(18-Sep-94 MST)
Hi Richard!

The previous letter you sent is sidetracked. Patty gave it to a mutual
friend to route to me and I still haven't been able to get my hands on it.
Attempts to reach you via internet have been bouncing and there's been
a lot of unwelcome interpersonal and material distress impinging on me
for the last few months.

Its funny how we seem to be thinking about the same classes of ideas
much of the time even when out of contact. Modular hierarchies were
much on my mind (pun not intended, but acknowledged) a few weeks
ago when I was reading Minksy's "The Society of Mind". I've also
been thinking about non-hierarchical models for government and reality.
Heterarchy is a fairly powerful term that may become increasingly trendy,
and I coin the term `reticulocracy' to describe non-heirarchical forms of
social organization.

The idea that reality is modular seems a slight mis-statement.
What appear to be modularly hierarchical are models of reality.
If one substitutes model for the term reality your exposition makes
a lot of sense to me.

A few days ago I was thinking about the nature of mathematics... how
different, apparently unrelated fields within mathematics are frequently
fused together in astonishing ways by new theorems. These often resemble
weird inferential puns. The best example i can think of is Euler's Formula,
which unifies trigonometry, complex numbers, and calculus.

                      cos(theta)= e^(i*Pi*theta)

Another thought catalyzed by your letter is that heirarchies may not be
the best term for the this process of progressive integration. Even though
existing models can be seen as subsets of new, broader models (your
example of newtonian mechanics being a subset of general relativity
is a really good one: Kepler's orbital model can be derived from
Newton's gravitational formula. Newton's model can be derived from
General Relativity - previous modules become special cases of the
newer model, derived by setting the novel variables introduced by
the more inclusive models to zero or one.)

The idea of hierarchy may not be applicable to situations that
Douglas Hofstadter labels "Strange Loops". These are circular structures
in which feedback exists, and which frequently lead to inferential
oscillations. There is nothing that prevents such structures from being
constructed, either in meme-space or in physical/neural reality. In fact,
much of the brain and the electronic design depend on such circular
feedback loops.

One of the early cyberneticists, Warren McCulloch, in his book
`Embodiments of Mind' (chapter: "On the Topology of Neural Nets")
shows an interesting example of a non-hierarchical
form of logic: The children's game "rock/paper/scizzors".
In this sort of circular hierarchy (is that an oxymoron?)
a>b and b>c and c>a. This violates transitivity. The transitive rule
is that if a>b and b>c then a>c. McCulloch goes on to demonstrate
that intransitive logic cannot be modelled by a two-dimensional
neural network. The smallest neural network that can model intransitive
relationships maps onto a donut.

Godels' Proof is a mathematical proof that demonstrates that any
non-trivial system of logical inference (that is, one capable of expressing
arithmetic) is either incomplete or inconsistent. The upshot of this
is that there is no such thing as ultimate truth. A system can not be
closed and consistent at the same time. If the system is consisten you can
always construct a paradox or a true statement that cannot be proven
true within that system - it is not closed. If the system is closed
you can always construct a paradox - it is inconsistent. This strongly
resembles the physical models of the electron proposed by Heisenberg
and Shroedinger - knowledge of an electron's position and momentum
are mutually exclusive.

Another interesting model/metaphor from physics is David Bohm's implicate
order. There are certain high-energy plasmas that are describable by
a single wave-function. The upshot is that a plasma of fundamental particles
behaves as though it were a single particle, as though the particles
were communicating instantaneously - faster than the speed of light.

This kind of single-wave-function integration seems non-hierarchical
to me, and it also resembles the process of inferential fusion or
meme-integration, or meta-modelling, or modular hierarchy that you
mention.

Thanks again for pursuing our dialog.
                                      -Mark



----------MISCELLANEOUS NOTES----------------------------------------
----RE: Modular/Hierarchical Reality----

Gregory Bateson - "Steps toward an Ecology of Mind"

Bateson proposes a learning model. (this seems to be, in away, an
extension of Bertrand Russel & Whitehead's theory of logical types.
In order to resolve a paradox, you have to move to a more-inclusive
system of logic. Russel also suggests that paradoxes are a form
of fallacy that comes from applying operators or framing questions
about propositions of one logical type in terms of a higher or lower
logical type. The classic example from Whitehead&Russels' Principia 
Mathematica is: "Is the set of all sets that are not subsets of themselves
a member of itself?")

 Learning 1
  acquiring facts and skills.
  rote learning.
  imitation.

 Learning 2
  learning how to learn.
  strategy acquisition.

 Learning 3
  learning new models of reality.
  transcendental experiences.
  resolution of deep crises.
------------
Douglas Hofstadter: "Godel, Escher & Bach - the eternal golden braid"
Douglas Hofstadter: ""

Discusses various wiggy notions of nested and infinite hierarchies,
recursion, etc. Pretty rewarding in the meme-mining department.
Hofstadter took over the Mathematical Games column of Scientific American
for a while, renaming it "Metamagical Themas".
---
Marvin Minsky: A Society of Mind.

This is a somewhat reductionist approach to intelligence and artificial
intelligence full of really useful and meaty ideas about interacting
hierarchies of agents that may compose and be intrinstic to the structure
of minds, models of reality, and the processes of intelligence. 

-----------------------RE: Flannigan Neurophone---------------------------
"Would the Buddha Wear a Walkman?"
compendium of trendy mind machines, consciousness altering technologies
and various wacky and useful stuff. Fairly recent, paperback, still in print.
I think this book may have a schematic of the Flannigan Neurophone.
I had a copy of the coversheet of the patent somewhere, but can't find it.
It used copper wool inside of plastic bags as electrodes, and used
a high-volatage RF carrier wave modulated by an audio signal.
One electrode was placed on the foot, the other on the temple.
Flannigan claims that this device allows people with inner ear
damage rendering them physically incapable of hearing any acoustic signal
to hear speech and other sound signals.
---
There are confirmed cases of human radar technicians and rats being able
to hear microwave pulses. Apparently this is due to thermal-acoustic
events inside the ear. Imagine the juices, tissues or bones in your
head expanding briefly when they are heated by a pulse from a microwave oven.
---
A related phenomenon is that some people claim they can hear a crackling
sound from meteorites. This can't possibly be due to acoustic sound waves
as the phenomenon occurs simultaneously with the meteor streak. It would
take more than a minute for high-altitude sound waves to reach a listener.
I have experienced this phenomenon once, as a boy scout, and it does seem
impossible. I recall reading somewhere that this may also be due to
electromagnetic phenomena triggered by a passing meteor in the ionosphere.
-----------