Author: 7stones_blog

Francesca, my brilliant wife, was raised Catholic.  She entered my life as my student at a Catholic college for girls.  This was my first foray as an adjunct physics instructor after getting my PhD.  I was not good at it.  Teaching a class full of teenage Catholic girls taught me a great deal about teaching, and more about how wary I needed to be when teaching girls, a lesson I had not fully incorporated when a few years later I taught a math class at Wellesley College.  “Do tell, do tell”,  I hear you say.  Well too bad.  That’s not what I’m here to discuss.  

Francesca has recently revived her Catholicism.  It had never died – there are cathedrals all over France and Italy in which she has lit candles for family and friends – but until recently I had the impression it was just simmering.  

Attending mass at the Duomo in our favorite coastal Italian town was, I believe, a part of the reason for her revival.  She is presently reading the bible – all of it.  Her Harvard PhD in material sciences applied to archaeology is helping her connect what she is reading to actual places and events for which we have good evidence for their existence, supporting her forays into the bible as history.  

Still, she is a hard scientist, and she has delved into ideas like this one (quoted from google): “The fine-tuned universe hypothesis is the observation that several fundamental physical constants must fall within a highly narrow range for any form of life to exist. If these constants were changed even slightly, the universe would be completely hostile to biological matter.”  This is certainly true, and suggests there is a hidden hand adjusting the dials just so, because the mind behind that hand wants life to exist.  Contrarians suggest there are actually infinitely many universes, all set perhaps randomly, and that some must inevitably be set to allow biological life.  (Personally, I hate this idea; it’s a “nothing more to see here; move along” cop out.)  And of course one can always argue that our knowledge of physics is insufficient to explain the constants, but that a sound physical explanation does exist that will rule out Intelligent Design.

Francesca sought further evidence supporting her desire to reconcile religion and science.  She found it in the works of Stephen C Meyer, who used information theory, probability theory and chemistry to argue that the universe is far far too young for life to have evolved by mere chance.

Edward J. Steele, a molecular immunologist summed it up in a paper published in Progress in Biophysics and Molecular Biology 136 (2018), 7: “The transformation of an ensemble of appropriately chosen biological monomers (e.g. amino acids, nucleotides) into a primitive living cell capable of further evolution appears to require overcoming an information hurdle of superastronomical proportions, an event that could not have happened within the time frame of the Earth except, we believe, as a miracle (Hoyle and Wickramasinghe, 1981,1982,2000). All laboratory experiments attempting to simulate such an event have so far led to dismal failure (Deamer, 2011; Walker and Wickramasinghe, 2015).”

Personally, I am a polytheistic agnostic.  At the very least, to my untrained eye, there is in our universe (its biophysics) a gradient of sorts that enhances the odds for the evolution of multicellular life – even intelligence.  Happily I am too ignorant to be willing to ascribe to this gradient an intelligent helping hand.  Nor would I be unhappy if that proved to be true.  It would explain a lot that I will not discuss.  

What I firmly believe 

There are only three nontrivial parallelizable spheres: 1-sphere; 3-sphere; 7-sphere.  This implies (given my 40+ years of incontrovertible published work in mathematical physics) that we must live in a Standard Model (mostly) universe, and that there is an antimatter twin, and the two are connected by a 6-dimensional space which carries color charges.  Now that is Intelligently Designed. It is, at the very least, the framework, rigid, immutable and glorious, on which any higher creative power must build.  It is a stainless steel pot: the chemicals of life, and the various physical “constants”, etc., are ingredients being stirred about within.  God is a mathematician (but most of us already knew that).

Musk: “People are mistaken when they think that technology just automatically improves… it will, by itself, degrade.”

That sentence should keep you up tonight.

We treat progress like gravity. Like it pulls us forward whether we try or not.

It is the opposite.

Progress is a boulder on a hill. The second you stop pushing, it rolls back over you. And it never announces itself.

My input

In theoretical physics, on the other hand, the mainstream gatekeepers ensure that unsanctioned progress may occur like a boulder on a hill, but the hill is hidden in a cloud of obfuscation. ChatGPT, the last time I looked, claimed the physics arising from the “Dixon algebra” predicts nothing. Well, how about the existence of an antimatter twin universe, just for starters. So, uh, what – at this late stage in my life – the fuck am I doing?

Theoretical knickers are presently in a twist about the threat of AI rendering theorists obsolete (or such is the impression I’ve gleaned from article headlines).  But, while only vaguely interested in AI, I suspect it’s only really good at extending extant ideas.  Does it get curious on occasion, even playful, and try out ideas well outside its database, the information in which is likely established by people without the playful gene.  

For example, many many moons ago my interest in number theory led me to wonder what the graph of the natural log of the least common multiple of the integers from 1 to n would look like. I am not a number theorist; this was just inspired playfulness. And this is what I found:

ln(lcm{1,…,n}) ❤️ n-1

This is more than just a good, or best fit; it is Nature’s intended fit.  The ❤️ connotes “Nature’s intended fit”. (I will go to my grave believing this.) I used this to derive an astoundingly good formula for the number of primes from 1 to n (I believe Riemann got the same result in a more rigorous way; my write up on this is on researchgate).

So anyway, yeah, can an AI be inspirationally playful? I think of AIs like graduate students, who attach themselves to some eminence grise. This exalted being has a vested interest in seeing to it that their charge stays in a lane that will enhance their … ok, so, in general inspirational playfulness will be met with censure.

My work applying the division algebras (C, H, O) to elementary particle physics arose from pure inspirational playfulness (and obsession; can an AI obsess?). Let’s assume that work is fundamentally correct. I don’t see an AI taking an initiative to try something new like this.

If you’re curious, the “Dixon algebra” is just the “Dirac algebra” on steroids.

So, anyway …

The idea of a Deep State pulling the strings of culture and economics is not an unverifiable conspiracy theory; it’s a mathematical socio-political inevitability.  The deepest of them will resort to assassination, either real, or just of reputations, to protect their entrenched interests.  All I can say is: thank the gods he missed; and the attacks on his reputation were so transparent.  For had the ditherer won, we’d be in fucking deep shit.

All human endeavors gravitate to a Deep State that, once established, will resist changes to its low energy state. Theoretical physics is not immune, as anyone who has followed its glacial progress over the last 50 years can attest; this despite the efforts of those who have attempted to nudge it with novel ideas (blush).

Being a Contrarian

When I was 7 years old, and my younger brother, Eric, 5 or 6, a similarly aged girl living on our street in Norwalk, CT, walked up to my brother and me and told us that her mother thought we were the bad boys of the neighborhood.  My brain did a Spock-like “Fascinating”, and it stuck in my memory banks.  But – and this is the point – it had utterly no effect on my behavior, nor my brothers.  It’s quite possible she was right, but it was our nature to be that way.  We did not have genes for behave-normally-and-responsibly.  We were just who we were.

A couple years later we were living in Redding, CT, and the elementary school we attended would give out yellow slips to misbehaving students.  These meant detention.  In our first year I got 7, and Eric 5.  Called into the principal’s office one day, the principal looked at Eric, and said, “Another of the Dixon boys.”  (We were not incorrigible; the remaining 2 years at that school we never exceeded 1 or 2 yellow slips.)

My first year in college I grew my hair long (1966), overdosed on LSD, then dropped (and flunked) out, leaving my family in the dark as to where I’d gone.  As it turned out, along with a friend, I headed to California, seeking a kind of Haight-Ashbury environment.  But I had just turned 18, was largely clueless as to how widespread California’s hippy movement was, and we ended up at Newport Beach, devoid of hippies, but having some excellent body surfing waves.  

After 3 months I returned home, now Wilton, CT, much to the delight of Eric.  I behaved, went to 3 different colleges of increasing prestige, and finally graduated, with dual mathematics and physics degrees.  I spent 2 years in NJ getting an MS in mathematics.  I did not behave well, and not for the first or last time was warned that my misbehavor would go on my permanent record, and so mar my future.  It never did, but it could have, I suppose.  

I then became aimless for a while, and – long story short (it’s all in the book) – ended up entering Brandeis University as a physics graduate student.

The physics theory faculty was getting into SUSY at the time, and one professor in particular was keen that I get involved and build an academic future in – what I even then considered – this very misguided notion.  I did publish a paper or two that contained a smidgeon of SUSY, but by and large I ignored my mentors’ advice, got interested in division algebras, then proceeded to build a PhD degree based upon these mathematical objects, being completely mentor-less for the rest of my years as a graduate student.  The arc of my graduate career was viewed with opprobrium by at least one faculty member, and curious unconcern by the rest, including my advisor.

Then, for the next 40 years, plus or minus, I continued to badly misbehave by researching the (obvious) link between the division algebras and the standard model of elementary particles.  I published many articles, with few exceptions against great resistance (bad Geoffrey), and two books.  I never collaborated, and at the time I did not understand exactly how much of an outsider I was considered by the mainstream … at least not until prior to my talk at a conference at Notre Dame I was introduced as “the maverick”.  What?  

The point I’m making, I think, is that those 40 plus years of working way outside the box of what is considered proper theoretical physics were not an act of rebellion.  I didn’t even realize it was considered outré until that conference at Notre Dame.  That moment was akin to being told at age 7 that my brother and I were thought to be the neighborhood bad boys.  As was true at that time, when labeled “the maverick”, I did not immediately understand why that should be thought to be true.  But upon deeper reflection, all of my publications were single author, and while they likely never would have existed without the prior works of Gürsey and Günaydin (Yale, late 1970s), they veered sharply from their work, which attempted to shoehorn division algebra mathematics into the box of proper theory.  I ignored the box.  Not intentionally, but it was 100% clear to me what role the division algebras are intended to play.  Nature wrote the script.  I just translated it.

Fewer and Fewer Fucks to Give

A recent internet meme:

“How many relationships are you willing to ruin because you won’t shut up about freedom?”

“All of them.”

I worked many jobs to keep myself financially above water after receiving my PhD, and after 3 postdocs, one of which ended acrimoniously because I resisted doing the mind numbing work I was supposed to do (there were no problems with the other two as no one gave me instructions to do anything other than what I wanted to do).  But now I am retired.  I live in a university town.  I briefly taught at the local university, one, that it is generous to say, is not highly ranked.  Some of the old timers from that university gather for a biweekly lunch at a nearby restaurant.  I am close enough to one of them (a fellow nerd) to cadge invitations to these friendly meets.  It periodically bordered on pleasurable, and Francesca felt I needed socializing, so she used to push me to attend, despite my frequent reluctance.  

I am not like these people.  They are politically liberal in an academic bubble sort of way.  As is frequently true of many MAGA conservatives, I try my best to hide my beliefs.  This necessity is annoying.  It grates.  And at a recent luncheon my pent up frustration burst forth and I released some prime opinions.  Francesca was there, and in the ensuing conversation she got very annoyed with the replies generated in response to my vituperative verbal vomit.  She no longer thinks that my attendance at these meets is necessary.  It’s the wrong sort of socializing, akin to banging my head against a wall.  Not fun, at least not anymore.  

I’m not going to add political bumper stickers to my car, for rabid liberals feel they are doing the world a service by damaging property they deem aligned with conservative values (like firebombing a Tesla dealership … I mean WTF).  I saw a pickup truck the other day sporting big ass American and Trump flags.  But I strongly suspect the rabids would think twice about damaging that vehicle, for it exudes fuck-with-me-and-I-will-respond-violently, maybe-even-lethally.  My Subaru does not exude much of anything of the sort.  Its two bumper stickers label it as the Rocinante, Legitimate Salvage.  I will not explain.

Cafe Culture

I am a fan of cafe visits.  It is a culture in France and Italy, but here in seacoast NH we also have a pleasant one 4 miles from home.  Frappuccino and banana bread is my usual morning order.  But there is a drawback at this particular cafe: the vibe is distinctly progressive, and I am not progressive. – not even remotely.  Neither is Francesca, my wife.  We both have science PhDs, and our views on many matters that trigger progressive alarm are based on sound science. 

Recently we had just finished ordering when a middle-aged woman and her 11-ish year old daughter entered.  They both were dressed in Covid-chic: heavily masked, the mother sporting Rachel Maddow glasses, and the daughter had some sort of splint on her lower right arm.  My initial reaction was exclaiming internally, “Oh for fuck’s sake”.  

Now to be fair, they may both be suffering from some rare disease that requires them to take steps to avoid as much as possible the exhalations of other humans.  Not likely, but I have no way of knowing.  The Rachel Maddow glasses, in my mind, did not support the rare disease hypothesis.  And further filling me with doubt, they were both – as seems so often true of woke progressives – physically weedy, and clearly timid.  In my biased opinion, MAGA people tend to be noticeably more vital than progressive wokes.  Were a study to be done, producing trustworthy statistics, I would be very much surprised if it did not support my weedy woke, vital MAGA, conjecture, at least on average.

The Situation at Columbia MIX, and Elsewhere 

Meanwhile, speaking of weedy folks, most academics seem to be of this sort.  For example, P Woit at Columbia, who – as of this writing – has blogged (excoriated) 30 times about the evil dictatorial Trump administration’s efforts to rein in the anti-Jewish, keffiyeh wearing, antifas at Columbia.  As is true of all such weedy fanatics, Woit seems to be completely immune to any evidence that does not support his views.  For example, he eagerly quoted a NYT’s Op-Ed that said it was clear that Israel’s actions in Gaza supported the notion that Israel is involved in a systematic genocide of the Palestinian people.  Then, a couple days later, the NYT published a counter Op-Ed saying that calling Israel’s actions in Gaza a genocide was patently, and historically, absurd.  Woit did not deem this worthy of mention.  Interestingly, the list of people willing (or allowed) to comment on his blog entries has – or so it seems to me – diminished greatly.

Some time ago I got into a texting debate with my remaining sibling, an older sister, who was adamant that there was nothing wrong in trans-males competing against biological females.  I quoted Francesca, whose chemistry/anthropology Harvard PhD was sufficient to cement my own opinions on the matter: anyone who goes through puberty as an XY will develop a bigger heart, lungs, muscles, and higher bone density, than a biological XX.  This is confirmed science, to which my sister replied, “Well…”.  

As to the views of J.K. Rowling, this beloved sister said: “She should mind her own business.”  This, frankly, floored me.  Why should Rowling be excluded from this debate?  Why should anyone?  Anyway, beloved sister is in her mid-80s, and her primary source of news and opinion has for years been MSNBC.  Her sons are evidently even more woke, one having lost a cushy job at a private high school for teaching the spawn of these elites a woke version of history.  Francesca’s niece went to this school and mentioned that everyone knew of the dismissal of this radical history teacher whom she named by name.  She did not know that the offending former teacher is my nephew.

And then there’s my Swiss friend (former?), whose views on Israel’s conflict with Hamas are derived in part from the leftwing Israeli publication Haaretz.  My views are approximately 180° out of phase with his.  I am in favor of brain.  One side in this conflict has a surfeit of brain; the other side has a surfeit of bile, with very little brain … and they seem to loath any people who possess brain.  (While at Harvard Francesca learned that maybe 95% of the great achievements of the Islamic world are due to the Persians, a distinctly non-Arab people.  The Palestinians have accomplished zilch.  Everywhere they’ve gone as refugees they’ve caused civil wars.  The Jordanians killed off 25,000 of them on Black September because they annoyed.  Many were pushed into Lebanon where they started another civil war.  Egypt, eager to avoid their spiteful, disruptive presence, built an enormous wall on the border of Gaza and Egypt.  No one in the Middle East wants them, although many in the Middle East would like them to disarm, surrender, and shut the fuck up.  (But, you know, I’ve not been there, do not intend to go there ever, and my knowledge – if knowledge it is – is second hand, at best.))  

Speaking of Harvard (and I suppose Columbia), Francesca is strongly convinced that her Alma Mater has noticeably diminished.  No more does she receive an annual letter extolling the virtues of the incoming class of Valedictorians (> 98%).  When they started acceding to the progressive screams of more campus DEI, standards – as is always the case when DEI is forced upon an institution – plummeted.  Francesca has zero sympathy for the travails that that university is presently undergoing at the hands of a very unsympathetic POTUS and his administration.

Common Thread

None of the people mentioned above – even Francesca and I – are persuadable.  I have tried to persuade those with opposing viewpoints, because I am very stubborn, and perhaps an idiot.  This morning a great miasma fell upon my spirit.  It left me feeling disconnected to almost everything but Francesca.  It was a good feeling.  I must nurture this feeling.  No more pointless debates. I will continue to text my sister amusing memes, mostly involving dogs.  We both enjoy those.  Common ground.  And having recently lost her husband, she needs some brotherly levity (lovity).

Do you as well?  If so, I leave you with this:

“Is there a nicer feeling than being in a room full of people and the dog chooses to come sit next to you?

“I think not.”

Saw a youtube video one morning about Porto Cervo, a town of sorts on the northeast coast of Sardinia.  This is a place concocted by the ultra wealthy, accessible primarily by yacht, and in this – and other ways – protected from intrusions from the outside world, those great masses of unwashed and yachtless.  

Porto Cervo is – I cannot help but imagine – a sterile place: a collection of highend stores; probably a few carefully crafted cafes staffed by people exuding carefully crafted subservience; and as to naughtiness, there’s probably a shitload, but rarely if ever in the open.

I have painted – possibly inaccurately – an unattractive picture, one that had I not written it, but encountered it at some random moment in my peripatetic life, would have dissuaded me from visiting the place, even if I had a ghost of a chance of being allowed in.  At least such would have been my attitude 2 months ago.

But in early May, 2025, Francesca and I flew to Paris, where we spent 4 weeks in an Airbnb across the street from Le Bon Marché, our favorite shopping destination in Paris containing Paris’s best grocery store.  This particular neighborhood – the 7th Arrondissement – I discovered when researching the area, is inhabited by many wealthy Frenchies, even billionaires, or so I read (certainly many influential members of the Parisian elite).  So this Arrondissement is better protected from riffraff  than most.  This is offered in explication of what dominated our stay here.

This being France, and Paris in particular, we arrived in strike season.  Taxi drivers were upset.  Their chagrin revolved around some financial issue, and ride-share companies like Uber.  So they took thousands of taxis and parked them on major thoroughfares, one of these being about a block from our apartment.  And by parked, I mean they took over all lanes, thereby blocking the entire thoroughfare to all but 2-wheeled vehicles and pedestrians.  Then, in an effort to drive home their presence, lest the nearby billionaires should try to ignore them, they would set off small explosive devices throughout the day.  These were more powerful than the Cherry Bombs I grew up with, and I learned these devices were illegal.  This did not dissuade the disgruntled drivers in the least.  

Francesca and I went to a cafe on this street one day, wanting to witness this spectacle in person.  In addition to explosive devices, they set various stuff on fire at several places along their strike route.  And we noticed that the majority of those involved in these disruptive activities looked distinctly of North African extraction.  And before you point your quivering finger of disapproval at me and call me racist, let me put your mind to rest: I am racist.  My racism is based on pattern recognition; it is rational, even mathematical.  This either makes sense to you, or it doesn’t.  I don’t care.  But I dislike Islam vehemently, and the vast majority of its adherents.  

So our second day sitting at that cafe watching the anger manifesting in front of us, there was a cluster of Parisian Gendarmes near us on a side street.  One of the North Africans set off one of these explosive devices near us.  The Gendarmes rushed out and grabbed the guy and dragged him down the side street a short way. The reaction of his cohorts was to rush at the police, and the only reason a violent fray was avoided was because the fellow the Gendarmes had grabbed raised his arms toward his cohorts in a universal signal of “Not to worry”.  

Anyway, our interest in witnessing any further acts of dissidence on the part of these angry toads plummeted to zero at this point, not least because detonation of the aforementioned explosive device had damaged my one good ear.  The primary effect of this damage is that when I stick a finger in that ear I hear a chirping noise, like that I experienced as a child in Redding, Connecticut.  There was a pond behind our house inhabited by thousands of little peeper frogs, and during mating season they set up a loud and constant chirping.  Long story short, they’ve moved into my ear, and I become aware of them when I yawn, or cover that ear (fortunately lying on that side on a pillow does not initiate the mating frenzy.)

The other major effect of this nearby ensemble of disgruntled was the frequent “bedoo bedoo …” of police and ambulance vehicles passing by in the vicinity.  Eventually the police decided to park their vehicles at the striker end of our street, likely at the behest of our wealthy Parisian neighbors.  Only once did the strikers make a brief foray onto our street, when they got half a block into our neighborhood and set fire to a bunch of crap – including tires – that ultimately melted into the roads surface.  Fucking hell.

Then France won some sort of sports competition, and the Parisians reacted as Parisians do; the white Parisians celebrated; the black (subSaharan immigrant) Parisians, seeing a chance to riot and break stuff, did just that.  Francesca and I visited the Champs Elysée 2 days later.  Many storefront windows had been damaged, but we saw only one that failed to withstand the mindless assault: a Footlocker store (looting blacks do love some good footwear … pattern recognition).  

Then there are the pickpockets.  From our apartment window we watched one Arab-looking fellow standing casually at the entrance of the nearby Metro.  He held a cell phone in front of him, but never once looked at it.  Every so often he would spot a likely mark, follow them into the Metro, then come back a short while later and take up his watchful position again.  Finally he must have scored big, for when he reappeared he raced off into the distance.  

OH!  And two years ago we were in Paris at the end of June during the annual citywide music festival.  It was a total scene, but not violent.  This year, while safely in Italy, I read that the Africans found this to be a valid excuse to rampage again, and – probably not connected – over 250 people during the festival were stabbed with hypodermic needles.  Fuck fuck fuck fuck.

Anyhum, we had visited Paris every year but one (2024, Olympics year) since 2016.  But no more, we think.  Its luster has been tarnished beyond recall.  In my possibly overly dramatic opinion, Paris has experienced a catastrophic change of state, from The City of Light, to The City of Watch Your Back, lest horny frogs take residence in your ears.

And that brings me back to Porto Cervo.  Initially having no allure for me, it now sounds like a great place, the wealth of its inhabitants almost certainly used in part to keep out undesirable immigrants.  Alas, I do not own a yacht, and had I a yacht, I could not afford its upkeep.  So … 

A final word on pattern recognition (a very apt phrase for my condition someone else used on the internet in the same way I am using it). Nerds, and most STEM folks in general, regardless of ethnicity, are immune to my pattern recognition induced racism, because nerds are my people.  Both Francesca and I have worked with North African Berbers, an intelligent people conquered by the rapacious Arabs spreading Islam by the sword (so much quicker than proselytizing).  We approve of Berbers, and other Amazigh (“Free People” in their original language). We approve of brain, and curiosity. You can be black as night; if you’re a science interested nerd, then welcome aboard.

Float to the top or sink to the bottom. Everything in the middle is the Churn.

I wrote a paper, and, when requested, I published it (https://link.springer.com/article/10.1007/s00006-018-0820-8). It’s a very pretty paper, extending the notion of 8-d Bott periodicity in Clifford algebras to a 24-d periodicity. This mirrors the exceptionality of the dimensions 2, 8, and 24 in lattice theory. Hyper-cool.

“There was a button,” Holden said. “I pushed it.” 
“Jesus Christ. That really is how you go through life, isn’t it?”

As is true of almost everything I’ve written and often published in theoretical and mathematical physics, the paper linked to above (call it Bobbie) utilizes the 3 division algebras, C, H, O, which are linked to even more fundamental topological objects, the parallelizable spheres of dimensions, 1, 3, and 7.

I frequently encounter papers exploiting the split octonions in their theory building. This requires replacing 4 of the 8 basis elements of O with i times those elements, where customarily i is taken to be the imaginary unit of C. One can also make split versions of H by similarly modifying 2 of its basis elements. But this method does not extend to C, as i is an element of C already. This is rather annoying.

In Bobbie this problem was remedied by replacing i by a new imaginary unit ι, and supplementing C,H,O with a distinct complex number field, C. Via the imaginary unit ι, all 3 of the division algebras have split versions. It’s very cool.

I am that guy.

Then it occurred to me …

C is generally assumed to be the number system from which arises all of complex analysis. C is recognized to be part of a unique and exceptional finite series of division algebras, and inspired by this fact over the past several decades many have tried to turn H and O into analytical doohickeys in the manner of C. These efforts have met with varying degrees of failure. And why?

Because C is not the foundation of complex analysis, C is. C,H, and O, are a set of mathematical objects relating to topology, geometry, and algebra. They are architectural. They can be viewed as real algebras, but they are really C algebras, where C is the mathematical field from which all our nice analysis – Green’s functions, Cauchy-Riemann equations, QFT, … – arise. So, because something is true of C does not mean it can be generalized to H and O. The field C is separate; it is not part of a series of mathematical objects.

Got it? All the division algebras have split versions. H and O are not the foundations of higher dimensional analytical theories. And C isn’t either.

Mother Nature suspects you will doubt this obvious Truth. Punishment is being prepared to meet your obstreperous petulance. In a private conversation with Mother Nature, she told me, rather firmly: “This is not a suggestion.”

A brief word on futility. There is a high probability that everyone who might have found this entry of interest is someone I’ve met, or connected to someone I’ve met. The degrees of separation are small. And none of these fellow hapless mavericks is in a position to influence the currents of scientific history. Anyway, I don’t know about the rest of you, but I’d not have done anything differently even knowing that recognition of such ideas as these will not even occur posthumously.