»  National Review Online Diary

  September 2002

Child abuse     I am on record as having said: "In the matter of parental discipline, I'm a parents-rights extremist. All but the very worst parents are better for kids than institutional care. I would smack my kids in public if I thought it necessary, though it never has been." So where am I on the case of Madelyne Toogood, who walloped her 4-year-old in an Indiana parking lot and was caught on videotape?

In the same place, that's where. For God's sake let the kid go home. Mrs. Toogood slapped the child around, which is a thing some parents sometimes do. It ain't nice, but to read the newspapers and watch TV, you'd think the silly woman was Bluebeard reincarnated. The child suffered no harm — not even a bruise, so far as anyone has been able to discover. I think Mrs. Toogood should be punished: a nasty fine, or some humiliating parole procedure. But to put the kid in care? To be molested by low-grade community-college-diploma "social workers" and have her poor little head filled with gibberish by crank anti-family "child psychiatrists"? Not on my dollar. I once worked with kids from these kinds of families, and I can tell you with no doubt at all, that poor tot cries herself to sleep every night, missing her mother.

I'm not defending Mrs. Toogood, who I have already said I'd like to see punished: but she'd have to do a whole lot worse than that to the kid before I'd surrender that child to the tender mercies of institutional "child care." Let the poor little thing go home.

A man is not a pot     So said Confucius (Analects, 2.xii). I am certainly not a pot, but I have recently acquired a pot. It was a gift from a friend, a collector of old and beautiful things.

This one is old all right: It is Chinese, and dates from the Han dynasty — I would guess, from the painted design, the Western Han, which makes it over 2,000 years old. It is by far the oldest thing I have ever owned, and I am filled with awe every time I look at it.

Imagine: a man, kitted out with the same basic appetites, longings, joys, miseries, dreams, and toothaches as myself, yet living in a society inconceivably remote from mine, made this thing with his hands, and decorated it from his own imagination, and sold it for profit. (Well, perhaps I shouldn't over-romanticize this. They guy was probably running some sort of primitive pot production-line, and using designs he'd used so often he could paint them in his sleep. Still …)

The thing about antiques is, you don't feel you own them; you have just borrowed them. After I'm dead, gone, and forgotten, someone else will own this pot. I have "my" pot for a while; then someone else will have it. It gives you some perspective, having a 2,000-year-old painted pot in your wall unit.

Grace notes     We are one of those families that sit down together round a table for dinner every day, come hell or high water. No TV, just a little background music if we feel like it, and some exchanges of views and the day's experiences over the cruet.

Before commencing the meal, we bow our heads and thank our Creator for what's in front of us. I generally say the grace, and most often it's just the basic English one: "For what we are about to receive, may the Lord make us truly thankful." Sometimes I vary it a bit. If I'm really hungry, or if we have visitors whose precise confession I am unclear about, I chop it down to the all-purpose grace we used to say for lunch at my secondary school: Benedictus benedicat — "May the Blessed One bless." Very handy, that; suitable for Christians, Jews, Muslims, Hindus, Buddhists and Zoroastrians. (Don't know how it would go down with a Wiccan guest; but when it happens, I'll let you know.)

Sometimes I let the kids say grace. My seven-year-old particularly likes the Marine Corps Grace that I picked up from an ex-USMC buddy and transmitted to the child: "Good food, good meat, thank God! — Let's eat." So far I have spared my family my own personal favorite, the Selkirk Grace. I am on the lookout for some new graces, though, so any reader with an especially original or colorful grace is welcome to send it in.

R-E-S-P-E-C-T     I am devastated, shattered and discombobulated. SurfControl, which filters out web sites that might bring a blush to a maiden's cheek, has flagged occasional-NR-contributor SteveSailer's site as "hate speech"; but they haven't flagged mine!

What's going on here? What do I have to do to get respect from these people? I urge those readers — they are legion — who have taken gross offense at something I have written, to get in touch with SurfControl and demand that I be accorded the same privilege as Steve. I want to be "hate speech." If I don't get my rights here, I shall be even more offensive. You have been warned.

The London Times columnist Bernard Levin threw a party when he learned that the apartheid government in South Africa had banned him from entering the country. He considered it a great honor. I feel the same way about being flagged by the PC police. Get on it, readers.

(Added later in the month:  Steve tells me he got in touch with SurfControl and complained. They looked at his site again and agreed that it is "news," not "hate speech." Still, you have to wonder how they came up with that original judgment. Steve is the nicest guy you'll meet in a month of Sundays, and as far as I know doesn't hate anybody. This "hate" business is totally out of control.)

Niggardly     In my September 17 column about the word "niggardly," I said that the whole controversy started with a piece in The Economist seven years ago. Reader Kevin Hawley in Ohio has trumped that with a much earlier reference: In Sinclair Lewis's 1947 novel Kingsblood Royal, there is a character named Winthrop Brewster, son of the Reverend Evan Brewster, a black Baptist preacher and Columbia PhD. Winthrop, back from his freshman year at the University, greets Neil Kingsblood's recent discovery of his 1/32 black heritage with enthusiasm, expanding upon the positive contribution that Neil might make to the cause of civil rights for blacks. In this regard, he then says:

Neil! Maybe you'll really get into the race-struggle and be able to give us some new slants. I wish you could do something with the racemen that are too touchy, and insist that the colored press spell That Word as n-blank-r, and have a cat-fit when they hear a bunch of innocent white kids doing some corny old song like "You could hear those darkies singing." I'll bet some of 'em insist that Niggardly ought to be pronounced Negrodly. Couldn't you make fun of them? Gee, you know, you could maybe become one of the leaders of the race.

Knowing where to look     "Knowledge is of two kinds: there is knowing a thing, and there is knowing where we may find information upon it." Thus the great Samuel Johnson. I'm constantly discovering new sources of information. One of the best I've got acquainted with recently is the China e-Lobby, an e-mail list sending out news clips about China and North Korea from an anti-communist viewpoint. Their mission statement says: "The China e-Lobby is an organization dedicated to exposing the abuses of human rights, threats to American security, and attacks on general decency committed by Communist China, and to influencing U.S. policy to ensure these egregious acts do not go unopposed." They are currently organizing a petition for a U.S. boycott of the 2008 Olympic Games in Peking. Lots of luck, guys … but it's a praiseworthy effort, and should be supported by all who love liberty. To sign up for the China e-Lobby postings, send an e-mail to them at "china_e_lobby@yahoo.com."

The Dreadful Daylight     Several readers wanted to know where I got the snippet of verse in my August blog, the bit about "the peace, before the dreadful daylight starts …" Well, it was from a poem by the English poet John Betjeman (1906-84). I have put up the poem, with a sound clip of me reading it, here.

September 11th     I KBO-ed, as promised. Finished some book reviews that had been hanging over me for weeks, did my end-week column for NRO on a totally non-war-related theme, got a little further with a speech I'm giving in England next month, got a little further with my current D.I.Y. project, scraping and sanding my front door. No break from regular routine. Defiant normality.

From the cutting-room floor

I have just lost a minor battle with the editors of my book about math. I wanted to add a 6-page appendix on Chebyshev's Bias. They: "No! The darn book is already too long! No! No! NO!!!"

OK, fine. Chebyshev's Bias deserves to be much better known than it is, though, so to get the word out, I'm going to blog it, right here. This is absolutely the only conservative web site where you get serious math.

Write down the first few prime numbers:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 …

Divide each one by 4 and note the remainder:

2 3 1 3 3 1 1 3 3 1 3 1 1 3 3 1 3 …

Once you get past p = 2, the remainder must be either 1 or 3. Which one is "ahead" at any point? Denoting the answer by 1, 3, or T (for "tie"), the answer is:

T 3 T 3 3 3 T 3 3 3 3 3 T 3 3 3 3 …

That's a Chebyshev bias. Do the 1's ever take the lead? Yes, they do; but not until p = 26,861. And that's nothing: if you divide by 3 instead of 4, the remainder (once you get past p = 3) must be either 1 or 2. The bias is to 2; and that bias doesn't get violated until p = 608,981,813,029! (This result wasn't found until 1978, by Carter Bays and Richard Hudson.)

If you divide by 10 instead of by 4 or 3, you will just get the last digit of your prime number. (659 divided by 10 leaves remainder 9.) Once you get past p = 2 and p = 5, every prime number must end in 1, 3, 7, or 9. Is there a Chebyshev bias?

I ran through all the primes up to p = 100,711,433, which is as many as I keep handy on disk. That's the first 5.8 million primes. Threes and sevens were in the lead roughly 2.8 million times each, ones had 113,922 leads, nines had 357, and there were 26,776 ties.

Notice, by the way, that these "who's ahead" biases arise from very small margins. The actual counts for ones, threes, sevens and nines as last digit in those first 5.8 million primes were: 1,449,824 ones, 1,450,185 threes, 1,450,153 sevens, and 1,449,836 nines — a variation of only 361, a niggardly 0.025 percent.

The situation resembles those "first past the post" election systems, where a nationwide majority of 51 percent can give your party a landslide in terms of parliamentary seats; or a foot race with very well-matched runners, in which one runner manages to stay slightly ahead for most of the race, and gets all the glory.

The English mathematician J.E. Littlewood proved in 1914 that any Chebyshev bias gets violated infinitely often, if you go far enough. Michael Rubinstein and Peter Sarnak proved in 1994 that the violations have nonzero density, a fascinating and counter-intuitive result … But that's about as much math as I can get away with on NRO. You'll have to read the amazing Rubinstein-Sarnak result for yourself: "Chebyshev's Bias," in Experimental Mathematics, Vol.3, 1994 (pp. 173-197).