relationships and perspectives for all things, were missing, then the thing would not be defined.

The theory of the universal network sides with Nietzsche and quantum physics, and against Einstein's idea of an objectively, rationally ordered world.

    The real problem with the quantum theory of consciousness, however, is the trouble of connecting it with the biology and psychology of consciousness. It is clear that, if the quantum theory/consciousness connection is to be taken seriously, something further must be done beyond merely equating consciousness with reduction. How does reduction from superposition to certainty correspond with the solidification that, in the dual network model, is the key function of consciousness? Unfortunately I will not resolve this question here. However, a bit more background regarding quantum theory should make the issue clearer.

11.4.1. Synchronicity

    The paradox of quantum measurement ties in with the phenomenon of nonlocal correlation, which is surprisingly closely related to Carl Jung's notion of "synchronicity." In his book Synchronicity: An Acausal Connecting Principle, Jung suggested that coincidence is not always the result of chance; that there is an additional force in the universe which causes "appropriate", "meaningful" things to happen at certain junctures. This is not, strictly speaking, a psychological hypothesis. To many it seems more metaphysical than scientific. But, taking into account Bell's Inequality and the quantum theory of measurement, one may see it in a rather different light.    

    Bell's Theorem from quantum physics implies that systems which have interacted previously will be correlated in the future. The simplest example is two electrons, once coupled but now very distant -- if one is observed by some consciousness to spin one way then the other one automatically spins the other way. But this example is only the easiest to visualize; the same sort of thing happens with complex systems that interact then separate. When the entropy of the probability distribution of the possible states of one system is decreased through observation, the entropy corresponding to the other system is automatically decreased as well.

    Stated a little differently, Bell's Theorem is about emergent pattern. It does not state that patterns in one part of the universe will cause similar patterns to emerge in other parts of the universe. But it does state that emergent patterns will spontaneously form, spanning distant systems which have been "physically unrelated" for a long time. That is what coincidence is: it is a pattern emerging between apparently unrelated events.

    Therefore, according to accepted principles of quantum physics, looking at the world will in general cause certain emergent patterns -- certain coincidences -- to form. This scientifically validates Jung's basic intuition, in the abstract. I have trouble believing some of the examples which he gives in Synchronicity. I suspect that virtually all of the coincidences that occur in everyday life are genuine chance phenomena. But, interms of quantum physics, the scientific possibility is there for some coincidences to be more than that.

11.4.2. Wheeler's Vision

    Over the last two decades, John Archibald Wheeler -- a leading gravitational physicist and the originator of the term "black hole" -- has become a sort of radical activist within the theoretical physics community. His goal is a physics which acknowledges the fact that, while physical reality creates observers (such as humans), observers also create physical reality. And he has argued that contemporary scientific ideas are largely inappropriate for this goal.

[N]o alternative is evident but a loop, such as: Physics gives rise to observer-participancy; observer-participancy gives rise to information; and information gives rise to physics.

    Is existence thus based on "insubstantial nothingness"? Rutherford and Bohr made a table no less solid when they told us it was 99.99... percent emptiness. Thomas Mann may exaggerate when he suggests that "we are actually bringing about what seems to be happening to us," but Leibniz reassures us that "although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough if, using reason well, we were never deceived by it...."

    Directly opposed to the concept of universe as machine built on law is the vision of a world self-synthesized. In this view, the notes struck out on a piano by the observer-participants of all times and places, bits though they are, in and by themselves constitute the great wide world of space and time and things....

    First, elementary quantum phenomena brought to a close by an irreversible act of amplification. Second, the resulting information expressed in the form of bits. Third, this information used by observer-participants -- via communication -- to establish meaning. Fourth, from the past through the billennium to come, so many observer-participants, so many bits, so muchexchange of information, as to build what we call existence.

    In the language of hypersets and functions, what Wheeler is proposing is that

a) mind = f(physical reality)

b) physical reality = g(mind),

for some functions f and g. In totally non-mathematical terms, this just means:

a) mind is defined in some way by physical reality

b) physical reality is defined in some way by mind

This proposal, made by a leading physicist, is obviously very much in the spirit of this chapter. I am not the only one to consider the possibility of reconciling of the psychological view of external reality as a belief system, and the physical view of external reality as a medium of specific dimensionality obeying specific dynamic equations.

11.4.3. Physics and Pattern

    In recent years, a new approach to quantum measurement has emerged -- the statistical approach, pioneered by the physicist Asher Peres (1990). In compressed form, the essence of the approach is that measurement is related to the statistical coupling of the measuring system and the object being measured. This idea, I suggest, may be precisely what is needed in order to connect the physical world with the psychology of belief systems.

    As Peres puts it, "a measuring apparatus must have macroscopically distinguishable states," where macroscopic is defined to mean "incapable of being isolated from the enviroment." Peres's thermodynamic arguments show that what is physically meant by "macroscopic" is nothing other than "statistically coupled with the environment." But a measurement device is defined as something with macroscopic states. Therefore, measurement is conceptually bound up with statistical correlation.

    The same idea was hinted at years earlier by no less a physicist than Richard Feynman:

Proposal: only those properties of a single atom can be measured, which can be correlated (with finite probability) with an unlimited number of atoms.

Let us think about this carefully. A correlation is, essentially, a way of predicting the behavior of a whole group of entities from the behavior of a small subset of the group. In other words, a correlation in a collection of particles is a pattern in that collection. It is an "approximate pattern," according to the technical definition; but it is a pattern nonetheless.

    What are we to make of Feynman's reference to an infinite number of atoms? Obviously there is not an infinite number of atoms in the universe, so if taken literally this implies that measurements never exist. But if one thinks in terms of pattern, the role of the infinite number of atoms here is easy to understand. A correlation among an infinite collection of atoms is bound to be a pattern in the collection of atoms, no matter who is determining what is a pattern and what is not. But a correlation among only finitely many atoms is, to a much greater extent, a matter of opinion: some observers may recognize it as a pattern, while others may not.

     Thus, the statistical approach to quantum measurement implies that every property of a single atom which can be measured is actually a pattern emergent between the atom and other atoms. And how can one tell if a group of atoms are statistically correlated? Well, only by measuring them. But if measuring means detecting a statistical correlation -- then it follows that the atoms themselves are never directly measured, only collections of "properties" that are in fact statistical correlations among large groups of atoms.

    One thing that this suggests is the radical possibility that the physical universe is an attractor for the "cognitive equation." It is known that each particle may be produced by certain configurations of other particles -- this is shown by the well-known catalogue of scattering diagrams. Capra, in his Tao of Physics, has illustrated this point for a nontechnical audience in a masterful way. The statistical approach to measurement implies that, furthermore, each particle is in fact definable as a collection of patterns among other particles (the specific patterns in question are statistical correlations).

    This may seem to be a somewhat extravagant conclusion. If one wants to be less ambitious, however, one may at least conclude the following: if mind is pattern, and if all that we can physically measure are emergent patterns, then it follows that physical reality is in no way separate from mental reality. Insofar as we can measure it, physical reality is just a certain subset of the collection of patterns that makes up the mind. The only question is how the mind came up with the temporal patterns governing the behavior of those patterns that we call particles. For these "temporal patterns" are nothing other than the laws of physics.

11.4.4. Consciousness Revisited

    Finally, what does all this have to say about quantum theory and consciousness? The verdict is unclear.

    If the physical world consists of patterns, then the difference between the quantum world and the classical world has to do with the transition probabilities between patterns. In other words, it has to do with whether, given the problem of computing the joint probability of two independent events A and B, one

    1) multiplies the probability of A by the probability of B (the classical view), or

    2) uses the path summation formula (the quantum view)

    The latter method involves the interpenetration of the two distinct events, A and B. The quantum theory of consciousness states that conscious intervention renders this kind of interpenetration impossible. In the context of the theory of consciousness given earlier, this implies that the barriers erected by consciousness around the patterns it processes somehow prevent quantum-physical interpenetration, as well as memory reorganization. Is this a sensible idea, or merely a surface correspondence between two fundamentally different things?

11.5. FEYNMAN INTEGRALS AND PATTERN PSYCHOLOGY

    The previous section was one long sequence of suggestive speculations. Now I will cap the chapter off with an appropriate grand finale -- the biggest and most suggestive speculation of all. I will put forth theradical possibility that the laws of mind may be used to partially deduce the laws of physics, and perhaps even to resolve some of the pressing problems of modern physics.

    This may seem to be a crazy idea. But one must recall that the hottest physical theory of the decade, string field theory, implies that the universe is a 26-dimensional space rolled up into a very thin 4-dimensional cylinder. In this light, it is hard to pronounce any approach to fundamental physics overly bizarre.

11.5.1. Perception and Paths

    The early Gestalt psychologists showed that, given a number of possible ways of perceiving a figure, the mind will tend to choose the simplest. Similarly, the philosophical axiom called "Occam's razor" states that, all else equal, the simplest of a collection of competing explanations should be preferred. Phrased in terms of pattern theory, these two insights boil down to the same thing: that the mind tends to make the choice of least algorithmic complexity (where algorithmic complexity is measured relative to the perceiving mind). In The Structure of Intelligence, this view of induction and perception is discussed in great detail.

    What if, then, one applies this rule of perception to particle paths? In quantum physics, a particle does not take one definite path from point A to point B; it takes "all paths at once." An action is assigned to each path; then these actions are summed up in a special way, yielding the probability that the particle goes from A to B. But there are numerous technical problems with the standard methods of assigning probabilities to the different paths. If one considers that the various paths do not exist except as perceived by some mind, then one immediately arrives at the conclusion that the probability of a path should be chosen proportionally to its algorithmic information, relative to the mind which is observing the path.

    This would provide a "psychological" derivation of the dynamics of the physical world: the Schrodinger equation, Newton's Laws, special relativity and perhaps even general relativity. It would not immediately resolve the question of where the spacetime containing the paths comes from. However, Wheeler (1979) has proposed that spacetime itself may be obtained by amethod formally similar to path summation; this is the concept of "quantum foam." Perhaps, given a spacetime A at time t, all possible spacetimes for time t+1 exist at once, each one with a certain "generalized action." Then, summing up these actions according to the Feynman formula, one obtains the probability of going from spacetime A to spacetime B.

    Whether this idea yields acceptable physical conclusions is not yet clear. At very least, however, it illustrates the viability of combining physical and psychological ideas. The two views of external reality are complementary and perhaps synergetic; they do not contradict one another.

11.5.2. The Feynman Path-Summation Formula (*)

    Let qiti denote the proposition that a quantum system is in state qi at time ti. In his classic 1948 paper, Richard Feynman showed that the quantum-mechanical probability of a transition from q1t1 to q2t2 is given by |(q1t1|q2t2)|2, where I denotes the integration functional and

    (q1t1|q2t2) = I [eiS(q)/h]     (*)

The integral is taken over all classical paths from q1t1 to q2t2; S(q) is the Lagrangian of the path q, and

    h =      (**)

is the normalized Planck's constant.

    This version of quantum dynamics is not only elegant but remarkably generalizable. All contemporary theories of particle physics -- from quantum electrodynamics to electroweak theory, chromodynamics, grand unified field theory and even string theory -- can be cast in the form of equation (*), with different interpretations for q and different forms for S (Feynman, 1950; Bailin and Love, 1986; Rivers, 1987; Ramond, 1981; Green, Schwartz and Witten, 1987). The integration variable q becomes not a classical path but a classical field, or a field defined over a Grassmann algebra, etc. -- but the basic concept remains the same. In a general context, equation (*) says that a quantum system assumes all possible spacetime configurations consistent with its observed behavior -- it is a "sum over all possible spacetime configurations." But, for simplicity's sake, I will continue to refer to (*) as a "sum over all possible paths."

    Given the tremendous importance of oscillatory integrals of the form (*), it is a curious fact that the entity "dq" has received no proper definition. As a standard particle physics text puts it, this differential is "just a fancy way of hiding our lack of knowledge about the measure" (Ramond, 1981).

    Because (*) is purely oscillatory, one cannot define it directly using Wiener measure. Attempts to get around this problem have been few and far between. Feynman himself simply used approximations to the integral, without formally taking the limit. And that is still a common approach. But among more theoretically inclined physicists, the most popular strategy for understanding (*) is analytic continuation: one removes the i to obtain a real integral, defines the real integral in terms of Wiener measure, then obtains the integral in (*) as the continuation of this real integral onto the imaginary axis. This allows one to study Feynman integrals using standard methods from statistical mechanics (Simon, 1979). But it is intuitively most unsatisfactory. It does not represent (*) as a sum over all possible paths.

    In 1967, Ito came up with a clever functional-analytic definition for "dq," but his method only works for a limited class of action functionals S; it does not generalize to relativistic quantum theory. A little later, Morette-deWitt (1974) suggested an interesting variation on Ito's approach. And, most impressively, in 1976 Albeverio and Hoegh-Krohn used the Parseval relation to give a fairly general Fourier-transform-theoretic definition of (*). But none of these tricks is really satisfactory from a physical, intuitive point of view. They still do not represent (*) directly as a sum over all possible paths.

11.5.3. The Psychological Connection (*)

    So, what is the solution? How can the gap between equation and intuition be bridged? One option which has not been explored is to introduce the physical Church-Turing Hypothesis -- the idea that the physical world must be computable. This principle, pursued by Joseph Ford (1985), Edward Fredkin (Fredkin and Toffoli, 1982; see also Wright, 1989) and others in different areas of physics, states quite simply that uncomputable entitiesdo not physically exist. If one accepts the computability principle, then it follows that, when computing path integrals, one should not integrate over uncomputable paths. But the number of computable paths is only countable, and thus the computability principle may well render (*) much less formidable.

    There is, of course, a catch. The problem of defining (*) has typically been cast in the form: find a measure on the space of all possible paths from q1t1 to q2t2, under which oscillatory integrals of the form (*) can exist under general conditions. But if one is to make sense of the concept of integrating over computable paths only, one must weaken the concept of measure to that of finitely additive measure. A finitely additive measure (f.a.m.) is a nonnegative-valued set function m which obeys the rule

    m( A union B) = m(A) + m(B)

whenever A and B are measurable and disjoint. As the name suggests, to go from a measure to an f.a.m., countable additivity is replaced by finite additivity. One can easily define the Lebesgue integral with respect to an arbitrary f.a.m. Many of the nice results of measure theory do not carry over; but if one could obtain convergence, this would be a small price to pay.

    What sort of f.a.m. might be appropriate here? This is where the psychological connection comes into play. If one accepts that physical reality is psychically constructed, then it follows that those paths that are simpler to the constructing mind should have a higher probability of being followed. In other words, the probability of a path should be proportional to its algorithmic information content relative to the mind doing the measuring. This idea imposes the pattern-theoretic analysis of mind on the physical world, in an elegant, if technical, way.

    The Feynman path summation formula itself may be seen as an incredibly intense pattern in the lower levels of the mental network. The Feynman formula implies that P[ A and B ] need not equal P[A]*P[B]; but nothing in the dual network model implies that the classical rules of probability must hold. In our everyday world, ordinary probability theory approximates the quantum probability formulae tolerably well. But the dual network model would apply just as accurately were this not the case.

    A specific particle path is a somewhat less intense pattern in the lower levels of the dual network. But thesimpler a path is, the more intense it can be as a pattern. Gestalt laws of perception specify that, out of many possible ways of seeing something, the simplest will tend to be chosen. This is also implied by the pattern-theoretic analysis of induction: given a number of possibilities, the mind will automatically assign a higher probability to the algorithmically simpler choices. What is being suggested in the section is that this rule of perception should be included as a part of the laws of physics. For, after all, the physical world does not exist until it is perceived.

11.5.4. Perturbation Theory (*)

    To see the possible usefulness of this kind of f.a.m., let us recall how (*) is actually used to study concrete examples of particle behavior. At present there are two fundamental strategies, perturbation expansions, and lattice approximations; but the former is by far the more popular. In the perturbation approach, one first lets t1 and t2 tend to infinity in (*), thus arriving at an entry of the "scattering matrix" S. Then, one expands the integrand in a Taylor series in terms of some coupling parameter, and integrates the series term by term, obtaining a "perturbation expansion" of (*). Finally, Feynman diagrams are read off from the first two terms of this perturbation series, giving an excellent intuitive and quantitative model of particle interactions.

    The trouble is, when one proceeds in this way, one tends to obtain infinite integrals. Thus one must use the technical procedure of renormalization, which allows one to "subtract off" these infinities, leaving only finite integrals. In the case of quantum electrodynamics, renormalization gives results that agree with experiment to a remarkable degree. The results for chromodynamics, electroweak theory and grand unified theory are not so clear, partly because for the Lagrangians involved in these theories, tractable perturbation expansions are very difficult to come by.

    But it seems quite plausible that, if one uses an appropriate f.a.m. defined in terms of algorithmic information, one might be able to get (*) to converge for the action functionals involved in physics. This would imply that the infinite integrals which necessitate renormalization are not inherent in (*), but are rather an artifact of the method of perturbation expansion.

    The reason to suspect that algorithmic-information f.a.m.'s might allow one to bypass these divergences is quite simple: these f.a.m.'s have a certain natural decay property. They are not smoothly peaked like Gaussian measures, but they are peaked on a very coarse scale. In short, algorithmic-information f.a.m.'s impose an effective cutoff on (*) in a natural way, an effective cutoff which is qualitatively quite different from the artificial cutoffs imposed in renormalization theory. Lacking a detailed analysis, one can at least say that these f.a.m.'s suggest that, once one commits oneself to a computable universe, an effective cutoff point is inevitable.

11.5.5. Conclusion

    So, what's the bottom line? The jury is emphatically out on the speculative physical theory of this section, on the use of algorithmic information f.a.m.'s to simplify Feynman integrals. But my purpose in outlining this theory here is to illustrate in detail the possibility of integrating psychology with physics. The view of the physical world as a belief system does not contradict the existence of detailed theories of physics. Far from it: the two views are complementary, and beyond this they have an immense potential to enhance one another.