The power of the keys

. As deplorable as we Badwhites are, our medieval forebears were deplorabler.

Here's one: Geoffrey le Barbu ("the Bearded"), Count of Anjou, around a.d. 1065:

The bishopric of Séez was vacant; by feudal custom the lord, Count Geoffrey, might appoint the next bishop; but by strict canon law, which was increasing in influence, the chapter of Séez, without lay interference, should fill the vacancy by election. This they did, in defiance of the count; whereupon he ordered all the canons to be castrated, and with them the bishop-elect. [Devil's Brood by Alfred Duggan, Chapter 1.]

Now that's Badwhite! (Geoffrey, by the way, was a great-granduncle of the English King Henry II , first of the Plantagenet Dynasty . His younger brother, who rejoiced in the epithet Fulk the Surly , was Henry's great-grandfather.)

What got me thinking of Geoffrey was a conversation with a friend who'd been listening to an audio version of Bertrand Russell's History of Western Philosophy.

In his introductory overview Russell points up the contrast between the rough, illiterate "kings and barons of Teutonic descent" who held secular power in medieval Europe and the churchmen who carried literate civilization forward, often — as the case of Geoffrey shows — in the teeth of fierce hostility from the fighting, drinking, hunting, bishop-castrating secular lords.

Of those lords Russell writes:

The Church could never produce in them the quiet regularity of good behaviour which a modern employer demands, and usually obtains, of his employees. What was the use of conquering the world if they could not drink and murder and love as the spirit moved them? And why should they, with their armies of proud knights, submit to the orders of bookish men, vowed to celibacy and destitute of armed force?

All the armed force was on the side of the kings, and yet the Church was victorious. The Church won, partly because it had almost a monopoly of education, partly because the kings were perpetually at war with each other …

But:Is not this (my friend asked) somewhat parallel to our own Cold Civil War? Are not our own gentry liberal Goodwhites "bookish men … destitute of armed force?" ("Vowed to celibacy" doesn't fit; although given the goodwhite-badwhite birthrate differential , from a strictly Darwinian viewpoint, it might as well.)

Well … there's somewhat of a parallel there. "Almost a monopoly of education"? Check.

At any larger scale, though, the parallel breaks down, mainly because, as Russell says, "Monarchs … were sincerely pious," whereas our own Badwhite leaders don't believe the Goodwhite ideology — the dogmas about there being no such thing as race, sex, etc.

Here's another medieval badass, Fulk the Black, Count of Anjou around a.d. 1000 and maternal grandfather of the aforementioned Geoffrey.

Fulk was one of the baddest Badwhites that ever lived, badder even than his grandson. (There was a slow decline of badassery as the generations rolled on; although Henry II reverted to type, offing an archbishop and locking up his Queen for 16 years.) Suspecting his wife of having committed adultery with a goatherd, Fulk had her burned alive in public, wearing her wedding dress.

(That boy in the back of the class who called out, "Serve her right!" … Yes, you … Go directly to the Principal's office, please …)

After twenty years of such delinquencies, Fulk one day realized that his immortal soul was in peril. He begged for forgiveness. It was granted, provided he did penance. William Manchester describes the penance in his book A World Lit Only by Fire:

Shackled, he was condemned to a triple Jerusalem pilgrimage: across most of France and Savoy, over the Alps, through the Papal States, Carinthia, Hungary, Bosnia, mountainous Serbia, Bulgaria, Constantinople, and the length of mountainous Anatolia, then down through modern Syria and Jordan to the holy city. In irons, his feet bleeding, he made this round trip three times — 15,300 miles — and the last time he was dragged through the streets on a hurdle while two well-muscled men lashed his naked back with bullwhips.

I dunno, I can't see Richard Spencer putting himself through that.

Russell again, continuing my last quote from him:

… but mainly because, with very few exceptions, rulers and people alike profoundly believed that the Church possessed the power of the keys. The Church could decide whether a king should spend eternity in heaven or in hell; the Church could absolve subjects from the duty of allegiance, and so stimulate rebellion.

That phrase "the power of the keys" is certainly suggestive. I'm sure that's how today's Goodwhites see themselves, as holding the power of the keys, at least in the earthly realm.

They can't condemn a recalcitrant Badwhite to eternal damnation, but they can wreck his business, terminate his employment, or cancel his PayPal account. Power of the keys!

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Mocking goodwhites in other languages. I've been using the Chinese internet slang term baizuo (pronunciation here) which translates as "white left," used by Chinese bloggers to mock ethnomasochist whites.

A Russian-speaking friend advises me that the Russian equivalent is либерасты, pronounced liberAHsty, a portmanteau word combining либералы (liberAHly) and педерасты (pederAHsty). All three of those Russian words are plural nouns. Both the latter words mean just what they sound like they mean.

I think I like the Russian word better than the Chinese one. It's ruder.

Presumably other languages have derisive terms for smug virtue-signaling goodwhites. I'd be interested to learn them.

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The bug wars. Back in my June Diary I recorded my troubles with small biting insects, and wondered if I should emulate the late great Jomo Kenyatta and get myself a fly whisk.

What I actually got, following a helpful suggestion from a reader, was an electronic bug swatter — an irresistible bargain at $3.99. It looks like a tennis racket, but with a three-layer metal mesh in place of the strings. You put two D batteries in the handle and wave it around where there are bugs.

Does it work? Eh, somewhat. You need to be brandishing it constantly around your exposed areas. A few moments' inattention and the little blighters get through … kinda like what we've been reading recently about the nation's missile defenses.

It is, though, mighty satisfying to hear the TSST! sound when a bug hits the mesh. A small bug, that is. The bigger critters — flies and wasps — die a more lingering death, writhing and burning while the mesh fizzes and sparks around them. A lot of these bigger guys are non-biting, and I regret their suffering; but it's hard to avoid collateral casualties in war.

Oh, you want bug-related news? Here you go:

Texas has launched aerial attacks on mosquitoes swarming coastal regions of the state and threatening to spread disease and hinder disaster recovery in the aftermath of Hurricane Harvey. U.S. Air Force C-130 cargo planes began spraying insecticides over three eastern Texas counties over the weekend and will expand to other areas over the next two weeks, officials from the Texas Department of State Health Services (DSHS) said. About 1.85 million acres have been treated as of Tuesday. [Texas calls in U.S. Air Force to counter post-storm surge in mosquitoes by Devika Krishna Kumar; Reuters, September 12th 2017.]

Perhaps some public-spirited billionaire or celebrity could fund a mass air-drop of my $3.99 electronic flyswatters to the afflicted areas.

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Bug Lit. Before the advent of modern bug repellents, electronic bug swatters, and the U.S. Air Force, people suffered mightily from insect bites. You could make an anthology of writers' complaints.

Mrs Trollope, in her 1832 book Domestic Manners of the Americans, took a break now and then from scoffing at those manners to grumble about the local insect life:

A cloud of mosquitoes gathered round, and while each sharp proboscis sucked our blood, they teased us with their humming chorus, till we lost all patience, and started again on our feet, pretty firmly resolved never to try the al fresco joys of an American forest again. [Chapter 10.]

About this time we began to experience the greatest plague of Manchuria, one to which former writers have alluded — I mean the midges and gadflies. The misery caused by insect pests is a stock theme with travellers, too common perhaps to call for sympathy. And yet if there be a time when life is not worth living, I should say it was summer in the forests of Manchuria. The midges … come out in countless millions, and bite like fiends. Mules and cattle are picketed at night to the leeward of fires, so that the smoke may protect them … Men at the plough wear circlets of iron on their heads, on which are stuck bits of burning touchwood, and they carry pieces of it in their hands as well … [The Long White Mountain, Chapter VII.]

Charlie had always used the term below the gnat line as a piece of Down Home humor. But this time it didn't strike him as funny. As he hobbled on his aluminum crutches from the Cadillac to the Big House, black gnats were dive-bombing his eyes in waves, without any letup. Why the eyes? Probably the water. They wanted to drink the water out of his eyes. Because of the crutches he couldn't lift his hands high enough to shoo them away. Now he could hear them singing in his ears. Turpmtine was not the place to be in the summertime. In the summertime South Georgia bowed down, helplessly, abjectly, to her rulers, the insects. "Owooooh!" That was Serena, who was just behind him. "Charlie! A bee stung me!" "Wasn't a bee," said Charlie, without looking round. "'Sa fly." Probably a black fly, thought Charlie. Mean little bastards. They were mottled, mostly black, in an unhealthy-looking way, and their wings were swept back like a jet fighter's or a Stealth bomber's. They never missed. But it could have been a yellow fly or a horsefly. [A Man in Full by Tom Wolfe (1998), Chapter XXXI.]

The grimmest complaint I've read is this one, from H.E.M. James' 1886 travels in northeast China:The complaints didn't altogether stop with the coming of modernity.These darn pests have been our companions on Earth through the entire history of our species, and we are stuck with them for ever …

… Or are we?

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Exterminate the Four Pests! Encouraging news:

Wildlife experts have been warning about the alarming decline in insects for decades. But the fall in numbers of bugs in Britain has now reached such a troubling extent that even motorists are noticing that their windscreens are clear of squashed flies, gnats, moths and wasps. ["The windscreen phenomenon" — why your car is no longer covered in dead insects, Daily Telegraph, August 26th 2017.]

After extrapolating data from a mile of highway in Ontario, researchers from Laurentian University calculated that hundreds of billions of pollinating insects were probably being killed by vehicles each year in North America.

Chris Shortall, an entomologist from Rothamsted said they had found evidence that the number of flying insects is falling, but said "the windscreen phenomenon" was difficult to prove. "The loss of insects from our windscreens is a well-noted anecdote, however actually demonstrating it is very tricky, if not impossible," said Mr Shortall.

Experts offer various opinions about the cause of the windscreen phenomenon. The most common explanation is the increased use of pesticides killing off the insects. Some dissenters blame the road traffic itself.Others deny that the phenomenon is real:For obvious personal reasons I am sanguine — all right: gleeful — about the mass slaughter of insects. As a science-literate adult, though, I really shouldn't be. Once you mess with the balance of nature, consequences are unpredictable.

The ChiComs found this out back in the 1950s. They launched a nationwide campaign to "Exterminate the Four Pests" (除四害), the Four Pests being mice, sparrows, flies, and mosquitoes.

Sparrows were especially targeted because they ate grain while it was growing.

Chinese citizens were mobilized in massive numbers to eradicate the birds by forcing them to fly until they fell from exhaustion. The Chinese people took to the streets clanging their pots and pans or beating drums to terrorize the birds and prevent them from landing. Nests were torn down, eggs were broken, chicks killed, and sparrows shot down from the sky. Experts estimate that hundreds of millions of sparrows were killed as part of the campaign.

Unfortunately nobody had told Chairman Mao (who knew nothing about agriculture) that sparrows didn't only eat grain, they also ate insects that lived on the grain. With no sparrows to keep their numbers down, insect populations boomed, eating far more grain than the sparrows had.

The list of Four Pests was hastily revised. Sparrows were rehabilitated; bed bugs took their place on the list.

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One kind of American. The ChiComs might have saved themselves a great deal of trouble by reading the letters of Benjamin Franklin.

Writing to his London friend Peter Collinson in 1753, Franklin observed that: "Whenever we attempt to mend the scheme of providence we had need be very circumspect lest we do more harm than good."

Franklin was mainly ruminating on the matter of social welfare. While it was admirable to want to relieve the misfortunes of others, he wondered if doing so might encourage laziness. Then:

He added a cautionary tale about New Englanders who decided to get rid of blackbirds that were eating the corn crop. The result was that the worms the blackbirds used to eat proliferated and destroyed the grass and grain crops.

I took that extract from Walter Isaacson's biography of Franklin , which I read this month.

(Yes, I know: I recorded buying the book last Christmas. So I'm behind with my reading, OK? The mills of Derb grind slow, but they grind exceeding small.)

Franklin's life is sufficiently interesting to read about, but Isaacson's last chapter, surveying the man's posthumous reputation, is the book's most thought-provoking.

Franklin was an instance of an American type: an exceptionally striking instance, with all the "points" (to borrow a figure from Orwell, who was thinking of dog shows) very highly developed.

There are several American types: the rambunctious cowboy, the solitary mountain man, the Southern gent, and so on. The intellectual life of late-colonial America, though, was dominated by just two types. Isaacson:

The literary critic Van Wyck Brooks distinguished between America's highbrow and lowbrow cultures, and he placed Franklin as the founder of the latter.

On the other, highbrow, side, Isaacson places people like Jonathan Edwards and the Mathers, who "tended to have a religious fervor, a sense of social class and hierarchy, and an appreciation for exalted values over earthly ones."

There is of course an underlying division of all humanity here, or at least of all the reflective portion of humanity. To put a Chinese spin on it: there are people of Heaven, and people of Earth. It is only that the division was especially visible in Franklin's time and place.

I'm with Ol' Ben on the earthly side of that divide. If I'd needed any confirmation of this — I didn't, but if I had — I would have found it in D.H. Lawrence's attack on Franklin, from which Isaacson provides a longish quote.

Isaacson calls Lawrence's essay "vicious and amusing — and in most ways misguided … a stream-of-consciousness rant that assaults Franklin for the unromantic and bourgeois nature of the virtues reflected in the Autobiography."

Fifty years ago every college-educated girl in England had read and swooned over Lawrence's novels. To give myself an edge in the dating market I thought I'd better read them too, so I tried to. I don't think I got more than twenty pages into any of them. Should I ever acquire state secrets that need to be forced out of me by torture, just strap me to a chair and play an audiobook of Sons and Lovers to me on a repeating loop.

If this self-obsessed literary poseur, this dime-store mystic, this timid Freudianism-for-Dummies voyeur (Malcolm Muggeridge, whose insights in this zone were deeper than the average, thought Lawrence was impotent), … if D.H. Lawrence hated Franklin, then Franklin's my guy.

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Adventures in fiction. The only novel I read this month was P.L. Gaus's Broken English, a murder mystery set in the Amish country of northern Ohio.

Yeah, I know: an Amish murder mystery, wha? It was an impulse buy. I was browsing the 75¢ box of second-hand books outside my local bookstore and it caught my fancy. I'd never read a book about the Amish. Gotta try one, at least.

How was it? Not bad. I'm not really a murder-mystery guy, though, and this one's a bit more contrived than most. You don't get much insight into the Amish and their ways, either. The main character is an "English" (i.e. non-Amish) college teacher.

What you do get is a lot of very detailed gun talk.

On the wall above the rifles there was a fully automatic H&K MP5 machine pistol with a long, thin 9 mm magazine mounted in front of the trigger guard. A fully automatic MAC 11 machine pistol hung shoulder high on the wall next to the secret door …

This author knows his guns. Still, the dénouement, which involved an exceptional piece of marksmanship, seemed to me a stretch. But then, as I said, this is not really my genre. (It's my sister's . I think that by the time she went to college she had read every word Agatha Christie ever wrote.)

OK, I've read an Amish novel. Onward and upward!

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Geezerism vindicated. What's happened to music? I mean, what the hell has happened to it?

I'm not talking about concert music. We know what happened to that: The human race's ability to write concert music that any large number of people would pay concert-hall ticket prices to listen to, disappeared around 1960. That's a totally lost cause, RIP. We have the legacy music of our ancestors: that's enough.

There went on being new pop music, though: songs, and even instrumental pieces, that millions of people liked to listen to, sing in the shower, karaoke along to, accompany on air guitar … That went on until the 1980s; then … it stopped.

Yes, this will be a geezerish segment. The vintage demographic has been grumbling about the musical tastes of their juniors for ever, of course. In my mind's ear I hear the voice of my mother, trying to deal with my sister's nonstop playing of an Elvis Presley LP: "Why, he can't even enunciate …"

That's not quite what I'm doing, though. At least my mother heard Elvis. I don't hear the music of millennials. Where is it? All I can find on the car radio is concert music (I'm including opera in there), oldies, country, and the Latino tune (there seems only to be one). The piped music at the mall is just concert music and oldies.

Sure, I know: the blacks have their own music. It's theirs, though. Nobody else much wants it. The days when blacks wrote and performed music for the rest of us are long gone — like the days when we dreamed of a united, harmonious nation without legalized race discrimination, without race favoritism or preferences — a nation in which race no longer mattered and we just looked each other in the eyes, citizen to citizen. Remember those days? How naïve we were!

And yes, I know there are musicians writing and performing good songs. Any time I go on this particular rant I get patient emails from readers recommending this one or that one. Some of them I like. They have no widespread recognition, though, the way Elvis had, or Nat King Cole, or Elton John. The karaoke boxes in public places don't carry Hayes Carll numbers.

Is this just another aspect of our spoiled-for-choice affluence, like having 45 varieties of breakfast cereal? Or is there a real issue here?

The latter, according to Scientific American.

A group of researchers undertook a quantitative analysis of nearly half a million songs to look for widespread changes in music's character over the years … [Is Pop Music Evolving, or Is It Just Getting Louder? by John Matson; Scientific American, July 26, 2012.] After peaking in the 1960s, timbral variety has been in steady decline to the present day, the researchers found. That implies a homogenization of the overall timbral palette, which could point to less diversity in instrumentation and recording techniques.

Similarly, the pitch content of music has shriveled somewhat. The basic pitch vocabulary has remained unchanged — the same notes and chords that were popular in decades past are popular today — but the syntax has become more restricted. Musicians today seem to be less adventurous in moving from one chord or note to another, instead following the paths well-trod [sic] by their predecessors and contemporaries. Finally, it comes as no surprise that music has gotten louder …

… [Lead researcher Joan] Serrà and his [sic] colleagues found that the loudness of recorded music is increasing by about one decibel every eight years. It's an interesting study, and it seems to support the popular anecdotal observation that pop music of yore was better, or at least more varied, than today's top-40 stuff. (A recent study also found that song lyrics are darker and more self-focused than they used to be.)

Less diversity! Eeeek!Actually it does come as a surprise. If today's pop is louder, why aren't I hearing it?See? You can be geezerish and right! I call this solid scientific support for the thesis that since around 1985, pop music has sucked.

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The decline of stuff (cont.) On the same geezerish note, and also bug-related:

Back in 2004 I wrote an essay titled "The Decline of Stuff," about how flimsy and ephemeral the substance of our material world was getting. The essay was inspired by a talk with my plumber.

From faucets the plumber's monologue broadened out into a mighty river of complaint, covering building materials of all sorts. Roofing! — time was, a roof would last you thirty years. Now, with these new, lighter materials, figure ten. Paint! — the health lobbies and environmentalists had pushed oil-based paints out of the market in favor of latex-based. Now even the latter were under attack from some group of busybodies. "Pretty soon we'll be down to watercolors — you'll have to repaint your house every time it rains!" Bathtubs and toilets, window frames, wallboard, siding — all the stuff of the world was becoming lighter, flimsier, less potent, less durable.

Paint-wise, that plumber's "pretty soon" has arrived. I recently needed to paint a door. It was white: I wanted it green. This took six coats of paint!

(Although I'll admit there's an upside. Cleaning up your brushes and rags after painting can now be done with soap and water. Clean-up from a domestic paint job fifty years ago involved using something from the same general family as concentrated sulphuric acid.)

Back to the bugs. Their severest assaults on my person have required dressing. That's where I came up against the decline of stuff again: band-aids no longer stick!

One of the damn things fell off. It fell off. I hadn't done anything to cause it to fall off: no immersion in water, no heavy sweating, no untoward stretching. The wretched band-aid just gave a weary sigh and fell off.

Again, I'm old enough to remember band-aids from the 1950s. Fall off? You had to scrape 'em off with a putty knife and some of that same stuff you used for cleaning paint brushes. A patch of skin came off with 'em. Sure, it hurt like hell, but whaddya want? Sissyfied Social Justice band-aids that fall off? Feugh!

I'm really not crazy about the 21st century.

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Since when I have used no other. Construction materials may have degraded, but you can still get good work clothes.

My source is Duluth Trading. They already had my loyalty from the excellent jeans and shirts I've bought from them … and the log carrier! — how did I cope without it?

Then came the September catalog. Check it out. The cover shows Charles Darwin — anachronistically old but forgivably so, for purposes of recognition — with ruler and notebook, measuring a Galapagos turtle (with a bird — possibly one of Darwin's finches — perched on its shell). In the background is a sailing ship, an early 19th-century British brig-sloop, presumably HMS Beagle. Accompanying legend: "Evolve to more flexible work pants."

This is bold and righteous. Bold, because some nontrivial proportion of Duluth's customer base must be creationists, to whom Darwin is a hate figure. Righteous, because the old boy was in fact a great scientist — one of the greatest! — a master observer of nature, who can never be celebrated enough by lovers of truth.

We're not suppose to endorse commercial products, but … Duluth, you have a customer for life here.

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Math Corner. Just a couple here, arising from email conversations with readers.

• Reverse Pythagoras. If you know any math at all above the level of multiplication tables you know that the square on the hypoteneuse of a right-angled plane triangle is equal to the sum of the squares on the other two sides. This is the famous Theorem of Pythagoras.

The fact that all P are Q does not of course mean that all Q are P. All fishes live in water, but not everything that lives in water is a fish.

So it does not follow from Pythagoras' Theorem that every plane triangle whose sides obey the square rule a² + b² = c² is right-angled. This needs proving. Can you prove it?

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• The unexpected e. I have a random number generator, turning out random numbers between 0 and 1. (The one I'm actually using is Microsoft Excel's RAND function.) All but an infinitesimal proportion of them are irrational, of course; but for simplicity's sake I'll write only the first five digits after the decimal point.

Cranking the handle, I turn out ninety-nine random numbers: 0.92790 0.67893 0.79095 0.53678 0.19888 0.52829 0.19171 0.17022 0.47515 0.69975 0.08601 0.26982 0.54203 0.77918 0.18747 0.86099 0.75765 0.59906 0.95829 0.47767 0.94781 0.14177 0.57876 0.12951 0.84301 0.43297 0.07585 0.82101 0.73445 0.85010 0.21542 0.58199 0.74636 0.86282 0.57630 0.57085 0.60895 0.96853 0.51443 0.28028 0.89657 0.90503 0.26371 0.20702 0.34562 0.60644 0.33043 0.67741 0.20685 0.64001 0.47067 0.88562 0.62047 0.67311 0.07255 0.00753 0.43275 0.38942 0.63936 0.44277 0.47971 0.33036 0.65948 0.15774 0.34070 0.09512 0.73409 0.05247 0.85472 0.78847 0.89409 0.81861 0.25608 0.66603 0.19968 0.98716 0.68478 0.51438 0.28965 0.20739 0.12033 0.91731 0.25106 0.92609 0.40161 0.58241 0.83912 0.88722 0.92054 0.80994 0.22021 0.11370 0.65511 0.33697 0.80295 0.80357 0.51119 0.36196 0.38856 …

Now I shall plod through those random numbers, adding them up as I go … but only until the total exceeds one. When that happens I'll start over with the next random number. Here you go:

0.92790 + 0.67893 = 1.60683 0.79095 + 0.53678 = 1.32773 0.19888 + 0.52829 + 0.19171 + 0.17022 = 1.09759 0.47515 + 0.69975 = 1.17490 0.08601 + 0.26982 + 0.54203 + 0.77918 = 1.67704 0.18747 + 0.86099 = 1.04846 0.75765 + 0.59906 = 1.35671 0.95829 + 0.47767 = 1.43596 0.94781 + 0.14177 = 1.08958 0.57876 + 0.12951 + 0.84301 = 1.55128 0.43297 + 0.07585 + 0.82101 = 1.32983 0.73445 + 0.85010 = 1.58455 0.21542 + 0.58199 + 0.74636 = 1.54377 0.86282 + 0.57630 = 1.43912 0.57085 + 0.60895 = 1.17980 0.96853 + 0.51443 = 1.48296 0.28028 + 0.89657 = 1.17685 0.90503 + 0.26371 = 1.16874 0.20702 + 0.34562 + 0.60644 = 1.15908 0.33043 + 0.67741 = 1.00784 0.20685 + 0.64001 + 0.47067 = 1.31753 0.88562 + 0.62047 = 1.50609 0.67311 + 0.07255 + 0.00753 + 0.43275 = 1.18594 0.38942 + 0.63936 = 1.02878 0.44277 + 0.47971 + 0.33036 = 1.25284 0.65948 + 0.15774 + 0.34070 = 1.15792 0.09512 + 0.73409 + 0.05247 + 0.85472 = 1.73640 0.78847 + 0.89409 = 1.68256 0.81861 + 0.25608 = 1.07469 0.66603 + 0.19968 + 0.98716 = 1.85287 0.68478 + 0.51438 = 1.19916 0.28965 + 0.20739 + 0.12033 + 0.91731 = 1.53468 0.25106 + 0.92609 = 1.17715 0.40161 + 0.58241 + 0.83912 = 1.82314 0.88722 + 0.92054 = 1.80776 0.80994 + 0.22021 = 1.03015 0.11370 + 0.65511 + 0.33697 = 1.10578 0.80295 + 0.80357 = 1.60652 0.51119 + 0.36196 + 0.38856 = 1.26171

In the first case there I just had to add two random numbers to get a sum greater than one. Starting over with my third random number, again I needed to add only two. For the stretch starting with 0.19888, though, I had to add four numbers before the sum exceeded one. Then again two … then again four … then again two … then again two … then again two … then again two … then three …

You get the idea. The number of random numbers I have to add before the sum exceeds one is: 2, 2, 4, 2, 4, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 4, 2, 3, 3, 4, 2, 2, 3, 2, 4, 2, 3, 2, 2, 3, 2, 3, … The average there is 2.53846.

Now suppose I were to go on doing that for a very, very long time, using random numbers to way, way more than five-digit approximation. What would the overall average be?

The unexpected answer is 2.718281828459045235360287 … That is Leonhard Euler's fabulous number e, the base of common logarithms — a number that is so important in math, people have written biographies of it. It is unexpected here because it doesn't commonly show up in problems like this of a straightforward kind, involving only addition.

I included this curious little fact as an endnote in my book Prime Obsession, but without a proof. Then, badgered by readers, I sketched a heuristic argument in the blog for that book.

A Radio Derb fan has directed my attention to a discussion about the result in a math blog here. It includes four, count 'em four, different proofs, of which the second, by Yuval Peres, is closest to my heuristic argument.

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John Derbyshire [ email him] writes an incredible amount on all sorts of subjects for all kinds of outlets. (This no longer includes National Review, whose editors had some kind of tantrum and fired him. ) He is the author of We Are Doomed: Reclaiming Conservative Pessimism and several other books. He has had two books published by VDARE.com com:FROM THE DISSIDENT RIGHT (also available in Kindle) and FROM THE DISSIDENT RIGHT II: ESSAYS 2013.

For years he’s been podcasting at Radio Derb, now available at VDARE.com for no charge.His writings are archived at JohnDerbyshire.com.

Readers who wish to donate (tax deductible) funds specifically earmarked for John Derbyshire's writings at VDARE.com can do so here.