Category Archives: Mathematics

NL XIX: Two Senses of the Word “Society”

Executive summary (below) | Index to this series

After a break of half a year, I return to reading Collingwood’s New Leviathan. Being on holiday at an Aegean beach gives me the opportunity. While here, I may also return to Chapman’s Homer’s Iliad. Last winter I finished Part I of the New Leviathan, the part called “Man.” Here I continue with the first chapter of “Society.” I have reason to look at what Mary Midgley and Albert Einstein say about science. Collingwood’s investigation suggests a way of thinking about prejudice and discrimination.

Part II of the New Leviathan is “Society,” and the first two chapters of this, XIX and XX, concern the distinction between society proper and two more general notions. In Chapter XX, the more general notion will be community. In Chapter XIX, the more general notion has not got its own proper name, and so Collingwood denotes it by writing “society,” in quotation marks.

A “society” of chairs at the beach (Altınova 2017.08.31)

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Hypomnesis

When is a help a hindrance? The Muses have provoked this question. They did this through their agents, the cicadas, who sang around the European Cultural Center of Delphi, during the 11th Panhellenic Logic Symposium, July 12–5, 2017.

     Cicada, European Cultural Center of Delphi, 2017.07.15     
Cicada, European Cultural Center of Delphi, 2017.07.15

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Victor Vasarely

Tophane-i Amire
Tophane-i Amire, 2017.03.25

Last week I wrote about the Turkish Impressionist Feyhaman Duran, born in 1886. Now my subject is the Hungarian-French Op Artist born twenty years later as Győző Vásárhelyi. His “Rétrospective en Turquie” is at the Tophane-i Amire Culture and Art Center in an Ottoman cannon foundry.

Vasarely show Continue reading

Şirince January 2017

Having enjoyed spending a January week at the Nesin Mathematics Village in 2016, this year I came back for two weeks. My spouse will join me for the second week. Meanwhile, here are some photographs from this amazing place. Continue reading

Confessions

This is about G. H. Hardy and Sylvia Plath: Hardy quâ author of A Mathematician’s Apology (1940); Plath, The Bell Jar (1963).

Photo: the Hardy and Plath books

I first read Plath only recently, after encountering The Bell Jar by chance in the Istanbul bookshop called Pandora. Continue reading

The geometry of numbers in Euclid

This is about how the Elements of Euclid shed light, even on the most basic mathematical activity, which is counting. I have tried to assume no more in the reader than elementary-school knowledge of how whole numbers are added and multiplied.

How come 7 ⋅ 13 = 13 ⋅ 7? We can understand the product 7 ⋅ 13 as the number of objects that can be arranged into seven rows of thirteen each.

Seven times thirteen

Seven times thirteen

If we turn the rows into columns, then we end up with thirteen rows of seven each; now the number of objects is 13 ⋅ 7. Continue reading

Thales of Miletus

This is about Thales of Miletus and what it means to study him. I am moved to ask what history is in the first place. It is a study of the freedom in which we face our conditions. Thales had his way of understanding the world, and we may benefit from trying to learn it.

“The Thaleses of the future are meeting in Didim, September 24,  2016”

“The Thaleses of the future are meeting in Didim, September 24, 2016”

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Happiness

If only tangentially sometimes, this is about living in Turkey, especially under the ongoing official state of emergency.

Aristotle, Marx & Engels, and Collingwood

Aristotle, Marx & Engels, and Collingwood

A blog article on Medium recently struck me for its treatment of science. Dated October 3, the article is called “The Purpose Of Life Is Not Happiness: It’s Usefulness,” and its opening section is as follows.

For the longest time, I believed that there’s only purpose of life: And that is to be happy. Continue reading

Thinking & Feeling

This essay is written as a distraction from current events, though I make some reference to them. I am prompted by questions of analogy provoked by

  1. the similes of Homer, and
  2. a recent theater review in Harper’s that mentions the parables of Jesus.

DSC06654 (2)
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Academic Freedom

Yesterday (March 24, 2016) was the first day of the sixth Models and Groups Istanbul meeting. There were participants from the Middle East, Europe, and America. Kıvanç Ersoy was to speak about his own mathematics. He could not speak, because he was in prison. He, Esra Mungan, and Muzaffer Kaya were in prison, because the three of them had publicly insisted that the government of Turkey make peace in the southeast of the country. Absurd, but true. Continue reading