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

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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