Police against all

May 31, 2013 – 1:48 pm

I returned again this afternoon (Friday, May 31, 2013) to Gezi Park, or rather to its vicinity. Since yesterday the police had fenced it off.

Northern end of Gezi Park

Northern end of Gezi Park

The police fences can be seen on the left above. I think the woman here was just trying to make her way to Taksim. Presently I noticed that my eyes were stinging. It was the same with other people nearby, even in front of the ritzy Hotel Intercontinental adjacent to the park. Some young men I consulted with there confirmed that the police were using tear gas.
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By David Pierce | Posted in Gezi, Istanbul | Tagged | Comments (0)

Occupy Istanbul Taksim Gezi Parkı

May 30, 2013 – 1:35 pm

When the last tree has been cut down, the last fish caught, the last river poisoned, only then will we realize that one cannot eat money.

They took all the trees and put ’em in a tree museum
And they charged all the people a dollar and a half just to see ’em

Don’t it always seem to go
That you don’t know what you’ve got til it’s gone
They paved paradise and put up a parking lot

Taksim Square is the cultural heart of Istanbul.  Most of it is paved, but nearby is Gezi Parkı, shaded by many trees.  It is somewhat out of the way and hidden from view: from the Taksim side, one must climb steps to reach it, and between it and the main road north, Cumhuriyet Caddesi, there are restaurants and a Turkish Airlines office.  As a tourist in Istanbul, I was only vaguely aware of the park.  Now, as a resident, whenever I walk from home to Taksim, I pass through the park.

The Turkish Prime Minister Recep Tayyip Erdoğan intends to replace the park with buildings of some kind.  His words are translated by Hürriyet Daily News:

If you have respect for history, first you need to learn the history of Gezi Park.

He is supposedly referring to the Topçu Kışlası or Artillery Barracks that used to stand on the land of the park.

It is a bad joke. Continue reading →

By David Pierce | Posted in Gezi, Istanbul | Tagged | Comments (3)

Learning mathematics

May 14, 2013 – 11:23 am

This is mostly reminiscences about high school. I also give some opinions about how mathematics ought to be learned. The post originally formed one piece with my last article, “Limits.”

I learned calculus, and the epsilon-delta definition of limit, in Washington D.C., in my last two years at St Albans School, in a course taught by a peculiar fellow named Donald J. Brown. The first of these two years was officially called Precalculus Honors, but some time in that year, we started in on calculus proper.

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By David Pierce | Posted in Archimedes, Calculus, Education, Euclid, G. H. Hardy, Logic, Mathematics, Philosophy of Mathematics, Strunk and White | Tagged , , , , , , , , , , , | Comments (5)

Limits

May 4, 2013 – 12:54 pm

This is about limits in mathematics: both the technical notion that arises in calculus, and the barriers to comprehension that one might reach in one’s own studies. I am going to say a few technical things about the technical notion, but there is no reason why this should be a barrier to your reading: you can just skip the paragraphs that have special symbols in them.

Looking up something else in the online magazine called Slate, I noted a reprint of an article called “What It Feels Like to Be Bad at Math” from a blog called Math With Bad Drawings by Ben Orlin. Now teaching high-school mathematics, Mr Orlin recalls his difficulties in an undergraduate topology course. His memories help him understand the difficulties of his own students. When students do not study, why is this? It is because studying makes them conscious of how much they do not understand. They feel stupid, and they do not like this feeling. Continue reading →

By David Pierce | Posted in Archimedes, Calculus, Education, Mathematics, Philosophy of Mathematics, Plato | Tagged , , , , | Comments (6)

Self-similarity

April 12, 2013 – 2:41 pm

Animation: circles within circles

From the poster depicting a few von Neumann natural numbers, I created this animation. The moving image no longer depicts natural numbers in the sense of the poster, since there is no infinite descending chain of natural numbers. There is an infinite ascending chain of them; but the poster does not actually depict such a chain as nested circles. So running the animation in reverse would not give a correct suggestion of the original poster, even if it were of infinite size. Continue reading →

By David Pierce | Posted in Exposition, Mathematics, Visual Art | Tagged , , | Comments (3)

The von Neumann natural numbers: a fractal-like image

April 10, 2013 – 2:20 pm

See the next article, “Self-similarity,” for an animation of the image here.

I have long been fascinated by von Neumann’s definition of the natural numbers (and more generally the ordinals). In developing axioms for set theory, Zermelo used the sets 0, {0}, {{0}}, {{{0}}}, {{{{0}}}}, and so on as the natural numbers. Here 0 is the empty set. Zermelo’s method works, but is not so elegant as von Neumann’s later proposal to consider each natural number as the set of all natural numbers that are less than it is, so that (again) 0 is the empty set, but also n + 1 = {0, 1, …, n}.

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By David Pierce | Posted in Exposition, Mathematics, Visual Art | Tagged , , , | Comments (8)

Similar images of different saints

March 1, 2013 – 10:38 am

I have been impressed by the similar depiction of the two saints here; first, St John Chrysostom, from the Byzantine collection of Dumbarton Oaks:

Image

and then St Cyril of Alexandria, in an image taken from Wikipedia, though apparently the original image is in Chora, here in Istanbul.  (I visited Chora once, maybe 14 years ago, but hope to visit again soon.)

Image

I was originally impressed by how the blue and red crosses of the vestments of Chrysostom were repeated in his halo; then I happened upon the image of Cyril, with crosses similar in form, though not color, again repeated about the head.

By David Pierce | Posted in Visual Art | Tagged , , | Comments (0)

The Point of Teaching Mathematics

December 26, 2012 – 12:24 pm

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):

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By David Pierce | Posted in Education, Mathematics, Philosophy of Mathematics | Tagged , , , , | Comments (3)

On reading too much into words

November 22, 2012 – 11:47 am

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 →

By David Pierce | Posted in Education, Facebook | Tagged , , | Comments (0)

Science and anti-science

November 21, 2012 – 12:34 pm

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 →

By David Pierce | Posted in Aristotle, Collingwood, Facebook, Philosophy, Science | Tagged , | Comments (0)