The Ring that Binds and Grinds


“There is geometry in the humming of the strings,
there is music in the spacing of the spheres.”


Grind and Crack the Dirac,

Paul Dirac and Richard Feynman



“So I tried to find what the observables had to be in order to manifest this “information”. The shock was in discovering that the families of observables I characterized in that way could not contain anything which behaved like a Hamiltonian. And, of course, without a Hamiltonian, you cannot even get started in doing traditional Quantum Mechanics. In a sense, what I then showed was that Quantum Theory and Quantum Mechanics do not coincide, and that the former was much bigger than the latter.” — Robert Rosen (AUTOBIOGRAPHICAL REMINISCENCES)



“It seems clear that the present quantum mechanics is not in its final form” — Paul Dirac

Beach and Leech the Landau

Leech Lattice and Global Dynamic Networks

I was brought up in an interesting time, in the 1950’s and 60’s. Not that I mean this was socially interesting (e.g., Post World War II social ferment of young people), nor politically interesting (e.g., the protests of the sixties), but rather it was scientifically interesting transition from the Analog (0.000 – 1.000) of radios and TVs  to the Digital (0 or 1) of computers.


I went from a slide rule, superheterodyne circuits, calculus, and cybernetic world to an information bit, digital circuit design, and computer world.

Initially I thought that the intersection of those two world views (Weltanschuung) would be where I could make my name: stake my intellectual claim. But I was wrong. Most of my career was in that new world, the world of the Robots and Internet: on the bleeding edge wave of the “digital revolution”.

But I have come back to that intersection.what_is_information_and_figuring_out

The combination of Science, Mathematics, and Information Science in a systemic way.



Exposed Leach Field


Evolution of Evolution

The Edge of Chaos

The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA) [Finite state machines]. As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept..

Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics have shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.

“Nobody understands Quantum Mechanics” — Richard Feynman

Particle physicists have a simple notion (ala Susskind, d’Hooft, and Hawking) of Information; that is, Shannon information.

“Everything should be made as simple as possible, but not simpler.” — Albert Einstein

“This brings up an interesting question: Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with the positive sign? We apologize for the fact that we cannot give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. He has shown that the two must necessarily go together, but we have not been able to find a way of reproducing his arguments on an elementary level. It appears to be one of the few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation. The explanation is deep down in relativistic quantum mechanics. This probably means that we do not have a complete understanding of the fundamental principle involved. For the moment, you will just have to take it as one of the rules of the world.…The principle seems so simple… I cannot help you, we understand it more mathematically than physically… Richard Feynman [Lectures in Physics]

“If you don’t understand something said, don’t assume you are at fault.”
 — David West Keirsey


In the Lost and Found of Mathematics and “Information” Theory

There has been a lot of progress in Information and Computer Science that can now be used to further understanding in relating discoveries in cosmology and particle physics. Adding some Discrete Mathematics (in the form of Group Theory and Number Theory, for example) that has been developed in the later part of the 20th century, a relational complexity approach can be effective in making a meaningful correspondence between physical concepts and information [and mathematical] concepts.

However, the entrenched paradigm of using differential, integral, and tensor calculus to approximating or/and correlating to particle physics concepts needs to step aside, so Formatics can try to pass them by. Abandon the Shannon. Embrace the Hamming and Golay

“We can’t solve problems by using the same kind of thinking we used when we created them.” — Albert Einstein

“Now Moufang it and Emmy ring it twoMake Lise Bind. Oh, Dedekind bother, it’s a unReal hard cut.”


Dynamic information bubbles, within dynamic information bubbles, within …


The Non-Abelian Simple Finite Sporadic Groups


2D Dynamic Symmetry and Asymmetry

180 degree dynamic symmetry demo, Courtesy of the Mathologer

What is the nature of Spin?  What are the kinds of Spin?  Isospin?  What is the meaning of Quantum Spin Up? Quantum Spin Down?


Beach and Leach the Ort

Ultima Thule in the Ort Cloud

Golay and Hamming the Hawking


to be continued… and added to

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