»  VDARE.com Monthly Diary

  February 2021


Politicians with courage.     In the Senate impeachment trial of Donald Trump, February 9th-13th, video footage was shown of events in the Capitol building during the January 6th protests.

I had things to say about that video footage in my February 12th podcast. They were not very kind things. I spoke of the congressfolk "scampering off to safety under the guidance of armed Capitol Hill cops while an un-armed mob filled the corridors."

I quoted a friend's email from earlier in the year, one that had made such an impression on me, I'd posted it here on VDARE.com at the time. Here it is again.

Not a single person had the courage to go out and confront a man wearing buffalo horns flanked on either side with what looked like cast tryouts for Duck Dynasty. Had one person done so, he would now be the frontrunner for the presidency in 2024.

That February 12th podcast brought in an email from a different friend, reminding me of a real attempted coup forty years ago this month.

This was in Spain, February 23rd 1981. Francisco Franco had died five years previously after almost forty years of authoritarian rule. His chosen successor was Juan Carlos of the old Spanish royal family, who set about liberalizing Spain in the direction of a constitutional monarchy. Juan Carlos appointed 43-year-old Adolfo Suárez as Prime Minister in mid-1976.

A free election was held a year later, the first since the civil war of 1936-39. Adolfo Suárez' party won a plurality and he continued as Prime Minister. The following year a new constitution was approved, fulfilling Juan Carlos' goal: Spain had become a democratic state under constitutional monarchy. In the next election in 1979, Adolfo Suárez' party again won a plurality and he again continued as Prime Minister.

It's an uplifting story of an old, proud nation making the transition from authoritarian rule to representative, constitutional democracy in just four years, 1975-79. It was a rocky road, though, as I guess it was bound to be. There were some seriously disgruntled factions in the new Spain, especially on the political right.

In February 1981 one of those factions staged a coup: a real, armed coup, not just some comedians in buffalo horns committing trespass. Antonio Tejero of Spain's Civil Guard (approximately a uniformed equivalent of the FBI) with armed colleagues entered the lower chamber of Spain's parliament while it was in session.

What they were in session about was the swearing-in of a new Prime Minister. Adolfo Suárez had resigned a month earlier, facing a revolt in his party and plagued with health problems. The swearing-in roll call was being taken when Tejero and his pals stormed into the chamber.

Quote from Adolfo Suárez' 2014 obituary in the London Guardian:

Suárez displayed remarkable physical courage, being one of only three parliamentarians who refused to obey Tejero's order to lie on the floor.

One of the other two was Deputy Prime Minister and former army General Gutiérrez Mellado; the other was Communist Party leader Santiago Carrillo. Concerning the former, the coup's Wikipedia page records that:

Undeterred, arms akimbo in defiance, 68-year-old General Gutiérrez Mellado refused to sit down, even after Tejero attempted, unsuccessfully, to wrestle him to the floor. Their face-off ended with Tejero returning to the rostrum and Gutiérrez Mellado returning to his seat.

From a review in the Irish Times of Javier Cercas' 2011 book about the event:

For Cercas the iconic image of the 1981 coup is the refusal of Spain's beleaguered prime minister, Adolfo Suárez, to obey Tejeros' order to lie on the floor. Suárez sits resolutely in his seat while his deputy, Gen Manuel Gutiérrez Mellado, challenges Tejero's men to put down their weapons. Out of camera shot, the leader of the Spanish Communist Party, Santiago Carrillo, also stays put, impassively smoking a cigarette.

There is video footage here.

I wonder, primero, which, if any, of our own federal legislators would display such fearless defiance in the face of a real coup?

And then, segunda: Was smoking still permitted in our own House of Representatives as late as 1981?

Antonio Tejero, by the way — the coup leader — is apparently still among us, now aged 88. At any rate, I have been unable to find any obituaries. He served fifteen years for his armed attempt to overthrow democracy, which is probably less than the capering clowns of January 6th will get for disturbing the solemn deliberations of our brave legislators.

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Make America Ordinary Again.     The friend who emailed in to remind me of that attempted coup in Spain forty years ago actually lives in Uruguay. His email stirred my longstanding but remote and possibly ill-informed infatuation with Uruguay, a country I have never actually been to.

That in turn got me thinking that I am really not on board with MAGA. I mean, I don't particularly want to live in a country that's great. I'd be happy to live in a country that is … ordinary, so long of course as it is well-governed and socially harmonious, with proper respect for personal liberty and a firm rule of law equally applied to all.

Are there any advantages to living in a country that is great? Certainly there are, although they tend to come with dis-advantages attached.

Being militarily great, for example, means you don't have to worry that other countries will seize your territory. In the case of the U.S.A., however that hardly applies. Two wide oceans protect us; Canada and Mexico are not significant threats; and being militarily great is awfully expensive. We could probably be secure in our territorial integrity while reducing our military expenditures by ninety percent — perhaps ninety-nine percent if we're willing to take chances with Hawaii and Alaska.

And then there is financial greatness, with everyone else in the world wanting to do business in our national currency. I'm on weak ground here, having no deep understanding of economics. Still, a lot of nations with non-reserve currencies seem to cope just fine; and who knows how things will shake out when currencies go digital, as they seem fated to do?

I grew up in a nation that stopped being great just about the time I was born, although the psychological adjustment to non-greatness took a couple of decades. The main downside of no-longer-greatness for Britain was the mass immigration of people from places the Brits had once practiced their greatness on.

There was no need for that, and plenty of sensible people opposed it — Winston Churchill, for example. It was a misplaced sense of post-greatness noblesse oblige that inflicted the dreadful nation-killing blight of diversity on late-20th-century Britain. If the Brits had listened to Churchill and opted for demographic stability, Britain could have been a really nice harmonious country by now, happy and secure in non-greatness — an ordinary country.

Wait, though (I hear you cry): The U.S.A. has never been an ordinary country. We have always been a nation with a mission, haven't we? Shining city on a hill, and so on? Even when demographically, militarily, or economically not great, we aspired to greatness, didn't we?

Arguable. Did Americans in our spells of national ordinariness — in the 1890s, say, say, or the 1920s — dream of bestriding the world like a Colossus? Yearn for national greatness? Some of them did, I suppose, but many?

I feel sure that greatness is, to say the very least, much overestimated. There are of course some seriously crappy non-great countries, but there are some very nice ones, too: Switzerland, Iceland, Hungary, Uruguay (on my friend's testimony), Japan, …

The immigration boosters tell us that to stay great, we need to import lots of smart people from elsewhere. Really? With a third of a billion in residence, we surely have all the talent we need to maintain our prosperity and security, even if we end up not leading the world in this, or that, or anything — not being great. If the rancors and disruptions caused by mass immigration are the price of greatness, perhaps our citizens would, like me, prefer to settle for cheerful national mediocrity. Perhaps we should ask them.

I think I shall get some caps made up with the initials MAOA, for "Make America Ordinary Again." How should MAOA be pronounced, though? "Mao-ah"? "Mah-oh-ah"? Eh, the complications never end …

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Home life at the Derbs'.     People like Mrs Derbyshire, speaking English as a second language, come late to the terms of rhetorical art. So:

Mrs D, reading our daily New York Post:  "This word "hyper-BOWL," is that right? Tell me again what it means."

Me:  "Exaggeration, honey, exaggeration for effect when speaking or writing. 'I've told you a million times …' That kind of thing. And it's 'hy-PER-bo-lee.'"

Mrs D:  "Ah. And the adjective is 'hy-PER-bo-lic,' right?"

Me:  "Sorry, no. It's 'hy-per-BOL-ic.' The stress shifts, like 'PHO-to-graph, pho-TOG-raphy, photo-GRAPH-ic.'" (I spared her "photgrav-URE.")

Mrs D:  "'Hy-per-BOL-ic,' got it." (Resumes reading.)

Me, now flipped into schoolteacher mode:  "What's the opposite of 'hy-PER-bo-lee,' do you know?"

Mrs D (after a 1.5-second frown, morphing to a mischievous grin):  "'Low-PER-bo-lee'?"

(Aw, come on, I can be sappy about the Mrs once in a while. This was mid-February, actually the day after St. Valentine's Day. If I can't be sappy then, when can I be?)

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Defund (some of) the police!     Back in August 2019 I reported on being the victim of New York State's Red Flag law. My handguns and my license to own them were taken away from me because my son, who lives at my address, got involved in a barroom scuffle. A reader wants to know if there has been any further news on that.

Not really. Junior's still living with us. So long as he is, the county cops get to keep my handguns. He's been nursing vague plans to move out to a place of his own, but the plans haven't come to anything yet.

I did do a couple of rounds with the county police department's Pistol Licensing Bureau a few months ago. My pistol license expired on July 1st last year. I failed to notice this because I no longer had the damn license in my wallet: It had been confiscated the year before under the Red Flag law. In September, out of the blue [sic], I received a stern NOTICE OF CANCELLATION from the PLB.

I sent a letter to Sgt. Walsh, the Executive Officer in charge, pleading for an exception. When, after three weeks, he had not deigned to reply, I filed a formal complaint with the PLB.

That got me a phone call from one of Sgt. Walsh's minions affirming that my license was canceled and that I had no recourse but to apply for a new license when Junior moves out.

I pointed out that the Fifth Amendment to my country's Constitution forbids my property being taken from me without just compensation. What, then (I asked) would happen to my handguns if I just decided not to apply for a new license?

This flunky had dealt with argumentative nuisances before, though, and had an answer for anything. The guns would then be sold, he said, and I would receive a fair price. OK?

[Added August 2021:  He was lying. In some exchanges with the local police Property Department I was assured that guns are never included in their auctions, and everyone concerned knew this. If I decided not to apply for a new license, I could arrange for the guns to be transferred to a dealer, or to a private person holding a pistol license. If I did nothing, the guns would be destroyed without compensation.]

My next question was: Couldn't the PLB have done what every other bureaucratic operation issuing time-limited licenses does — send me a reminder notice that my license was about to expire? Flunky: "We don't do that."

No, I guess you don't.

This was all happening last fall, when the nation's air was ringing with calls to Defund The Police! Were those calls returning an echo from my bosom? You bet they were.

On sober reflection of course I'll allow that the guys out there on patrol have useful functions to perform and need the support of law-abiding citizens. So no, I wouldn't defund them. When it comes to paper-pushing bozo seat-warmers like Sgt. Walsh and his commissars at the Pistol Licensing Bureau, though, I have to admit, if they were to be defunded and put out to grass on their extravagant pensions, I wouldn't mind at all.

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Checking in with the Bard.     Here's a headline from The Washington Times, February 15th: Woke teachers want Shakespeare cut from curriculum: "This is about White supremacy".

Well, yes, of course it is. What isn't?

My own reaction to the headline was mild surprise that Shakespeare is still being taught. Wasn't he canceled years ago, when the Great Awokening first got under way? Yes he was: It was back in December 2016 that Shakespeare's portrait was removed from a common area at the University of Pennsylvania.

In place of the Bard, the students put up a photograph of Audre Lorde, the black feminist poet who died in 1992. ["Making a Point by Moving Shakespeare's Portrait" by Scott Jaschik; Inside Higher Ed, December 14th 2016.]

Like (I think) most educated people of my generation, I suffer from occasional spasms of Shakespeare guilt. I don't know half as much about the man's work as I really should. The fruit of those spasms can be seen in my study: a shelf holding DVDs of all the plays, purchased piecemeal through the last few years, along with Peter Saccio's Great Courses lectures on — hoo boy, it has been a few years — cassette tapes.

The main effect these periodic news stories about canceling Shakespeare have on me is, to prompt me to sit and watch one of those DVDs. This month's choice, more or less at random, was Love's Labour's Lost, the DVD of which I think must have arrived when the guilt spasm had already passed. At any rate, I have no recollection of having watched it.

So I watched it. This was the 2015 production from the Royal Shakespeare Company.

I read the play up beforehand, of course. You don't watch unfamiliar Shakespeare cold, any more than you go to an unfamiliar opera cold. You need to know in advance what's going on, at least in outline; and it doesn't hurt — well, I don't think it hurts — to hear what the judgment of wise critics has been.

My wise critics were, (a) Dr Johnson of course, and (b) Alfred Harbage of Harvard University, who supplied the preface to this play for The Complete Pelican Shakespeare 1981 edition, which I used as a crib for the obscure words and allusions.

Both these learned gents agree that LLL is down at the lower end of Shakepeare's achievement, but both allow that, in Johnson's words: "There are scattered, through the whole, many sparks of genius."

(Of the Princess' "None are so surely caught …" lines in Act V, Scene ii, Johnson remarks that: "These are observations worthy of a man who has surveyed human nature with the closest attention." That's not bad from one of the Bard's more severe critics, the guy who dismissed the plot of Cymbeline as "unresisting imbecility.")

I'm not sure this was 2½ hours well spent. The problem, as with all Shakespeare's comedies, is that much of the comedy is fast wordplay, with words and references a 16th-century audience would understand instantly but which I have to look up in my crib … which soon gets tiresome.

The RSC also mucked the play about too much. There's a weird selection of costumes neither contemporary nor modern: the "Muscovites" in V.ii wear Stalin-era Red Army uniforms. That lovely snippet of verse at the end — "When icicles hang by the wall …" — is submerged in a Broadway-musical-style song'n'dance routine.

Johnson was right about "sparks of genius," though. I could, after all, have spent those 2½ hours listening to the works of a black feminist poet … except that, if I'd tried, I would have run outside and thrown myself under a passing truck after 15 minutes.

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Ideology's downward slide.     We see the different human races exhibiting different social and civilizational outcomes. Why?

Until about fifty years ago the common belief — I mean, the belief held by most persons of middling intelligence and decent education — was that the different outcomes are caused at least in part by innate biological differences. The human races are, most people supposed, like breeds of dog or cattle, divergent from each other as a result of localized inbreeding over many generations.

That belief was easier to maintain then than now because many more people back then had some experience of country matters. In particular, they were better acquainted with animal breeding, if only at second or third hand. You see this plainly in Chapter One of Darwin's On the Origin of Species. There was a general, widespread familiarity with practical biology that people in today's sophisticated electronic societies no longer have.

Up into the middle 20th century, for instance, horse racing was much more popular than it is today. I have seen it written somewhere that the two most popular sports in 1940 America were horse-racing and boxing. In my own childhood in mid-20th-century provincial England, dog racing was also popular. One of our neighbors bred racing dogs. (The local track, a mile and a half from my childhood home, closed in 1964.) Pigeon-fancying was also a common hobby among adult men, … and so on.

Biology was understood to encompass human beings, too. Rough, approximate ideas about inherited characteristics among humans — the Habsburg Jaw, the Bourbon nose, the Romanov hemophilia — were universal.

This general, unsystematic acquaintance with practical biology was not restricted to the animal kingdom. Botany used to be a common hobby. Having spent many hundreds of hours in the middle and later 20th century browsing in second-hand bookshops, I can report that it was a very common experience, on opening some dusty old volume, to find a dried leaf or flower pressed in its pages.

Churchill again: The normal occupations of mankind, he told Siegfried Sassoon, are war and gardening.

I am speaking of ordinary people, not academics. Adolf Bastian, back in the later 19th century, had already laid down his principle of the psychic unity of mankind for Franz Boas, "the father of American anthropology," to pick up and transmit to the 20th.

By the time the 21st century arrived the reigning dogma had, in the words I employed in Chapter Seven of We Are Doomed, passed from "Biologism" to Boasian "Culturism." The only innate, biologically-determined race differences, said the Culturists, were the superficial ones: skin color, hair texture, and so on. The BIP traits — behavior, intelligence, personality — were statistically identical for all races, at any rate in potential. Different social and civilizational outcomes were caused by culture: by factors geographical, historical, and social.

It was all ethereal and abstract, but in tune with the times. Technology has carried us into a world of abstractions. Even our wealth is abstract: printed stock certificates and bonds have long since turned into numbers scrolling down luminescent screens, metal coins and paper bills are giving way to cryptocurrency. Where human nature is concerned, the ultimate abstraction is the Universal Person: a raceless, sexless, immaterial phantasm with no biological essence whatsoever.

In We Are Doomed, which came out in 2009, I declared myself a Biologian and engaged in some gentle mockery of Culturism:

It's not that Biologians can't get a hearing. They have even appeared in the best-seller lists: most famously with Herrnstein and Murray's 1994 book The Bell Curve [1994]. Public displays of Biologism are, though, always sure to excite angry controversy. Compare the fevered responses to The Bell Curve with the placid reception given to Culturist best-sellers like Jared Diamond's Guns, Germs, and Steel [1997] or Malcolm Gladwell's Outliers [2011]. A Biologian who wants to write a best-seller is well advised to just leave out the really fever-inducing stuff, however good it looks scientifically; or at very least to put some Culturist lipstick on his Biologian pig.

For all the pessimism trumpeted in my book's title, I was not pessimistic enough. I did not foresee see that Culturism was merely a phase in the ongoing downward ideological trajectory of Western society.

Today, twelve years later, we have slid down below Culturism to something darker, stupider, and even further removed from reality. Culturism now dwells in the odium of ideological heterodoxy, just as Biologism did in the 1990s.

Case Study A:  Jared Diamond's Culturist bestseller Guns, Germs, and Steel is now on the Index Librorum Prohibitorum of the Church of Wokeness. As Steve noted here in reference to the New York Times firing of veteran Times-man Donald G. McNeil:

As us oldtimers recall, Guns, Germs, and Steel was a Pulitzer Prize-winning bestseller for seeming to refute The Bell Curve … But by now … both books seem pretty much the same to the Youth of Today: crimethink!

Case Study B:  The defenestration of NYU political scientist Larry Mead. In 2019 Prof. Mead published a carefully Culturist book titled Burdens of Freedom: Cultural Difference and American Power. I have read the book and can testify that it contains no trace of Biologism.

I can in fact double-testify to that. I saw Prof. Mead in person addressing a promotional event when the book was launched. Speaking of his book, Prof. Mead again maintained strict Culturist propriety.

In the Q&A after his talk I actually challenged him on it. I asked: Didn't modern studies in population genetics rather strongly suggest that biology plays some role in differences of outcome by race? Prof. Mead replied with a firm negative: "It's culture. They're just not thinking straight …"

The witch-hunters descended on Prof. Mead none the less. Today, since the 2013 Great Awokening, it's not enough to be Culturist. Indeed, Culturism is racist.

You can get the general tone of criticism from this tweet by Spencer Piston, a PoliSci professor at Boston University:

disgusting and reprehensible … vile … his racism is inseparable from his classism …

Etc., etc. For a fuller exposition of Prof. Mead's sins of heterodoxy, see this piece by Colleen Flaherty at Inside Higher Ed last July. She implicitly denounces Culturism in the piece's sub-heading:

A leading voice on welfare reform is accused of racism after he publishes an article linking poverty to "culture." Journal faces calls for retraction.

(The journal there is Society from the Springer academic publishing house. Prof. Mead had published an article with a condensed version of the ideas in his 2019 book. The article was indeed retracted by Springer soon afterwards.)

So where The New York Times and academic social sciences are concerned, we have gone from Biologism into Culturism, then through Culturism and out the other side, to … what? What, under the new orthodoxy, accounts for different outcomes by race? If the causal factor is not Biology or Culture, what is it?

This being the U.S.A., we are talking about blacks. What explains their stupendous levels of criminality and their doggedly dismal academic performance? The over-representation of Northeast Asians in the winner lists of the International Math Olympiad is just as glaring as the black crime statistics, but no-one's much interested.

So what causes these differences in outcome? The orthodox post-Culturist answer seems to be: white malice, dressed up of course in cant phrases like "systemic racism" and "white supremacy." Dress it up how you like; it's white people making it happen, we are supposed to believe.

So in just these few decades — well within my own lifetime, and I'm not that old — we have gone from Biologism, to Culturism, to Anti-Whitism. That's a downward trajectory: from sensible empirical inferences, to aery notions of all-pervading, all-determinative "culture," to primitive race hatred — mostly self-hatred, since it is white people taking the lead in promoting the current Anti-White orthodoxy.

Will the downward slide continue? What comes next: laws to handicap whites? Oh wait: We already have those …

Seriously, though: What is the end-point of this slide? If it were just a case of one race hating on another you might reasonably predict genocide; but this ideology is driven by white people hating on themselves — on their own ancestors, their own civilization. Where does that end? Mass suicide? — auto-genocide? I guess we'll find out.

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Suburban story.     In my daily walk of the dog round our leafy suburban neighborhood, I pass an empty lot in a street otherwise full of houses. It's half an acre of nothing — rough grass and weeds, some bare patches of stony soil, with a board out front erected by the firm that owns the lot. The board begs passers-by to LET US BUILD YOUR DREAM HOME HERE, with some fetching colored pictures of dream home options.

The lot has been empty for a couple of years, to my vague recollection. Before that there was a house on it, of which no trace now remains.

This morning I walked past the lot as usual. Three or four houses further on there was a lady in her front yard. We exchanged some pleasantries, in the course of which I asked about the empty lot. "Oh," said the lady, "That was old Joe's house."

She told me about old Joe. He'd married and moved into the house way back in the 1960s, perhaps 1950s. They'd raised a family there. The kids had grown up and left. Joe and his wife had lived alone in the house for many years. Then Joe's wife had died, aged 80-something. Joe had soldiered on by himself for some more years. When the house became too much for him to manage, he'd sold up and moved to a care home in Florida. The purchasers, or someone they'd sold the property on to, had leveled the lot.

Joe kept in touch with his old neighbors. He'd occasionally call to chat. The neighbors swore a solemn oath among themselves to not mention the fate of the house, thinking it would be too upsetting for Joe, after all those years he'd lived and raised his family there.

Somehow, though, he found out — Google Earth, perhaps. The lady I was talking to got a call from Joe's number in Florida one day. She picked up and identified herself. Joe's very first words were: "YA DIDN'T WANNA TELL ME, DID YA?"

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Math Corner.     I belong to both big math associations, the AMS (American Mathematical Society) and the MAA (Mathematical Association of America). I get each one's monthly journal: the AMS Notices and the MAA Monthly.

In this space last month I compared the AMS Notices unfavorably with the MAA Monthly. The former is far gone in wokeness, I said. The MAA publication, by contrast, is still solidly mathematical, some minor virtue signaling aside.

In this, too, I was not pessimistic enough. Mid-February my March issue of the MAA Monthly arrived. Cast your eye down the front cover — all the way down to "Reviews."

Yes: When you've finished nourishing your mind with news about the Trapezoidal Rule, Morikawa's unsolved problem, Fermat's Last Theorem, countable metric spaces, and cyclotomic polynomials, you can relax with a review of Ibram X. Kendi's How to Be an Antiracist.

To an old math geek, this is pissing on the altar. There is no longer any refuge, not even in mathematics. This poisonous gibberish is everywhere. Should Ibram X. Kendi be nominated for a Fields Medal? Nothing would surprise me now.

In the Editor's Note attached to the review we read that:

During the summer of 2020, events including the murders of George Floyd and Breonna Taylor …

"Murders"? Excuse me? When and by whom were determinations of murder arrived at in either case? The matter of George Floyd's death has not come to trial yet. Nobody has even been charged with murder in the Breonna Taylor case; nor, on the evidence, should anyone be.

For an editor at a journal of mathematics, the most precise of all disciplines, the author of that Editor's Note is awfully sloppy with words.

No, I haven't read Ibram X. Kendi's book, and don't plan to read it, unless someone pays me to. I did read Anthony Daniels' portmanteau review of Robin DiAngelo's White Fragility and Kendi's How to Be an Antiracist in last September's issue of The New Criterion, and I am satisfied that I now know all that a sane person needs to know about both books.

I hope Dr Daniels won't mind me quoting the closing words of his review.

Perhaps the most interesting question raised by these books is why, when they are so badly written, self-indulgent, and intellectually nugatory, when they are so plainly written in the spirit of what Karl Popper called reinforced dogmatism, they should be so popular among the Western intelligentsia. Let us hope that this is not a question for an Edward Gibbon of the next millennium to answer. ["Hypocrite hector" by Anthony Daniels; The New Criterion, September 2020.]

Last month's not-really-a-brainteaser.  I am no nearer to a solution. Commenters over at the Unz Review, whither these diaries get cross-posted, have made helpful suggestions about some particular cases, but no-one has come up with a full general proof.

I myself have continued to diddle with the problem in an empirical, breaking-rocks kind of way, just working out terms of the series in hopes of spotting patterns.

To do this in full you need to double the number of possibilities for each new term of the sequence. You start with x1, x2, and x3; I have called them just A, B, and C for simplicity. For x4 there are two possibilities, for x5 four, for x6 eight, and so on. I took it as far as x9, for which there are sixty-four possibilities.

The conditions that define the possibilities yield to a lot of simplification. Look at line 122 in my spreadsheet for example. (My spreadsheet shows the conditions in columns A thru F, the corresponding sequences in columns J thru R.) Among the conditions for line 122 are both B < 0 and B > 0. Since all my less-than and greater-than signs come with understood "… or equal to"s, that means B is zero. Since, by the same token, 2B − C is zero, C must also be zero.

You get a lot of nifty special cases like that, but a general theoretical approach has so far escaped me.

I shall diddle some more with that problem. Meanwhile it's high time I directed your attention to YouTube, where there are now many, many excellent math presentations.

A kind reader just sent me one that I hadn't seen before (thank you!): Matt Parker's Standup Mathematician. Here is Matt having some fun with pi. Here he is on the inner mysterious workings of the humble ellipse.

The first YouTube math site I ever got to know was Numberphile. For this month I offer you one of Numberphile's not-too-heavy brainteasers; but you must promise not to cheat and watch the video in advance. Promise? OK:

Brainteaser.  Write down the numbers from 1 to 15:  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Now rearrange them into a new order such that any two adjacent numbers add up to a perfect square.

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