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November 22, 2010
Revised: December 17, 2013
Notes on Programming Neural Systems

Nataraja, dispeller of Darkness
Fill my mind with your veil of Light

A Personal Note

I've been blessed to have learned physics from Satosi Watanabe. I heard he had studied as a student under Werner Heisenberg doing research on nuclear statistical mechanics. I was fortunate enough to have attended his classes on statistical mechanics and quantum theory. He used the text book on quantum theory written by David Bohm in his class. The first day of his lecture on quantum theory he spoke about wave packets and pilot waves.

I remember one sunny day when he was sitting on the lawn on campus. I was 18 years old, filled with my own ideas on particle physics, so I told him all about it. He always smiled, and graciously told me to write it up. I never wrote anything, and since then never remembered anything about the theory I talked with him about. But I always remember his smiles.

In 1985, he published a book [1] on pattern recognition in which he wrote:

... emphasize the fact that the interval between two spikes is a continuous variable, hence the all-or-nothing theory (i.e., the characterization of a neuron by a binary variable) is inadequate.

Nature is too efficient to waste information in the spikes produced by the neurons. Every bit of matter or energy created by the neuron will be used intelligently for the purposes of relaying information to other neurons. This is a statement of faith. So how do we analyze this. How far down do we go?

I remember Satosi Watanabe's lectures on entropy, where he explained that attributes of entropy is essentially information. Statistical mechanics rules the universe. So information is embedded in energy. Abstracted physical energy has an infinite (a word humans can't really understand) array of properties, but fortunately the idea (or the mess) can be be simplified in a nice little equation. Note that information is not the same as energy. Information exists inside the energy's distinct states. An energy system with a few states means information must be dispersed.

The idea is that dynamical energy, in the unfolding of physical processes, is constrained by an exponential suppression in the number of physical states available to this particular system in the instance of time before it makes its state transitions. The energy states of a physical system viewed at statistically will tend to settle into fewer states in time. The information will be dispersed among these fewer states. Entropy also gives a direction to the flow of time. It's in the statistical laws of the universe to diminish the complexity or number of "information states" in localize matter by dispersing it. I do not know why this is so [2], but this is one of the basic laws of the universe.

But Nature is really divine. Although the entropy equation says the rate of change of order is limited (localize, closed system, micro-entropy always increases), fundamental forces in Nature get order to increase (forces, open to energy, global macro-entropy over a long period of time decreases). Why this is so seems like a paradox; subtle and beautiful, only what the seemingly divine would do.

Physical systems are forced into higher complexity states all the time, that is, entropy decreases [3], and information is congealed. Forces in Nature like gravitational energy reshapes the atoms, planets and galaxies. Einstein would say that gravitational forces are caused by space-time itself. The atoms like silver and gold are created inside the core of stars because Nature (as described by the law of entropy) has eliminated certain states where energy could propagate. The law of entropy works inside of stars and black holes. It is this seemingly divine paradox that leads to complexity.

Inside the core of stars, the energy density is extremely high, but information states must be moderated by entropy. A rise in energy does not mean a proportional rise in information. Although the energy is great inside of stars, the law of entropy says that the number of states cannot be proportionally as high. The creation of states is suppressed by the law of entropy. So inside of stars there are essentially only states of high energy matter. The complex atoms like gold that's created in stars is a consequence of this.

The electron is small in mass or energy compared to a proton which are attributes of atoms. I think of the elementary particles inside the atom as attributes of the atom, that is, an atom is a whole unit. The electron is much harder to isolate than the proton because it has so little energy. If you're trying to measure the electron around the atom, it would be dispersed in a relatively wide area around the center occupied by the proton. A stationary outer electron of the atom (in quantum mechanics this means a coherent electron with nearly zero energy) could be dispersed over an enormously wide area orders of magnitude away from the center (in the atomic world it's better to give really rough descriptions if you cannot make an exact measurement). Whenever you move away from the center of energy, complexity falls and uncertainty increases. This is another consequence of entropy, information and the uncertainty principle.

For awhile, I carried around a book [4] written by David Bohm. In the beginning of this book, chapter 1 on Fragmentation and Wholeness, he wrote:

The new form of insight can perhaps best be called Undivided Wholeness in Flowing Movement. This view implies that flow is, in some sense, prior to that of the 'things' than can be seen to form and dissolve in this flow. One can perhaps illustrate what is meant here by considering the 'stream of consciousness'. This flux of awareness is not precisely definable, and yet it is evidently prior to the definable forms of thoughts and ideas which can be seen to form and dissolve in the flux, like ripples, waves and vortices in a flowing stream.

I think that what David Bohm is talking about is the current of energy flowing in our neural circuits. It's the energy which gives rise to our thoughts and creates our consciousness. The source of this order from which this flowing movement arises is what the ancient Hindus would call Dharma. David Bohm's "flowing stream" is the what the Hindu sage Ramana Maharshi calls "The Self".

So we end here focused on our thoughts. It's the only possibility. If you wanted to stretch this, like I do, then you could say that the Hindu ascetics were right, and that nature's gift to each of us is our consciousness. If there were no dynamic movement, there would be no thoughts. My first impression on reading "Wholeness and the Implicate Order" is Bohm's words about movement as the essence of being. "Movement" is transformation and metamorphosis, and a constant theme throughout his book.

In his introduction David Bohm wrote:

Such harmony is seen to be possible only if the world view itself takes part in an unending process of development, evolution, and unfoldment, which fits as part of the universal process that is the ground of all existence.

This is my personal note. It's the ideas that has keep me doing this and like Satosi Watanabe used to say always with a smile: "It is a quest!"

Kali Ma, goddess of change and time
Mother of the universe
I fear the stillness, and the cold
I fear the chaos, and the fire
Move me along, when I'm beyond time.


1. Satosi Watanabe, Pattern Recognition: Human and Mechanical, 1985., p. 470

2. Understanding the language of statistical mechanics takes awhile. Entropy is a measure of the order in a physical system. It is the only general law of we have of Nature that explicitly constraints the propagation or transition of a system's energy states as a function of time. Entropy exists to put very broad limitations on what is possible. But it does this in a subtle way which requires deep thinking. For example, the law of entropy does not tell us if there is a limit to the amount of order which is being created or destroyed. We essentially know from the mathematical formulas for entropy, that it describes the rate of change in the order of things, but not absolute quantities.

3. Think of entropy increase as a rise in disorder, or decrease in complexity or information. But if you transfer energy into a system, then entropy will decrease, and the complexity or information will rise. Erwin Schrodinger spoke about negative entropy while referring to biological systems in which he meant that order or complexity in a system was increasing. Some people called this "negative entropy." It's negative because positive entropy originally meant an increase in disorder. Very confusing at first, in fact, it still confuses me sometimes.

4. David Bohm, Wholeness and The Implicate Order, 1980.