. 8
( 10)


conspiracy which has nothing to do with conspiracies in the external world: the belief system of

Christianity is a highly complex belief system, and I will not attempt to dissect it in detail.
Instead I will focus on some very simple belief dynamics, centering around the following
commonplace example of circular thought:

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God exists because the Bible says so, and what the Bible says is true because it is the Revealed
Word of God.

This "proof" of the existence of God is unlikely to convince the nonbeliever. But I was
astonished, upon reading through a back issue of Informal Logic, to find an article attempting its

The author of the article, Gary Colwell (1989), reorganizes the argument as follows:

(1) The Bible is the Revealed Word of God

(2) The Bible says that God exists

(3) God exists

His most interesting thesis is that, in certain cases, (1) is more plausible than (3). If one accepts
this, it follows that demonstrating (3) from (1) is not at all absurd. Therefore, Colwell reasons, in
practice the argument is not circular at all.

I do not agree with Colwell's argument; in fact I find it mildly ridiculous. But by pursuing his
train of thought to its logical conclusion, one may arrive at some interesting insights into the
creativity, utility and self-perpetuating nature of the Christian belief system.

10.4.1. The Bible and Belief

Let us review Colwell's case for the greater plausibility of (1), and pursue it a little further. I
contend that, rather than removing the circularity of the argument, what Colwell has actually
done is to identify part of the mechanism by which the circularity of the argument works in

Colwell's argument for the greater plausibility of (1) is as follows:

It is not uncommon to hear of believers who relate their experience of having encountered
God through the reading of the Bible. Prior to their divine encounter they often do not hold the
proposition "God exists" as being true with anything approaching a probability of one half.
Indeed, for some the prior probability of its being true would be equivalent to, or marginally
greater than, zero. Then ... they begin to read the Bible. There in the reading, they say, they
experience God speaking to them. It is not as though they read the words and then infer that God
exists, though such an inference may be drawn subsequently. Rather, they claim that the
significance of the words, the personal relevance of the words, and the divine source of the
words are all experienced concomitantly. In reading the words they have the complex experience
of being spoken to by God. The experienced presence of God is not divorced from their reading
of the words....

Given that this experience of encountering God in the reading of the Bible is a grounding
experience for the believer, from which he may only later intellectually abstract that one element

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that he refers to by saying that God exists, proposition (1) for such a believer may actually be
more plausible than proposition (3).

Putting aside the question of how common this type of religious experience is, what is one to
make of this argument?

I think that Colwell is absolutely right. It probably is possible for a person to find (1) more
plausible than (3). For a person who has had the appropriate religious experience, the argument
may be quite sensible and noncircular.

After all, when told that a young man has long hair, and asked to rate which of the following
two sentences is more likely, what will most people say?

A: The young man is a bank teller

B: The young man is a bank teller and smokes marijuana

The majority of people will choose B. Numerous psychological experiments in different contexts
show as much (for a review, see Holland et al (1975)). But of course, whenever B is true, A is
also true, so there is no way B is more likely than A. The point is, intuitive judgements of
probability or plausibility do not always obey the basic rules of Boolean logic. Even though (1)
implies (3) (and in fact significantly implies (3) in the sense of Chapter Four), a person may
believe that (1) is more likely than (3). Why not -- it is known that, even though B implies A, a
person may believe B to be more likely than A.

What this means, I believe, is that the human mind is two-faced about its use of the word
"and." If asked, people will generally make a common-language statement equivalent to "'and'
means Boolean conjunction." But when it comes down to making real-life judgements, the
human mind often interprets "and" in a non-Boolean way: it thinks as if "A and B" could be true
even though A were false. Thus, God exists and the Bible is the Revealed Word of God" is
treated as if it could be true even though "God exists" were false. In judging the plausibility or
likelihood of "A and B," the mind sometimes uses a roughly additive procedure, combiningthe
likelihood of A with the likelihood of B, when on careful conscious reflection a multiplicative
procedure would make more sense.

But it seems to me that Colwell's argument contains the seeds of its own destruction. I grant
him that in certain cases the inference from (1) to (3) may be reasonable -- i.e., given the a priori
judgement of greater plausibility for (1). But nonetheless, the argument is still fundamentally
circular. And I suspect that its circularity plays a role in the maintenance of religious belief

I have known more than one religious individual who, when experiencing temporary and
partial doubt of the existence of God, consulted the Bible for reassurance -- in search of the kind
of experience described by Colwell, or some less vivid relative of this experience. But on the
other hand, the same people, when they came across passages in the Bible that made little or no
intuitive sense to them, reasoned that this passage must be true because the Bible is the

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Revealed Word of God. Certain passages in the Bible are used to bolster belief in God's
existence. But belief in the validity of the Bible -- when shaken by other passages from the Bible
-- is bolstered by belief in God's existence. The two beliefs (1) and (3) support each other
circularly. Considered in appropriate context, they may be seen to produce one another.

This psychological pattern may lead to several different results. In some cases the intuitive
unacceptability of certain aspects of the Bible may serve to weaken belief in God. That is, one
might well reason:

(1) The Bible is the Revealed Word of God

(2') The Bible is, in parts, unreasonable or incorrect

(3') Thus God is capable of being unreasonable or incorrect

And (3'), of course, violates the traditional Christian conception of God. This is one possible path
to the loss of religious faith.

On the other hand, one might also reason

(1'') God exists and is infallible

(2'') The Bible is, in parts, unreasonable or incorrect

(3'') The Bible is not the Revealed Word of God

This is also not an uncommon line of argument: many religious individuals accept that the Bible
is an imperfect historical record, combining the Word of God with other features of human
origin. For instance, not all Christians accept the Bible's estimate of the earth's age at 6000 years;
and most Christians now accept the heliocentric theory of the solar system.

Finally, more interestingly, there is also the possibility that -- given appropriate real-world
circumstances -- these two circularly supported beliefs might lead to increased belief in God.
We have agreed that it is possible to believe (1) more strongly than (3). So, for sake of argument,
suppose that after a particularly powerful experience with the Bible, one assigns likelihood .5 to
(1), and likelihood .1 to (3). Then, what will one think after one's experience is done, when one
has time to mull it over? Following Colwell's logic, at this point one will likely reason that, if (1)
has likelihood .5, then the likelihood of (3) cannot be as low as .1. Perhaps one will up one's
estimate of the likelihood of (3) to .5 (the lowest value which it can assume and still be
consistent with Boolean logic). But then, now that one believes fairly strongly in the existence of
God, one will be much more likely to attend church, to speak with other religious people -- in
short, to do things that will encourage one to have yet more intense experiences with the Bible.
So then, given this encouragement, one may have a stronger experience with the Bible that
causes one to raise one's belief in (1) to .8. And after pondering this experience over, one may
raise one's belief in (3) to .8 -- and so forth. The circularity of support may, in conjuction with

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certain properties of the real world in which the believer lives, cause an actual increase in belief
in both (1) and (3).

So, whereas Colwell expresses "curiosity about the prominence that the putatively circular
Biblical argument has received," I see no reason for curiosity in this regard. The Biblical
argument in question really is circular, and it really does play a role in the maintenance of
religious belief systems. The religious experience which he describes is indeed real, at least in a
psychological sense -- but it does not detract from the circularity of the argument. Rather, it is
connected with this circularity in a complex and interesting way.

10.4.2. Christianity as a Belief System

Let us rephrase this discussion in terms of pattern. "God exists" is a certain way of explaining
events in the world. It explains some events -- say, a child being hit by a car -- very poorly. But it
explains other events fairly well. To give an extreme example, several college students have
reported to me that they do better on their mathematics tests if they pray beforehand. This
phenomenon is explained rather nicely by the belief that God exists and intervenes to help them.
My own preferred explanation -- the placebo effect -- is much less simple and direct.

Two related examples are the religious ecstasy some people experience in church, and the
experience of "talking to God" -- either directly or, as discussed above, through the Bible. These
subjective psychological phenomena are well explained by the hypothesis that God exists.
Alternate explanations exist, but they are more complex; and the religious belief system is rather
vigilant in sending out "antimagicians" against these alternatives.

Believing that "the Bible is the Revealed Truth of God" explains a few other things, in
addition to those phenomena explained by "God exists." And, more importantly, it gives the
believer a set of rules by which to organize her life: the Ten Commandments, and much much
more. These rules promote happiness, in the sense defined above: they provide order where
otherwise there might be only uncertainty and chaos. They actually create pattern and structure.
They are a very effective "psychological immune system" -- protecting valuable high-level
processes from dealing with all sorts of difficult questions about the nature of life, morality and

So, one has an excellent example of internal conspiracy: belief in the Bible supports belief in
God, and vice versa. And in very many cases this internal conspiracy is also a structural
conspiracy: the two beliefs create one another. Belief in the Bible gives rise to belief in God, in
an obvious way; and belief in the Christian God, coupled with a certain faith in the trappings of
contemporary religion, gives rise to belief in the Bible. It is certainly possible to believe in the
Christian God while doubting the veracity of the Bible; but in nearly all cases belief in the
Christian God leads at least to belief in large portions of the Bible.

This is a useful belief system, in that it really does deal with a lot of issues at low levels,
savinghigher levels the trouble. It is psychologically very handy. For example, it mitigates
against the mind becoming troubled with metaphysical questions such as the "meaning of life."

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And it does wonders to prevent preoccupation with the fear of death. It serves its immunological
function well.

Next, as anyone who has perused religious literature must be well aware, the Christian belief
system is systematically creative in explaining away phenomena that would appear to contradict
Biblical dogma. It is precisely becuase of this that arguing evolution or ethics with an intelligent
Christian fundamentalist can be unsettling. Every argument receives a response which, although
clever and appropriate in its own context, is nonetheless strange and unexpected.

So, to a certain extent, the Christian belief system meets both the criteria for survival laid out
at the beginning of the chapter. It is an attractor for the cognitive equation, a structural
conspiracy, and it is creatively productive in the service of the dual network.

However, the Christian belief system clearly does have its shortcomings. It entails a certain
amount of awkward dissociation. For instance, the Bible implies that the Earth is only a few
thousand years old, thus contradicting the well-established theory of evolution by natural
selection. In order to maintain the Christian belief system, the mind must erect a "wall" between
its religious belief in the Bible and its everyday belief in scientific ideas. This is precisely the sort
of dissociation that leads to ineffective thinking: dissociation that serves to protect a belief from
interaction with that which would necessarily destroy it.

The prominence of this sort of dissociation, however, depends on the particular mind involved.
Some people manage to balance a Christian belief system with a scientific world-view in an
amazingly deft way. This is systematic creativity at work! For others, however, Christianity
becomes stale and unproductive, separate from the flow of daily life and thought. The value of a
belief system cannot be understood outside of the context of a specific believing mind. Just as a
cactus is fit in the desert but unfit in the jungle, Christianity may be rational or irrational,
depending on the psychic environment which surrounds it.

Chapter Eleven


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

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"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


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 cons ciousness 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

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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

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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

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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

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

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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,

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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

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

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-

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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.


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

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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

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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

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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

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

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

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

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

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

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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. 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."


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

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

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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

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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

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.

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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.

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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

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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.

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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.

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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?


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

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

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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

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,

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,

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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

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.

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