Sep 9 2021

Bach’s Art of the Fugue (and its Counterpoint)

Mark Twain in Athens

Really digging Bach and counterpoint these last few weeks, good logical to stuff to read something like Alice’s Adventures in Wonderland to, etc.

Mar 5 2017

You Don’t Have to be a Mathematician (to be British)

But the age of chivalry is gone. That of sophisters, economists, and calculators has succeeded. –Edmund Burke

Lewis Carroll, a.k.a. Charles Dodgson, (1832-1898) is perhaps England’s best known mathematician. But many British writers were not so inclined. Consider a passage about C. S. Lewis (1899-1963) in Philip and Carol Zaleski’s The Fellowship: the Literary Lives of the Inklings (2015):

The Latin and Greek portions of Responsions presented no problem, but Lewis failed the section on mathematics. He had a terrible head for numbers and was unable to handle even the simplest arithmetical problems—counting change was a daily ordeal—much less algebra, a prominent part of the exam. Algebra is defined by the OED as “a calculus of symbols,” and Lewis’s failure to master it is worth bearing in mind, in light of his later controversial forays into the application of logic to metaphysics and theology. Nonetheless, he was accepted into University College and returned to Oxford on April 26, 1917, enrolling as an undergraduate on April 29.[1]

Compare philosopher and Prime Minister Arthur Balfour (1848-1930):

I wish I were a mathematician. There is in the history of the mathematical sciences, as in their substance, something that strangely stirs the imagination even of the most ignorant. Its younger sister, Logic, is as abstract, and its claims are yet wider. But it has never shaken itself free from a certain pretentious futility: it always seems to be telling us, in language quite unnecessarily technical, what we understood much better before it was explained. It never helps to discover, though it may guarantee discovery; it never persuades, though it may show that persuasion has been legitimate; it never aids the work of thought, it only acts as its auditor and accountant-general. I am not referring, of course, to what I see described in recent works as “modern scientific logic.” Of this I do not presume to speak. Still less am I refer ring to so-called Inductive Logic. Of this it is scarce worth while to speak.1 I refer to their more famous predecessor, the formal logic of the schools [i.e. of John Stuart Mill].[2]

Compare Balfour’s colleague Winston Churchill (1874-1965):

All my life from time to time I have had to get up disagreeable subjects at short notice, but I consider my triumph, moral and technical, was in learning Mathematics in six months. At the first of these three ordeals I got no more than 500 marks out of 2,500 for Mathematics. At the second I got nearly 2,000. I owe this achievement not only to my own back-to-the-wall resolution for which no credit is too great but to the very kindly interest taken in my case by a much respected Harrow master, Mr. C. H. P. Mayo. He convinced me that Mathematics was not a hopeless bog of nonsense, and that there were meanings and rhythms behind the comical hieroglyphics j and that I was not incapable of catching glimpses of some of these. Of course what I call Mathematics is only what the Civil Service Commissioners expected you to know to pass a very rudimentary examination.

I had a feeling once about Mathematics, that I saw it all Depth beyond depth was revealed to me the Byss and the Abyss. I saw, as one might see the transit of Venus or even the Lord Mayor’s Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and. I let it go![3]

Finally, there’s G. K. Chesterton (1874-1936):

A great deal is said in these days about the value or valuelessness of logic. In the main, indeed, logic is not a productive tool so much as a weapon of defence. A man building up an intellectual system has to build like Nehemiah, with the sword in one hand and the trowel in the other. The imagination, the constructive quality, is the trowel, and argument is the sword. A wide experience of actual intellectual affairs will lead most people to the conclusion that logic is mainly valuable as a weapon wherewith to exterminate logicians. [4]


[1] Zaleski and Zaleski. The Fellowship: the Literary Lives of the Inklings 75.

[2] Balfour, Theism and Humanism: Being the Gifford Lectures 176.

[3] Churchill, My Early Life: a Roving Commission. NY: Charles Scribner’s Sons. 1930. Ch. III.

[4] Chesterton, Twelve Types. 1906. “Thomas Carlyle” p. 125.