Looks like Khan found his girlfriend!
Posted on 07/21/2018 6:18:51 PM PDT by DUMBGRUNT
New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.”
“Octonions are to physics what the Sirens were to Ulysses,”
Decades on, no particles beyond those of the Standard Model have been found. Meanwhile, the strange beauty of the octonions has continued to attract the occasional independent-minded researcher, including Furey, the Canadian grad student who visited Günaydin four years ago. Looking like an interplanetary traveler, with choppy silver bangs that taper to a point between piercing blue eyes, Furey scrawled esoteric symbols on a blackboard, trying to explain to Günaydin that she had extended his and Gürsey’s work by constructing an octonionic model of both the strong and electromagnetic forces.
Surely, you jest or is it Shirley, you jest?
Is brain damage from strain cumulative?
If nothing else. staring at the E8 Petrie projection; was soothing.
... The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 21435527 = 696729600....
Looks like Khan found his girlfriend!
Mathematicians have taken over and destroyed the field of physics.
+++++++
Well you caught my eye with that one. Einstein, Schrodinger, Godel, Planck, von Neuman and others just might disagree with you.
But you might be right.
“I know when I’m over my head.”
Just trying to read this thread and the accompanying article, confirms that for me.
Is that like an Octopus with an Abacus?
Same thing, only different!
Or with eight Abaci?
I always enjoyed Dr Feynmean’s barroom contest with the abacus salesman. IIRC the final question came down to the cube root of something near 1728, most might recognize as a cubic foot. The Abaci wizard was crushed.
From “Surely You’re Joking, Mr. Feynman!” (??? Having memory errors this evening).
A great read.
Nothing particularly profound about octonions. They’re simply 8 dimensional numbers with 4 real and 4 imaginary dimensions. Just an extension of complex numbers.
I am fascinated by mathematics, but I completely suck at it. I did pretty good in electronics school with my trusty Hewlett Packard RPN calculator, but I still have to count on my fingers. For some reason, numbers are a struggle for me. I hate it.
You make a good point. But I don't think it is that hairy at the undergraduate level. Usually the last math course most people take as undergrads would be differential equations, which sort of tops out the applied calculus sequence. Unfortunately, that is just a hair short of the "cool" stuff.
It is a shame that the calculus sequence is not followed by a semester or two in "abstract algebra" (or "modern algebra" if you prefer). That should be sufficient background to follow these developments in physics, the same way an ordinary chess fan can follow and appreciate the game of a grand master.
For the contemporary world such a course is really invaluable and touches not only on the theoretical but also solidly practical applications like cryptography as well. And a lot of folks find it easier and a breath of fresh air after slogging through the calculus long march.
A drawing would indeed be possible, all that’s needed is eight dimensional paper.
Thats me, and most engineers probably, topped out at differential equations, the calculus long march indeed.
I’m not sure Lax would hit that...but let’s hear him speak for himself.
I am rather certain that every single one, were he alive today and NOT dependent on grant money to eat, would be wholly in agreement and without reservation.
Pretty cool article. Takes a little while (for me, anyway) to digest. But the rules governing the Fano Diagram seem to make a weird kind of sense. Or that could be the beer.
Wonder what Stephen Wolfram might have to say about this?
Operations using base 8 still follow real number rules of commutation and association. The other divisional algebras mentioned in the article do not. And that just dances right past the edge of my comprehension. There are hints of a more vast and deeper reality than we know.
Stephan Wolfram. I hope you are an expert and can perhaps answer your own question. Because I don’t think I can.
But you did pose your question to the right guy since I am probably the only Freeper with an official copy of “A New Kind of Science”. Of course you might be the second.
I pulled the book off my bookshelf and had a look. I read a bit of it quite some time ago but I don’t believe I ever “Got It”. Thumbing through it you don’t see any equations but you do see lots of mosaics.
But you got me interested. I’ll give it a better look tomorrow.
Sounds exciting. Intellect over emotion.
These folks need to get together...
https://www.quantamagazine.org/mathematicians-chase-moonshine-string-theory-connections-20150312/
Many here never made it past A ... let alone to the esoteric heights of D ...
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