Algebra

In Sunday's New York Times, Andrew Hacker asks "Is Algebra Necessary?" and answers, Generally, no. The reactions to this article that I noticed (over at Hacker News, as it happens) were strongly negative.

I find that I am of several minds about this one.

First, I have seen algebra fetishized by some. The Washington Post used to carry a columnist who was sure that 8th-grade algebra was necessary to the nation's future. She wrote well and set forth her arguments forcefully. Yet I wondered. The Montgomery County schools--which she covered--had more problems than under-enrollment in 8th grade algebra; students were getting to high school not knowing arithmetic they should have learned in the middle grades. I came to think that eventually there would be a movement for third grade algebra, which would have predictable results: the schools would teach what they could, and call it algebra; the parents of the young Gausses and Noethers would write furious letters to the Post about deficiencies in the algebra teaching; and the rest of the parents would shake their heads and wonder what came next.

Second, Hacker's proposal matches many I see. If something turns out to be hard, let's not do it. I don't know that this is the best way to run school systems.

Third, some of his reasoning seems questionable to me:

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Or could it be--as the folks at Hacker News suggest--that algebra can't be fudged with easy grades for bad work, the way softer courses can?

Fourth, good teachers are scarce, and good math teachers are scarcer. Some of what Hacker describes must no be  a deficiency in the students so much as in the teachers and the curricula. Of course, it would be easier to write an outstanding algebra text than to reform mathematics education in a school system, let alone a state or nation.

Fifth, can one consider a college student academically ready if he or she cannot master the rudiments of logic? And if not, are the rudiments of logic easier to master than algebra?

Finally, it is hard not to recall the numbers of obviously intelligent persons who have confessed--the boasters I don't count--that they could not master algebra. I suspect that many of them simply encountered bad teachers, and were too young to know how to ignore the teacher and work from the text. Yet some probably could not manage it, others didn't, and many went on to useful careers in academia or elsewhere.

Fuhrer Meets Geyser

Thirty years ago, I worked with a delightful woman, then a copy editor, who had started her working life as a proofreader at a vanity press. The excellence of her author queries--one jotted these in the margins of galleys--got her promoted to copy editor fairly quickly. The one publication she mentioned from this press was called something like My Three Weeks with Hitler in Yellowstone National Park. The plan of the book was simple: during the 1920s, Hitler visits the US, and while sightseeing in Yellowstone discusses with an interlocutor his plans for world domination. Hitler's dialogue, my coworker said, was rendered as if spoken in broken English by a German: 'Und zen ve must einother var fight mit die Englitsch und French." She was droll, but not I think given to just making stories up, so somewhere out there--perhaps in a storage shed owned by the writer's descendants, there must be copies of this book.

It's Greek to Him

In the essay "The Greek Conquest of England", collected in Essays Ancient and Modern, Bernard Knox writes

Ben Jonson, who sneered at Shakespeare's "less Greek," had none too much himself and Samuel Johnson [said] of the young Alexander Pope that "it was not very likely he overflowed with Greek" . . .

Here Knox is writing of how Greek displaced Latin as the most esteemed language of antiquity, something that occurred with the Romantic generation Still, it brought to mind other instances of writers being happy to say hard things about one another's mastery of Greek.

In his biography Thomas More, R.W. Chambers cites and argues against

the gibe, to which Gibbon gave currency, that Erasmus learned at Oxford the Greek which he subsequently taught at Cambridge.

(Though in context this appears to me to be a gibe aimed at Cambridge, not at Erasmus.)

In Eothen William Alexander Kinglake reports Lady Hester Stanhope's remarks on Byron:

The first whom she crucified in my presence was poor Lord Byron; she had seen him, I know not where, soon after his arrival in the East, and was vastly amused at his little affectations; he had picked up a few sentences of the Romaic, and with these he affected to give orders to his servant in a sort of ton d'apameibomenos style ...

And Stendahl reports the remarks of a Milanese professor on Byron to the same effect.

Macaulay is happy to demolish the learning of John Wilson Croker at some length, including

 Johnson was not a first-rate Greek scholar; but he knew more Greek than most boys when
they leave school; and no schoolboy could venture to use the word thnetoi in the sense which Mr. Croker ascribes to it without imminent danger of a flogging.

(To be sure, he is as hard on Croker's Latin and command of facts and dates.)

Knowing better was Macaulay's and Gibbon's stock in trade, of course.  Johnson, evaluating Pope's versions of Homer, had good reason to judge Pope's knowledge. Byron, I suppose, had only himself to blame for unkind attentions.

The amusement of maligning someone else's mastery of Greek must by now be purely a specialist's treat, to be carried out in academic journals, rather than in widely circulated magazines or in books with the print run of Johnson's Lives of the Poets or The Decline and Fall of the Roman Empire. I sat through the commencement of a large college of arts and sciences last year, where the students came up by department; there was one classics major. The attempted coup against the University of Virginia's president came in part because some on the Board of Visitors thought her too reluctant to shut down dwindling departments, one of them, of course, being Classics.

Oh, to be in Texas, Now That August's Here

Today's Washington Post notes that Larry McMurtry is closing down his Booked Up store in Archer City, Texas. The store's web site confirms this: on August 10 and 11, the store will auction off several hundred thousands of books by the shelf lot. The stores will be open for browsing the week before.

Unfortunately,

• I don't have a lot of shelf space for shelf lots.
• I lack the experience needed to buy efficiently when somebody is auctioning off tens of thousand of lots in two days.
• I have other commitments those days.

The books, then, that I remember from Booked Up's Georgetown days, if still with McMurtry, will be somebody else's prize. To those who have the time, the space, and the money, I can only quote Booked Up:

EXPERIENCE TEXAS IN AUGUST. 

An Odd Perspective

In an opinion piece, "The Inequality of Opportunity", in yesterday's Washington Post, Lawrence Summers remarks that

The number of children not born into the top 1 percent who move into it must equal the number of children born into the top 1 percent who move out of it over their lifetimes. So a serious program to promote equal opportunity must seek to enhance opportunity for those not in wealthy families and to address some of the advantages currently enjoyed by the children of the fortunate.

True enough, yet I found the notion that inequality is about the top 1 percent very odd. One could smooth out the curve considerably within the top 10 or 50 percent, yet leave troubling inequalities in place.

But Summers was president of Harvard University, where he remains a professor of economics. As viewed from the Harvard admissions office, or from the admissions office's chain of command, equality of opportunity is about the 1 percent. Those who graduate from high school functionally illiterate or innumerate aren't sending in applications. Perhaps the president of a decent state school or community college would put matters differently.

To be fair, Summers does mention the need to improve public education; still, the ending of the paragraph in which he does so doesn't quite reinforce his point.

The Slot in the Cabinet

In the houses where I grew up, there was a slot in the back of the medicine cabinet in the bathrooms, made so that one might dispose of old razor blades. Yet I have never shaved with a razor that took such blades. My first razor used a band of metal that one wound on the a fresh stretch when the edge became dull. Not long after, I began to use razors with the two blades in a plastic cartridge, which I have used since. All are much too big for a slot made to receive a flat, unenclosed blade.

Yet a row ouse where we lived, built in the early 1980s, had that slot in the medicine cabinets, though by then most American men must have moved on to the bulkier razor cartridges. I was a little disappointed, when we painted the bathrooms, to find that there was no special receptacle for the blades to fall into; anything pushed through simply dropped to onto the ceiling below. I knew that it was unlikely anyone would ever have collected years of old razor blades, but there was something unsatisfying in thinking of them falling onto old plaster, dusty drywall, and construction debris.

Parallel Texts: Waugh and Diogenes

Evelyn Waugh, in a letter to his wife, October 13, 1940, from a troopship

... In fact I am friends with all on board but I do wish sometimes I could meet an adult. They are all little boys. Some of them naughty little boys like the Brigadier, most of them delicious & just what I want Bron to be at the age of ten, but not one of them a mature man.

Diogenes, as translated by Guy Davenport in 7 Greeks:

Men nowhere, but real boys at Sparta.

Versatility

I am musically illiterate, so my opinions on music hardly deserve the name--they are prejudices. One is that Mozart is the greatest composer ever. Start my Desert Island mix with Symphony #40 and The Marriage of Figaro, and I'll consider it solid.

Yet a couple of times a year I admire Tchaikovsky's versatility. Around Christmas he is the favorite composer of girls between 5 and 7; on Independence Day he is the artillerist's favorite composer. At least, I think he must be the latter; maybe the gunners had rather pass in review to "The Caissons Go Rolling Along" than fire off Long Toms in the 1812 Overture. Of the former I can't doubt, after having seen a lobby or two of dressed up little girls spinning during the intermission of The Nutcracker.

The Middle of Next Week

In the introduction to his Essays Ancient and Modern, Bernard Knox writes

I remembered often the man in Lewis Carroll's poem who "thought he saw a rattlesnake,  / that questioned him in Greek, /He looked again and found it was / The Middle of Next Week." Though it had taken me a long time, I had finally realized that when you read Thucydides, or Sophocles, or any of the great Greek writers, you may think you see an ancient text that speaks to you in Greek. You look again, and find it is The Middle of Next Week.

 The book is absorbing, surprisingly so when I consider that it consists largely of extended book reviews. Of them, I so far like best "The Greek Conquest of England" and "Thucydides and the Peloponnesian War: Politics and Power."

Knox, who died just two years ago, led a remarkable early life, sketched out in the introduction. In 1937 he was wounded serving with the International Brigades at Madrid. In 1943 he was an officer of the U.S. Army, training for infiltration behind German lines with such men as William Colby, Lou Conein, and John Singlaub, all later notable Cold Warriors. He served behind the lines in Brittany, with Italian partisans ("party-jans" according to some less linguistically gifted generals) on the front lines of a then secondary front, and was fortunate not to be landed in Honshu to seek out Japanese party-jans.