Tag Archives: 2012

The point of teaching mathematics

This essay was provoked in part by a New York Times opinion piece by Andew Hacker (July 28, 2012) called “Is Algebra Necessary?” (the suggested answer being No):

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t. Continue reading

On reading too much into words

First let it be noted that nothing I say here will have any effect on hostilities in the so-called Holy Land or anywhere else. I have no need here to take any particular line; no reader should assume that I do or do not elsewhere follow any particular line.

I do wish to promote clear thought. I should like to think that my friends and colleagues have a similar wish, especially when they are academics like me.  Of course, what counts as clear thought may vary. I am a mathematician, professionally; I work in the mathematics department of a university. Certain modes of thought are therefore habitual with me; they may not be habitual in other departments, not to mention other walks of life. I may adopt my modes of thought at the expense of others.

I feel compelled to say such things, having been shocked to find that what I say here may be at all controversial. Continue reading

Science and anti-science

I published most of the following as a Note on Facebook, Wednesday, October 3, 2010.

Is there an ongoing or perhaps an increasing antipathy to science, and if so, are scientists to blame? The passage below treats this question, but was written 75 years ago, in December, 1935. The author could remember the war of 1914–1918, a war that he described in his Autobiography as “an unprecedented disgrace to the human intellect”, but “an unprecedented triumph for natural science.” Continue reading

Michael Psellus on learning

The value of learning was in question, a thousand years ago, during and after the reign of Emperor Basil II, in what was to become Istanbul. When learning has no purpose, it may flourish; when it has, it may be abandoned when the purpose is not achieved soon enough. Michael Psellus suggests this in Fourteen Byzantine Emperors (London: Penguin, 1966).

Michael Psellos
Michael Psellos (left) with his student, Byzantine Emperor Michael VII Doukas (from Wikipedia)

Basil died in 1025. Michael was born in 1018; here is what he says.

Continue reading

Strunk and White

The following is a lightly edited concatenation of some emails I wrote several years ago, in response to “50 Years of Stupid Grammar Advice,” Geoffrey K. Pullum’s article in The Chronicle of Higher Education (April 17, 2009). [I returned to Strunk and White in March 2018; I supplemented the present post in July 2018.] Continue reading

Logic (notes on the finger-wagging Cratylus)

The senior essay that I wrote at St John’s College was called something like ‘An account based in Aristotle of the Law of Contradiction’. I do not know now what the point was. I had read the Metaphysics in a preceptorial, so I decided to spend even more time with this book in writing my essay. I remember noting ultimately that humans could indeed be self-contradictory. Hector was an example. To Andromache he described two incompatible expectations: that their son would win renown, and that the boy would die as an infant when the Greeks took Troy. Continue reading

Aristotle on Heraclitus

Along with various fellow alumni of St John’s College (Annapolis and Santa Fe), I am currently reading Eva Brann, The Logos of Heraclitus (Paul Dry Books, 2011). This may inspire some incidental posts, such as the present one, which considers the same sentence about Heraclitus by Aristotle in three languages, mainly because of the oddity of a published Turkish translation. The oddity is in the treatment of opinion and knowledge. The distinction between them is important in, for example, Plato’s Republic; but I shall not really have anything to say here about the distinction as such.

Miss Brann spends III.A (pages 15–19) considering Fragment 50 (by the Diels reckoning):

οὐκ ἐμοῦ, ἀλλὰ τοῦ λόγου ἀκούσαντας ὁμολογεῖν σοφόν ἐστιν ἓν πάντα εἶναι

Continue reading

The swift

This is about the bird and its appearance in the Quran.

We (my wife and I) live at the edge of the upper reaches of a stream valley on the European side of the Bosphorus. The stream drains a plain where Sultan Abdülmecid (1839–61) once invited immigrants to settle. That area is now called Mecidiyeköy (village of Mecid), and until the 1950s, it was mostly open fields. Continue reading

Basil II

One reason for this blog is to avoid being enclosed by the wall of the garden called Facebook.

Sometimes I enjoy reading the history of where I live, and lately I have been working slowly through Judith Herrin, Byzantium: The Surprising Life of a Medieval Empire. The work is not chronological like that of John Julius Norwich (I have read only his Short History of Byzantium); but it does have a chapter on Emperor Basil II, the so-called Bulgar-Slayer, who apparently led the Byzantine Empire to its apogee. Reading this, I could not remember having read about Basil before, in Michael Psellus; but I had, as I could see when Herrin mentioned the latter. Continue reading

Hello world!

When I learn things that might be worth remembering, and when I have thoughts that might be worth pursuing, it may be useful or convenient to type them up as here. I begin with the opening paragraph of the third of the 77 short chapters of W. Somerset Maugham’s book called The Summing Up (published in 1938 when Maugham was about 64): Continue reading