Math, Archetypes, etc. (was Venus, etc.)

Reilly Jones (
Fri, 31 Jan 1997 05:14:18 -0500

Omega wrote 1/30/97: <The problem with archetypes is that they can not be
approached rationally, because each system of archetypes will define
its own mutually incompatible logic, thus we have what we call dogma,
political correctness, ideological purity, holy wars, witch hunts...>

There is anecdotal evidence for this if one chooses the anecdotes carefully
to fit the theory. In reality, if archetypes are turned towards truth,
then even though they may be approaching truth from all directions, there
will be at least *some* compatible logic at the borders of the meanings of
the archetypes. If, on the other hand, archetypes are turned away from
truth, then "each system of archetypes will define its own mutually
incompatible logic." Systems of archetypes that are turned away from truth
can still have the appearance of rationality to those who subscribe to
coherence theories of truth (the Quinian stance), though not the reality of
rationality. Systems of archetypes that are turned towards the truth, even
if only striking a tangentially glancing blow, will contain a shred of
potentially discoverable rationality, at least to those who subscribe to
correspondence theories of truth (the Kantian stance).

<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.>

I would like to point out that this technique was in the "philosophical
air" at the time of Feynman's early productive years, not to take anything
away from Feynman's accomplishments at all, but to show the connection
between *what* he thought and *how* he thought, specifically his ideas
about summing-over-the-histories that eventually made QED so successful. I
got the following quoted material from "Analytic Philosophy" Ed. Barry
Gross (1970):

>From Leibniz's "Monadology", Bertrand Russell took the idea of each mind
viewing the world from a unique perspective at any given moment. "Each
observer has a space private to him in which all his sense data appear and
the totality of these data at any time make up the perspective. The
history of all perspectives of such an observer is just the history of
certain of his mental functionings. On the other hand, the thing or object
in the world is a bundle of all the events which consist of the various
appearances of it ­ the sum of all its actual and possible appearances.
The table, or physical object, is now defined as the class or system of all
the possible perspectives of it. The appearances are not in the object nor
are they parts of its surface. Rather, what we call the object is the sum
of all its possible and actual appearances."

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

"Russell postulates a single space in which all the points of view or
perspectives are themselves located. There are many actual private spaces,
an infinite number of possible ones, but only one public space or
perspective space which contains them all."

"Only one perspective space" is the same idea as the space-time point
common to all events referred to in other recent posts, published the year
before Einstein's "General Relativity."

<...the incompleteness of one coordinate space for defining in a simple
form all possible localizations and correlations that can exist within
mathematical reality. In math these are the spaces that are defined by the
myriad Fourier waveform families.... [T]he brain is well known to be
loaded with data patterns that have been through Fourier transforms
(leading to the periodic talk about "holographic" memory/processing).
However when we add in the intracellular microtubules which operate in the
low GHz range, everything falls into place now as we now find integrated
together in the wetware of the brain, the necessary structures for working
in two conjugate waveform spaces; exactly what we would suspect would be
needed for a cognitive device that operates within a generalized set of
Fourier spaces.>

Between your Fourier spaces description above, and your later use of
"memes" (which I'm skeptical of), I believe I recognize what I refer to as
"conceptual attractors," or something closely related to it. We're in
neighboring Fourier spaces looking at a similar problem set, is how I
believe you would put it.

I am not sure how generalized the set of Fourier spaces is that we operate
within. Evolutionarily, we should expect that the overall set should not
be very large, because we haven't been subjected to an excessively mutable
environment in our brief history.

J.A. Scott Kelso, in "Dynamic Patterns: The Self-Organization of Brain and
Behavior" (1995) reported on using SQUID arrays to capture spatial patterns
of brain activity and then applied a decomposition technique (the
Karhunen-Loève (KL) expansion) to model how these evolved in time. "The
idea is to see whether an essentially infinite-dimensional system, the
human brain with around 100 billion neurons and 60 trillion synapses,
exhibits a small (or at least restricted) set of time-varying global modes.
The patterns or modes of brain activity are spatially coherent, but their
temporal evolution is complex. By modeling switching dynamics and its
multistability, this theory connects brain events (internal behavior) to
behavioral events (overt behavior).... the waxing and waning of modes is a
result of nonlinear coupling between the outside world and the internal
spatial modes of the brain. One can see... that at least seven coherent
spatial modes are present in the brain, the contributions of which may vary
dynamically according to the kinds of tasks people (and brains) have to
perform. It's tempting to speculate that each of us is born with a brain
that operates globally in a relatively small set of basic modes whose
contributions vary with life's trials and tribulations."

Only seven sets! The tests are only beginning, but I would be very
surprised if we turn out to be operating in many diverse patterns, our
environment does not present us with utter chaos, rather with temporally
stable packages of constraints.

<This is next leads us into the problem of "archetypal rationality". For
small problems, holding a few dozen Fourier spaces in ones head simultan-
eously, and picking an answer from some suitably localized one is no big
deal, but as the problems get larger and larger, our ability to hold simul-
taneous viewpoints decreases accordingly.>

This is quite an apt description of how my thought processes work, I have
this huge ball of working concepts gyrating throughout many frameworks of
structured dormant concepts, performing inter-Fourier-spatial translations
and intra-Fourier-spatial recognitions. The problem sets in play at any
one time dictate the viscosity and diffusion of the working concepts
throughout the whole mess.

Technically, it is not the case that "as the problem sets get larger and
larger, our ability to hold simultaneous viewpoints decreases," it is the
old uncertainty principle at work, or the depth vs. breadth nonsimultaneity
principle. No brain, no matter what its capacity, can escape the physical
constraints (really the linear temporal constraint) of what David Gelernter
referred to as the "spectrum of focus," that sliding scale of attention
from high-focus analytic to mid-focus emotional to low-focus associative
imagination. Any thought, no matter how potent the intelligence is, will
land at only one point on this attention scale at any moment in time. A
superintelligence that could plunge to an incredible analytical depth of a
problem would be a high-falutin' geek; that could spread to an incredible
imaginative breadth of a problem would be a hepped-up mystic.

<Along this line, brain plasticity may well function by simply reinforcing
certain Fourier spaces at the expense of the general set.>

I think you mean just the opposite of this, brain plasticity, which is at
maximum levels in utero and in infancy, is more closely related to the
general set. The process of reinforcing certain spaces describes not brain
plasticity, but brain sludge. Evolutionarily, brain sludge enhances the
potential for preservation if the environment is not changing too rapidly,
brain plasticity is preferable only in chaotic environments.

<Each Fourier space has, quite simply, its own logic.>

This is an important consideration, the nature of knowledge systems,
including scientific knowledge, is radically local. It's why physicists
should never become biologists, or worse yet, neuroscientists. It's why
mixing computer and human metaphors is so cludgy. However, we must be very
careful not to fall into compost-modern relativism and get lost in pure
coherency theories of truth. We must be aware that each Fourier space will
be turned towards or away from truth, that not all Fourier spaces are
created equal with respect to their utility for our preservation.

To help show what I mean, by expanding into a few other Fourier spaces, I
would like to start with the example from above about the preferred seven
coherent brain activity spatial patterns. Then, a couple examples about
preferred protein folding pathways and preferred protein design pathways.

>From "Science" 2 August, 1996: 595-602. Holm, Lisa & Sander, Chris.
"Mapping the Protein Universe":

"Conceptually, each protein structure may be imagined as a point in an
abstract, high-dimensional fold space. At close range in this fold space,
clusters represent protein families related through strong functional
constraints... At intermediate range, clusters are related by shape
similarity that does not necessarily reflect similarity of biological
function. At long range, the overall distribution of folds is dominated by
five densely populated regions, which we call attractors. [W]e put forward
the hypothesis that these attractors represent both dominant folding
pathways and evolutionary sinks that are the result of physical
constraints. Selective pressure in evolution from random or partially
random sequences would be more likely to result in specifically folded
stable structures in one of these regions."

Only five preferred protein foldability regions here. The next example is
from the same issue of "Science" pg. 610. Kardar, Mehran. "Which Came
First, Protein Sequence or Structure?":

"Whereas 'foldability' focuses on the [amino acid] sequence, selecting
potentially functional ones... 'designability,'... is based on the
structure of resulting protein. This concept is quantified by measuring
the number of sequences that uniquely fold into a particular structure
(foldability is thus implicitly included). A great technical achievement
of these authors is that they are able, for the first time, to compute the
energies of all 103,346 structures, for all 2^27 possible sequences of
27-mers.... Some structures are not designable as they do not correspond
to the ground state of any sequence; the best structure is obtained from
3794 sequences. Several interesting patterns emerge from the enumeration.
(i) At the tail of the distribution, there are structures that are highly
designable: the number of sequences that fold into them is much greater
than expected from simple probability distributions. (ii) These structures
have, on average, a larger gap to their first excited state, making them
thermodynamically more stable. (iii) The well-designed structures are
also more robust against simple changes in the sequence (random mutations).
Thus, a major claim... is that the designability principle unites several
properties (thermodynamic stability and mutational plasticity) occurring in
real proteins."

Here we have only a few thousand preferred protein designs out of over a
hundred thousand possible. Also, the linkage of stability and plasticity
at the protein level is exactly analogous to the depth vs. breadth
situation in the cognitive focus of attention. Finally a short example of
preferred evolutionary pathways from Stuart Kauffman's "Origins of Order"
(1993): "Whether one is comfortable with the idea or not, the existence of
preferred 'directions' of alteration of developmental pathways implies
something like 'orthogenesis' ­ a tendency of evolution to occur in
preferred directions not because of selection constraints but because the
underlying system has preferred directions of change in the face of
*random* mutations."

<...the frequency component of this generalized Fourier processor is not
limited to the brain, but exists in all eukaryotic cells, thus easily
spilling over into the rest of the body (and possibly beyond the body).>

This would be helpful in explaining the increasingly well documented
cognitive experience of tacit knowledge and implicit perception.

<We may yet find that building efficient AI and upload capable devices
requires the use of at least some "wetware" as this meat in our bodies is

If each Fourier space is discrete, then the boundaries between them must be
analog for jumping to occur. Thus, I would agree with you that an upload
capable device must be a mix of digital and analog computers, most probably
in roughly the estimated 20% digital-80% analog mix of neurochemical
interactions we currently possess. Perhaps it is four times more
evolutionarily important to jump boundaries than it is to settle into a
Fourier space. Perhaps each Fourier space is at minimum a tetrahedron with
four faces. Who knows? Maybe Bucky Fuller had a few useful guesses at
what is going on, the shotgun approach is not a bad one when trying to hit
large, amorphous objects. As he monotonously said "Angle and frequency
modulation exclusively define all experiences."

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