Bog of Despair

I despair. However, to be frank, when it comes to theoretical physics (TP) I began to despair about 50 years ago. So it’s nothing new. And, in fact, nowadays it doesn’t bother me too much. Despair is like a lukewarm bath suffused with epsom salts – swelling is reduced; muscles relaxed.

It’s my own fault, really. I continue to monitor the end-of-days blather about the sorry state of TP, mostly following Peter’s blog, but a lot from hyped up stories online from the popular press.

The latest brouhaha arose from an article in Quanta Magazine entitled Why the Laws of Physics Are Inevitable. (Quanta Magazine, you may recall, last year published an article entitled The Peculiar Math That Could Underlie the Laws of Nature. The Peculiar Math the article article refers to is an algebra (T = C ⊗ H ⊗ O) I began using some 40 years ago to explain stuff in particle physics. However, the focus of the article was a talented young woman (Cohl Furey … probably … she has a tendency to change that moniker from time to time) who began to exploit this algebra in her own work some 10 or more years ago. For reasons that remain not at all mysterious to me, while seminal work with this algebra was attributed to me, the article basically all but killed me off in the early 1980s, a decade before my first book on the subject, and over 35 years before before my second. From this I conclude that I may be a zombie. You might want to put on a helmet to protect your brain if you plan to read further.)

Anyhum, this recent Quanta Magazine article gave rise to much righteous spluttering, its title leaving one little alternative. Spluttering was called for. Part of Peter’s response was a very cogent summation of how we got to where we are, mentioning how Lie group representations had been used in conjunction with analytical methods, including QFT, to exclude a lot of things that were thought not to be a part of our universe’s description. Well, if you know anything about my work (ok, right, you don’t, but never mind), you’d not be surprised to discover that I offered my own comment on this (which, as is true of many of my comments, was rejected; I understand why, so no hard feelings):

DB wonders “when everyone in that world will acknowledge that they’re totally stuck”, etc. I wonder if the problem is “the world” is not really stuck enough. The QFT/representation theory playground is a messy morass that allows too much freedom to wallow without clear direction. Try: if fail, try again; if success, lock in place. Repeat.

IMħO, if “representation theory” is an integral part of your theoretical tool chest, then you’re working from a blueprint that is far too loose and unconstrained. Representations should be forced by the blueprint, along with much else that is presently achieved by trial and error.

This critique arises from my own blueprint (T = C ⊗ H ⊗ O), from which, in particular, all the Lie groups and representations that the Standard Model exploits arise naturally. There is no room to test other groups or representations, so the morass is made considerably less messy. (However, I was labeled a crackpot in a blog following the Quanta Magazine article on the subject. That word, “crackpot”, was used several hundred times (just an impression; that number may be wrong) in the blog (the first of two), mostly aimed at Cohl, but also liberally slathered on myself, as well as Gürsey and Günaydin, whose work at Yale on applying the octonion algebra in TP predates mine by several years. In that blog I learned that I am not Lance Dixon, so it wasn’t entirely without merit, for this was previously a source of some confusion for me.)

Ok, ok. Where was I? Oh, right, TP end times. One of Peter’s commenters posted this:

I listened to a sobering piece on NPR this weekend (Living Lab, you can look it up). The subject was “Planck’s Principle”, i.e., roughly, “Science advances one funeral at a time.”

Someone actually attempted to test this notion with some rigor. The field was bio-medicine, but there likely are implications for other fields.

The conclusions were actually worse than Planck thought: Even if a Superstar scientist dies, their proteges keep up the rear-guard, stifling progress about as effectively. It’s not enough for the ossified to die off. You’ve got to worry about all the people still around who agree with them.

Seems relevant to Multiverse Madness and its otherwise inexplicable staying power.

(Multiverse Madness? I offered this photographic evidence in support of the notion that it is not madness at all:

Well, that was a very grownup non sequitur.)

So, yeah, in Planck’s day one could point to a couple of prominent examples of Kuhnian paradigm shifts that were in part able to shift because of a few funerals. The efficacy of these funerals in shifting paradigms was helped in no small measure by the small population of hidebound resistors. Add to this a not significantly lesser number of supporters of some new paradigm, increasingly backed up by persuasive experimental results, and there you have it. What? What do you have?

Well, you don’t have something even remotely able to be replicated today. The same number of supporters of some new paradigm today would be vastly outnumbered by the old guard – orders of magnitude. And as to experimental results, they are presently millions of times more expensive, and are prone to give results intended to support old guard ideas – which they haven’t, so there’s an end to that. No one is going to suggest the machines be retooled to investigate some new paradigm. Even I wouldn’t suggest that. There are just too many alternative paradigms, each with a supporter who wants to be Einstein, not Minkowski or Eddington.

Meanwhile the mainstream bloggers give lip service to TP end times, and the need for a catastrophic change of state, but heaven forfend that it exploit any but tried and trusted tools, and comfortable paradigms.

Another of Peter’s commenters:

I understand that the idea of continual scientific progress has always been understood to be problematic. But what I’m referring to is something different than the Kuhnian “normal science” leads to “crisis” leads to “revolutionary science” and then “paradigm shift”, which is a model of progress with forward jumps.

What if the “crisis” of no progress goes on so long that the field loses its best people and instead attracts those happy with a bogus “revolution”, one that is not in any sense progress? As far as I know Kuhn or Kuhnians haven’t looked at this possibility, which may describe where we are now.

Sigh. Well, I gain some solace from the computer games to which I’m presently addicted. While comments made here will be lost, “like tears in rain”, in a computer game my daily efforts to effect change are actually awarded. And the NPCs are virtual, not poorly programmed mushy bags of DNA.

Tacit Prediction

So, the grownup TP (theoretical physics) community – a community to which, I confess, I do not belong – is all a dither about impending cuts to federal spending on “speculative” TP. (Incidentally, while some might argue I should not be counted a member of any TP community, I myself simply meant that I am not sufficiently grownup to be counted a member of that slightly more exclusive group.) Peter’s take on the situation can be found here. Peter quotes a study:

The situation is becoming increasingly unstable.

University-based theory is suffering its most serious crisis in decades.

Its future is in jeopardy.

Sabine comments (as usual, pleasantly caustic):

As I have tried to tell particle physicists for 5 years or so, even the dumbest politician will eventually see that they don’t live up to the promises they’ve been making …

I offered my own comment, inspired by Sabine’s:

Sabine’s statement concerning “even the dumbest politician” has me confused. I was unaware that a lower bound had ever been established. 

As to me personally, I was fearing all this might mean cuts to my research funding of 50 to 90%, but then I did the math and determined in either case it would result in no change. :-))

Alas, not being a grownup, I find it hard constructing comments that make the cut, and this little nugget was deemed to be pyrite, and so dismissed.

Anyway, speculative TP has a history of funding woes as long as the field itself. Decades ago I remember attending a colloquium at Harvard given by a prominent younger member of their particle physics group. At the time the relevance of TP was under question, and spending cuts were feared in the offing. The subject of the talk was on the potential to use neutrinos to find oil deposits. Gosh. That certainly has the verisimilitude of relevance. Of course, nothing ever came of this, and no one in the audience – and probably the speaker himself – took the suggestion seriously.

Some time after this, during my years as a perennial slave … oh, I mean, adjunct … the Texas based SSC was cancelled. At the time this had a direct effect on my life. One of the professors at one of the many universities at which I was adjuncting was relying on SSC funding. When it evaporated I lost one of my courses to said prof.

And that’s a point made in Peter’s blog. Not about me personally, mind, but that it’s the little people who suffer the most immediate effects of money evaporation. In this present case, “little people” refers to speculative TP-ers at all but elite universities.

Do I care? Not so much. Fearing adjuncting would lead to a life in retirement sleeping in a cardboard box under a bridge, I eventually quit and ended my professional life as a web developer. So I’ve already been there, and done that.

Hell, in one of the last physics conferences I attended I was introduced prior to my talk as “the maverick”. This shocked me a trifle, but not being a grownup I was largely clueless as to how I was perceived by the larger TP community. (Still, “maverick” is better than “contrarian”, a more dismissive term I recently encountered online in reference to, well, people with thoughts on TP that are contrary to the mainstream.) So, anyway, my life on the fringes of TP has instilled in me a deep seated desire to see pruning shears applied liberally to mainstream TP. Indeed, one of Peter’s commenters suggested that funding cuts are long overdue:

Theoretical HEP is in failure mode and deserves its funding cut. Period. Full stop.

You know, as a TP maverick, one of many whose ideas are at variance with the mainstream, it occurs to me that the present funding fears are a tacit prediction of my work, and the work of anyone whose TP models bring into question the value of highly funded speculative TP. Sadly, verification of this tacit prediction is insufficiently focused to do contrarians much good, as they are likely being viewed by the powers that be no less leerily – probably much more leerily – than your average elite university string theorist.

Which reminds me: the Boston Area Physics Calendar, to which I subscribe, has in recent times had a dearth of string related talks listed. Unsurprisingly, quantum computing, which “even the dumbest politician” has come to view as in the national interest, now dominates listed TP talks. Or such is my impression. You should check with grownups for verification.

Bread and Circuses

Ground State

In need of a possibly trite metaphor for the human intellectual condition, but wanting it to be accurate, I googled “low energy state”. This came up at the top, probably a wiki:

“The lowest energy state an atom can be at is called its ground state. When an electron in an atom has absorbed energy it is said to be in an excited state. An excited atom is unstable and tends to rearrange itself to return to its lowest energy state.”

Applied to theoretical physics (TP) the lowest energy state is blind acceptance of the status quo – or at least that’s what I originally wrote. It’s not quite right, though. That word “blind” is wrong, methinks. “Willing” is more apropos – or even “eager”. The vast majority of individuals who’ve made careers in physics, while relishing stories of the disruptors of the past, are largely indifferent to disruption in the present, and occasionally aggressively against it. The lowest energy state is where security lies.

Of course, too much stability and there is a risk that funding may dry up. But excitement can be generated by a kind of scientific yellow journalism.

“The Universe Might Be a Giant Loop”

“Is a New Particle Changing the Fate of the Universe?”

“Even In A Quantum Universe, Space And Time Might Be Continuous, Not Discrete”

“Quantum physics: our study suggests objective reality doesn’t exist”

“A Link Between Dark Matter and Antimatter Could Be Why the Universe Exists”

These are actual titles of pop-sci articles strewn about the internet. Such titles often end in a question mark, or have one or more of the conditional words, “might”, “may”, “could”, etc. The titles are clickbait. My favorite type of clickbait title begins with words similar to these: “Scientists now believe [something moderately outrageous].” My first reaction – the reaction the title is intended to elicit – is, “Really?” And for a brief flash I am filled with self doubt, wondering how I missed word of this revelatory story. But wait a minute. What does “scientists” mean? It’s plural, so accepting the story’s accuracy the number of scientists sharing the moderately outrageous idea is greater than or equal to two, and less than or equal to the number of all scientists. The impression generated, in the absence of specificity, is that the number is close to all, which is a big deal. But it rarely if ever is nearly all. It’s usually two or three researchers who were overheard postulating something outrageous while sitting at a bar in an advanced state of inebriation – which is another metaphor.

Anyway, while I have nothing against a bunch of brainy folk having job security, I’m also a big fan of intellectual disruption. For several decades the ground state of TP was string theory. That ground state would have been cemented in place for many more decades, if not centuries, had the LHC found any evidence for anything SUSY related, but alas, it did not. Absence of evidence is not really disruption though. Had there been evidence of anything else, something requiring new ways of thinking, well, that might have boosted the atom to a higher energy state. Still, in finding nothing, the notion that there likely are higher energy states has not been precluded.

The Disruptor Meme

Disruption in TP can in fact negatively impact funding and careers, unless you are the disruptor, and you are already a member in high standing of the TP ecclesiastical bureaucracy. You know, I saw an article recently about the last scientist who knew everything. It doesn’t matter who the article’s author thought this person was, but the idea that things have now gone well beyond what any individual can mentally encompass is a valid one. There will be no more Swiss patent clerks overturning tired ideas, although many people – myself included – would love to be that. Some 50 years later, though, the illusion/delusion on my part has largely dissipated. It’s not all – or even mostly – my fault. I still believe in the core value of my body of work. But no matter.

What reputation I still have is that of an obstinate maverick. I am occasionally sent links to new articles by authors who want feedback on their potentially disruptive ideas. Their thought is: you (me) have been writing counterculture physics articles for decades, so your (my) sympathy is assured. The message I get from most of these is: your (my) work is counterculture, but let’s ignore it entirely and look at mine, which is different and unrelated to yours (mine, again). Your (my) feedback is requested.

The problem is, I believe with every fibre in my mind and body that my work is fundamentally correct, and that there are not many truths, but just one; so if your (not my) work is not building on mine, then, frankly my dear, …

The Wall

A couple days ago I encountered an online article about philosophers who believe there are limits to what we as a species can achieve intellectually. I quote:

“‘Mysterian’ thinkers give a prominent role to biological arguments and analogies. In his 1983 landmark book The Modularity of Mind, the late philosopher Jerry Fodor claimed that there are bound to be ‘thoughts that we are unequipped to think’.

“Similarly, the philosopher Colin McGinn has argued in a series of books and articles that all minds suffer from ‘cognitive closure’ with respect to certain problems. Just as dogs or cats will never understand prime numbers, human brains must be closed off from some of the world’s wonders. McGinn suspects that the reason why philosophical conundrums such as the mind/body problem – how physical processes in our brain give rise to consciousness – prove to be intractable is that their true solutions are simply inaccessible.”

So, yeah. But never mind that mind/body stuff; the idea also applies to TP. I must relate a quick anecdote. In my youth, full of a kind of boundless and obstinate enthusiasm stemming from a deep well of hubris, I visited a professor at Dartmouth to tell him about my burgeoning division algebra ideas. He shared a thought with me, that there may be limits to what humanity can achieve in TP. Did I mention the deep well of hubris? Yes, I see I did. Anyway, some time later I encountered him again, and I remembered some time in the past that someone had suggested there may be limits to what we can achieve in TP, an idea that my youthful arrogance totally dismissed, and I told him so. His reaction led my memory cells to the unfortunate recollection that he had been the one to share that opinion with me. Idiot! Me; not him.

Ok, let’s accept that there is a species specific TP wall, and we are close to it. The problem is, rather than admit that some mainstream idea shared by the ruling elite and their minions is wrong, this body of individuals has a vested interest in proclaiming the wall reached before it actually is … at least from an intellectual perspective. From a sociological perspective, maybe they’d not be wrong. If the ruling collective refuses to consider heretical ideas, then a wall – not the wall, just a wall – will have been reached. Happiness will ensue as we slide back to the ground state, a soup of exoplanets, dark matter speculation, and multiverses. Bread and circuses.

Game of Arya

Before the Game of Thrones (GoT) became an international television sensation, and prior to the publication of books 4 and 5, a friend suggested I might like the then extant books.  I dipped into book 1 and quickly encountered a description of a wall of ice hundreds of feet high intended to protect people living to its south from some horror to its north.  The island (Westeros) upon which most of the GoT takes place has a shape and size similar to Great Britain’s, and the wall in GoT was placed roughly where Hadrian stuck his wall in GB.  Clearly, however, whatever lay to the north of GoT’s wall was more frightening than a bunch of obstreperous Scottish clans.  I don’t think we were told what it was, but I needed to find out.  I was hooked.  

Were this a conventional work of epic fantasy fiction, such as the Lord of the Rings (LotR), the introduction of a mature, strong, and somewhat heroic character would have led one to sit up and take notice, for the story arc clearly would involve this character … oops.  He’s dead.  Well, that was unexpected, but he has two fine strapping boys, the elder of whom would don the heroic mantle, with an added touch of motivating revenge thrown in to … WTF.  He’s dead, along with his charming fiancée, his mother, and a whole slew of kin.  

This Red Wedding, when it aired on TV, shocked a great many people who’d not read the books and were unprepared for the death of a character they’d assumed was being groomed to take a central role in the story, a la Aragorn in LotR.  I mean, he was of semi-royal blood, was strong, handsome, and his fiancée was gorgeous and of an exotic foreign extraction.  The elements were all there for an entertaining if conventional fantasy with a happy ending in a castle.  But then these elements went and got their throats cut.  Many viewers vowed never again to watch the show.  I doubt many stuck with that vow.  

Meanwhile I had become intrigued by two characters, neither of whom in a conventional fantasy tale would have played central roles (hobbits are an exception, I suppose).  One was the dwarf, Tyrion, a scion of the most powerful family on Westeros; and the other was the smallish daughter of the fellow who lost his head early on and thereby lost all chance of being central to the story, save as a source of vengeance.  The former, Tyrion, was intelligent and thoughtful, traits that endeared him to me despite his foibles.  The latter, Arya, was expected, like her elder sister, to behave dutifully, marry well, and so on.  But she was having none of it.  She was feisty, rebellious, wanted to learn to fight with weapons, and in general avoid ladylike gentility.  Her father was not unsympathetic, to his credit, but he carelessly lost his head early on and Arya’s life was shortly thereafter swept up in a storm of chaos.  

As the story continued (speaking mostly of the episodic TV show from now on), neither Tyrion nor Arya seemed like central characters, but I found episodes without them tedious.  The plot got ever more convoluted, and I cared less and less about the cast of conventional characters most of whom seemed intent on achieving the titular throne for themselves, or at least their clan.  And that throne was made from a bunch of swords welded together.  What?  Well, no accounting for taste.  

Speaking of convoluted, I did not read every word of books 4 and 5 (as I write this, expected books 6 and 7 have not been published).  Characters would appear, dominate a chapter, then disappear, never to reappear.  Still, amidst all the death and mayhem, Arya and Tyrion would occasionally bubble to the surface, and I was happy to read those bits.  And I developed a theory.  

The author of GoT (GRRM) is not physically heroic – more Beorn than Aragorn.  I suspected, with no real evidence, that he sympathized with Arya and Tyrion, and relished killing off, or in other ways discommoding, the pretty boys and girls who his audience kept expecting would achieve conventional hero status.  I commented on this idea on Facebook:

“If you’re not an outcast, deformed, or picked on, you are not safe.  Look at the author.  These books are revenge books against everyone who demeaned him in school.

“Anyone who seeks to rule, however pure their motives, and however good looking … Whom the gods would destroy they first make mad (or proud).  From the beginning my two fav characters were the outcasts, Tyrion and Arya.  I predict they will survive.”  

A Irish friend of mine took exception to my view.  She commented:

“Sometimes I worry about you. I think the airs too thin where you are at. Please descend to correct mental imbalance.”

Years later, the TV show now complete, she wrote again:

“You’re prediction was correct …”

I replied:

“I thought show was great.  I never had any interest in pretty boys and girls and their thirst for power.  Red Wedding left me unmoved.  Oh well, I’m thinking, now there are fewer people to distract show from Arya and Tyrion.  

“When Arya brilliantly stabbed Night King the show was basically over.  However, they needed 3 episodes to completely destroy Kings Landing, the Iron Throne, and Dany (dragon go bye bye).  Then an episode to select unlikely king, and show elites squabbling over what was more important, ships or brothels.  This exemplified how trivial elites are and always have been.  Arya heads west on a voyage of science and discovery.  Excellent.  Jon Snow, the eternally befuddled supposed hero (in eyes of 99% of viewers), heads north, ignoring Black Watch, to be with people who actually like him.  

“I mean, once threat from north done, only thing to do was to destroy everything almost everyone (but me) thought the show was about.”  

And that’s it.  Arya overcame so much – even herself – to become the person she became, the hero of the story, as I see it.  And the game?  It is the Game of Thrones, after all.

The game is enforced by our genes, which shapes our societal thinking.  In rebelling against society’s expectations, society takes the self-preserving step of marginalizing the rebel – removing the offending part from the game.  Arya did not fit all but a very few viewer’s expectations of the hero.  Small, female, and rebellious, she transcended every obstacle put in her way, while simultaneously learning from each, becoming greater from each.  In the end only her highly trained, savvy, and intense focus could have brought down the Ice King.  As for him, he was justifiably smug in the face of the conventional foes conventional society threw in his way.  He would have easily defeated them.  But Arya was something outside his experience, as a living man, and as a dead one, and she had talents of which he could never have had any familiarity.  

Arya could then have stayed in Westeros, a person revered by (almost) all.  But that notion did not interest her.  She’d spent a life learning all she needed to learn, and Westeros had nothing more to offer.  No one there knew what was to the west of Westeros across the sea.  No one had any interest.  But Arya did, and she left squabbling Westeros (including Tyrion, who does all right for himself in the end), and she sails to the west on a voyage of discovery, ever the maverick.  

The show’s ending was deeply dissatisfying to a majority of viewers, taking only 3 episodes to tidy up the stories of everyone else, including the last surviving pretty boy (referred to above as befuddled).  He wanders off to the north and out of history.  The throne gets melted down.  The two strongest female contenders to the iron throne die.  And even the great city in which the throne once rested was largely destroyed.  Basically everything and everybody about which the vast majority of viewers really wanted the story to be about, in the end, it’s all gone.  And my fav character, Arya, does the perfect thing at the end: she lets curiosity and a thirst for knowledge lead her away to new adventures.  

It is rumored the screen writers, in finishing a story whose literary version was never (will never – ought never – be) completed, well, to mollify upset viewers they confessed they had no clear idea where they were going.  Now they want to make a prequel, about a time before Arya was born.  Personally, in the absence of Arya, I just don’t give a damn.

Reality and Tools

Theoretical physicists are presently waiting impatiently for any kind of experimental clue that there is still something to explain – something significantly beyond the Standard Model.  In the recent past there have been some notable close calls.  I direct your attention to Sabine’s take on the diphoton anomaly in her book, Lost in Math, and this recent article in Quanta Mag.  In particular, the point of highlighting these two short-lived instances of giddy excitement is that not only did these ephemera give rise to hundreds of papers with ready explanations of false data, but the theoretical milieu in which the authors work and strive was able to give rise to such nonsense.  The reason for this is simple: that milieu lacks sufficient constraints to limit these potential Nobel prize winners’ theoretical ramblings.  

Ideally they ought to have been able to tell the experimentalists that they should recheck their results, for they are inconsistent with accepted and proven theoretical canon.  But this is not – and seems unlikely ever to become – the case.  

In my lifetime numerous Nobel Prizes have been awarded to people who realized that crazy noncommutative Lie groups could help explain the structure of reality.  This was initially a huge OMG moment for science, made all the more mind boggling when it was recognized that after 1 (U(1)) and 2 (SU(2)) comes 3 (SU(3)), and 3 also had a role to play.  Shortly after that some mathematician, presumably, pointed out to the celebrating physicists that the set of integers extends beyond 3.  And so the merry chase was on: SU(5); SO(8); SO(10); SO(32); E8; …  This was diphoton anomaly stuff on a majestic scale, stemming, of course, from the fact that no one understood where the first three groups came from, or why they worked.  So, having no architecture to limit their brilliance, off they went in a decades long chase after the next big thing (group).  They could console themselves that they were doing hard science, because it was hard, relying on QFT, where the T there stands for theory.  

In reality it isn’t a theory, though, is it?  It’s a tool, and one that is only vaguely understood (“shut up and compute”).  And it rests on a collection of quantum ideas whose meaning has defied over a century of deep philosophical blather.  Peter Woit’s blog is my favorite, but every time his latest screed touches on anything quantum the comments section blossoms into a rich weedy field of “No, you’re not thinking of it right; you want to think of it my way!” debate that can have no resolution, because evidently all ways of interpreting QM lead to the same real world conclusions – or at least those that get any attention.  

Still, if you want a career in physics the quantum road is paved in gold, especially now with quantum computing receiving so much attention, and Sky Net just around the corner.  As to me, well, I ignored all those road signs that indicated “Exit here for QFT and Career”.  As a graduate student every time I dabbled in QFT my spidey sense went crazy, warning me that immersion in its arcana would not take me where I wanted to go, which – although I did not realize this then, despite repeated warnings from the well-meaning – was not to a sinecure in academia.  

There’s nothing wrong with QFT (well, …), but it lacks rigidity.  It’s a tool.  SU(2) and SU(3) were ok, but nothing in the way we did (do) physics was up to the task of limiting further speculation along these lines.  Our theoretical foundation (TF) was powerful enough to say, well, if we want SU(5) then the proton should decay, and if it doesn’t (and it doesn’t) then we need to throw out SU(5).  But the TF wasn’t even remotely sufficiently constrained to preclude SU(5) from the outset.  And that’s because we never understood where the 1,2,3 came from in the first place, and as physicists (and not mathematicians) we didn’t concern ourselves with such issues.  We apply; we don’t explain.

Ok, so now let’s do a Gedanken Experiment a la Thanos (warning: you are not alive in this experiment; oh, and failure to connect with past and future pop-culture references is of no concern to me). With a snap of his gauntleted fingers all sentient life … oh, hell, let’s make it all life … throughout this or any universe is gone. Eradicated. There’s still matter, and said matter clumps into balls, and the surfaces of these balls are what we called 2-spheres (before our eradication). And it’s still true that if one of these 2-spheres were really really smooth and hard, with a one atom thick atmosphere of He, the motion of these He atoms (the planet’s wind) could not be everywhere nonzero (speed units unspecified, as no life exists to specify them). For a similar reason no grid could appear on the surface of the 2-sphere that did not have poles. Indeterminacy in one of the two dimensions at some position is certain.

For the 1-sphere (circle) this is not the case. We use degrees or radians to indicate position, and there are no indeterminate coordinates. Were this not the case the Fourier transform would be impossible, and quantum theory would cease to function.

But in a universe without life there would be no QM, or QFT, or hammers, and for much the same reason. They’re all tools. But there would still be parallelizable spheres (1-sphere), and nonparallelizable spheres (2-sphere), with real lifeless universe physical consequences in both cases. And it would still be true that of all possible n-spheres only those of dimension 1, 3, or 7 (and arguably 0) are parallelizable. These dimensions (and the associated 1, 2, 4, and 8) are what I call resonant. If we allow for the existence of one sentient creature (which for purely selfish reasons I choose to be me), then I would find dealing with this resonance easiest were I to develop algebra (a tool), and these algebras in particular: real, complex, quaternion, and octonion. And after a bit more solitary cogitation I discover the sequences of Lie groups: SO(n), SU(n), Sp(n), and a few exceptional groups, all associated with the respective division algebras. The list of mathematics that bubbles up from these algebras goes on, and try as I might I would find little of interest completely unconnected to these mathematical resonances.

And what of physics? Well, in my pocket I discover some notes on Dirac theory. Generalizing from that, I discover (predict): spinors constructed from T = CHO reduce to a family of quarks and leptons existing in my 1,3-dimensional universe; and there is a mirror universe dominated by the antiparticles of those fermions; and vector bosons arise from gauging what I’d call the Standard Symmetry which arises naturally from T-maths; and connecting the two mirror universes is a 6-dimensional space carrying SU(3) charges. Then, if I felt really bored, I might invent QFT with which to generate numbers. Or, I might not, as I suspect that there’s something wrong with it. No point getting carried away and risking yet another universe-wide eradication of all life, albeit at this point just me.