{"id":174,"date":"2020-04-19T20:17:41","date_gmt":"2020-04-19T20:17:41","guid":{"rendered":"http:\/\/7stones.com\/?p=174"},"modified":"2020-04-26T14:42:13","modified_gmt":"2020-04-26T14:42:13","slug":"the-art-of-being-a-humble-adult","status":"publish","type":"post","link":"http:\/\/7stones.com\/?p=174","title":{"rendered":"The art of being a humble adult"},"content":{"rendered":"\n

Brevis Gravitas<\/strong><\/p>\n\n\n\n

My attitude in these blogs has often been flavored with a soup\u00e7on of flippancy, occasionally falling well short of conventional adult seriousness that let\u2019s one know where one is, what to expect, and signifies there is a shared notion of what it is to be a grownup. Starting right now I shall attempt to mend my ways for an extended period of time during which I shall exude gravitas. … There. Done. I hope that suffices.<\/p>\n\n\n\n

Conway in the 24-dimensional celestial sphere<\/strong><\/p>\n\n\n\n

John Horton Conway died recently, sadly succumbing to the fucking covid-19 virus that hovers like the cloud belched forth from Mount Doom at Sauron\u2019s behest over Mordor and surrounding counties. I don\u2019t do heroes, but Conway comes very close.<\/p>\n\n\n\n

A couple decades or more ago, having already spent a couple of prior decades demonstrating that the very resonant (Hurwitz) division algebras (C<\/strong>, H<\/strong>, O<\/strong>, with resonant dimensions 2,4,8) provide a natural architecture for the Standard Model of elementary particles, I happened upon Conway and Sloane\u2019s book, Sphere Packings, Lattices and Groups<\/em>. In this I discovered that in lattice theory the resonant dimensions are 2, 8, and 24 (1\u00d72, 2\u00d74, 3\u00d78), associated with the lattices A\u2082, E\u2088, and \u039b\u2082\u2084. That last one is the Leech lattice. It is remarkable, and there are a few people in the world who understand why, to some extent. I am not one of them. I\u2019m like a fan of a sports team, not willing (able?) to put in the years of work needed to become a proficient player, but still able to write about the sport, which I did most recently here<\/a>.<\/p>\n\n\n\n

I never met Conway, nor ever communicated with him, but my readings in Sphere Packings<\/em>, and elsewhere, convinced me that the fellow was beyond brilliant. In an online obituary I encountered this:<\/p>\n\n\n\n

“During what Dr. Conway called his \u2018annus mirabilis,\u2019 roughly 1969 to 1970, he discovered what\u2019s known as the Conway group, an entity in the realm of mathematical symmetry that inhabits 24-dimensional space. He discovered a new type of number, \u2018surreal numbers.\u2019 And he invented the cellular automaton Game of Life, which is among the most beautiful mathematical models of computation. He described it as a \u2018no-player never-ending\u2019 game.<\/p>\n\n\n\n

“\u2019In mathematics and physics there are two kinds of geniuses,\u2019 Dr. Kochen said by phone from his home in Princeton, echoing something once said about the physicist Richard Feynman. \u2018There are the ordinary geniuses \u2014 they are just like you and me but they are better at it; if we\u2019d worked hard enough, maybe we could get some of the same results.<\/p>\n\n\n\n

\u201c\u2018But then there are the magical geniuses,\u2019 he added. \u2018Richard Feynman was a magical genius. And the same always struck me about John \u2014 he was a magical mathematician. He was a magical genius rather than an ordinary genius.\u2019”<\/p>\n\n\n\n

By the way, Conway wrote another book (with Derek A. Smith) – On quaternions and octonions: Their geometry, arithmetic, and symmetry<\/em>, and quite a few years ago, at the request of an editor of The Mathematical Intelligencer<\/em>, I wrote a review of that book, which appeared in that journal. Something odd happened as a consequence – a glitch in The Matrix – and if you do a search for that title you will sometimes see my name listed with Conway and Smith\u2019s in a way that gives the impression I was a coauthor. I was not. In life Conway inhabited a more rarefied plane of existence than do I, and now – sadly – it is even more rarefied.<\/p>\n\n\n\n

And speaking of being humble: WPP<\/strong><\/p>\n\n\n\n

Stephen Wolfram, polymath, genius, and a model of self effacement we would all benefit from emulating, has initiated “a project to find the fundamental theory of physics”: The Wolfram Physics Project<\/a>.<\/p>\n\n\n\n

Let\u2019s look into his bona fides, and things he has let go to his head:<\/p>\n\n\n\n

> He published his first physics paper when he was 15. I misremembered that number; I thought he had said it was 2, but upon rereading his backstory I discovered that that was just a general impression he was generating. The real number is 15, which is still impressive.<\/p>\n\n\n\n

> He got seriously involved with physics in the 1970s. He evidently frequently rubbed elbows with Feynman, an association that he definitely let go to his head, and one that I suspect prevented him from thinking more out of the box at that time. “Not that I was trying to find a fundamental theory of physics back then. Like essentially all physicists, I spent my time on the hard work of figuring out the consequences of the theories we already had.” So, that phrase – “essentially all” – is, methinks, intentionally dismissive of any theorists – like G\u00fcrsey and G\u00fcnaydin at Yale – who were not “figuring out the consequences of the theories we already had”, but were involved in a search for the mathematical roots of “theories we already had”. (Their work inspired mine, and although they surrendered their efforts when faced with mainstream ridicule, I participated in keeping the flame alive in the wilderness, and although it took decades, that flame is now pretty much self sustaining.) Anyway, it\u2019s just a guess, but the problem with being young, bright, AND a friend with the likes of Feynman, is that such friendships dampen the potential of youth and brilliance, leading one to avoid any thoughts or actions that could jeopardize the friendships and diminish the perceived respect those theory gods might have for your malleable young mind.<\/p>\n\n\n\n

> The siren call of computers became un-ignorable at some point, and SW succumbed to the allure of its dulcet tones. He founded Wolfram Research, and used the Wolfram Language (See? Humble.) programming language to create the kernel of Mathematica, a now nearly ubiquitous STEM computing research tool. But he never forgot physics.<\/p>\n\n\n\n

> And now we have the WPP. Ideas gleaned from decades of thinking digitally have led to this inherently digital approach to solving some – or all – of the big mysteries of physics. According to wikipedia it was Abraham Maslow, writing in the book The Psychology of Science<\/em>, who used the phrase: \u201cI suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.” I suspect that the WPP is a classic example of this. That doesn\u2019t mean it\u2019s wrong, or misconceived, but … well, you know, if it doesn\u2019t involved the C<\/strong>, H<\/strong>, O<\/strong> trio at some point in its architecture, then even if the WPP succeeds in explaining everything, I won\u2019t care, and I\u2019ll lose all respect for Mother Nature. So, that\u2019s my opinion; it\u2019s not humble. I don\u2019t do humble opinions. And just to be clear, the WPP has to do more than succeed; it has to explain why its success – and the particular path to that end – was inevitable.<\/p>\n\n\n\n

> SW also says: “But what about other approaches to finding a fundamental theory of physics? Realistically I think the landscape has been quite barren of late. There\u2019s a steady stream of people outside the physics community making proposals. But most of them are deeply handicapped by not connecting to quantum field theory and general relativity. Yes, these are mathematically sophisticated theories that pretty much take a physics PhD\u2019s worth of study to understand. But they\u2019re [QFT and GR] the best operational summaries we have right now of what\u2019s known in physics, and if one doesn\u2019t connect to them, one\u2019s basically throwing away everything that was achieved in 20th-century physics.” It may be just my own ego speaking, but this blanket dismissal of things that do not include QFT and GR might include my own work. Keep in mind, I\u2019d be happy to have another lifetime with which to shoehorn those notions into my work, and I\u2019ve never dismissed their utility, but … I\u2019m reminded of the excitement I felt years ago when I saw I was cited in a Roger Penrose tome, only to discover he felt my work, by involving division algebras beyond C<\/strong>, was thereby rendered unworthy. But maybe Wolfram is unaware of my dabblings. Is that better? Maybe I\u2019m just being sensitive. Sniff.<\/p>\n\n\n\n

Anyway, Stephen, good luck with that. It\u2019d be nice were a ToE developed before I die, even if my efforts are beside the point. But please hurry.<\/p>\n\n\n\n

More ABC conjecture humility<\/strong><\/p>\n\n\n\n

Although Peter Woit\u2019s latest blog has taken a small step away from the ABC conjecture proof controversy, the debate that played out in his ABC blog comments – by some of the preeminent mathematicians in the field – was fascinating. I can\u2019t pretend to understand much more than a small fraction …<\/p>\n\n\n\n

“What my post above attempts to show, is: if passing to poly-isomorphism has the effect of doing no gluing\/no identification of ring structures (arising from \u03c0\u2081, just the gluing from the actual log map), then the only gluing left is the actual log map, which gives one global chart, and no transition functions needed, essentially(?) since just one chart. I before never really seriously considered that full poly-isomorphism could have the effect of \u2018no gluing arising from this part\u2019 (instead of \u2018choose your favourite gluing\u2019), but a similar thing is (I think) asserted for the case of the theta-link in …”<\/p>\n\n\n\n

… Holy crap. Anyway, Peter W is adamant that the purity of mathematics would be sullied by the publication of a “proof” of the conjecture that is viewed by many as flawed. (My comment that physicists publish flawed work all the time did not go over well, and it was dismissed.) I don\u2019t disagree with PW, but I do wonder if this >500 page proof – the semantics of which is not understood by its critics, according to its author – has entered a zone of near unknowable-ness. I suggest we create an AI that can not only look into this vexing problem far more quickly than can a human, but also far more dispassionately.<\/p>\n\n\n\n

You know, I\u2019m only half kidding. Actually I\u2019m not at all kidding. We then should turn the AI\u2019s attention to physics, and turn the attention of mathematicians and physicists – who\u2019ll no longer be needed doing what they\u2019d been doing – to other areas, like farming, and web design.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n