C for Cute

Helpful extraterrestrials need not apply

My brain, as is its wont, has latched onto an old idea, ignored the multiple times in the past I’ve presented it as new, and, well, you get the idea (pull my finger). So, this highly original reboot is to (re)imagine some cluster of nattily attired super intelligent aliens – or, if you want to get picky, some other sort of nattily attired entities inhabiting some other sort of unassailable intellectual pinnacle – although to be politically correct in the strictest sense, it should be stressed that they needn’t physically inhabit an actual pinnacle; I mean, they might be Mole People, or practically any kind of entity that isn’t human (totally out of the running; sorry) …

Where was I? Right. They pop to the nearest internet cafe and submit to the arXiv an actual correct TOE. The arXiv gatekeepers give it a gander, observe that it varies significantly from 99% of the ideas arising from the mainstream, and even 95% of fringe ideas, and they reject it. Of course they fucking would. What does the community of theoretical physicists have to gain? A negative amount of good things.

It should be added – although it ought to go without saying (but doesn’t) – this TOE exudes inevitability; it could not be other than it is. And no part of it could be left out without threatening the entire edifice. That’s not to say all questions are answered by this work of overarching genius, but all questions that are answerable are answered. And there would be mathematical explanations – or proofs – of why there are limits to what is knowable, and, as much as is possible, what those limits are. So, cool.

Having personally seen only a small bit of this masterpiece – written in Québécois – I decided I could use it to grade various notions floating around Middle Earth (human lands; not homes to Space Entities or Mole People) that promote themselves as efforts to find a human TOE. Peter W has been blogging about the Atiyah-Singer Index Theorem, and all things Langlands, which I give a grade of C for Cute, but that’s unfair. These things brush up against theoretical physics, but they are really pure mathematics, and cutting edge at that. They may be part of the TOE, but I’m not qualified to judge.

However, I give Category Theory a D for Dewey Decimal System, and because as a mathematics graduate student the subject made me sleepy every time I encountered it.

String Theory, of course, gets an F for Failing to give up the ghost.

And finally, Division Algebras and Parallelizable Spheres get an A for Apotheosis. And, of course, although strictly speaking I’m not supposed to share this, these bits of mathematics are integral to … but I’ve said too much.

Meanwhile on the fringe: a rambling discourse full of holes

I am widely (?) regarded as an exemplar of the scientific maverick carrying on a Sisyphean struggle to blah blah blah. LM suggested that Tony Smith (now passed) and I are/were founding fathers of what he views as an uncomfortably large pool of abhorrent crackpots unwilling to adhere to accepted dogma. But Tony and I approached theorizing rather differently. I had a small idea that was pure mathematics. It was a doorway (Speak friend, and enter); and I did enter, and I followed its mathematical path deep into Moria. There were obvious connections to physics, but – and here’s the nub – not all of physics; the connections are strongest to the groups and fields of the Standard Model. There were many side tunnels that would have led to deeper Truths, but I did not – and do not – feel competent to follow them. If the mathematics, as I understood it, did not explain some aspect of physics, I tried assiduously not to push it where it didn’t want to go. It’s a pretty little mathematical gem. It seems to me it has profound things to say about physics, but that’s just me.

And why is it just me?

Consider Tony. Unimaginably bright, he also had an abiding need to explain everything. During the years that I knew him I can’t think of any theoretical physics mystery that he did not try to encompass in his ever expanding model building. He would sometimes exhort me to expand my ideas to encompass a bigger picture. He seemed to admire my devotion to my little gem, and he wanted it expanded, merged with his own ideas. I never outright refused, but also never came close to acceding. Not my thing. Quantum gravity? Uh, yeah, hmm. Dark matter? Uh, yeah, soooo mysterious (although Tony had an explanation).

Tony was an exemplar of something that seems quite common today: a theorist intent on building models that explain everything. This may be just because such theorists’ works are those I most frequently encounter on Researchgate, so my view of what’s going on in the fringe is quite narrow.

Still, throughout the history of Middle Earth, great thinkers have convinced themselves, and occasionally many others, that all that was knowable was known. That presupposes that all mathematical ideas originating in the future may at best fine tune what is already known. And so, just to be entirely clear, because the idea is eternally resisted, the Middle Earth we are presently inhabiting is part of this long history of self-delusion. The odds that we know everything we need to know to duplicate the Mole People TOE in any but a small part are vanishingly small.

I early on internalized this notion, and it helps explain why, as a graduate student of theoretical physics in the late 1970s, I resisted efforts to get me involved in supersymmetry and QFT. The former I felt from the outset was a goofy idea. Immersion into the latter would have made me better able to judge the massive amount of work arising since QFT’s inception, but I’d have become a technician, carrying around a useful bag of tools with which to test …

Sigh. What I did instead was to follow my intuition. And when that landed me on the Dixon algebra, T, I settled down for years and studied that one thing (and a few other things that were similarly mathematically resonant). Any piece of theoretical physics that the mathematics of T did not encompass, I mostly ignored. I assiduously tried to avoid incorporating notions I felt didn’t belong in order to expand T’s explanatory power, although I was often exhorted to do so. Working with T was clear. The jungle of stuff outside of T was not clear, and my intuition said little about it. I’d be guessing – and given what I see coming out of big explainers – guessing again, and then again.

Yeah, so the Mole People could tell you why T is inevitable, that it is forced by field theoretic ideas we do not presently employ. I’d like to be around when they do, but, you know, the odds are not in my favor. And the Mole People have nothing to gain in pointing out the failings and fallacies of narrow-minded Middle Earth dogma. Au contraire …