Category Archives: Prose

Math, Maugham, and Man

September 1, 2019 – 7:49 am

Note added, August 28, 2023. The main purpose of this post of September 1, 2019, seems to have been to assemble some information about the etymologies of “man” and “woman,” because of ongoing controversy about what the words even mean today. I started to take up the controversy itself on December 30 of that year, in “Sex and Gender.” Meanwhile, this post suggests, or points out:

  • a generic “person” may still be male in people’s minds;
  • becoming a woman may be like becoming Jewish;
  • there are no gendered pronouns in Turkish;
  • the series freshman, sophomore, junior, senior is like pinkie, ring finger, middle finger;
  • Greek does not have such an interesting series for the fingers;
  • Greek mathematics includes Thales’s Theorem and Pappus’s Hexagon Theorem.

There does not seem to be any connection between the mathematics and the etymology here, except that I was studying both at the same time. I must have been reading The Razor’s Edge too, where Maugham

  • places himself in a tradition founded by Herodotus;
  • uses “he/him” for for somebody who can be a woman as well as a man.

More themes I took up:

  • what it means to be natural;
  • that I don’t consider myself ADHD;
  • the etymology of “squirrel”;
  • the Etymological Fallacy.

A dog lying in the shade of a beach umbrella looks at us; behind him are a woman and a man sitting facing away from us, towards the sea
Woman, man, and dog
Friday, August 18, 2023
Altınova, Balıkesir, Türkiye

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By David Pierce | Also posted in Collingwood, Language, Mathematics, Maugham, Plato, Sex and Gender | Tagged , , , , , , , , , , | Comments (5)

On Causation

August 20, 2019 – 5:10 am

Causation seems commonly to be understood as a physical concept, like being a fossil. The paleontologist seeks the one right answer to the question of when a particular dinosaur bone became part of the fossil record; likewise readers of international news seem to think there is one right answer to the question of whether Donald Trump or Ali Khamenei caused the shooting down of Ukraine International Airlines Flight 752 on January 8, 2020.

There is not one right answer. If you are Trump, you caused 176 civilian deaths by attacking the Iranians and provoking their response. If you are Mitch McConnell, you caused the deaths by inhibiting the removal of Trump from office. If you are Khamenei, you did it by meeting Trump’s fire with fire.

Being a cause does not mean you deserve condemnation or praise: that is another matter.

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By David Pierce | Also posted in absolute presuppositions, Aristotle, Causation, Collingwood, Descartes, Plato, Thoreau | Tagged , , , , , , | Comments (11)

We the Pears of the Wild Coyote Tree

April 15, 2019 – 9:12 pm

This is a preliminary report on two recent films:

  • The Wild Pear Tree, by Nuri Bilge Ceylan;
  • We the Coyotes, by Marco La Via and Hanna Ladoul.

The report is preliminary, not because there is going to be another, but because I have seen each film only once, and I may see one of them again.

I remember that François Truffaut liked to see films at least twice. I believe I read this in The Washington Post, and I might have guessed it was in an appreciation published when Truffaut died; however, he died on October 21, 1984, during the first semester of my sophomore year at St John’s College in Santa Fe, and I would not have been reading the Post then.

While in college, I did enjoy seeing some films twice, or a second time; Truffaut’s own 400 Coups was an example, a French teacher having shown it to us in high school.

The two films that I am reviewing now concern young adults trying to find their own way in the world, in defiance of their elders. We all have to do this. In every generation, some will do it more defiantly than others. Heraclitus can be defiant, he of Ephesus and thus one of the Ionian philosophers, whose spirit I imagine to haunt the Nesin Mathematics Village. A further reason to bring up Heraclitus will be a theme that is explicit in Pear Tree, implicit (or metaphorical) in Coyotes: gold.

A book, whose cover shows a bonfire, sits on a rock dampened by waves of the sea, which laps on the sand beyond
A copy of The Logos of Heraclitus,
by Eva Brann,
on Marmara Island, July, 2012

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By David Pierce | Also posted in Film, Freedom, Philosophy, Plato, Thoreau, Turkey | Tagged , , , , , , , , , , | Comments (3)

Logic of Elliptic Curves

January 6, 2019 – 8:49 pm

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. Continue reading →

By David Pierce | Also posted in Aristotle, Exposition, Hitchens, Mathematics | Tagged , , , , | Comments (1)

On Gödel’s Incompleteness Theorem

December 15, 2018 – 8:43 am

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

I shall review the mathematics of the theorem, first in outline, later in more detail. The mathematics is difficult. I have trouble reproducing it at will and even just confirming what I have already written about it below (for I am adding these words a year after the original publication of this essay).

The difficulty of Gödel’s mathematics is part of the point of this essay. A person who thinks Gödel’s Theorem is unsurprising is probably a person who does not understand it.

Next to a slice from a tree trunk, a worn copy of the book Frege and Gödel: Two Fundamental Texts in Mathematical Logic, edited by Jean van Heijenoort

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By David Pierce | Also posted in Archimedes, Categorical Thinking, Descartes, Euclid, Exposition, Hitchens, Mathematics, Philosophy, Philosophy of Mathematics, Science | Tagged , , , , , , , , , , , , , , , , , , , , , | Comments (16)

NL XLII: The First Barbarism: The Saracens

October 1, 2018 – 5:49 am

Index to this series

Executive summary: The barbarians who overran the Western Roman Empire were not barbarists in Collingwood’s technical sense. However, “in the seventh century a movement inspired by hostility towards everything Roman … and everything Christian, flared up on the south-eastern frontier of the Roman world” (42. 22). This movement was therefore barbarist. Failing to conquer Europe, either from the east at Constantinople, or from the west at Tours, the movement settled down and ceased being barbarist—by the account in Chapter XLII, “The First Barbarism: The Saracens,” and later, in Collingwood’s New Leviathan. I check this account against more recent sources; it is barbarist to think that the “movement” in question, or indeed any movement, must always be barbarist; I look at the “civilization” of the British Empire as portrayed in a story of Maugham, and I compare a character of the story to Collingwood.

Collingwood’s historical account of barbarisms is a minefield, if one wishes not to sound like a barbarist oneself. The four examples will be

  1. the Saracens,
  2. the “Albigensian Heresy” (or the Bogomils),
  3. the Turks, and
  4. the Germans.

The very formula “the X”—definite article followed by national or quasi-national adjective—this has a barbaric use in branding a people with indelible features. A retort then is “not all X,” as in “not all men.” Collingwood issues such a proviso himself:

45. 68. Please observe, Reader, that I am not talking about all Germans. I do not say that all Germans are liars. I know of some who are not; those heroes, for example, who continue in spite of everything the Nazis can do to run their secret wireless station and keep on printing Das Wahre Deutschland.

Das wahre Deutschland, from a Swiss antiquarian bookshop, Antiquariat Peter Petrej

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By David Pierce | Also posted in Collingwood, dialectic, Galileo, History, Maugham, New Leviathan, Philosophy, Philosophy of History, Plato | Tagged , , , , , , , , , , | Comments (4)

NL XXVII: Force in Politics

September 1, 2018 – 7:09 am

Index to this series

Executive summary (added September 12, 2018): When persons cannot rule themselves, they are ruled by force, as a duty, by other persons, for the benefit and pleasure of all. Force includes fraud and deceit; but their use must be limited, if those persons who are being ruled by force now will one day join the ruling class themselves. If a liberal and a conservative party take up respectively the ideals of democracy and aristocracy discussed in the last chapter, the parties must understand that each needs the other, in order to engage in the dialectic that aims for the best society. If somebody thinks the two parties waste energy, either in pretending to be in opposition to one another, or in actually being opposed, then that person is effectively wishing for tyranny.

In my last post on the New Leviathan (which was my first for this year), I said Collingwood would discuss the British parliament in Chapter XXVII. That chapter is now my subject.

The ruling class must incorporate new members from time to time, whether anybody thinks about it or not (27. 75). Anybody who does think about it may take up one of two goals (27. 77).

27. 79. To hasten the percolation of liberty throughout every part of the body politic was the avowed aim of the Liberal party; to retard it was the avowed aim of the Conservative party.

27. 8. The relation between them was consciously dialectical. They were not fundamentally in disagreement. Both held it as an axiom that the process of percolation must go on. Both held that given certain circumstances, which might very well change from time to time, there was an optimum rate for it, discoverable within a reasonable margin of error by experiment.

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By David Pierce | Also posted in Collingwood, dialectic, History, Hitchens, New Leviathan, Philosophy, Philosophy of History | Tagged , , , , , , , , , | Comments (10)

Writing and Inversion

July 14, 2018 – 7:55 am

Executive summary: The “voice” of a transitive verb may be active or passive. A piece of writing may be vigorous or torpid. There is not an exact correspondence between passive verbs and torpid writing. However, a passive verb is used to effect inversion of subject and object. One may also invert subject and auxiliary verb, subject and predicate, or two clauses, always adding new words. Each inversion may lead to torpid writing. This is what Strunk warned about in The Elements of Style, by issuing the command, “Use the active voice.” The command must be followed with discretion. Williams makes the same case, more elaborately, in Style: Towards Clarity and Grace. There is no foolproof executive summary of how to write well.

When E. B. White revised William Strunk’s original Elements of Style, he did not retain Strunk’s “Introductory,” whose first paragraph said of the book,

The experience of its writer has been that once past the essentials, students profit most by individual instruction based on the problems of their own work, and that each instructor has his own body of theory, which he may prefer to that offered by any textbook.

Perhaps many students today cannot receive individual instruction. They are just given textbooks that try to spell out everything. Continue reading →

By David Pierce | Also posted in Education, Grammar, Maugham, Strunk and White | Tagged , , , | Comments (2)

Effectiveness

May 17, 2018 – 6:36 pm

Preface

First posted May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are

    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically – and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.

  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.

  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.

  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.

  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.

  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)

I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.

Papers on a table with a view of trees and a distant hill between stone columns

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By David Pierce | Also posted in absolute presuppositions, Collingwood, Galileo, Harper’s, Leo Strauss, Mathematics, Maugham, New Leviathan, Philosophy, Plato, Principles of Art, Science, T. S. Eliot | Tagged , , , , , , , , , , , , , , , , , , , , , , , | Comments (18)

Some Say Poetry

November 6, 2017 – 5:00 pm

In a poetry review, a remark on being a student has drawn my attention:

In My Poets, a work of autobiographical criticism with occasional ventriloquial interludes, McLane recalls two “early impasses in reading,” freshman-year encounters with Charles Olson and Frank O’Hara. She writes about not “getting it” but wanting to get it, about a desire to get it that was left wanting by code-breaking and analysis and satisfied by hearing and feeling.

This is from the second half of a “New Books” column by Christine Smallwood, in the Reviews section of Harper’s, July 2017. After quoting Smallwood’s review, I want to say something about learning and creating, in poetry and also in mathematics.

Potted palms with plaster farm animals on hillside behind
Kuzguncuk, 2017.11.05

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By David Pierce | Also posted in Collingwood, Education, Harper’s, Midgley, Plato, Poetry, Principles of Art, Sylvia Plath | Tagged , , , , , , , , , , , , , , , , | Comments (6)