Category Archives: Mathematics

The geometry of numbers in Euclid

January 2, 2017 – 6:34 pm

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.

Bottlecaps arranged on a desk in seven rows, thirteen columns
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.

The same bottlecaps, now seen from another side as thirteen rows, seven columns
Thirteen times seven

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By David Pierce | Also posted in Education, Euclid, Exposition, Philosophy of Mathematics | Tagged | Comments (11)

Thales of Miletus

December 24, 2016 – 11:01 am

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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By David Pierce | Also posted in Archeology, Collingwood, Education, Euclid, Freedom, History, Leo Strauss, Nesin Mathematics Village, New Leviathan, Philosophy, Philosophy of History, Principles of Art, Tourism, Turkey | Tagged , , , , , , , , | Comments (29)

Happiness

November 3, 2016 – 9:07 am

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.

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By David Pierce | Also posted in Causation, Collingwood, Education, History, Istanbul, New Leviathan, Philosophy, Philosophy of History, Principles of Art, Science, Turkey | Tagged , | Comments (3)

Beykoz, Istanbul

August 16, 2016 – 4:22 pm

After five years in Istanbul, we continue to learn how much there is still to discover here. Now we have been to the Asian borough of Beykoz. Much of what we saw there was rural, and the topography and flora reminded me of Appalachia. I have nothing to say about the poverty and ignorance that might be suggested by this term; for me, Appalachia was always a locus for holidays, mostly at my late uncle’s place in West Virginia, but also in the form of bicycle tours. Travelling now to Beykoz, “Country roads,” I could think, “take me home, to the place I belong!” We got there by public bus from our European borough of Şişli.

Polonezköy, Beykoz, 2016.08.14

Polonezköy, Beykoz, 2016.08.14

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By David Pierce | Also posted in History, Istanbul, Nature, Philosophy, Pirsig, Science, Tourism, West Virginia | Tagged , , , , , , | Comments (2)

Thinking & Feeling

July 20, 2016 – 2:16 pm

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.

With sea in the background, on the sand of a beach sits Chapman’s Homer: The Iliad, the cover featuring a 16th-century Flemish tapestry (framed by a circle), Scene from Roman History, showing a number of men, the one in the middle armored; a horse is in the foreground

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By David Pierce | Also posted in Archeology, Collingwood, coup, Education, Harper’s, History, Homer, Language, Maugham, Midgley, Nature, Nesin Mathematics Village, Philosophy, Philosophy of History, Principles of Art | Tagged , , , , , , , , , , , | Comments (11)

Academic Freedom

March 25, 2016 – 7:18 am

(See also other articles in the Freedom category.)

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 →

By David Pierce | Also posted in Education, Freedom, History, Philosophy, Philosophy of History, Philosophy of Mathematics | Tagged , , , , , | Comments (7)

Nesin Matematik Köyü, Ocak (January) 2016

January 26, 2016 – 6:33 pm

DSC05976

My first visit to the Nesin Mathematics Village was in the summer of 2007. My first course there was in the summer of 2008. I have been back every summer since, sometimes more than once. Now I have visited for the first time in winter. I am in awe. The photographs here are supposed to give you an idea why. Continue reading →

By David Pierce | Also posted in Nature, Nesin Mathematics Village, Turkey | Tagged , , , | Comments (6)

The Facebook Algorithm

March 17, 2015 – 3:36 pm

I thank all of the friends who sent me birthday greetings on Facebook this year. [But see note at end.] One friend noted that I was not likely to see his birthday greeting, since I do not pay attention to Facebook these days. I usually do not pay attention; but since so many friends apparently continue to use that medium, I have not closed my account. I recently posted on Facebook a couple of photographs showing a friend from Washington who was visiting Istanbul. These photographs were “liked” by friends of that person or of me. Thus I suppose I used Facebook for its best purpose. Continue reading →

By David Pierce | Also posted in Facebook, Philosophy, Plato, Psychology | Tagged | Comments (5)

Equality Is Not Identity

January 26, 2015 – 3:20 pm

I want to record here an account by Collingwood of Aristotle’s theory of knowledge. The passages quoted below are relevant, both to something I have learned from reading Euclid with students, and to the considerations of consciousness that led to my recent article “Body and Mind.”

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By David Pierce | Also posted in Aristotle, Collingwood, Euclid, Nature, Philosophy, Plato, Science | Tagged , | Comments (2)

The Academic Battery Cage

January 22, 2015 – 4:42 pm

The purpose of this article is to record a couple of paragraphs by Mary Midgley about academia today and its judging of people according to numbers of papers published. I have become something of a fan of Midgley. Her field is philosophy, though I think her complaint applies to mathematics or anything else:

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By David Pierce | Also posted in Istanbul, Midgley, Nature, Philosophy, Turkey | Tagged , , , , | Comments (0)