There are two broad categories of mathematics: concocted; and fundamental. Concocted mathematics helps with the “how” of physics. Fundamental mathematics can give us the “why”.
Most of fundamental mathematics arises from the two finite series of integers: 1,2,4,8; 1,2,8,24.
The starting point of the first series is the set of parallelizable spheres; the second intersects with modular forms, Fourier transforms, and laminated lattices … at a minimum.
Sour old hamsters would advise you to ignore these quarter baked ideas, if you want a job in academia. And since they are in control, you would be unwise to ignore them. And on your deathbeds you will possibly – at best – be able to say: “I had a job.”
So, if science media had a plethora of exciting articles about theories that Bigfoot is alive and well and lives in a cavern 43.14 miles beneath Paris, would you be inclined to read them? If so, well, that puts a damper on the point of this Gedanken experiment. But read on, if you care to.
The point is, do you get excited by vaguely scientific stories the bona fides of which are likely beyond convincing verification now, and for the rest of human history? For example, anything regarding black holes a la Einstein, with maybe a smattering of QM kludged in. And speaking of kludges, almost anything regarding the foundations of QFT, itself a kludge.
For example, I encountered this a few days ago: “An Entire Swarm of Black Holes Has Been Caught Moving Through The Milky Way”. Well, yikes. There is no room for doubt in that title. And yet, I wondered, if true, how could we possibly know that? We have just barely the technology to capture a picture of a reddish area around a black smudge, and claim it is a black hole, all the while having only the vaguest of ideas what that really means. And speaking of means, by what means have we “caught” a swarm of black holes moving through anything? Well, unsurprisingly, we have not. It is yellow journalistic conjecture – blatant clickbait, florid and sensational.
Had the story been about a swarm of Bigfoots I should likely have read past the first sentence, finding entertainment in how the story justified its central premise. But black holes? Much of our work in this area is tantamount to attempting to make a computer chip with a hammer and screwdriver, for we are comfortable with such tools, and are hesitant to admit that these tools, which have got us so far, may not be adequate to get us any further.
Recently PW’s blog informed me that the greatest minds in theoretical physics continue to gather and confabulate about the sorry state of this science. PW quoted LM, who was quoting some bigwig at Princeton:
“…Millennials are a generation that prefers to hide in a herd of stupid sheep and remain at the surface that is increasingly superficial…
“So most of the stuff that is done in ‘quantum information within quantum gravity’ is just the work of mediocre people who want to keep their entitlements but who don’t really have any more profound ambitions.”
Sigh. Swarms of bigwigs, but nary a Bigfoot to be seen. I thought I might comment on that blog, but I could only come up with a single word to describe my thinking: chortle.
As is frequently the case, when I have got most of the way through one of my peevish online screeds, like this one, I am wondering if I am covering old ground. And of course I am, but then, those about whom I write do nothing but that. If only I had the strength to ignore them.
There is a saying, neither a platitude nor profound, just obvious: creativity lives on the border between order and chaos. The manner in which this may apply to what is written above is left as an exercise for the reader.
As for me, it’s nearly vaca time, and I think I’ll turn my writing to another book. To my avid reader: Ciao!
There is a difference – vast actually – between having preconceptions about how physics should work and applying some new mathematical fad to it; and, on the other hand, having some mathematics and following it in hopes it has fuck all to do with reality, doing your best to ignore all preconceptions. One of those paths is pure. (That’s what I tried to do. Succeeded nicely, but, you know, attack ships on fire off the shoulder of Orion, and all that.)
Or, alternatively, you could partake in an effort to make QFT mathematically rigorous, or something equally monkish and onanistic. For sure the universe is craving that. But let’s move on to anime.
This is for those who believe all anime not stemming from Studio Ghibli consists of angstvoll youngsters with big eyes and bigger swords battling the forces of darkness while screaming. Indeed, there’s a lot of that, and some isn’t half bad, but then there’s Girls’ Last Tour, about which I’ve written before, and Made in Abyss, which I’ve almost certainly mentioned in the past. But now we’re going to do a deep dive, and if you have uninformed preconceptions (unrelated to theoretical physics), then I hope to rend them into tiny pieces, and take those pieces and subject them to searing heat, rendering the rent whole into plasma which will congeal into something unrecognizable, unless you’re familiar with Venetian gondolas; it may remind you of one of those. So, my plan is to rewatch the series and describe stuff.
Change of plans
So, yeah, no. In the meantime my psyche has become more fragile. Not flower-like, but maybe akin to a sand castle made near the water line at low tide.
The thing is, the artwork in the anime is as good as any I’ve ever seen, including Ghibli. The heroes of the story (Made in Abyss) – as far as I’ve gone – are a girl, a boy (who is actually at least mostly a robot), and another girl (who is part rabbit). She was not born like that, but … just wait. All these children are around 12, hovering on the edge of puberty.
Now, the age of 10 is my ideal age, and I often think that when I surpassed that age my spirit clung on to 10 like a limpet, and it would not let go. It’s the perfect age. Far enough from puberty that its echoes are faint, but old enough to recognize that the world, in the hands of a 10 year old, can be a really fun place, if the environment in which you live does not make soul-crushing demands. So, yeah, … crikey. But the point is, the kids in Made in Abyss are close enough to that age that … You know, I still read the occasional bit of YA literature. Quelle surprise, right?
Where were we? Cute kids; adventurous; all somewhat mysterious; big cute anime eyes, living in a place that oh-my-gods-is-that-ever-hyper-super-mega-cool! You see, it’s a very large city built in a circle that is some kilometers in diameter. The city has no structures inside the circle, because there’s nothing upon which to build them there. There is a hole. And not a dank hole, nor even a hobbit hole, but an entire ecosystem of levels going down down down – no one knows how far, because those that go past some point never come back, although sometimes they send balloons up. And you’re likely wondering, if they can send balloons up, why not themselves in bigger balloons. Just wait.
So, the Abyss is full of plants and animals, many of which – especially the animals – are not found on the surface. It should be added that this Abyss is full of structure: places you can walk and explore and even – should you be so inclined – build a home. There is weather: clouds and such like. And it is also full of relics, and many surface people go down a short ways into the Abyss daily in search of same, for they are sometimes powerful. And all are valuable.
And there I am, when first watching the first two or three episodes of season 1, so thoroughly enthralled by kids like me – just a tad older – exploring an enormous, gigantic, tremendous and mysterious Abyss, even the existence of which is a tremendous mystery … golly. It had just about everything I find most addictive in fiction, or nonfiction (I’ve entered a few enormous caverns in the past; they enthrall me). But this is way way way beyond caverns.
After season 1 of the show, a film was made to continue the story: Made in Abyss: Dawn of the Deep Soul. I plan(ned) to get it as soon as available in the States. And I still want it, but no longer with bounce up and down in your chair eagerness. Why the hesitation?
You see, the Abyss looks paradisiacal, but those looks are somewhat deceiving. Some who go into the Abyss get eaten, by large flying snake-wormy things, or spiders (big ones), or this large elegant bird-like thing that while feeding on some hapless child – as witnessed by our heroes – will imitate the voice of that child in a call for help to lure others to feast upon. The artwork at this point is still stunning, but whoa. What the fuck? This is all unsettling. And we haven’t even met the bunny girl yet, and her best friend. Just wait.
So initially it’s just our primary girl heroine, and she discovers the robot boy, who is an extremely powerful relic (maybe; he is extremely powerful, but I’m not sure he’s a relic). He has extendable robot arms, and can emit a beam from his palm that can vaporize (almost?) anything, but conks him out for some time after to allow regeneration. Our heroine’s life is saved early on by this beam, and that is how they meet.
But the biggest danger of the Abyss is in exiting it. Even if you had an elevator, this could ruin your day. It’s kind of like the bends on steroids. Ascend too rapidly and you start vomiting, and your eyes bleed. And if you go beyond a certain depth and then ascend too rapidly, your DNA gets altered. And it’s excruciating. An accumulation of such environmental maleficence overcame our heroine at one point, and robo-boy, overcome with grief and fear, began crying and wailing in a deeply chilling way.
Bunny girl was bunny girl because her DNA had been restructured, but not because she ascended too quickly. Nay nay. A character who dominates the film sequel had captured bunny girl and her best friend, and performed an experiment on them. I suppose this experiment simulated a rapid ascent – you know, it’s been a while since I watched season 1. The bunny girl got bunnified – a kind of cute result, and I guess she became immune to further changes. I’m not sure. But her best friend in the whole world was turned into a living gelatinous mass with eyes and a sort of mouth. During the transformation process – awful to watch – before she lost the ability to speak, she looks at her friend and begs, “Please kill me.” Pretty horrific, actually.
When our two heroes first encounter bunny girl, she takes them to her home – a really cool eco-friendly sphere – where they meet gelatinous girl. But here’s the thing. Bunny girl made this home to be a place where she could care for her best friend, but bunny girl is mortal. She will die someday, but by some perverse Abyss logic, her friend will not. Gelatinous girl is immortal, and almost impossible to kill by ordinary homicidal means. And this fact hovers over bunny girl like a cauldron of molten awfulness, for when she is gone, gelatinous girl – bunny girl’s bestest friend in the whole world – will spend eternity alone, and … the mind boggles.
Anyway, long story short, bunny girl convinces our heroine and robo-boy that this situation is horrifically untenable, and the solution is to have robo-boy vaporize her best friend with his beam. This done, bunny girl experiences profoundly deep grief, and she wails in a manner that was far too like the sound of real grief. Ma femme freaked at the sound, which resonated with her grief when her mother passed, and could watch no more.
The killing of gelatinous girl was necessary, and even wanted by gelatinous girl herself. Everyone recognized this, and after some time our heroine and robo-boy need to carry on their journey. Bunny girl, having nothing but memories of heartbreak in her home, and no further obligations, decides to leave it and travel with our duo as they descend ever deeper into the Abyss. The goal is to find our heroine’s mother, who descended very very deep some years before.
So, now we have this hyper-cute trio exploring the depths of this awesome mystery, and it’s all fun and … But fucking hell? Does anyone even remember the unceasingly traumatic journey that got them to this point?!
So, season 1 ends with the cuteness trio traipsing down into the Abyss, and everything looks great; the artwork is still stunning; the mysteries no less compelling; which is just as well, as my PTSD couldn’t take much more at the time.
Meanwhile, having become aware that there was a film that followed the story from the end of season 1, I began googling like crazy, and failed to determine when it would be available over here. Very frustrating and all, but my googling eventually led me to uncover some plot points of the film, and that the film revolves around the character who did the experiment that resulted in bunny girl and gelatinous girl. I read some comments by some lucky viewers. The gist of these is that the film is even more traumatic than the series. What? Upon discovering that I immediately became a lot more patient. I’ll see it when I see it, and if I die first, well, I can live with that.
And if by some miracle of inanity you’re still thinking this is a kid-friendly chunk of entertainment, let me just add that robo-boy can – and does at one point at least – get an erection. Maybe the Japanese are more ok with this than your typical red or blue state American. I’m neither red nor blue, and, so, anyway.
I think in my next blog, as an antidote to this disturbing and unnecessary pile of mind seepage, I’ll discuss my favorite Jean Paul Belmondo film. But I needed to discuss Made in Abyss, a stunning work of anime, and by far the most nontrivial I’ve ever watched. Maybe it’s just me.
So, yeah, David Hume wrote something that I discovered many years ago and have more than once quoted in my own rambling prose. In particular:
“Abstruse thought and profound researches I prohibit, and will severely punish, by the pensive melancholy which they introduce, by the endless uncertainty in which they involve you, and by the cold reception which your pretended discoveries shall meet with, when communicated. Be a philosopher; but, amidst all your philosophy, be still a man.”
I haven’t a clue who he was writing about, but I’m guessing his circle of acquaintances included many contemporary intellectuals, and many of these would have been young and driven; firebrands. Their eager neediness to have their groundbreaking discoveries recognized by a viscously entrenched body of mainstream luminaries would have driven many close to or beyond madness. Hume evidently found such behavior annoying, and in response wrote what he wrote. The tl;dr version is: “Cut it out.”
We’ll never know the names of the majority of such roadkill, and it isn’t only failing to achieve recognition that drives these individuals to the brink and beyond. The “abstruse thought and profound researches” alone can, even if recognized, eat at the soul and leave the mind gasping for air (I do love my metaphors).
The really good – if rather too dramatic – BBC series, Dangerous Knowledge, focuses on four well-known researchers in mathematics and physics: Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing. All ended their lives deeply disturbed. Cantor and Boltzmann confronted the dual foes of deep obsessive thinking, and a resistant mainstream. Turing’s case is somewhat unique, and his inclusion doubtless had much to do with his British nationality, a nationality that contributed greatly to his downfall. Gödel, on the other hand, was showered with acclaim throughout most of his life, but in the end he starved himself to death, subject to profound paranoia.
PW recently linked to an excellent article about the life and work of Alexander Grothendieck. Who?
In the early 1970s, as a graduate student in mathematics, I had heard his name, but knew very little about him. A fellow graduate student, who I remember meeting at least once, would eventually become his nth wife, but I was – and am – largely clueless as to what he did to achieve international acclaim. But I am including him in this blog because of his life, and how it ended. The essay begins:
“Alexander Grothendieck started out as the greatest mathematician of the Twentieth Century, and ended up as a destitute hermit, lost in a labyrinth of ideas, dreams and maybe delusions that we still haven’t been able to decipher.”
And near the end:
“In June of 1990, Grothendieck stopped eating for 45 days. He was found by one of his children in a semicomatose state and subject to violent hallucinations, afraid for his life. Miraculously Grothendieck, who was 62 years old, survived without any physical consequences.”
Shortly after that he disappeared.
“The great mathematician, who had let his beard grow long and almost always wore a strange arab-style caftan, had taken refuge in a tiny village at the foot of the Pyrenees, where no one knew him. He lived there for 23 years, in a shabby abandoned farm, in total isolation. The village’s 200 inhabitants, who didn’t know who he was, soon got used to his presence, respecting his privacy. He received very few visits, all of them from the few people who knew about his new residence, and soon not even from them.”
Because of his parents, his life was far from uneventful; it was fraught. The weight of that life, on top of the heavier weight of his immersion into extremely abstruse thought, where no one had gone before, well, yeah, so there it is.
I’m not done, so listen up
My favorite book on 20th century theoretical physics, is The Quantum Ten: A Story of Passion, Tragedy, Ambition, and Science, by Sheilla Jones. If you’re suffering from the delusion that the founders of quantum mechanics lived happy adventurous lives – a kind of nerd Ibiza – and not prone to suicidal thoughts, when not actually committing suicide, or being institutionalized due to mental and emotional burnout, then this is the book for you.
Still, they had each other, and Solvay was not Ibiza, but it was not nothing. People like Grothendieck, Cantor and Gödel – or such is my impression – produced their groundbreaking work alone. They interacted with others, even teaching, but their intellectual labors were solitary. That kind of thing takes its toll.
I became interested in this whole genre when, after 40 years of solitary work in mathematics and physics, I realized I was teetering very close to the edge of what my mind could endure. And I had no interest in adding myself to the many famous, and much more numerous nameless, theorists who teetered off their edges. So I quit. I briefly went back to it, at Cohl Furey’s urging, but this did not end well:
“And anyway, I can’t do the work anymore. I mentioned somewhere–possibly in another book–that I told Cohl I found it psychologically difficult to work on my ideas in mathematical physics. She expressed doubts, and suggested that that would be too bad. Prodded by her reaction, I started thinking about a way of combining some ideas I’d had in pure mathematics with notions I’d had in physics. Very quickly I had a result I found rather exciting. I pursued it rabidly for a couple of weeks, and quit finally when I realized I was getting close to a mental breakdown. Such work seldom gives your brain any rest, even when asleep. I simply could not do it. I am used up.”
The great mass of conventional theorists are to all extents and purposes a book club, meeting periodically over tea to discuss arcana. I approve. But there will always be some few who look too deeply into the abyss. My advice to them: if you notice the abyss looking back into you, avert your gaze. This advice will not be heeded.
So, what’s going on? I still have cancer. Well, since I’ll have it for the rest of my life, that’s hardly a surprise. It may kill me some day, or something else may, like giant mutant angry frogs intent on punishing me for my mistreatment of their normal sized brethren when I was 9 years old. And I’d deserve it. And truth be told, I’d rather go out via frogs – big ones, and angry. As they came rushing at me, I would relax in the knowledge that weirdness does exist, and not everything is dominated by gaslighting world leaders, and – closer to home – gaslighting pop sci proponents like Kaku and Greene in their desperate attempts to stay relevant and admired by a world of fuzzy, quadrupedal, ruminant muggles. Oh, well, it’s a living. And theoretical particle physics is dead now anyway. (Ignore all pop sci articles that look like this: “Blah blah blah LHC blah blah fifth force blah blah new physics blah dee blah muon blah?” Well, ignore them until they appear in reputable places without the question mark, or words like “may”, “could”, “might”, “god”, or “cwazy wabbit”.)
You know, I’ve never been part of the human race. It took me a long time to realize this, that people with whom I associated viewed me as an amusing oddity, but always something separate. True, I spent nearly 6 decades with annoying hormones – the gundam pilots I wrote about earlier – attempting to turn me into a biological puppet, periodically wresting control of my life and will to serve their own selfish ends. But, yeah, once told I had an incurable disease, and presented with a series options for how to confront and control it, using the advice of my oncologist, and lots of googling, a therapy was devised – and very quickly implemented – that has left me pilotless, a gundam with free will. I’d always wondered what it would be like, and here, in the final years of my life, I am finding the experience fascinating. It has definitely removed me still further from humanity, the collective. Age gave me a change of perspective, but this change was more profound. At times I feel like one of MCU’s Watchers, and the odds are slim that you know what this means, but I look upon humanity, and all the fucked up crap they get up to, as an analytical cosmic intelligence might. Whoa! WHOA! Where are you going with this, Geoffrey? Take a chill pill and let’s get back to what you’d planned to do with this blog. Fuck’s sake. You’re just this guy writing on an iPad. (No, I’m not.) What? What did you say? You had better behave yourself, young man. (Pfft. [Gestures rudely.])
Great equations in physics … fuck
Before I carry on, I have to rectify a misapprehension you almost certainly harbor regarding the Dirac equation. As noted recently by PW, this is pretty much universally acknowledged to be one of the great equations of theoretical physics. Sure, and of course it is, but what makes it great – even revolutionary? There are lots of such equations that involve derivatives, ultimately integration, and a slew of analytical methods. Theoretical physicists are addicted to analysis, occasionally sniffing topology, and many harbor a conviction that more and deeper applications of analytical methods will cause unification to be born Athena-like from the forehead of analysis. But the Dirac equation is not great for the ways in which it is similar to everything else, but the manner in which it is different, and that difference is algebraic. It is architectural. This algebraic/architectural aspect of the Dirac equation is generally minimized by mainstream analytical TPers; it is an embarrassment. “And that is why you fail.”
As I have mentioned elsewhere once or thrice, upon retiring I wondered how I would take it, being set adrift after an adult lifetime of something resembling labor. Within little more than 24 hours I realized I had become Bertie Wooster, whose independent and labor-less lifestyle I had always found so attractive in the many works of P.G. Wodehouse revolving around this character. I began to write books that no one would ever read, but which brought me joy in their creation. Then I shifted to blogging when covid shut down foreign sources of memoir inspiration.
Wodehouse’s oeuvre is light on deep philosophical musings, and of horror and science fiction there is none. Still, in my technical writing I have droned on frequently on mathematical resonance; Wodehouse’s writing, in my cranium, creates a literary resonance that comes close to simulating an almost chemical addiction. So, for example:
“His whole attitude recalled irresistibly to the mind that of some assiduous hound who will persist in laying a dead rat on the drawing-room carpet, though repeatedly apprised by word and gesture that the market for same is sluggish or even non-existent.”
I mean, see? If you don’t, that’s ok. For many people, especially in theoretical physics, I am, to all intents and purposes, that hound, and the dead rat is my collected works in maths and physics. Cornell tried to shoo me out of the arXiv, and, failing that, shunted me into gen-phys, basically the doghouse out back. Still, I will persist in laying the dead rat on their drawing-room carpet in hopes they will see its superiority to their dead mouse, which is looking considerably more oogy than my rat.
I’ll finish with more Wodehouse, to lighten the mood of those deserving of mood lightening. You will know who you are by whether or not your mood is lightened.
“When I entered the establishment, he was leaning over the counter, his gaze riveted on some sort of merchandise which was being shown him by the gentlemanly assistant. To prod him in the hindquarters with my umbrella was with me the work of an instant.
“‘Ahoy, there, Stilton!’ I cried.
“He spun around with a sort of guilty bound, like an adagio surprised while watering the cat’s milk.
“‘Oh, hullo,’ he said.
“There was a pause. At a moment like this, with old boyhood friends meeting again after long separation, I mean to say, you might have expected a good deal of animated what-ho-ing and an immediate picking up of the threads. Of this, however, there was a marked absence. The Auld Lang Syne was strong in me, but not, or I was mistaken, equally strong in G. D’Arcy Cheesewright. I have met so many people in my time who have wished Bertram was elsewhere that I have come to recognize the signs. And it was these signs that this former playmate was now exhibiting.
“He drew me away from the counter, shielding it from my gaze with his person, like someone trying to hide the body.
“‘I wish you wouldn’t go spiking people in the backside with your beastly umbrella,’ he said, and one sensed the querulous note. ‘Gave me a nasty shock.’
“I apologized gracefully, explaining that if you have an umbrella and are fortunate enough to catch an old acquaintance bending, you naturally do not let the opportunity slip, and endeavored to set him at ease with genial chit-chat. From the embarrassment he was displaying, I might have been some high official in the police force interrupting him in the middle of a smash and grab raid. His demeanour perplexed me.”
Aaah. It’s like reading a good book while lounging in a hammock in the dappled shade of a palm tree that bends to and fro in a light tropical breeze off an azure sea. A refreshing drink, perhaps sporting a miniature umbrella, is sitting within reach at a nearby table. Bliss.
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 …
Like addicts recognizing the need to correct misbehavior, but unable to do so – unable to break the constricting addiction, or even anymore able to imagine what that might be like – the theoretical physics elite occasionally recognizes the need to introduce ideas from the wastelands, but then they get immersed in discussions of the intricacies of QFT, or the injustice of SUSY’s failure, or [long list of 40 year old debates and failures]:
Thus the comforting bed of familiar old ideas, it does make uninspired NPCs of them all, And thus the native hue of resolution Is sickled o’er with the pale cast of ennui. And enterprises of great pith and moment — With this regard their currents turn awry And lose the name of action.
But I may be in error. Other than Peter Woit’s blog, and the occasional email from friends and strangers out in the broader world, I am not really sure what’s going on the the cranium of your above average TPer … well, there is the Boston Area Physics Calendar, which gives the impression that the vast majority of theorists have moved away from HEP. And PW continues to blog about what he encounters in the media, strongly filtered by his expertise in QFT, a filter used by virtually everyone else who counts, in the estimation of everyone else who counts, as it were. One of the readers of Peter’s latest (as I write) commented:
“Il est dangereux d’avoir raison dans des choses où des hommes accrédités ont tort.” Voltaire
That is: “It is dangerous to be right where accredited men are wrong.” I absolutely love this quote. In its spirit I offered the following comment:
“Il est aussi dangereux d’avoir raison beaucoup de temp avant le bon moment, mais beaucoup plus triste.”
This may mean: “It is also dangerous to be right a long time before the right time, but much sadder.” This is what a few years of Duolingo French will get you. Maybe I should have used “longtemps”. But anyway PW didn’t like it, and for reasons with which I can’t cavil: the comment was self serving, directly relating to my own work, which he recognized. Such comments are not allowed. Still, I was pleased with it, and … whoa … I have my own blog, which is frequently self-serving, and I don’t really care how often I serve myself.
Moving on. I get most of my news online, and much of that with the Flipboard app on one of my many Apple devices. I subscribe to a variety of different feeds, like Travel, Science, Physics, Science Fiction, Humor and Memes. Animation too; mustn’t forget animation. And I’ve created a few of my own feeds: collections of stuff I find insightful, fascinating, and/or entertaining. I use a pseudonym.
But let’s focus here on Travel. And let’s recognize that article writers have to make a living, and the majority of them cut corners to get things out as quickly as possible. This often means that when they see one writer use an idea, they frequently glom onto it, becoming a vector in its viral spread. And the shared idea that irks me a lot (maybe not the most, but a lot) is the Bucket List.
This all started, as I recall, with the eponymous 2007 film about some old geezers (like me) who had lists of things they wanted to do and accomplish before kicking the bucket. (And here I am reminded of something that thoroughly astonishes me every time I think about it: the iPhone – and so smart phones in general – was introduced in 2007; this is, like, yesterday, right? Yet it feels like 50 years ago, so great and transformative is this technology. It has dilated time, dude! So, yeah, WTF.)
The travel articles … wait; let me find one … just a moment … just a moment (click here if you’re not HAL) … ok, back. That didn’t take long. But I found an article guilty of this transgression: “Bucket list worthy places in Japan’s scenic northeast”. But why is this a transgression? Well, of course, it may be so only to me. Ok, it is only me … maybe.
I recently read what turned out to be an autobiographical graphic novel, except it wasn’t really a novel, then, was it. It was called, We Saw Scenery, the title deriving from the parents of the author taking her on childhood trips where scenery was seen. Scenery can be cool, and when you’re a vapid young Millennial or Z, it’s an essential accoutrement to your need to plaster your face on the intertubes, with scenery in the background, at which you may never look directly. But I’m a colorful, lively and exciting (all antonyms of vapid) elder Boomer, and if I photograph scenery, the scenery takes up 100% of the photo. Still …
After a point one has to wonder, what is the point? Were I to go to Japan’s scenic northeast, in what way will I die more contentedly having done so? Of course, my attitude may be a little soured by the fact that I have a terminal illness, so anything that reminds me of that – like a 10 foot long bucket list – is moderately annoying. Scenery is nice. I like scenery. But as I have mentioned once or thrice in previous blogs, if there are not nearby cafes and interesting people walking dogs, well, I’m just not sure. Here’s my bucket list, in entirety:
Sit in cafe and watch world go by; Read; Write; Make friends with every encountered dog willing to be friendly.
Yesterday at the beach I encountered a young black Labrador retriever wearing the cone of shame. I asked the owner why. She said he’d recently been “fixed”, and was still healing, so the cone was there to prevent him licking his greatly diminished privates. I got down on my knees in the sand and said some commiserating things to the poor guy, and I reached into the cone and scratched his ears, behind his ears, and everywhere else in the cone. His reaction was basically this: “Uh, excuse me. This is a little forward of you. What are you doi … oh, gods, that feels so good; you know, I can’t get to those spots myself because I’ve got this ridiculous piece of headwear, and, oh, yeah, the neck, quite itchy; I am so so grateful.” If you’re a dog person, it’s not hard to understand what they’re saying. And if you don’t understand, then you could still be a dog person, but not a person dog, like me.
In 1986 two Chicago based film critics (Siskel and Ebert) took their reviewing skills to the little screen (much littler then than now, although those CRT pigs weighed a lot more than today’s flat screens). So, this is the misty past. Universities were starting to get internet connectivity that year, but the WWW was but a gleam in CERN’s eye. Still, time does pass, and eventually Siskel succumbs to illness. Ebert carries on, and after a while he – or some management type, more likely – finds a new cohost, named Roeper, who is a younger more peevish version of Siskel. In 2001 they review The Lord of the Rings, part the first, subtitled, The Fellowship of the Ring.
Keep in mind, by this time I had read that book, and the others in the trilogy, more than 10 times (total to date: 13; once in German, and once aloud to some nephews), and not because I disliked them and had a monk’s need to punish myself for past sins. No, au contraire, I was, and am, a fan. Roeper was clearly not a fan, leaning more towards the likes of Claire’s Knee, I strongly suspect. And if his take on LoTR is any indication, it is clear he had never read any of Tolkien’s works. Indeed, it seems likely he had never heard of the trilogy, and dismissed the entire genre as insignificant twaddle.
So, the LoTR episode is in full swing, and they’re bantering back and forth. Ebert has said some positive things about this grandly epic film. And then Roeper chimes in, and he says at one point: “The characters are getting tedious after a while … they go on one adventure after another …”. From this I conclude that he also thought the Iliad and the Odyssey were tedious drivel. He continues: “… this hobbit character, who’s, you know, in this elfin world, or whatever, and he’s wide-eyed and …”. Yikes. Holy fuck. I mean, he’s not strictly speaking saying anything wrong in any of this. He makes semi coherent English sentences and phrases, but yikes. And yes, “this hobbit character” – that would be Frodo – does live in a world in which elves also live, or whatever; and sure, Frodo was born and raised in the Shire, so perhaps a tad naive, but … Roeper carries on like this, utterly and entirely dismissing the film for its great sin of not pertaining to Claire’s knee, but instead continually introducing places and creatures that do not exist, and are evidently unimaginable (I mean, what next? A cyclops whose eye was put out by Noman?). And then, oh, crap, in summarizing the story he talks about “this silly little ring”, which everyone seems so preoccupied with for some bizarre reason.
Three rings for the Elven-kings under the sky, Seven for the Dwarf-lords in their halls of stone, Nine for mortal men doomed to die, One silly little ring for the Dark Lord on his dark throne; In the Land of Mordor where the shadows lie.
One silly little ring to rule them all, one silly little ring to find them, One silly little ring to bring them all, and in the darkness bind them; In the Land of Mordor where the shadows lie.
Well, I must confess, had the book and the movie used this modified description, I would have found it entertaining, but in being less ominous, I’d likely have stopped at 3 or 4 reads of the epic. Perhaps Roeper’s view was warped by Wagner’s opera, Der Silly Little Ring des Nibelungen. Or the Norse saga upon which it was based. Sigh. Still, Roeper by this point had given every sign that not only had he never read the books, but really seemed never to have heard of them. And it became clear at the end of his goofy tirade that he may not have known it was a “them” – that there was more than one book. Did he even know the film was based on a book?
So, yeah, finally, Roeper completely astonished me – and Ebert, who was getting more and more concerned for his cohost, who seemed to be foaming at the mouth – by complaining that the ending of the film left it so obviously wide open for a sequel to appear at some future date, draining the wallets of fans for this film number 2. At that point, in my original viewing in 2001, my jaw hit the floor. Did he just say that? WTF!?!?!? And an idea started growing in my younger – but not really young – brain: No one should be allowed to review any work of art if they have no interest in the genre, and may even disdain it.
By the way, Ebert – embarrassed for his cohost, and always the most cogent and insightful of all the critics who ever appeared on the show – did his best to help Roeper out of the hole of ignorance he’d dug for himself. He succeeded to some extent.
Alas, eventually Ebert also succumbed to illness, and the show was taken over by younger, less cogent and insightful critics. But without Ebert it was destined to fail, and although I continued to watch, albeit less regularly, I remember nothing about this later incarnation other than a general sense of annoyance.
That Reminds Me
Hollywood, like mainstream theoretical physics, is intent on diminishing the influence of any work outside their narrow purview. In the case of theoretical physics, this involves limiting exposure of the works of people like me, by keeping such works out of the arXiv, and when that is impossible, relegating the works to gen-ph, a kind of trash heap set aside for papers with which the mainstream is displeased, but can’t outright banish, because they have been published.
Hollywood doesn’t have an arXiv, but it does have film critics, and it rules them with an iron fist, if they are American, and if they want to maintain cordial relations with the mother ship. This manifests itself in generally awful reviews of good foreign films by American reviewers – especially science fiction blockbusters (Hollywood is less afraid of Clair’s Knee, for such films have a limited audience that Hollywood considers irrelevant), and a sure indication of such meddling can be found in the Rotten Tomatoes favorability numbers, which will look something like this: Critics – 22%; Viewers – 95%. Numbers like these, pertaining to foreign films, should be ignored, except for the Viewers score. (Example: Valerian and the City of a Thousand Planets. 82% of google users liked it; Rotten Tomatoes critics gave it 47%.) Ignore American reviews; see the film.
What else is going on?
Nothing, really. 2021 has been blissfully free of catastrophes and drama. The pandemic is at an end; climate change has stopped changing the climate; the peoples of the world are content with nearly everything, and they have promised to stop overpopulating your planet (not my planet – I want no part of this one – it’s a fucking nightmare); and bunnies and unicorns …
You know …
It isn’t really that mainstream theoretical physicists have formed a secret cabal to exclude everything that does not discuss, exploit, or promote QFT. It’s just that this is what they’re trained to do; they’re mostly goobers and nerds (I have some nerd-cred myself), and they like rubbing elbows at conferences while discussing familiar topics (my problem has always been that I like rubbing elbows at conferences while discussing unfamiliar topics). It’s all very comfortable, until someone outside the circle points out the lack of progress over the last 20 to 40 years in advancing our understanding of the universe. At that point they bring up the successes of QED, quarks, and quantum entanglement. If need be, more senior members may be called upon to address the outside world with stern and confident gravitas. This kind of thing still works in allaying the fears of those who suspect the theorists may not have a clue. For the time being, at least. But it’s really not a cabal. One hears talk of deep states nowadays, but really, quelle surprise. Deep states are inevitable, and they form organically, but … ooh, that’s a pretty cloud.
For this blog I’d originally written a series of global improvements that would come about in 2021, suggesting that many of the planet’s ills – like the incarceration or sentencing to death of rebellious people in doctrinaire nations; like slavery (at least 20 million people throughout the world presently enslaved); and drugs, the bad kind, that companies and cartels … well, you get the idea. Anyway, these various chunks of badness, and many more, would go away when the perpetrators would, in this new year, so full of hope, join hands around the world with bunnies and unicorns. However, I doubt I need to spell out how unlikely this is. I mean, unicorns are notoriously antisocial, and they don’t have hands. As to bunnies … let’s not go there.
Alas. My wife thought my original repetitive list was annoying. She reminded me how much I dislike lists that employ repetitive verbiage. Good point. I felt uncomfortable with what I’d written and discarded it, but I did have one hope for the new year that pertained to physics. It was this:
“Mainstream theoretical physicists, who have spent decades using their power and influence to suppress contrary ideas, and to ceaselessly promulgate the notion that facility with analytical (QFT, ST, …) and geometric (GR, ST, …) tools is the righteous and sole path to truth, under the bizarre impression that having tools, and knowing how to use them, makes you an architect with a profound understanding of design … 2021 finds them repenting and joining hands around the world with bunnies and unicorns.” So, yeah, sarcasm.
Let me just add a brief postscript to that, and then I’ll move on. In the sanctified popular science media it is occasionally admitted that theoretical physics has dug itself into a very deep hole over the last few decades. One encounters occasional mutterings from theorists themselves that what is needed are well-connected young geniuses to come along and bring us into the light … in some ill-defined future. In almost every instance it is supposed, assumed, hoped, that these young turks, having come up through the sanctified ranks, will carry on using the tools beloved by those who failed, viz., shovels.
Never once is it suggested that young turks, working outside the consecrated mainstream, may already have developed ideas that could lead the hidebound into a brighter future, and that they may have done so years ago – decades, even. The very suggestion that there may – could, at least theoretically – exist a potential evanescent future that has been assiduously disregarded in favor of a comfortably crusty past is beyond anathema (to be clear, it is the suggestion, should it be made – and it is being made; please keep up – that is beyond anathema; lots of nouns in that sentence). Anyway, I’m blushing now, so let’s stop here. Don’t want to annoy my wife.
And speaking of books …
In 1965, I think, I first encountered The Lord of the Rings trilogy at a bookstore in Wellesley, Massachusetts. I read the trilogy so often in the 2 or so decades thereafter that I was able eventually to read it in German, despite having only two college years of the language. But I knew enough of it, and more than enough of the books, to be able to follow the story easily in this foreign tongue.
In more recent years, my wife and I came to understand that our travels overseas needn’t be as broad and expansive as once they were, and we zeroed in on a very limited number of nations and places that gave us joy. As a consequence, she began to study Italian, and I French. Recalling how helpful LotR was in helping me improve my German, I recently ordered all three of the books of LotR, and The Hobbit, in French. I have begun with The Hobbit, and although French is less logical than German, and much harder to understand, still I am enjoying the experience. Bilbo Bessac (not Baggins – although sac means bag, so …) has just listened to the dwarves sing their haunting song about far away misty mountains, but he has not yet come to understand how pointed all these shenanigans are, and that he is expected to visit said mountains, despite having indicated to Gandalf that he has no interest in adventures.
Eventually Bilbo will go on adventures, but, like my wife and I, in the fullness of time he will come to feel he has had enough of the broadening influence of travel, and he will settle in Paris … er, I mean, Rivendell.
Gonads, or why there is no cure
Few of us are actually individuals, so how can we be judged as such? We are cyborgs … no, replicants … no, that’s not right either. Gundams! That’s what we are. And the pilots do not drive us from our heads, but from our gonads. In the midst of fierce battle, with the life of the male Gundam in jeopardy, if the gonad pilots get kicked they cause the Gundam host to topple over and curl up into a ball – a ball intended to protect the gonad pilots. The Gundam itself becomes immediately of secondary importance, for it is only a vehicle intended to aid the pilots in achieving their ultimate goal, a kind of immortality. The pilots are amoral, and they don’t believe in unicorns, so there will always be Gundams willing to suck the life out of other Gundams at the behest of their gonad pilots. Avoid them, if you can. It will be easier to do so once the life-sucking Gundams are isolated in Antarctica, which is the plan. Or on Mars. Mars would be best, as on Mars they would be less able to get up to mischief.
Having determined I was not rabidly partisan, the old guy – perhaps a bit older than myself – complained with more than a tinge of regret that no one would listen to his concerns about the state of the nation. I got the impression that lecturing his descendants had proven frustratingly and markedly lacking in efficacy. I cautiously suggested that the young people who had turned their deaf ears to him … well, it’s their world now, sort of. Still lots of elders in control of lots of stuff, but at least culturally the world belongs to the inheritors, so bemoaning the fading mores of yesteryear will change nothing. Well, that’s a bit strong perhaps. Let’s just say that there are no precedents, so the odds are slim to none.
The old guy craved a return to a world that he understood, but a world I strongly suspect only ever existed in verisimilitude. Still, were his perfect world spread out before me I rather think I’d find it attractive in many respects. But really, I’d prefer Paris in the 1920s: Paris, the Luminous Years. Woody Allen’s Midnight in Paris, as I’ve said before, and elsewhere, was an interesting depiction, but a character in it craved an even earlier time: La Belle Epoque. The main character suggested that such nostalgic cravings are natural, but they are will o’ the wisps, for the benefits attached to one age over another are illusory. Well, but you know, not always. I don’t crave America in the 1950s, nor much of anywhere in the world during the Great Depression (exception below).
The world I am gradually leaving has become uncomfortably factional, to the point that factions on the extremes wish extreme violence on factions on the opposite extremes, this involving – preferably – death. I was in college during a time of equal or greater factionalism, albeit more focused, I would say. I was the same age as those who died in the Kent State shootings. That sort of thing was less satisfying to the perpetrators than you’re maybe thinking, whichever extreme you favor.
Still, that event does not stand alone. The violent suppression of dissent is a time honored tradition throughout the world, and all of its history. Kent State is about as big an event on that list as is the murder hornet scare on the list of 2020 horrors. But, you know, crowds will go mad; and I will continue to resist going mad with them. I did that a little bit in the 1960s. Neither sorry nor proud.
Out of the line of fire in books
Speaking of yearning for other places in other times, I recently read a perfectly wonderful book: Harry’s Bar: The Life and Times of the Legendary Venice Landmark, by Arrigo Cipriani. I suppose I wouldn’t recommend it to the majority of millennials and Zs, for they will not understand why they are not the book’s focus, nor why this memoir has so many eccentric characters that are not excoriated for their lack of adhesion to modern doctrinaire …
Ooh, careful, Geoffrey. Careful. Put the old guy curmudgeon back in its box. Back away … slowly …
So, anyway, for those whose tastes are even remotely like mine, I recommend it. On the Cipriani website it has this to say:
“On May 13, 1931, Giuseppe Cipriani Senior opened Harry’s Bar in Venice. Over the years, Harry’s Bar became the place where writers, painters, artists, aristocrats, kings and queens would meet. Among them there were: Barbara Hutton, Katherine Hepburn, Gary Cooper, Giancarlo Menotti, Peggy Guggenheim, Orson Welles, Frank Lloyd Wright, Joe di Maggio, Truman Capote and Ernest Hemingway. The keys to the success of this tiny Bar were: service, freedom and lack of imposition.”
In particular, “freedom and lack of imposition”. That is, not woke. The book is hilarious, for its cast of characters includes delusional faded aristocrats, along with all the others of greater or lesser celebrity. The manner in which they all fit into this tolerant and forbearing milieu is a wonder to read, and occasionally very Fellini-esque, with the distinction that the story told in Harry’s Bar is true. It’s not Paris in the 1920s, but I’d be happy to be transported to Harry’s Bar in, say, 1932 or so.
But this is not possible. All these moments are “lost in time, like tears in rain. Time to die.” Well, maybe not time to die just yet. 2020 has been so bad in so many ways, but although it kept SWMBO and I home, foregoing our yearly trip to the EU, and it presented me with the uncomfortable knowledge that I had a brand of stage 4 cancer, in keeping us home, it also kept us close to MGH, where I initiated a connection with a couple of excellent doctors. Quick action, and efficacious (so far) treatment, has given me hope for future trip(s) to the EU. I won’t be able to put in the miles of walking I did previously, but my favorite memory is of sitting in a cafe on Rue Cler in Paris. The sun was out, we had a table outside next to the rue, and before us was a parade of locals walking their little boofie dogfaced beasties (my term for animals of the canine persuasion, for they are beasties, they have dog faces, and they go boof, on occasion). Anyway, that hour or so we spent there was bliss, involving not only a Paris cafe, but dogs – adorable ones. Such experiences will have to do until we figure out how to transport me back in time to ….
You know, never mind that. I’ll take Paris, sun, cafe, and fluff ball parade over that other stuff. Still, Harry’s Bar does sound attractive.
Where’s the science?
I intentionally left out the science this time, but recently I got an email request – from someone who is more highly regarded in the world of theoretical physics than myself – wanting my thoughts on why there are 3 generations of lepton/quark families. I responded:
So, 3 generations. I outlined my suggestion in my 2004 JMP paper. Basically anywhere the number 3 pops up in any mathematics that has been connected to physics there is an enthusiastic collection of supporters touting that 3 as THE 3. Triality; Exceptional Jordan algebra; E₈ (ahem); Cohl’s Clifford algebra thing; …
Anyhum, I’ll go to my grave in 3+ years still quietly repeating my mantra about resonant mathematics, and in particular the two finite resonant sequences: 1,2,4,8; 1,2,8,24. The first is connected to the parallelizable spheres and the division algebras; the second to lattice theory (a la my last publication in AACA). In my 2004 paper I used this second sequence to simultaneously explain why I couldn’t use just T, but needed T²; and to explain why we seem to have 3 generations. In particular, the starting point shouldn’t be:
T = C ⊗ H ⊗ O
It should be
T⁶ = C¹ ⊗ H² ⊗ O³.
This is a hybrid spinor space for which we presently do not have concomitant mathematical tools … as far as I know.
Anyway, this thrills me because it involves both 2,4,8 and 2,8,24. It is much harder to think about than triality, Jordan algebras, big groups, or Clifford algebras, all of which are comfortable notions with long histories … too long.
In my view, the nice thing about T⁶ is you don’t have to tack on spinors later. It is a spinor, incorporating 3 families of Dirac spinors, and their antifamilies, and all the groups fall out of the maths. But, as I made clear in 2004, we do not presently have the mathematical architecture or tools to make this a full fledged meaty model. It is skeletal.
But, like a lot of people now, I believe particle physics is at a minimum in a very deep coma, and I’m far from convinced that blather about black holes, dark mattergy, and 40 year old debates about the meaning of QM, are likely to end the coma. And I’m very ignorant in very many ways, but AdS/CFT? Is it not known that our universe is deSitter? But again, AdS is evidently so much easier to deal with mathematically, so …