Discrete Logarithms

In the fall of 2017, I created what I propose to consider as being both art and mathematics. Call the art conceptual; the mathematics, expository; here it is, as a booklet of 88 pages, size A5, in pdf format.

More precisely, the work to be considered as both art and mathematics is the middle of the three chapters that make up the booklet. The first chapter is an essay on art, ultimately considering some examples that inspire my own. The last chapter establishes the principle whereby the lists of numbers in Chapter 2 are created.

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An Exercise in Analytic Geometry

This past spring, when my university in Istanbul was closed (like all others in Turkey) against the spread of the novel coronavirus, I created for my students an exercise, to serve at least as a distraction for those who could find distraction in learning.

From Weeks & Adkins, Second Course in Algebra, p. 395

The exercise uses no more mathematical tools than may be found in an algebra course in high school; yet it serves the purposes of university mathematics, as I understand them.

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Be Sex Binary, We Are Not

Content warning: suicide.

The following sentence is bold in the last paragraph of an essay: “the science is clear and conclusive: sex is not binary, transgender people are real.” I don’t know what the writer means by this. As far as I can tell, as a biological concept used for explaining reproduction, sex has two kinds or parts or sides or aspects, and the essay tacitly affirms this; at the same time, obviously persons called transgender exist.

☾ ♂ ☿ ♃ ♀ ♄ ☉

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Poetry and Mathematics

This reviews some reading and thinking of recent weeks, pertaining more or less to the title subjects, of which it may be worth noting that

  • poetry is from ποιέω “make”;

  • mathematics is from μανθάνω “learn.”

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Return to Narnia

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My subject is the Chronicles of Narnia of C. S. Lewis (1898–1963). I consider this heptad of books (published 1950–6) as constituting (1) literature (2) for children (3) that I enjoyed in my first decade and continue to enjoy in my sixth.

  1. By literature, I mean a work of art whose medium is prose. Prose may also be a work of craft, intended to fulfil some purpose. This purpose could be to serve a market for fantasy or children’s books. Art as such has no purpose that can be specified in advance.

  2. Writing for children may take certain liberties that annoy adults.

  3. As with any post in this blog, I write out of my own personal interest. As a child, I read other fantasies, such as those of Lloyd Alexander, John Christopher, Ursula LeGuin, and J.R.R. Tolkien. Only the works of C. S. Lewis have stayed with me. This essay may be considered as an exploration of why, or least an example of how.

The seven books of the Chronicles of Narnia, Collier edition
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Thoreau and Anacreon

Gray clouds over blue sky over white clouds over buildings

At the beginning of Walden, the author says he wrote its pages, “or rather the bulk of them,” in the isolated house he had built by the pond of that name. He lived there, 1845–7. He wrote there also A Week on the Concord and Merrimack Rivers. He had spent the week of the title with his brother, who died of tetanus in January, 1842. Writes Laura Dassow Walls,

Into the narrative of his 1839 river trip with John, Henry had woven everything he ever felt, thought, and experienced …

This in Henry David Thoreau: A Life (University of Chicago Press, 2017). Weaving is Thoreau’s metaphor, used in Walden in a consideration of what is worth doing in life.

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Reading shallow and deep

Executive summary (added July 28, 2020): I read an article praising so-called deep reading, one of whose exponents is Henry Kissinger. The world is apparently being corrupted by people who do not read deeply; and this includes ourselves, if we allow ourselves to be distracted by social media. I myself find the article corrupted by references to neuroscience, and I am sorry that the writer, Adam Garfinkle, does not tell us about his own experience of reading. His article comes recommended by George Will, whose tenure at the Washington Post can be blamed on my grandfather. I reminisce about him and about my own deep or at least long reading, in college and more recently. I take a hedonistic view of this reading.

Seeing a tweet condemning the superficiality of Twitter, I could not pass up the challenge. I read the linked essay, “What we lost when we stopped reading” (The Washington Post, April 17, 2020). That was by George Will, summarizing and recommending a longer essay, by Adam Garfinkle, “The Erosion of Deep Literacy” (National Affairs, number 43, spring 2020). I read that, yesterday evening and this morning (April 21, 2020).

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Donne’s Undertaking

I was recently called on to recommend a poem. I chose “The Undertaking” of John Donne. I want to say here why.

  • The poem (quoted below) has a sound that impressed me when first I read it, more than thirty years ago.

  • The poem alludes to ideals:

    • of recognizing what is good for its own sake;

    • of climbing a rung or two on Diotima’s ladder or stairway of love, recounted by Socrates in Plato’s Symposium (211c):

      And the true order of going, or being led by another, to the things of love (τὰ ἐρωτικά), is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps (οἳ ἐπαναβαθμοί) only, and from one going on to two, and from two to all fair forms (τὰ καλὰ σώματα), and from fair forms to fair practices (τὰ καλὰ ἐπιτηδεύματα), and from fair practices to fair notions (τὰ καλὰ μαθήματα), until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is (ὃ ἔστι καλόν).

  • The sound of Donne’s poem may seduce one into thinking the ideals worthy.

Analytic Geometry and Donne's complete poetry

Two books that were my mother’s

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Mood

Executive summary. The English grammatical moods—indicative, imperative, subjunctive—were not understood till the nineteenth century, according to an 1882 doctoral dissertation, On the Use of the Subjunctive Mood in Anglo-Saxon. Considering illustrative passages that happen to be from Plato, Alfred Douglas, Evelyn Waugh, and especially John Donne; looking ultimately at John McWhorter’s 2015 essay, “English is not normal”; I review the subjunctive mood, grammar in general, and my own lack of understanding till I was in college.

Copyright page and table of contents, side by side, of Concise Oxford Dictionary Continue reading

Doing and Suffering

Edited March 30, 2020

To do injustice is worse than to suffer it. Socrates proves this to Polus and Callicles in the dialogue of Plato called the Gorgias.

I wish to review the proofs, because I think they are correct, and their result is worth knowing.

Loeb Plato III cover

Or is the result already clear to everybody?

Whom would you rather be: a Muslim in India, under attack by a Hindu mob, or a member of that mob?

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