Conway’s Mesh of Life

I saw him there as he sat, with his classic slightly bemused grin before his lecture.  I had never got a book autographed, until then. I am not easily enamored by fame, scientific or any other knowledge or skill domain. But I powered through my natural enryo, for I had brought his book with me intending to get him to sign it. I thought his book as one key to unlocking an important question.

I have studied the contents of the book for years. And continue to revisit and re-cycle his ideas contained within.


To Subquotient, or Not Subquotient,
That is the question!

The divisor status, of the lattice, oh my, Times, Rudvalis.
Crack the Dirac, Landau beseech the damp Leech.
It’s a Monster Conway Mesh, Mathieu’s Stretch, Jacques’ Mess, Janko’s Sprains, and Einstein’s Strain…

He had given me a quizzical look, since my hair was graying and I didn’t say anything.  He said it was his “best book.”  I nodded and I didn’t say anything.  I am not a mathematician by training, and I was working on a slow idea, not ready for Prime time On the nature of the universe.

Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.
No Tegmark or Linde, but
Verlinde in name. It’s all but Feynman’s streams,
and weigh.

Such a Prime rank, any such Milnor’s exotic sank
No mess, no Stress, but Strain.
Tensors Bohm and bain

John Horton Conway, Inventor Rational, FRS (/ˈkɒnweɪ/; born 26 December 1937 – April 11, 2020) was an English mathematician active in the theory of finite groupsknot theory, number theory, combinatorial game theory and coding theory. He had also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway was Professor Emeritus of Mathematics at Princeton University.

He was the primary author of the ATLAS of Finite Groups giving properties of many finite simple groups. Working with his colleagues Robert Curtis and Simon P. Norton he constructed the first concrete representations of some of the Sporadic groups. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice, which have been designated the Conway groups. This work made him a key player in the successful classification of the finite simple groups, which is considered one of the greatest quests in mathematics.

Now that John has passed from the scene, his Game of Life has ended, a new requestion will be continued. Conway’s Monster Mesh needs to be fleshed out and explained in more simple and complex terms: 1) in in-form-ation terms, 2) in phys-ical terms, 3) in mathe-mat-ical terms, 4) in in-volut-ionally and en-volut-ionally terms. But also explained with these four towers of Babel — integrated.

My slow idea was to use as a Framework based on Conway’s work on Symmetry and the Sporadic Groups, but also other mathematicians and scientists.

Many mathematicians including Conway regard the Monster Group as a beautiful and still mysterious object. Since there is no “physical meaning” attached to mathematical concepts and percepts, these “conceptual ideas” in mathematics will continue to be “beautiful and mysterious” and ABSTRACT. However, one can be more systematic in the use of ideas. It is about that Relational Thing: not only about Conway, Dirac, Einstein, Newton, or Hawking ideas.

Life Itself

When looking both at the details and the overall Gestalt, patterns can be seen. It might be called Existence Itself More and Less, A Gain.

The 27 Sporadic Groups with corresponding
Physical Ansatz Concepts and Percepts
Gestalt Science

Gestalt Science related blogs: Gestalt ScienceReimaginingFeynmanThat Relational ThingThe Digital Sand ReckonerTowards Quantum FormaticsThe Ring that Binds and GrindsPrimeOn the Question of Learning WordsOne Ring that Binds Them AllThe FunctionalWithin the Edge of…

Inventor Rationals include: Feynman, Atul GawandeLarry PageElaine MorganLynn MargulisElon MuskSteve JobsJoseph James SylvesterFrances CrickPaul AllenWerner Von BraunWolfgang PauliAbraham LincolnMark TwainHedy LamarrJulius Sumner Miller, and Zhang Xin

Using Reasoning to Learn New/Old Words

“Only strong characters can resist the temptation of superficial analysis.”

Albert Einstein

Quantum mechanics, with its leap into statistics,
has been a mere palliative for our ignorance.

Rene Thom

When logic and proportion fall soggy dead,
and the white knight is talking backwards,
with the Red Queen is on her head,
Remember what the dormouse said:
Feed your head.
Feed your head!

We typically learn many words from context, rather than looking them up in a dictionary. Each person knows and uses many words which they cannot define exactly. Most of the words we know are not learned by someone telling us the definition. More typically, we learn words by extracting its meaning from context. The first encounter with a given word is usually not sufficient to gain any real understanding of the word.

Understanding can be achieved by comparing several examples. Each successive example can either augment understanding, confirm the understanding, or in some cases, uncover misunderstanding.

Learn, Unlearn, Learn

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

Wandering towards Scientific Enlightenment

Understanding can always be improved.

Problem comes when learning old fast ideas.

The trouble with specialists is that they tend to think in grooves
Elaine Morgan

In 1900, Max Planck had created a theoretical explanation of Wien’s formula on black body radiation. But in that process, experimentalists aware of Planck’s interest in the matter, had recently looked into the matter at longer wavelengths and higher temperatures, and told Planck that the infrared region at high energies violated Wien’s formula — so his original explanation was wrong. To quickly solve the problem, Planck added a “correction” to his analysis. A resulting derived formula proved to correct, no matter the increase in frequency (looking at a wider range of energies) and the improved accuracy of experimental results. Planck went back to his quickly modified analysis and reformulated his ideas to justify the semi-ad-hoc correction and found that it implied that energy was emitted or absorbed in discrete units based on Boltzmann’s combinatorics. He had solved a problem by simply creating a “chimera:” adding a factor in his equation — but he did not realize its consequent was as significant until he tried to justify his change theoretically. Even then, he did not consider it as profound, until Niels Bohr and others started to apply his new idea “a quantum action” to atoms and molecules. Another problem was there was a flaw in Planck’s reasoning for which Satyendra Bose corrected later, but the idea of quantum action has proved to be one of the two key and major ideas of physics in the 20th century.

Niels Bohr became very successful in applying Planck’s quantum action idea when examining the spectrum of the hydrogen atom. The failure of Rutherford’s simple analog “orbit” model, whereas the precise predictions of Bohr using Fraunhofer spectral lines, signaled the death of 19th century physics in the realm of small. However, for more complicated atoms, Bohr’s model wasn’t as accurate, so his original fast idea [quantum theory] needed modification or to be added to. The initial progress of the ideas: Einstein’s 1) lichtquanten, 2) special relativity, 3) general relativity; 4) Schrodinger’s recursive function equation; and 5) Dirac’s delta functional; petered out into the “particle and force zoo” ending up with the not very well understood statistical and probability based Standard Model of particle physics.

Wandering towards Scientific Enlightenment 2.0

Time, Space, Mass, Energy, Charge, Spin? What do these words mean?

Gestalt Science related blogs: Gestalt Science, Reimagining, Feynman, That Relational Thing, The Digital Sand Reckoner, Towards Quantum Formatics, The Ring that Binds and Grinds, Prime, On the Question of Learning Words, One Ring that Binds Them All, The Functional, Within the Edge of…

Gestalt Science

modeling_relationA Viking Reader

Fearless Asymmetry and Symmetry

order_chaos_particle_biform
Chaos to Order,                                 Order to Chaos

My father died on July 30th, 2013 and I intend to honor him, if I can, by writing a blog about him and the consequences of me integrating his ideas every year.  First year,  Second YearThird Year, Fourth YearFifth Year, Sixth Year. this is the Seventh Year.

keirsey_seaweedMy father, near the end of his life, considered himself the last Gestalt Psychologist. When I was very young I was fearful of kelp seaweed: my father showed me that it couldn’t hurt me, so I shouldn’t be afraid of it.   I learned from him. If you understand something, you can reason about it.   If you only have a correlation, you can’t be sure of the factors. He was never afraid to question conventional wisdom or the current fashionable and entrenched ideas (however old or fast those ideas were).

As a clinical school psychologist he was on the front line against invasion of chemical psychiatry into K-12 schools, and he saw how they used “their pseudo-scientific expertise [and argot]” to fool and trap kids and parents into approving the use of brain disabling drugs, within the “educational system” and with the implicit pressure and blessing (and relieving of responsibility) of the teachers and administrators.  He also didn’t buy into the dominant paradigms of the first half of 20th century of Freudian psychology and the correlational “blank slate” behaviorism of Watson and Skinner.

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

Throughout my discussions and debates with him in my lifetime, he talked about ideas.   We talked about philosophy, science, mathematics, computers, people, and life. 

to_explain_the_world_cover 

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More Moore

I don’t remember exactly how it happened, but I was in his office.  I remember it to this day.  Think it was Sue Lapin who directed me to his room, but that’s another story.

wizard_child

He was a classic example of a gray haired, balding, absent-minded professor, his office shelves stuffed to the ceiling with books, papers, and other flotsam and jetsam of an academia life. There we were: two different generations —  he, my father’s generation, and me, a 50’s nerd baby boomer. The commonality was we were both computer nerds, interested in ideas and the nascent computer science field.   At the time I was just trying to get a job to support my education: a Masters degree at University of Wisconsin, Madison, far from my home in sunny SoCal.  I had driven the two thousand miles or so across the US for the first time in my life to get there.

We talked for about four hours non-stop about all kinds of things, the Chinese language is the only subject I remember: he was a fountain of knowledge, and both us could have gone on many Moore hours.  I probably didn’t know the significance of it at the time, except he did point me to a job which I got to support myself in that strange land.  A year and half later, I got a Masters in Computer Science, and left Madison to wander towards Enlightenment for the next 46 years, and hopefully beyond.

dmk_library_physics_math

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The Digital Sand Reckoner

To see a World in a Grain of Sand

And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

— William Blake

dave_grad_schoolarchimedes
New scientific ideas never spring from a communal body, however organized,
but rather from the head of an individually inspired researcher
who struggles with his problems in lonely thought and unites all his thought
on one single point which is his whole world for the moment.
Max Planck

elkies_power_five_formula

Connecting precise physical relationships between the finites and the infinites.

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Slow Ideas

Comparative Science and Relational Complexity

We would debate for hours.

Over decades.

Only the educated and self-educated are free.

My father died on July 30th, 2013 and I intend to honor him, if I can, by writing a blog about him and the consequences of me integrating his ideas every year.  First year,  Second YearThird Year, Fourth Year, Fifth Year  This is the sixth year.

When I was young, my father would introduce and discuss, around the dinner table, the ideas of philosophers, scientists, and historians: like Adam Smith, Charles Darwin, Herbert Spencer, John Stuart Mill, Georg Hegel, William James, Arthur Schopenhauer, Bertrand Russell, Oswald Spengler, Will Durant, Ayn Rand, Milton Erickson, and Jay Haley, to name a few.

I had a question early on “How and Why does the World Work?” He had a more difficult question: “What are the long-term patterns of an ‘Individual’s Human Action?” He was clinical school psychologist, who was identifying deviant habits of children, parents, and teachers. He was developing techniques aimed at enabling them to abandon such habits. His methods of research and reasoning enabled him to evolve his ideas into a coherent system. His model of Human Temperament has helped many people to better understand themselves and others.

He was good at qualitative reasoning, wholistic thought: the Gestalt (despite [and because] of having lots of training in statistics). I became good at quantitative reasoning: conventional science and mathematics. Between the two of us, as we debated, I realized that there was a middle way, much more powerful than ad hoc wholistic reasoning or ad hoc atomistic reasoning, when they are used separately. The new middle way, The Slow Idea, is using Comparative Science and Relational Complexity in conjunction as fields of scientific endeavor using systematic qualitative and quantitative reasoning together. To some extent: (hard and soft) science, mathematics, and computer science are towers of Babel, not able to understand each other’s argot and considered irrelevant to other.

The idea ofSlow Ideas <=> Fast Ideas

The root of this idea appeared just recently, thanks to Atul Gawande. He and Matt Ridley noted that ideas operate very much in an evolutionary manner.

Fast Ideas and Slow Ideas

FAST IDEAS WORK

eventually, SLOW IDEAS WORK BETTER, and longer

Atul Gawande introduced the idea of slow and fast ideas with an example from the 19th century. The fast idea was anesthesia and the slow idea was antiseptics. To quote him:

“Why do some innovations [ideas] spread so swiftly and others so slowly? Consider the very different trajectories of surgical anesthesia and antiseptics, both of which were discovered in the nineteenth century.”

“The first public demonstration of anesthesia was in 1846…”

“The idea [anesthesia] spread like a contagion, travelling through letters, meetings, and periodicals. By mid-December, surgeons were administering ether to patients in Paris and London. By February, anesthesia had been used in almost all the capitals of Europe, and by June in most regions of the world.”

Antiseptics, on the other hand, was a slow idea. It took decades for antiseptics to accepted by doctors, who had no incentives to change their practices that didn’t help them immediately. Blood stained clothes was a sign of a experienced surgeon; and washing hands, sterilizing instruments, and keeping hospitals clean seemed unnecessary. Germ theory was dismissed by doctors because the “germs” were not readily observed. Miasma Theory still was used as an excuse to not change.

Hey buddy, can you spare a Para-digm?

“Science advances one funeral at a time.” — Max Planck

“The trouble with specialists is that they tend to think in grooves” — Elaine Morgan

Establishment science needs to protect themselves from quacks, but it also resists slow ideas that are not easily incorporated into the current fashionable (often fast) ideas. This is natural, this is the way evolution works. However, Kuhnian revolutions (as in Margulian-Darwinian evolution) are necessary in science to progress and leap across the Quantum Gap.

Form

He didn’t get it.

I was surprised, kinda.  But it made sense, why he didn’t think much of my suggestion.  In fact, in his seminar at UCIrvine Information and Computer Science department (as tactic to get MIT to give him a better offer as a tenured faculty member), he dismissed my “idea”, quickly, even though he had asked (obviously rhetorically, in hindsight) for suggestions as a kind of Socratic presentation tactic in his talk.

My mentioning of Kirchoff’s law as a parallel in regards into information flow, he thought irrelevant, and was rather dismissive.  But who was I, just a graduate student from a west coast Podunk U [which eventually was a key university in the development of the World Wide Web].  He was an assistant Professor from MIT, angling for tenure.

kirchoff_law_1

This time I understood.  Although I didn’t have a name for it at the time.  I just shut up.

Now, I call it eucaryotic hubrisWe all have it, in the area of our expertise and our vast areas of ignorance.

This time, I had had enough encounters with these kind of guys to not be in awe of them. I didn’t assume I was at fault in not understanding, and not smart enough it “get what they are promoting”.  They were just as ignorant as I was.

And, Stupid, as me.  So when I was watching one of Geoffrey Hinton’s youtube talks…

carl_hewitt_stupid

I had interacted this “professor” before, in that seminar.   And I had listened to some of his other conference talks, he is very very very smart and accomplished.  So smart, these days, he is a distinguished emeritus faculty member, at the institution he got his BS and PhD at.  He has never had to move out of Massachusetts, or MIT.  No, this guy wasn’t Marvin Minsky, but his student.  So when Hinton told his offhand story, about Professor Carl Hewitt, I had to laugh.  Deja vu, all over again.

“Indeed, in their later years (after finding out that most others are faking an understanding of the laws of nature), INTPs [Architect Rationals] are likely to think of themselves as the master organizers who must pit themselves against nature and society in an unending effort to create organization out of the raw materials of nature.” – Please Understand Me II,  Keirsey, David. Please Understand Me II (Kindle Locations 4099-4107). Prometheus Nemesis Book Company. Kindle Edition.

As scientists, we all are struggling with understanding:

Formatics: Precise Qualitative and Quantitative Comparison. Precise Analogy and Precise Metaphor: how does one do that, and what does one mean by these two phrases? This is an essay, in the form of an ebook, on the nature of reality, measure, modeling, reference, and reasoning in an effort to move towards the development of Comparative Science and Relational Complexity. In some sense, this ebook explores the involution and envolution of ideas, particularly focusing on mathematics and reality as two “opposing” and “fixed points” in that “very” abstract space. As Robert Rosen has implied there has been (and still is going on) a war in Science. Essentially you can view that war as a battle between the “formalists” and the “informalists” — but make no mistake the participants of this war are united against “nature” — both are interested in understanding the world and sometimes predicting what can and will happen, whether that be real or imagined. So… I will ask the questions, for example, of “what could one mean” precisely by the words: “in,” “out,” “large,” and “small.” The problem is both Science and Mathematics are imprecise — but this sentence contains fighting words and is impredicative, to say the least. In my father‘s terms, it is important to distinguish between order and organization, and understand the difference. Lastly, for now, the concepts and their relations, in the circle of ideas of “dimensions of time” and dimensions of energy along with the dimensions of space and dimensions of mass will be explicated, as I evolve (involute and envolute) this ebook. SO WHAT IS HE TALKING ABOUT? Let me try to explain.

Formatics

Other Architect Rationals include:  James MadisonSrinivasa RamanujanEmmy NoetherPaul DiracRobert RosenDavid KeirseyAlbert EinsteinLonnie AthensDavid Bohm

Prime

Partitions: Exact Approximations

… there is something strange going on with Primes
Paul Erdös

champagne_bubbles

Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.

ramanujan_book

When Srinivasa Ramanujan wrote to G. H. Hardy in the 16th of January 1913, he had some remarkable formulas in that letter.  So remarkable are some of his formulas that mathematicians have been studying Ramanujan’s notebooks of formulas for new mathematical insights to this day, more than a hundred years later.
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras… I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling”. 
Hardy invited him to England because some of the formulas “had to be true, because no one could have the imagination to make them up”.   But there were no proofs.  However, when this poor vegetarian Indian Hindu came to England, eventually Hardy showed Ramanujan (thru Littlewood) that his formula on Primes was not EXACTLY correct. So Ramanujan had to bend to Hardy and work on his proofs of some of his formulas, so when they tackled the function of Partitions P(n), Ramanujan with the help of Hardy got to point where they “cracked” Partitions (and could prove it). They developed a direct formula that computed the number of partitions pretty accurately, and at the limit (infinity) it was “perfect” — and, could by truncating the number for high partition number to an integer could guarantee to be exact: since the number of partitions of integers is an whole number (i.e., the real number series “formula” converges with an deceasing error rate). Together they “cracked” the problem where neither man could do it alone. Ramanujan supplied the “intuition” (the finding of the hidden pattern) and Hardy provided the rigor to explain why the pattern is true.  The method they created, in this instance, was called the “circle method” — and it has been used ever since by numerous mathematicians for various other results.

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Thanks, I needed that.

Seasons change with the scenery
Weaving time in a tapestry

I was surprised.

I was just eating lunch by myself in the cafeteria.  I am attentive, not expressive, kind of guy.  Besides this was the first time I was visiting MIT, as a part of Artificial Intelligence (AI) conference.  No, my SATs were not good enough to get into CalTech (or MIT), and I am a west coast guy, anyway.

But, lo and behold.  He sat down next to me.  Obviously, to strike up a conversation.

Marvin Minsky.

Ok, now I wasn’t a kid anymore.  I was industry-based AI researcher (Hughes Research Labs, HRL) working at the time on Autonomous Vehicle research.   Minsky didn’t know me, but, I knew a fair amount about him.

Marvin Minsky, full professor at the Massachusetts Institute of Technology, and “one of fathers of Artificial Intelligence”, came to my table clearly because he was curious.  Minsky, a Fieldmarshal Rational, had been very successful in promoting his graduate students to getting academic professorships across the lands. The list of his PhD students is more than impressive. He had government and university funding. MIT is a technological power house.  Money, People, and Companies have been flocking to MIT well before I was born.

I tried to make our conversation as interesting as I could.  Hey, Marvin was a legend in my field: Artificial Intelligence.

After about 5-10 minutes of conversation, me doing most of the talking about the autonomous vehicle project that I had been involved with, Marvin excuse himself, and wandered over to another table with a couple of people and joined in that conversation.

He didn’t get any useful out of me, in his mind, no doubt.
Next.
He moved on.

Thanks, I needed that.

I did get something useful out of the encounter.
A slow idea. But not a fast idea.  A hint on a part of an idea on how the world works.
It was a Kuhnian moment for me, I knew some things that Marvin couldn’t imagine.

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An Odd Even Ode Log Rhythm

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

Find Structured Constant: A Ode to Wolfgang

in-form == 1

ex-form == 0

form == -1

Now Moufang it and Emmy ring it two. Make Lise Bind. Oh, Dedekind bother, it’s a unReal hard cut.

But,
Never mind, Hilbert doesn’t bother. Such a Dehn mine-d vater.

MJ Golay to the re-scue, the Hamiltons and Hamming to rearrange and recode, the 23th Prime Poincaré to re-solder.

 

Two notes of the chord, that’s our poor scope,
And to reach the chord is our life’s hope.
And to name the chord is important to some,
So they give it a word, and the word is:

Di-vision

To Subquotient, or Not Subquotient,
That is the question!

The divisor status, of the lattice, oh my, Times, Rudvalis.

Crack the Dirac, Landau beseech the damp Leech.

It’s a Monster Conway Mesh, Mathieu‘s Stretch, Jacques‘ Mess, Janko‘s Sprains, and Einstein‘s Strain.

Never mind the mock theta, Ramanujan‘s gap, Namagiri dreams.

No Tegmark or Linde, but Verlinde in name. It’s all but Feynman‘s streams,
and weigh.

Such a Prime rank, any such Milnor‘s exotic sank.

No mess, no Stress, but Strain. Tensors Bohm and Bain.

It’s Held together. Dr. Keirsey is here to re-frame.

It Works! Much to lose and A Gain.

It’s Life Itself, More AND Less, a game.