Math, Archetypes, etc.

Reilly Jones (
Sat, 8 Feb 1997 20:38:36 -0500

Omega, this is tying up loose ends, just in case you're peering in from the
disengaged ethereal limbo all lurkers inhabit.

First, we were exploring the curious coordination dynamics between the
physiological *way* in which Feynman thought, and *what* he thought of in
mathematically semantic terms. *How* he thought was *why* he described how
reality works. A section of this follows:

Omega: <The genius of Feynman was often attributed to the fact that in the
middle of a difficult problem, he would stop what he was doing and suddenly
shift to a different viewpoint.>

RJ: <Voila! Sum-over-the-perspectives/sum-over-the-histories describes
reality. Russell (the positivists) and independently Edmund Husserl, were
working on this line at about the same time roughly a full generation
before Feynman's breakthroughs, but Sartre picked it up and spread it
around more contemporaneously.>

Omega: <Strange that the very process that was responsible for the genius
inside of Feynman's head was what led him to confirm in physical reality
what these philosophers had been saying a generation before.>

Secondly, and very closely related to this, we broached the timeless topic
of the correlation between objective reality (physical spaces) and
subjective reality (mental spaces of mathematical semantics). A sample

Omega wrote 2/1/97 in "Von Neumann's Mistake": <Of course, this just begs
the question of the priority of, and relation between, mental spaces and
physical spaces. One of the biggest unanswered questions in the philosophy
of science is the uncanny correlation physical reality and the totally
arcane branches of mathematics that sometimes get discovered centuries
before they are shown to have any relationship to physical reality.>

The very short answer to these links, is that the universe is
self-consistent. As Kant put it in the chapter 'Analytic of Concepts' of
"Critique of Pure Reason": "The conditions *a priori* of any possible
experience in general are at the same time conditions of the possibility of
any objects of our experience."

The longer answer begins with what must be true for self-consistency to be
a property of the universe we know. We are purposeful, meaningful beings;
purpose and meaning cannot sneak into the universe, they precede us. No
existent region is not imbued with purpose, the universe is whole and
open-ended. If any speck of the universe is physically random, then it all
is, and no intelligibility can arise.

Those who believe the universe is random activity, purposeless and
meaningless, are in a Fourier space (in your terms) turned away from truth.
They have nothing meaningful to say in a meaningless universe. They are
not serious, only wastefully playful, in a purposeless universe. They are
barbaric, in that only might can ever be right in such a universe. I agree
with Boethius in "The Consolation of Philosophy" where he concludes that
they "not only cease to be powerful, but cease to be at all.... cease to
exist themselves." Those who deify chance do not have absolute, complete,
unqualified existence.

I am saying that the concepts of randomness and probability are virtually
synonymous with ignorance. They are of an epistemological order, not an
ontological order. The evolutionary growth of intelligence is measured by
a steady decline in aimless behavior, and a steady increase in coherently
purposeful behavior. Individuals drifting through life, or harboring
unresolved conflicting purposes, are not as intelligent as those who
doggedly pursue the truth, whether narrowly or broadly. Intentionality is
how we tap into the purpose that imbues the universe and gives rise to our
semantically meaningful concepts, such as mathematics. The intentional
movements of our bodies in relation to ourselves, our environment, and to
others taps into the design inherent in the universe. Semantically
meaningful information arises from the functional couplings with others,
produced by mutual intentions within a co-evolving environment.

We try very hard to statistically fit our mathematical symbols to reality,
but we cannot logically infer a fit, induction must be used not deduction.
The centrality of metaphors (and metonymy) to our semantically meaningful
exchanges is because we must use them when our symbols don't match a
reality which is simply too rich and fine-grained for our symbols to
closely approach.

Symmetrical translations of spacetime arising from our bodily behavior lie
at the foundation of our semantics; the priority of relations consists in a
metaphorical mapping from physical space to mental space. Whatever
statistical fit our mathematics has with physical reality is traced back to
this. Giambattista Vico in "New Science" (1744), put forth as an axiom the
"universal principle of etymology in all languages: words are carried over
from bodies and from the properties of bodies to signify the institutions
of the mind and spirit." This is now the foundation of modern cognitive
psychology (see George Lakoff, Ruth Millikan, Gerald Edelman, etc.).

Since our bodies move according to our intentions, which are formed within
our evolutionarily preferred value patterns, the linkages between
mathematical concepts, emotions, meaning, design, and aesthetics are
strong. Information specifying our coordinative relations amongst our
constituent parts and between ourselves and our environment is of high
order meaning to us. Such meaning is entirely contextual, specific to the
task before us. The movements of the body are inseparable from the
thoughts of the mind. The formation of our language itself depends on our
behavior. As we behave in specialized ways, our language and knowledge,
our thinking itself, branches away from each other; we think in different
Fourier spaces because we behave in different Fourier spaces. Mathematical
semantic technology and tautologies are in mental space alone; mathematics
is essentially the study of stable relations among stable or invariant
mental objects. That mathematics correlates at all to physical space is
because the universe is self-consistent, we pick up valuable concepts from
physical space and intentionally reapply them to it.

Omega: <And the pathways between the varying [Fourier] spaces could well
have varying degrees of constriction/resistance. Strange, how in the
purely abstract realm of memetics and cognitive process, that this gives us
such a remarkably strong basis for applying the metaphors of fluid dynamics
in such a meaningful way.>

It is very productive to think of patterns of thought in terms of river
channels, with "constriction/resistance" reflected in their curves, falls,
shallows, currents, floods, etc. The physiology of
"constriction/resistance" is what I was describing in my examples of
preferred evolutionary branches of ontogeny, preferred protein folding
spaces, preferred protein design spaces, preferred mental activity
patterns, etc. Virtually everywhere you turn in the biological sciences,
preferred physical structures and preferred dynamic patterns turn up; not
randomness, but design. The most highly adaptive dynamic structures, such
as our brains and immune systems, are most aptly described with liquid
realm metaphors, because the biophysical "constriction/resistance"
parameters force them to "flow" in between chaotic and ordered dynamic

Omega: <I find it amazing that so few of those interested in uploads are
paying any attention to this lack of analog in proposed upload schemes.
Digital is nice, but this business of waveform families and their associate
spaces is not in any way insignificant.>

This "learned ignorance" touches on the "free will vs. group-think" thread.
The unexamined metaphysical presuppositions of the age are greatly
inhibitory to creative breakthroughs in scientific knowledge or humanistic
wisdom. The pervasive digital/computer metaphor has made many otherwise
intelligent individuals appear to be "bit-drunk." I believe progress would
gain the fast track again when excitement over the latest "toy" wanes,
computers are taken for granted, and the search for novelty leads back to
the ever-fertile fields of analog devices. I weary of the "Digital Age"
media-hype already, I'll announce (perhaps prematurely) the dawn of, what
else, the "Post-Digital Age."

We also must keep in mind, that meaning arises from the movements of the
body as it functionally couples with others against the background of the
external environment. What forms of bodies uploads will inhabit, will
determine what meanings will arise within them. Certainly human meanings
will not arise or be sustained in non-human bodies.

Omega wrote 2/1/97 in "Von Neumann's Mistake": <With this comes an
understanding that a generalized math capable of reconciling all the
Fourier spaces within reality is going to require a system that combines
continuous differential equations with fractals and other forms of discrete
math into a seamless whole.>

Such a system would include difference equations, among other forms of
discrete math, and would require quite novel philosophical underpinnings to
seamlessly conjoin them all. Metaphysically, we would do well to jettison
the assumption that the universe is isotropic, assume that the Planck and
gravitational constants are only locally constant (if not downright
variable), and develop a physical explanation that would shore up the
legitimacy of Einstein's assumption of a constant light speed. Scientific
statements we make about reality should be radically local in their scope,
not universal, in keeping with the metaphysical presupposition of discrete
Fourier spaces with analog connections across boundaries.

Reilly Jones | Philosophy of Technology: | The rational, moral and political relations
| between 'How we create' and 'Why we create'