Dear List,
I ended my last note highlighting that Bits are strongly local and their
organization is arbitrary.
The “word” in my last post is the binary word, such as “1010” and not “THIS.”
The latter is more complex than the former, although they both depend upon an
arbitrary organization.
It may not seem that way to you but this is merely because we are familiar with
conventions that enable us to apprehend, to perceive or “feel,” a particular
organization. An 8bit or a 64bit word is equally arbitrary and has little
locality, except that which is useful for engineering, not science.
On BIT Locality
So a weaker view of Bit Locality concerns the width of organization and,
necessarily because we are dealing with Bits, the step-wise nature of their
transformation.
But let me point out that stated at its most dramatic nothing varies, the world
can be said to transforms. It moves from one distinct state to another. But
there is no “returning” to a prior state, there can be no variable state. These
are simply ways to speak about the world.
Clearly we can dig a hole in the ground and place a stone in it. Between us we
may call this hole a “Bit.” We may agree that when there is a stone in the hole
its value is 1 and when there is no stone its value is 0. We may dig a second
hole at your house and we can do the same. We can agree to combine the two such
that were a stone in each hole the value can be said to be “11” and when not
the value can be said to be “00.” We may also speak about the value “10.” To
increase our confidence, perhaps, we may pay a grandchild to stand by the hole
and shout out whether or not there is a stone in the hole.
By this means we may eventually build a computing system, grandchildren
shattered all over the neighborhood. But this organization has little locality,
it does not “scale,” and it is not sustainable. Children tire, holes eventually
fill and stones break.
And, this is especially challenging, each time a stone is placed in the hole it
is not, in fact, the same stone nor is it the same hole. Even though this will
not be how it will seem to our grandchildren. The reuse of the stone and the
hole is itself an arbitrary pragmatic.
Automated information processing varies from this scenario only as a matter of
degree. Reducing the problem to microelectronics enables us to put the machine
into our pocket but it does not change the locality question nor does it make
the states the same.
Every state is, in fact, new. The illusion that it is otherwise is transitory.
Now, obviously, engineers make best efforts to give us the impression that
things are other than this. And, of course, I understand that for practical
purposes we take the organization of machines to maintain repeatable states for
practical purposes. Indeed, we depend upon this fragile pragmatism.
The illusion is so pervasive that we call our time the Digital Age and we
attempt to explain everything in terms of illusory Bits. We are enamored.
On Step-wise Functions
At the core of the Bit issue is a dualism that extends back to the start of the
twentieth century. It is the dualism of “This” and “That,” “True” and “False.”
It was brought to us largely by Bertrand Russell, his advocacy of Logicism and
his celebrated authorship of the Principia Mathematica.
Gödel showed us in 1931 that this system is necessarily inconsistent and even
that the foundations of arithmetic based upon well considered but none-the-less
arbitrary axioms, like those of Peano, could express no truth.
I argue that the conventional axiomatic method is not well grounded and must be
replaced by one that has greater rigor. I suggest one that is explicitly
structuralist and covariant.
It has to be admitted, of course, that despite these problems we have achieved
remarkable success. But, again, we must shake off our love of this success in
order to see how things are.
Adoption of dualistic and strong bit-wise locality, arbitrary organization, and
step-wise functions (due to Alan Turing and Alonzo Church) define the effective
methods of modern computing. We have also finally accepted that the parallel
processing of large-scale data is required. But this acceptance does not help
us if we we are merely back to where I started 30 years ago.
In fact, step-wise functions are deeply flawed. The result of a step-wise
function is entirely unrelated to its former or subsequent value. In addition,
the parallel execution of such a function suffers the long known problems of
parallelism. Structure is hidden from such functions and is present only as a
matter of fait or deception and must be enforced or imposed by engineering or
mathematical artifice.
I can hear many software engineers and applied mathematicians crying out in
rebellion that this simply cannot be the case, but it is an imposition upon
their minds that is involved and the truth of the matter has likely never
occurred to them.
Holomorphism and at once “Functors”
I distinguish "step-wise functions” from “holomorphic functors.”
True Holomorphism (a continuous and whole dynamic structure) is simply
impossible for a computing machine to simulate.
The "at once” geometric transformation of a structure may only be simulated by
very fast machines using great electrical power burning and time consuming
step-wise functions for only small cases - or many such small cases. We can and
do fool ourselves into believing the magic by pointing at the movie or the game
screen.
But it is all artifice, a sham of Moore’s law, timing, and the miracle of
theatre.
There are important differences in the power profile of computing machines and
biology, two important differences that despite the clever short cuts and
mechanisms identified by Shannon and others demand that we accept that Turing
computation, in all of its forms (including neural networks), is excluded from
biophysics.
These are the low power requirements of biology and the absence of hotspots.
Hotspots occur in computing systems because of locality in their operation.
There appears to be no such “hotspot" locality in biology.
Alan Turing dismissed this lack of locality in his famous paper concerning
Computing Machines And Intelligence.
"I do not wish to give the impression that I think there is no mystery
about consciousness. There is, for instance, something of a paradox connected
with any attempt to localise it. But I do not think these mysteries necessarily
need to be solved before we can answer the question with which we are concerned
in this paper.” Alan Turing, 1950.
By dismissing locality Turing excludes a role for biophysical sensation, what
he calls “consciousness," in his mechanics. Of course, his paper concerned the
vague notion of “intelligence” and this really is a separate question to that
of sense.
But I believe that if we are to build truly intelligent machines, machines with
the strength of the uniquely human skill set - admittedly shrinking since the
time of Turing, I am thinking of the things that are truly unique: easy general
recognition, self-maintenance, reproduction and creativity, not chess,
arithmetic etc… - then we must find a role for sensation, feeling or
“experience” in our physical mechanics.
I make a pragmatic argument that Turing computation is necessarily excluded
from biophysics that runs along the following lines: The human brain dissipates
15Joules of power per second in a profile that is quite extraordinary. The
power dissipation is uniform across the brain to within 1degree everywhere.
There are no hotspots. Neurons and astrocytes work together to change blood
flow, they change the brain’s structure.
It has been widely predicted, although there is now a great deal of push back
from the neuroscience community, that the human brain can be simulated in a
machine with 10^18 operations (of some kind), the fabled “Exascale” machine.
Let us ignore the architecture of such a machine, and the hotspots, and simply
consider the numbers. If a brain possessed this much computing power it would
require 94eV per operation. Although estimates vary widely, projections for the
Exascale machine, with designs that are close to physical limits, are
60MegaWatts, a reasonably sized power station sufficient to power a moderately
sized city.
Biology has the locality problem solved, the Exascale machine does not. Plus
biology has the advantage of being able to function effectively on a couple of
burritos and a few cups of coffee per day.
Allosteric Conformance
The absence of locality in biophysics, generally refers to the variety of
biophysical conformances called Allostery. This is defined as "a fundamental
process by which ligand binding to a protein alters its activity at a distant
site.”
The truth is that biophysicists are still mystified by this effect, despite
putting their best foot forward to provide an explanation is conventional
terms. See, for example, the latest edition of Essential Cell Biology, 4th
Edition.
This absence of locality in biology defies Information Theory. If, however, we
listen to Brit Cruise closely we discover that he makes many assumptions
concerning locality despite the fact that he mentions the Bit as the foundation
of information theory. He fails, as do most information theory presentations,
to mention locality and existent structure as a consideration.
We speak about data structure, certainly, but data structure is not an
existential structure. Its various implementations are no less arbitrary than
the word.
If I confront a Tiger alone on the path I feel the entire experience at once
across my physical structure. My apprehension is bound intimately with my
responses. There is no time for reasoned thinking. I stand or run as one
entity, fully coordinated, no part of me is standing still while the rest of me
is running. This is not merely a matter of software, it is one of structure.
At the end of the day only holomorphic functors can describe biophysical sense
and actions, allosteric conformances, and it is only the binding of these as
hyperfunctors that they can describe my sense and response at all scales.
Shapes and Shaping
At its simplest, information in biophysics involves shapes and shaping. These
shapes are cell receptors and motor functions, changed and bound by genetic
mechanics in flexible closed structures (cells and membranes). We can describe
these shapes at all levels of the organism with dynamic holomorphic functors.
These describe the shapes upon the surface of cells, be they receptor clusters
or motor functions.
These are sensitized by a necessary new basis. A universal that is across all
flexible closed structure and is responsible for the associated range of
sensation, allosteric shaping and coordination across these structures.
I have one more piece to add, expanding information science into its proper
domain.
My apologies for the delay between posts. I am still in recovery and in
addition to the problems with the FIS server last week my Thyroid crashed (the
consequence of radiation treatment last year) leaving me feeling pretty ill.
Regards,
Steven
--
Dr. Steven Ericsson-Zenith, Los Gatos, California. +1-650-308-8611
http://iase.info
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