Category Archives: Archimedes

More of What It Is

September 21, 2020 – 7:08 pm

I say that mathematics is the deductive science; and yet there would seem to be mathematicians who disagree. I take up two cases here.

Page of Greek text with diagram
From Archimedes, De Planorum Aequilibriis,
in Heiberg’s edition (Leipzig: Teubner, 1881)

Continue reading →

By David Pierce | Also posted in absolute presuppositions, Calculus, Collingwood, Euclid, Mathematics, Philosophy, Philosophy of Mathematics | Tagged , , | Comments (3)

Salvation

February 24, 2020 – 7:06 am

Because Herman Wouk was going to put physicists in a novel, Richard Feynman advised him to learn calculus: “It’s the language God talks.” I think I know what Feynman meant. Calculus is the means by which we express the laws of the physical universe. This is the universe that, according to the mythology, God brought into existence with such commands as, “Let there be light.” Calculus has allowed us to refine those words of creation from the Biblical account. Credited as a discover of calculus, as well as of physical laws, Isaac Newton was given an epitaph (ultimately not used) by Alexander Pope:

Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light.

I don’t know, but maybe Steven Strogatz quotes Pope’s words in his 2019 book, Infinite Powers: How Calculus Reveals the Secrets of the Universe. This is where I found out about Wouk’s visit with Feynman. I saw the book recently (Saturday, February 22, 2020) in Pandora Kitabevi here in Istanbul. I looked in the book for a certain topic that was of interest to me, but did not find it; then I found a serious misunderstanding.

book cover: Steven Strogatz, Infinite Powers

Continue reading →

By David Pierce | Also posted in Calculus, Euclid, Mathematics, Philosophy of Mathematics | Tagged , , , , , , , , | Comments (5)

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.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification.

Continue reading →

By David Pierce | Also posted in Categorical Thinking, Descartes, Euclid, Exposition, Hitchens, Mathematics, Philosophy, Philosophy of Mathematics, Science | Tagged , , , , , , , , , , , , , , , , , , , , , | Comments (13)

Hypomnesis

July 30, 2017 – 6:35 pm

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

My question has two particular instances.

  1. At a mathematical conference, can theorems “speak for themselves,” or should their presenters be at pains to help the listener appreciate the results?

  2. When the conference is in Greece, even at one of the country’s greatest archeological sites, does this enhance the reading of ancient Greek texts, or is it only a distraction?

Continue reading →

By David Pierce | Also posted in Archeology, Art, Collingwood, Education, G. H. Hardy, Language, Logic, Mathematics, Philosophy, Plato, Principles of Art, Tourism, West Virginia | Tagged , , , , , , , , , , , | Comments (14)

Victor Vasarely

March 26, 2017 – 5:48 pm

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 →

By David Pierce | Also posted in Collingwood, Descartes, Education, Euclid, Istanbul, Mathematics, Midgley, Pirsig, Principles of Art, Tophane, Visual Art | Tagged , , , , , , , | Comments (2)

Bosphorus Sky

December 19, 2014 – 4:14 pm

This is about the morning of Thursday, December 18, 2014, a morning I spent by the Bosphorus, thinking mostly about poetry, and photographing the sky.

Seagulls against clouds and a brighter sea

Continue reading →

By David Pierce | Also posted in Bosphorus, Collingwood, Descartes, Education, History, Istanbul, Language, Mathematics, Nature, Nesin Mathematics Village, Philosophy, Poetry, Principles of Art, Psychology, Tourism, Turkey, Turkish | Tagged , , , , , , | Comments (5)

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.

Continue reading →

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