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AUGUST DIARY: Pachelbel and Nepalese In Japan; Derb In China; Dentists and Dieticians; Etc. [11 ITEMS]
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Cultural appropriation you can love

I like Pachelbel’s Canon in D. Sure it’s overplayed, but I like it, so I was stirred to action after hearing Prof. Greenberg pass some mildly snarky comments about it in one of his lectures. The precise action I was stirred to was, I used the Canon for sign-off music in my August 23rd podcast.

That brought an email from a listener. The email contained a link to a short video from Japan—a commercial, it says, so presumably run on Japanese TV.

I watched it. Then I called my wife in and we both watched it. There wasn’t a dry eye in the house. (Although I think the translation needs work.)

Here’s the clip.

Why don’t we have commercials as good as that?

How Japan works

My entire direct acquaintance with Japan consists of an aggregate few hours mooching around Narita airport on stopovers. I did once, long ago, make a brief and not-very-serious attempt to learn the language; but all I have retained from that is the mnemonic for the order of letters in the Japanese alphabets (they have two):

Kana Signs, Take Note How Much You Read and Write them.

The fact that I can still remember that after fortysomething years suggests that it’s a really good mnemonic.

My go-to guy for matters Japanese is a friend who does speak the language and spends much of his time in Japan. His observations about the place are interesting, HBD-realist, and sometimes contradict what I read in respectable news sources.

I recently tackled him with a question about Nepalese immigrants in Japan. There are a lot of them:

According to official data, as of the end of 2018, there were approximately 89,000 Nepalese living in Japan—up 11 percent from the previous year. There are 10 times as many Nepalese living in Japan compared with 10 years ago.

Welcome to Tokyo’s ‘Little Nepal’: A microcosm of Japan’s evolving identity, by Dave Hueston,, June 20, 2019

Most of these Nepalese are apparently doing low-level service jobs.

Now, I know that to get an immigrant visa for Japan you have to pass a Japanese-language test. My impression from my own feeble attempts so many years ago, fortified by many subsequent encounters and conversations, is that Japanese is a subtle and difficult language, hard for foreigners to learn. If that’s true of spoken Japanese, it must be even truer of the written language. They don’t just use two alphabets—three, I guess, if you count romanizations—they also use a non-alphabetic stock of Chinese ideograms.

Looking at David Becker’s table of mean national IQs (end of this post by James Thompson), I saw Nepal listed as one of the lowest: mean IQ 60, along with Sierra Leone and Guatemala.

Thence my question: How hard can the language test be, if so many service workers from Nepal, a nation with such a small Smart Fraction, can pass it?

I asked my friend in Japan. His reply, in part:

Everything in customer service follows a script. Everything. All the time. There is a script for everything. Sometimes the Japanese level is pretty good. Usually it’s just the script. And lately it’s almost non-existent. Asking if they are out of an item has gotten me confused looks …

One of my observations about Japan is that this country works because of the left half of the bell curve. Very low-IQ people are well behaved. They show up to work. They don’t steal. They don’t litter. They are not loud. When they speak they follow the script. You would think, “Oh, I am taking to a smart Japanese person. They are so smart and disciplined.” No. You are speaking to 90 or maybe 85 or even 80 IQ. Yet the outward behavior doesn’t show it.

Meanwhile Vietnamese and Nepalese have to be screened to function at the level of 85 or so IQ Japanese. The traits of patience, compliance, work ethic are the issue.

You occasionally hear or read someone telling you that the test of a civilized society is how well it treats X, where X is some comparatively helpless group: old people, animals, homeless, the poor.

I prefer Steve Sailer’s idea: the true index of civilization is how well you provide work, stability, respect, and the opportunity to feel useful to the left-hand side of your bell curve.

On that index, Japan seems to be doing something right.

Married a third of a century

How did I end up with a Japanese theme here? It must be the influence of August 6th—Hiroshima Day.

As it happens, August 6th is also the Derbs’ wedding anniversary. This year is our 33rd; so at some point in early December we shall have been married a third of a century. As a champion of three-ness and third-ness, I consider this a major milestone.

The coincidence of dates—I mean, our getting married on Hiroshima Day—didn’t occur to us at the time. If it had, and we’d mentioned the fact, the people around us would not have minded. We might even have gotten a round of applause.

We were married in Mrs. Derbyshire’s home region, Northeast China (always “Dongbei” in Chinese, never “Manchuria”), which had been occupied by Japan from 1931 to 1945. There was still anti-Japanese feeling there. One of Mrs. Derbyshire’s uncles had been drafted into a Japanese labor battalion during World War II and never heard from again.

(There still is anti-Japanese feeling all over China, carefully cultivated by the ChiComs, probably to divert their citizens’ attention from the fact that communism killed far more Chinese people than did Japanese imperialism—nearly six times as many, according to Prof. Rummel; although Prof. Dikötter gives higher numbers for deaths from communism, raising the ratio to seven or eight times as many.)


National character’s a funny thing. The Japanese of eighty years ago were regarded as ferocious savages. In my 1950s English childhood I occasionally encountered adult Englishmen who had been war prisoners of the Japanese. You wouldn’t want to be in the same room with one of those guys if a Japanese person walked in. Fortunately this never happened in the sleepy country town where I grew up.

Yet here I am a mere lifetime later gushing over the high civilizational level of Japan. I guess really, comprehensively, unmistakably losing a war—your cities fire-bombed to ashes, topped off with a couple of nukings—will do that.

My Jersey girl

China, where I and the Mrs. will be spending most of September, is a world within the world, complete with a whole set of regional prejudices and stereotypes.

The Economist ran an interesting piece about this recently:

People from Henan and the north-eastern provinces … are among those most commonly targeted, partly because those areas are such big sources of migrants …

Even among better-educated urban residents, north-easterners are often stereotyped as quarrelsome and pugnacious, and Henanese are commonly regarded as thieves and cheats.

[Province and prejudice: Many Chinese suffer discrimination based on their regional origin, April 13th 2019.]

I commented on anti-Northeastern prejudice in my 2001 China Diary. For the full stereotype, see page 33 of the 2010 book Dirty Chinese, by Matt Coleman:


Hailing from Dongbei, the frigid bit of China stuck between North Korea and Siberia, Northeasterners generally describe themselves as 豪爽 (háoshuăng; “extroverted,” “direct,” “fun-loving”) while people from elsewhere in the country typically describe them as “alcoholics prone to violent outbursts” and assume them to be affiliated with organized crime. This is unfair. Dongbei guys make great drinking buddies, if you’re a guy (if you’re a girl, you may want to carry pepper spray), and they’re good to have on your side in a fight. And with their big hair, heavy war-paint, piercing accents, negotiable virtue and square-headed boyfriends, Dongbei chicks are like the Jersey girls of China.

So I guess I’ve been living with a Jersey girl this past 33 years. That explains a lot.

Fun with lexicography

I’m pretty sure I must have mentioned somewhere my favorite page in the 1979 Xinhua Zidian Chinese-Chinese pocket dictionary—this page.

I don’t think, though, that I have ever mentioned my favorite page in the 1962 New Cassell’s German Dictionary from Funk & Wagnalls. That would be page 103, where you find the entry:

derb, adj. firm, solid, strong, powerful, robust, hardy, sturdy, stout; coarse, blunt, rough, rude, uncouth.

Sounds like just the guy for a Jersey girl.

More than I wanted to know about Dorothy Provine

More email on my podcast signoff music; not Pachelbel this time, but Dorothy Provine, who I featured in the August 16th Radio Derb.

A couple of listeners wanted to chide me for pronouncing the lady’s name as Pro-VEEN, when it should properly be Pro-VINE. I stand resolutely unchidden. Who can ever get the een-ine business right? The hell with it. Cue ancient showbiz joke.

A listener also reminded me that Ms. Provine closed out her showbiz career in a way some thought unseemly: by doing commercials for a vaginal deodorant spray. Wrote Nora Ephron:

By 1969, the market for the sprays had grown to $19.3 million and manufacturers were tumbling in. The boom in sales came largely because Alberto-Culver had succeeded in getting the National Association of Broadcasters to change its code and permit the sprays to be advertised on television. (The stations themselves exerted pressure, of course.) The ads were required to be totally bland and unspecific—the word “vagina” is not allowed on the air—and they were. A woman walked down the beach with her child. Or lit the candles for dinner. Or talked, haltingly, about this somewhat mysterious product she, uh, really liked a lot. Dorothy Provine emerged from what she calls semi-retirement to endorse Feminique, and returned to semi-retirement $100,000 richer.

I’ve located a clip of the relevant TV commercial: it is at 28 seconds into this. Incredibly, it seems to me, the commercial aired on The Brady Bunch—the wholesomest of all wholesome family sitcoms—around 1970. Truly, the past is another country.

Are dentists any good?

Lewis Thomas’s book The Youngest Science reminds us how primitive medicine was until well within living memory. Outside basics like bone-setting and amputation, there was nothing much the medical profession could do for you until around 1930 (when my own mother was already a trained hospital nurse).

Hygiene had advanced somewhat in the early 20th century; before that, doctors were more likely to kill you than cure you. Read up the last days of President Garfield, if you can bear to. [The dirty, painful death of President James A. Garfield, by Dr. Howard Markel, PBS, September 16, 2016](Garfield’s assassin said, probably correctly: “The doctors killed Garfield, I just shot him.” He was hanged anyway.)

Still, Lewis Thomas may have targeted the wrong discipline, according to a recent article in The Atlantic. The youngest science may in fact be dentistry.

When a dentist declares that there is a problem, that something must be done before it’s too late, who has the courage or expertise to disagree? When he points at spectral smudges on an X-ray, how are we to know what’s true? In other medical contexts, such as a visit to a general practitioner or a cardiologist, we are fairly accustomed to seeking a second opinion before agreeing to surgery or an expensive regimen of pills with harsh side effects. But in the dentist’s office—perhaps because we both dread dental procedures and belittle their medical significance—the impulse is to comply without much consideration, to get the whole thing over with as quickly as possible.

[The Truth About Dentistry by Ferris Jabr; The Atlantic, May 2019]

Hm. I can’t say I love dentistry, or dentists in the generality, but I love mydentist. Here’s a story from a couple of years ago.

The wall clock in our kitchen needed fixing. I climbed up on to the kitchen table via a chair, but underestimated the table’s overhang. The table tipped; I fell.

Mrs. Derbyshire was preparing food nearby. By sheer instinct she leapt forward to catch me: she, who weighs a hundred pounds soaking wet, to catch me, a 192-pound adult male.

I tell ya: A Jersey girl takes care of her man.

We crashed to the floor together. Somehow in the crash she hit one of her front teeth against the furniture. It was chipped and bleeding from the gum.

I experienced remorse at near-suicidal levels. By sheer careless stupidity I’d caused physical injury to the woman I love.

This was a Saturday evening. I called our family dentist at his home phone number. I promised to pay him a thousand dollars in cash over and above normal fees if he’d attend to Mrs. Derbyshire the next day, Sunday.

He: “Calm down, John. Don’t be silly. You’re like family. Have her come to the office at ten o’clock tomorrow morning.”

She went. He was there—with his wife, who is also his secretary. He powered up his equipment, did a marvelous repair job on the tooth, and billed us a very reasonable fee, refusing anything extra for coming out on a Sunday.


That evening I went to the nicest family restaurant in our town and bought a $200 gift voucher to cover a slap-up meal for my dentist and his wife. I put it in a thank-you card with some suitable words written. Monday I dropped it off at the office.

Those suitable words ended of course with: “Don’t forget to brush your teeth afterwards!”

The real youngest science

So no, I’m a hard sell for the idea that there is anything bogus about dentists.

Dietitians are another matter. Is diet advice actually any good?

That 192 pounds is more than I’d like to be and more than I should be on a skinny frame. I eat sensibly, dinners mostly “oriental”: rice (brown), fish, veg. I lift weights three times a week in the family gym, and walk a lot (I no longer own a car). Yet still I have incipient moobs, and I’m told the phrase “muffin top” has been heard murmured around the household servants’ quarters. So I’ve developed an interest in diet.

A few things are clear and straightforward. Sugar is bad; snacking is bad. I’ve cut out sugar and don’t snack. It’s made no difference.

Fasting got my attention. It’s easy to do—a not-doing, not a doing—and I have good self-control. I cut out lunch, except for a protein drink on work-out days. No difference.

Carbs are the enemy! people have told me. Really? OK, I gave up bread. I couldn’t give up my morning oatmeal, though. I look forward to it too much; without that bowl of Quaker Oats to head for, I wouldn’t get out of bed in the morning.

Surely oats can’t be bad for you? Oats? “A grain, which in England is generally given to horses, but in Scotland supports the people,” says Dr Johnson in his Dictionary. You don’t see fat horses; and the Scots are a lean, hardy race, aren’t they?

Then I heard about the Keto Diet. I bought a magazine with details and recipes. Kale chips … bone broth … mocha muffins … zoodles … It all seemed a bit precious: artsy, yuppie, Vermontish, perhaps even—euiw!—millennial.

While I was pondering I started noticing anti-Keto articles on the news websites. This one:

Last month, three doctors published an essay in JAMA Internal Medicine cautioning that the enthusiasm for the diet as a treatment for obesity and diabetes “outpaces” the evidence. They pointed to studies suggesting that it … could cause adverse effects like constipation, fatigue and, in some people, an increase in LDL cholesterol particles, a risk factor for heart disease.

[The Keto Diet Is Popular, but Is It Good for You? by Anahad O’Connor; New York Times, August 20th 2019.]

Then this one:

People following the ketogenic diet may be missing out on some of the healthiest foods in the world, an expert has warned …

Dr Shivam Joshi, a medical doctor and New York University professor, said people following the diet risk “throwing the baby out with the bath water.”

Carbohydrate-rich foods like brown rice, quinoa and oats have been proven to be healthy and risk being sidelined by people grouping them with white bread and cakes.

[Keto diet loved by A-listers cuts out ‘some of the healthiest foods on the planet’ by ditching whole grains like oats and brown rice, doctor warns by Sam Blanchard; MailOnline, August 5th 2019].


And then this one from Time magazine:

Different people, even identical twins (who have nearly the exact same DNA), may respond to the same foods very differently, the researchers found—complicating decades of weight-loss and health advice …

Researchers tracked about 1,100 U.S. and U.K. adults, including 240 pairs of twins, for two weeks … Foods that spiked one person’s blood sugar or kept their fat levels elevated for hours didn’t necessarily do the same for the person dining next to them—even if they were twins. Individuals even had different responses to the same meals when they were eaten at different times of day …

A major 2018 study … found that just as many people succeed (or fail) to lose weight on low-carb versus low-fat diets, with no clear reason why.

[A Study on Twins Offers Proof That We All Need Personalized Diets, by Jamie Ducharme; Time, June 10th, 2019.]

OK, got it: I need a personalized diet.

How can I get one? I can’t:

Scientists still don’t know enough about gut bacteria or diet-gene interactions to offer the type of personalized advice that would actually be helpful for dieters.

Looks to me like it’s not medicine that’s the youngest science, nor dentistry: It’s nutrition.

Outside basic obviosities like “Don’t gorge on Twinkies” and “Get up off the Barcalounger now and then,” dietitians have nothing to tell us.

Decline of the waiting-room magazine pile

My dentist has an actual magazine wall rack, which endears me to him even more.

Well, he had one the last time I went there, six months ago. Now I’m afraid to go and check. The zeitgeist may have swept that wall rack away.

Last week I was in the waiting area of a different doctor’s office in the next town over. It was a big establishment serving several physicians, seating for around thirty waiting patients. I registered at the desk, then went to get a magazine for browsing while I waited.

There weren’t any!

I looked around at the other patients waiting. A couple of the older ones were just staring into space. The majority, though, were fiddling with their accurséd smartphones. Of course. What use would they have for magazines?

Yes, it’s geezerish to grumble about these minor social changes. And yes, I’m sure that four thousand years ago some old fart in Mesopotamia was lamenting the change from good solid indestructible inscribed clay tablets to that new-fangled paper stuff—so flimsy! so flammable!

But I used to like the random, faute de mieux quality of the waiting-room magazine pile. If not for my doctors and dentists, I would likely never in my life have browsed a copy of Vogue or Ebony or People or Golf Digest. Whether my life is richer for having done so, I can’t say; but it might be.

I’m sure I can go to those periodicals using a smartphone; but why would I want to go to them? In the old dispensation they came to me:

We know you’re not much interested in us, but take a look! It’s an afternoon appointment and he’s backed up; he’ll keep you waiting half an hour at least; what else do you have to fill the time?

Note to self: For next doctor/dentist appointment, take a book.

Young Fogey takes Parliament

At month’s end I read that Boris Johnson, Britain’s new Prime Minister, has persuaded the Queen to prorogue Parliament.

I don’t have much clue what the significance of that is for Brexit; but it’s made all the Establishment cucks’n’commies foaming mad. [They’re HYSTERICAL: If you’re still wondering what to make of the PM’s bold gambit, revel in this over-the-top outbursts of anti-Boris weeping and wailing from Remoaner luvvies, Daily Mail, August 29, 2019] So I’m sure it’s a good thing.

Likewise Johnson’s pick for Leader of the House of Commons, Jacob Rees-Mogg.

Nicknamed the “Honourable Member for the 18th Century,” Mr Rees-Mogg is known for his formal dress and love of tradition.

[Jacob Rees-Mogg issues style guide to staff by Paul Brand; ITV News, July 26th 2019]

Rees-Mogg is what thirty years ago in my Spectator days we used to call a Young Fogey. That style guide mentioned in the title there instructs Rees-Mogg’s parliamentary staff to:

  • Use singular verb forms for organizations,
  • Double-space after periods,
  • Follow the names of non-titled males with “Esq.,”
  • Do not place a comma after “and,” (whoops) and, (darn it!)
  • Use imperial measures (pints, miles), not metric (liters, kilometers).

I like the cut of this guy’s jib. It doesn’t seem probable that Jacob Rees-Mogg, Esq. will have occasion to refer to the speed of light in vacuo during Parliamentary proceedings; but on the off-chance it comes up, I hope the proper British measures will be used.

It’s 1.8 billion furlongs per fortnight, Sir. British billion, of course.

Math Corner

That was a segue into my Math Corner.

Here’s a very striking, very weird math paradox. I had never heard of it until it was brought to my attention just recently by astrophysicist and polymath Michael Hart.

Michael is the author of The 100: A Ranking of the Most Influential Persons in History,Understanding Human History, and numerous other books including Restoring America, and The Rise and Fall of the United States of America. This particular paradox will appear in a book he has just finished writing: Mysteries and Paradoxes (©2019 by Michael H. Hart, publisher still in negotiation). I reproduce it here with his permission, though the exposition below is mine, not his. Writes Michael:

I first read about this paradox over 60 years ago. It seemed very strange to me then, and it still does.

The paradox concerns rational numbers, commonly called fractions. A rational number is the ratio of two whole numbers. The rational number ¾ is the ratio of 3 to 4. The rational number 23½ is the ratio of 47 to 2; you can write it as 47/2. The top number in a fraction (like the 47 in 47/2) is called the numerator, the bottom number (2 in that case) is called the denominator.

One of the greatest discoveries in ancient mathematics—by the Pythagoreans ca. 500 b.c., though not likely Pythagoras himself—was that some numbers are not rational. The square root of two is not a rational number; pi is not a rational number. Euler’s e is not rational; neither, probably (we don’t know for certain), is his γ.

Rational numbers can be as large as you please. They can also be negative: −47/2 is a perfectly good rational number. In what follows, however, I’m going to restrict my attention to rational numbers between 0 and 1. More precisely: between 0 exclusive and 1 inclusive.

The set of numbers I’m considering does not include zero or any negative numbers; it does include 1, and all numbers between 0 and 1, both rational and irrational; it includes no numbers bigger than one. In proper mathematical symbolism, it is the interval (0, 1], “open” at the left-hand end, “closed” at the right. You can visualize it as a line segment one unit long with a just-visible dot at the right-hand end but no corresponding dot at the left-hand end.

Note in regard to the rational numbers that they are everywhere densealong this interval: between any two of them, you can always find another one. The rational numbers 377/849 and 127/286 are very close together—they differ by only four parts in a million—but halfway between them sits 215645/485628.

One more wrinkle. When discussing rational numbers we commonly “cancel down.” If the number 4/6 shows up, we rewrite it as 2/3; if 35/60 shows up, we rewrite it as 7/12. In what follows I shall not do this. Far as I’m concerned, 4/6 and 35/60 are rational numbers in good standing. This means that each rational number in my line segment (0, 1] will be counted many times over, but I don’t care.

OK, let’s proceed.

Onto that line segment (0, 1] I shall impose some lesser segments, thus.

To every rational number n/d in (0, 1] I shall attach a teeny segment at its left. The length of this mini-segment will be 1/(10d3).

So, for example, the rational number ½ is now at the right-hand end of a teeny segment of length 1/80. (Meaning that the left-hand end of that segment must be at 39/80.) The number 1 itself, which you can write as the rational number 1/1, is at the end of a teeny segment with length 1/10, left-hand end at 9/10.

You can think of these teeny segments imaginatively as little shadows cast to the left of all the rational numbers by some light source over at the right, the length of the shadow cast by n/d being 1/(10d3).

The question I shall tackle is: How much of (0, 1] ends up “in the shadows,” as it were? (See, this is You can’t escape the immigration issue). How much of it ends up in one of those mini-segments attached to a rational number?

I shall call the answer L. If half of (0, 1] ends up in some mini-segment or other, L = 0.5. If all of it does (which seems, at first glance, more likely), L = 1.

I don’t actually know the value of L. Some quick paper-and-pencil work on denominators from 1 to 10 tells me that it is bigger than one-eighth; bigger than 0.13, in fact. Remarkably, though, I can prove that it’s less than one-sixth.

Proof that L < 1/6:

Consider some fixed value of d, say d = 4. Each of the four rational numbers 1/4, 2/4, 3/4, 4/4—think of them as dots evenly spaced out along the line from 0 to 1, with the fourth dot of course precisely at 1—will end a teeny segment of length 1/640. Total length of all four segmentettes: 1/160. In general, the total length of all the mini-segments for denominator d will be 1/(10d2). There are d of them and each one has length 1/(10d3).

The total length of all the teeny segments on (0, 1] for all possible denominators is therefore one-tenth of this infinite sum:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + 1/6² + 1/7² + 1/8² + 1/9² + …

As it happens, we have known the precise value of that infinite sum since December 5th 1735. The value is pi²/6, which is 1.644934066848226436472415266646…

The total length of all the teeny segments for all the rational numbers in (0, 1] is one-tenth of that: 0.16449340 …, a bit less than one-sixth.

And if you think about it, the actual proportion of (0, 1] covered by this infinitude of teeny segments must be less than that number, because the teeny segments overlap so much.

Consider the longest teeny segment, the one stretching to the left of 1. Its length is 1/10. Call it Joe. Halfway along it is the rational number 19/20 with its little segment, length 1/80000, appended to it on its left; and this little segment is totally covered by Joe—as, of course, are an infinity of other segments for other rational numbers in Joe.


There’s overlap like this all the way along from 0 to 1. The rational number 1/3, for instance, owns a teeny bit of real estate to its left, length 1/270. Call this one Sally. Halfway along Sally dwells the rational number 179/540 with its segmentino, length 1/1574640000, totally covered by Sally.

And that’s not even to mention the overlapping caused by my not cancelling down. The rational number 4/7 has a segment attached to it at the left, length 1/3430—call it Fred. The rational number 8/14, which is at exactly the same spot in (0, 1], has a segment of length 1/27440 attached—call it Daisy—but totally overlapped by Fred. The rational number 12/21, which is at the same spot again as 4/7 and 8/14, has a segment of length 1/92610 attached but totally overlapped by Daisy, … and so on.


With all that overlapping, the proportion L of (0, 1] covered by this infinitude of teeny segments must be a lot less than 0.16449340 …

Put it another way: The un-covered portion of (0, 1], has aggregate length well north of five-sixths. The great majority of (0, 1] is not covered by any of my teeny line segments.

All right: but what does that uncovered portion look like? You might imagine it as a lot of microscopic fragments—a little bit here, a little bit there, …

But that can’t be right because the uncovered portion can’t include any line segments. It can’t, because every line segment, no matter how short, contains rational numbers.

The interval from 403277185924/1000000000000 to 403277185925/1000000000000 (denominators one trillion) is short indeed, length only one-trillionth; but it contains 4032771859241/10000000000000, 4032771859242/10000000000000, 4032771859243/10000000000000, (denominators ten trillion) and an infinity of other rational numbers.

If the uncovered portion of (0, 1] can’t include any line segments it must be just a collection of isolated points (corresponding, of course, to irrational numbers like the square root of ½ or pi − 3).

And the only place one of these isolated points can exist is immediately to the left or right of some teeny segment. So the total number of isolated points, each with length zero, is at most twice the number of teeny segments, each with a finite length.

Since 2 N zeroes must add up to less than N finite lengths, the total length of all the isolated points must be less than the total length of all the teeny segments.

But we have already shown that the first total length is greater than five-sixths, the second less than one-sixth.


Moral of the story: Ordinary plain-vanilla real numbers, the critters we’ve been familiar with since 500 b.c., are stranger than you think, perhaps stranger than you can think.


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 authorof We Are Doomed: Reclaiming Conservative Pessimism and several other books. He has had two books published by com: FROM THE DISSIDENT RIGHT (also available in Kindle) and FROM THE DISSIDENT RIGHT II: ESSAYS 2013.

(Republished from VDare by permission of author or representative)
• Category: Culture/Society • Tags: China, Japan 
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  1. I like Pachelbel’s Canon in D. Sure it’s overplayed, but I like it

    I feel the same way about “Pomp and Circumstance”, as long as there are no gowns anywhere near. I have the car radio tuned to the classical stations to prevent road rage.

    people from elsewhere in the country typically describe them as “alcoholics prone to violent outbursts…” Dongbei guys make great drinking buddies, if you’re a guy (if you’re a girl, you may want to carry pepper spray), and they’re good to have on your side in a fight.

    All that’s missing is the tartans.

    Outside basic obviosities like “Don’t gorge on Twinkies” and “Get up off the Barcalounger now and then,” dietitians have nothing to tell us.

    The best book on diet I have ever read is by– sit down– David Reuben. Of course, the title is Everything You Always Wanted to Know About Nutrition, apparently released in paperback exactly 40 years ago today, and far more useful, and entertaining, than his similarly-titled bestseller. I’ve been happily consuming eggs, butter, and oats all these decades, and am in as fine health as anyone I know.

    It’s a real fun read. Especially the part about rabbits and cholesterol on pp. 99-100.

    One of the greatest discoveries in ancient mathematics—by the Pythagoreans ca. 500 b.c., though not likely Pythagoras himself…

    Read up the last days of President Garfield, if you can bear to.

    Read up on the early days of President Garfield. He was a teacher of mathematics. One of his achievements was an original proof of the Pythagorean Theorem.

    James Garfield Was the Only U.S. President to Prove a Math Theorem

    Of course, Derb probably already knew this. But how did the Greeks do all that complex rational-number (let alone irrational-number) math without a zero?

    • Replies: @Logan
  2. But I used to like the random, faute de mieux quality of the waiting-room magazine pile. If not for my doctors and dentists, I would likely never in my life have browsed a copy of Vogue or Ebony or People or Golf Digest.

    Allen Fahden, in the marketing book he wrote with baseball entrepreneur Mike Veeck (“the man who killed disco”):

    “While You Wait, Would You Prefer Fortune, Forbes, or Medical Aspects of Human Sexuality?”

    As senior vice president of a large advertising agency, I noticed that others with corner offices had Fortune, Forbes, and Business Week on their coffee tables. I like to be different. So I got the most bizarre magazines I could find for my corner office. American Funeral Director, Hog Farm Management and Diseases of the Colon and Rectum.

    Everything else was as corporate as I could make it. I wore a three piece, blue-pinstripe, vested suit and a very small patterned tie. If you want to get away with being crazy, look as sane as possible.

  3. dearieme says:

    four thousand years ago some old fart in Mesopotamia was lamenting the change from good solid indestructible inscribed clay tablets to that new-fangled paper stuff

    How remarkably far sighted of him. It would be more than a thousand years before some Chinese chap invented it.

    • Replies: @David
  4. David says:

    Papyrus, paper’s namesake.

  5. My wife went on the Keto diet, John, for about 2 or 3 weeks. She wanted to lose about the 3 or 4 lb. required (that’d be a wheelbarrow full of stones to you, I guess?). to be able to fit into one dress she bought on-line, or else she’d have to pay the shipping to return it. It was not about her figure, which is just fine, but about the shipping costs.

    Anyway, she is disciplined as all hell in this respect, and cut down her usual healthy diet, especially of all the fruits but the berries. It was ridiculous, as she already eats healthier than anyone I’ve ever seen. If she did not stay on this diet, which is the case, then it really sucks.

    Your metabolism is just changing – I’d recommend some other exercise at home, not the weight-lifting, but the kind that tones up muscles. I’m no doctor, but I play one on the internet. ;-}

    On the fasting, we’d gotten some videos by one Dr. Joel Furhman way back, to diet for health reasons (not for weight reasons). That guy is (was?) a fanatic, and tells you to go ahead and fast for about a month – “it’ll do you good!” Shoot, we made if 4 days, is all. I think he is aiming for people with 120 extra lb. on them. For you and I, your body will start eating up your muscle tissue by mid-week.

    • Replies: @Bardon Kaldian
  6. Destiny6 says:

    Things like this (Michael Hart’s paradox) long ago led me to believe that irrational numbers were just that — irrational — and not to be messed with. Whether they are in any sense real, I am agnostic about.

    The existence of a (completed) infinite set, as opposed to an unbounded (potentially infinite) set seems highly unlikely.

  7. To address 2 of your segments at once, with no irrational arguments in between, our family has been lucky to have good teeth. We all went to one dentist 3 years ago, and he recommended my wife and I both get this $500 (after insurance) 3-session deep gum cleaning. Yes, I got a 2nd and 3rd opinion, and from one doctor friend who knows a dentist (I got the x-rays and emailed them) I got “I don’t know, maybe he just wants the extra business.” and from a lady dentist at the pool, I got “Yeah, I know the guy, and he just wants the extra business”.

    So there you have it. Plus, the last time I went to a dentist, about 15 years prior, I remember telling him that I hadn’t been since the late 1980’s. (As they say, DO THE MATH – it’s all line segments nowadays!). He was impressed, and outside the door I remembered something, and walked back in to tell him “yeah, and I eat all the sugar I want.”, just to, you know, rub it in.

    Now, that leads to the magazines. I don’t usually read them, I LEAVE them. I bring already read copies of the NRA magazine and leave them in dentist’s/doctor’s offices and airport gate areas.

  8. I will address the math corner with trepidation, as I don’t usually have what it takes to follow it. First off, in grade school we would have made a line segment representing that (0,1] involved here in your paradox as a horizontal line with a solid small circle at the right end, the 1, and an open circle of the same size at the left end, the 0.

    Now, as to your small segments, did you ever explain why each tiny segment, though it contains an infinite number of rational numbers can’t contain ANY irrational numbers? Where did you prove that? I am probably lost, so if some other commenter can tell me, including the usual name-calling, that’d be fine too.

    • Replies: @blake121666
  9. jim jones says:

    Boris reminds me of Donald Trump, he loves to do things that drive Leftists crazy. He is also my MP so I had some small part in his rise to power.

  10. I used to change planes in Denver quite often.

    For some reason, there seem to be a fair number of Nepalese immigrants working in the Denver airport. It seems to be one of those things. An immigrant does well in a certain place, brings friends and family. Then it catches on. For example Madison Wisconsin has a lot of Tibetans, Northwest Arkansas has a lot of Marshall Islanders and Bartlesville Oklahoma has a lot of Taiwan Chinese.

  11. The average IQ of the Nepalese is not 60. That is simply absurd. The Nepalese do have a reputation for being diligent and hardworking, which are no doubt reasons why the Japanese have allowed them to come work in their country. And make no mistake, the Japanese are a very deliberate people.

    Although these global IQ statistics do possess an element of truth, I do think they fail in not being adjusted for people’s education levels. In South Asia in particular, there is still a vast amount of illiteracy and high drop out rates. Flooding, earthquakes, difficult terrain, and political instability have kept Nepal from developing, though progress is being made.

    Despite what these numbers claim about intellectual abilities, the Nepalese are not the level of places filled with sub-Saharans.

    • Replies: @Rex Little
    , @Truth
  12. Albertde says:

    Actually, you can further classify numbers. You have numbers like √2, which is the root of x^2 – 2=0, and other numbers like e. In general, a number, which is a root of a polynomial equation with rational coefficients is called an algebraic number. The other numbers like e (there is a long and complicated proof using number theory that shows e cannot be the root of a polynomial with rational coefficients) are called transcendental. The algebraic numbers (which, trivially, include the rational numbers) are countable. So √2 is part of a countable set. Since the real numbers are uncountable, this implies that “most” numbers are transcendental.

    Of course, for a believer in constructive mathematics, where there are allowed only proofs that involve building the answer, i.e., no proof by contradiction, there is only the subset of numbers that can explicitly be constructed. I am not sure whether that implies that this subset is countable or not or even whether countability is a valid notion. Some mathematicians take this to imply that there must be some algorithm to compute the value (or an approximation that can be extended to be more precise – not some asymptotic value that at first appears to be an approximation but on extending the calculation, diverges). These numbers are called computable and, so, taking it further, the numbers that are not computable do not exist for such a believer.

    From a classical standpoint, though, it is possible to prove that the set of computable numbers is countable. This implies, since the real numbers are uncountable, that most numbers are not computable and the set of such numbers is uncountable. (Note e is computable).

  13. Logan says:
    @Reg Cæsar

    Garfield was a pretty interesting guy. Ambidextrous plus.

    At parties he’d have someone give him an English tag line, like “Hell hath no fury.”

    He’t take a pen in each hand, put his hands together and simultaneously write out a Latin and Greek translation of the phrase, writing backwards with the left hand.

    Not a common accomplishment.

    • Replies: @Reg Cæsar
  14. @Logan

    He’d take a pen in each hand, put his hands together and simultaneously write out a Latin and Greek translation of the phrase, writing backwards with the left hand.

    Not a common accomplishment.

    There was a guy in Brooklyn who could do that. You wouldn’t have heard of him, but likely have of his son– Sandy Koufax.

    • Replies: @Logan
    , @PiltdownMan
  15. Looks to me like it’s not medicine that’s the youngest science, nor dentistry: It’s nutrition.

    Outside basic obviosities like “Don’t gorge on Twinkies” and “Get up off the Barcalounger now and then,” dietitians have nothing to tell us.

    True. I tried all that & came to the conclusion that essentially the only thing that works for me it to eat smaller portions (of anything I like) 4-5 times a day (not exactly, just – don’t overeat). It works- but for me, and only up to a certain point. It seems that a body has something like an equilibrium position of a pendulum, so that it takes time for body weight to stabilize.

    Perhaps the best advice is: be moderate, happy & do not pay too much attention to body.

  16. @Australoid

    The average IQ of the Nepalese is not 60. That is simply absurd.

    That was my reaction, too. People with Down’s Syndrome average 50-60. There’s no way a whole country averages 60–not even an African one like Sierra Leone, never mind Asian Nepal.

    Although these global IQ statistics do possess an element of truth, I do think they fail in not being adjusted for people’s education levels.

    That, and I’ll bet there are cultural factors involved in some cases. I know they try to make IQ tests culturally neutral, but some cultures may be too different from, or too poorly understood by, the test makers for the right adjustments to be made.

  17. Technomad says:

    I hope poor Mrs. Derbyshire is all right!

  18. @Achmed E. Newman

    Your extremely confused – and kind of have it backwards. The tiny line segments are real number line segments between two rational numbers (n/d – 1/10d^3 and n/d). All of those real number line segments only account for at most 1/6 of the real numbers between 0 and 1. Those numbers that do not fall within any of those line segments therefore make up the other 5/6ths-plus real numbers between 0 and 1. But those numbers are isolated because rational numbers are dense in real numbers (between any 2 distinct real numbers is a rational number). So all of those zero-length points (the points not in any of those line segments) account for over 5/6 of the real numbers between 0 and 1. This is counter-intuitive precisely because those numbers are merely isolated points before and after line segments. Do you see now?

  19. baythoven says:

    I don’t know Prof. Greenberg or his lectures, but if he made a particular point to disparage Pachelbel’s Canon it’s very much to his credit.
    As for that exquisite Japanese commercial, I took a pass.

  20. I saw Nepal listed as one of the lowest: mean IQ 60, along with Sierra Leone and Guatemala.

    This is more likely an artifact of the testing methodology, an indication of how it breaks down at the extremes, and doesn’t provide useful information.

    Neolithic pygmies from the Congo rainforest have IQs of 60. But the Nepalese have built things like those below and are able to serve in the British Army with distinction. They also got their first science and technology college in 1918. The Congolese pygmies don’t have anything of the sort.

    Nepalese may not be super-bright, like the Han Chinese or Ashkenazic Jews, but that IQ score of 60 is misleading.

  21. @Achmed E. Newman

    Forget it. All diets, eventually- fail. It is a change of the entire life that matters. If it is such that it is in the right direction of enhancement of one’s life, weight will follow -up or down. If it doesn’t, then it’s determined by other factors we don’t know about.

    One of the big mistakes one frequently encounters is almost religious, naive faith in practice, exercise. True, there are areas of life where exercises are crucial: sports, reproductive arts, surgeon training,….
    But there is no type of exercise that will give one a sense or humor (if one doesn’t already possess it); no exercise will enhance one’s IQ; nor will it change a person’s body type.

    I guess that, apart from a few common sense advice, nutrition & dietary “laws” are just an amusing chat…

    • Replies: @Achmed E. Newman
  22. On waking this morning and thinking about the math conundrum here, I think the problem is with the concept of “counting” Real Number “infinity”.

    If one were to refer to Real Number infinity as RI, and a countable set’s infinity as CI that might possibly resolve the problem.

    I think RI has the queer property that any countable manipulation of it is still that RI – it can never go away in a countable way.

    So when Derb says that L < 1/6 he is correct insofar that RI == 1/6 * RI (RI is identically equal to 1/6 times RI in his countable construction of it). But the set is uncountable – it is a collection of uncountable real number sets – that just so happen to be countably constructed.

    So although it would be the case that the numbers not in his countably constructed sets are isolated because of the countable construction, each one of those sets is uncountable.

    So you have a CI number of sets of length RI. And that is then RI.

    If you were to think about it as is done here, you'd of course think "where are those real numbers"? And the answer is that they are indeed as he described them – there just so happens to be RI number of them (not a CI number – even though those sets are indeed constructed CI times).

  23. Nepalis may have a mean IQ of 60. I have spent time in Nepal and can report that no such dimness is apparent, for what that’s worth. But if it exists, then half the population is below 60 and a substantial portion below 45. These couldn’t find their way home at night. Does anyone really believe this stuff?

    • Replies: @Logan
    , @Half-Jap
    , @JosephB
  24. Truth says:

    If one IQ number in a study is wrong, they are ALL wrong. That’s the way scientific method works, Old Sport.

  25. Truth says:

    33 years married huh? Well lucky you, “worshipful master.””

  26. anonymous[244] • Disclaimer says:

    I didn’t read carefully, but surely every line segment has to contain both rational and irrational numbers.

    The paradox is that an infinite number of line segments (tho to be sure, countably infinite) still has finite length (and less than 1 in total). The 1/6 part is just a detail.

    How does this relate to the Cantor set?

  27. Lots of fresh Derbyshire degeneracy to deal with.

    I’ll be commenting on this column and on his column about Haidt and Codevilla.

    First, his scribblings about a civil war. This is VDare nonsense. There will not be a civil war. What will happen is that blacks will get their own state. More and more blacks keep moving to the South – a very good thing. Negrophiliacs like Ann Coulter, Rush Limbaugh, the Kardashians will have to move to this state. Derbyshire and his Chinese family will be sent to China.

    He scribbled about Japan. He has yet to deal with the fact that the Japanese are the only intelligent Asians. China will always be a shithole.

    He scribbled something about being worried about “his country.” America is not his country. He tried make an analogy that his brown Chinese woman is a Jersey girl. She is not a Western woman.

    He scribbled nonsense about Jacob Rees-Mogg. Rees-Mogg is a practicing Roman Catholic who will OSCULUM INFAME black/Asian priests-popes.

    • Replies: @Truth
  28. Logan says:
    @Fred V. Reed

    That’s the problem with these amazingly low mean IQ numbers.

    Supposedly the US military has a rule forbidding the recruitment of anybody below 83 IQ because there is nothing they’re capable of doing in the military that isn’t counter-productive.

    83 IQ would be quite high IQ in Nepal, assuming a typical standard deviation. Yet Nepal is home to the Ghurkhas, renowned for about two centuries as among the best light infantry the world has ever known. High competence in modern combat is not associated with far below average intelligence.

  29. @Bardon Kaldian

    Mr. Kaldian, there are aerobic exercises that keep one’s lungs and heart in shape to last quite a bit longer. Just like man-made mechanical machines, you don’t leave these on low for years and expect them to work hard when your body needs them.

    There are other exercises, or more like changes of life, as you say, such as just everyday walking outside vs. going everywhere in the car, that can keep one from being dangerously overweight leading to driving around Wal-Mart on a scooter and getting diabetes early on, ruining one’s quality of life.

    I guess you can still have a sense of humor when driving around Wal-Mart on a scooter. It’s funny to me, anyway. IQ will probably go up if you sleep better due to working your body a bit.

    Take if from Sal in Dog Day Afternoon – the body is temple of the soul.

    • Agree: Bardon Kaldian
  30. Truth says:

    Rush Limbaugh and Ann Colter are “negrophiliacs”?

    • Replies: @attilathehen
  31. @Truth

    Hi Truth!!!

    Yes. Ann Coulter has stated that we owe black Americans for slavery and they have the right to order us around because of their past treatment.

    Rush Limbaugh’s unrequited love is Charles Barkley.

  32. I keep hearing that IQ tests provide some of the most replicable results in psychology; but then we have these unbelievable claims like ‘average Nepalese IQ is 43’. Something must be rotten in the state of psychometry…

  33. @Reg Cæsar

    Irving Koufax? Was that a parlor trick that more than one ambidextrous, multilingual and highly coordinated person knew how to perform, back in the day of parlor tricks?

  34. Half-Jap says:
    @Fred V. Reed

    The Nepalese here in Tokyo have all been good people, even unscripted. Perhaps we are contributing to a brain drain, even in services.

  35. Half-Jap says:

    Regarding our (Japs’) brutality, n-ga please. (2 spaces as always, as being proper here) Such complains were typical during the later phase of the war. Brits and mericans caught were treated as well as most of the wardens, or did not receive provisions or shelter because the japs lacked the supplies themselves.

    Torture, when it did happen, was pretty fcked up though. At least the allies had the most civilized decency of keeping things clean by indiscriminate bombings of any given civilian center and prison camps, ignoring factories producing munitions when they could, and had and still have such honesty to blame the Germans about the Jews they starved and bombed to death.

    • Agree: Tusk
    • Replies: @Achmed E. Newman
  36. @Half-Jap

    That’s quite a few lies packed into one comment. Nice one. At what point in the war was the Bataan death march?

  37. @attilathehen

    I gotta admit that last line there was funny, I don’t care who ya’ are! (excepting Ditto-heads, of course)

    You are right about Ann Coulter on that. Her belief in AA because “slavery”, along with her recent silliness about “the pot”, are about the only 2 things I’ve disagreed with her on in a decade or more. She is still batting .980 or so. I haven’t listened to Rush much since the 1990s.

    • Replies: @attilathehen
  38. Dan Hayes says:


    I believe that Ms Coulter’s latest squeeze is a black gentleman! Not surprising since her previous significant others covered all conceivable bases.

    • Replies: @attilathehen
  39. JosephB says:
    @Fred V. Reed

    I concur. For a population of 29.3 million and an SD of 15, the country would produce 8 or 9 people with an IQ of 135 or higher. I’m not gregarious and have never been to Nepal, but know 2 or 3 Nepalese who are above that threshold — one who is far above it (STEM PhD students / faculty at a solid STEM school).

    The response I’ve seen is there’s a high performing minority subgroup such as the Brahmins in India. But, I don’t recall anyone enlightening me as to the name of the Nepalese minority group.

    So yeah, I’m not buying this number either.

  40. @Achmed E. Newman


    Coulter is good on immigration, but she would always emphasize that the reason she was against immigration was because of blacks. I figured her out quickly. I’ve read her books in bookstores. They are easy reads and I knew most of what she wrote about so I never wasted money on her.

    She is right about pot though. I’ve never done drugs so all I know about drugs is what I read in articles. The pot that’s being peddled is apparently very powerful and causes serious health problems. The best thing for everyone is to stay away from illegal drugs, and legal drugs like Prozac and Ambien. E. Michael Jones is correct when he says that junk like this will just enslave and control you.

  41. @Dan Hayes

    I’ve heard the rumours for several years. Apparently, J.J. Walker of the “Dyn-O-Mite” fame is just a friend. I do know she said that she dated a Muslim. That’s a problem. I’ve heard she’s dating (((Bill Maher))), but that doesn’t add up. (((Bill Maher))) dates black women.

    She says she likes to keep her private life private, but that’s a little too private. Women don’t hide their boyfriends unless there is something unacceptable about them. She did her job getting Trump elected. She is not needed anymore.

    • Replies: @Dan Hayes
  42. Dan Hayes says:


    I respectfully disagree. Coulter is now needed more than ever. Her current critical task is to hold Trump accountable for his promises. During the 2016 Campaign her criticisms prevented the Orange Man from reneging on some of his immigration promises.

    • Replies: @attilathehen
  43. @Dan Hayes

    OK. We’ll keep her until November 2020.

    • Agree: Dan Hayes
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