Category Archives: Psychology

NL XXIX: External Politics

Index to this series

Executive summary (added September 13, 2018, edited July 19, 2019): Dealing with other bodies politic is the third stage of political life, after societies’

  • formation (as if by marriage),

  • dominion over non-social communities (as if by having children).

Having been used in the first two stages, dialectic can be used in the third. Being the eristic of external politics, war has no psychological cause. War is a state of mind, which does not think non-agreement can become agreement. Pacifism has this state of mind.

External politics are international relations. These represent the third of the “stages” in political life (29. 1), which we enumerate:

  1. The joining of wills into a society, which rules itself (29. 11).

  2. Such a society’s ruling over a non-social community in a body politic (29. 12).

  3. Dealing with other bodies politic (29. 13).

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The Tree of Life

My two recent courses at the Nesin Mathematics Village had a common theme. I want to describe the theme here, as simply as I can—I mean, by using as little technical knowledge of mathematics as I can. But I shall talk also about related poetry and philosophy, of T. S. Eliot and R. G. Collingwood respectively.

An elaborate binary tree, with spirals

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NL XIII: “Choice”

Index to this series

Adolph Gottlieb, “Centrifugal,” gouache on paperboard, 1961 (National Gallery of Art, Washington; gift of the Woodward Foundation)

Adolph Gottlieb, “Centrifugal,” 1961 (National Gallery of Art, Washington; gift of the Woodward Foundation)

The key idea of Chapter XIII of New Leviathan is the correct statement of the “problem of free will”:

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NL XII: “Happiness”

Index to this series

Judith Leyster (Dutch, 1609–1660), Self-Portrait, c. 1630, oil on canvas (National Gallery of Art, Washington; gift of Mr. and Mrs. Robert Woods Bliss)

Judith Leyster (Dutch, 1609–1660), Self-Portrait, c. 1630, oil on canvas (National Gallery of Art, Washington; gift of Mr. and Mrs. Robert Woods Bliss)

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NL XI: “Desire”

Index to this series

The four parts of Collingwood’s New Leviathan (1942) are Man, Society, Civilization, and Barbarism. From the first part, we are considering Chapter XI, “Desire.”

Pablo Picasso, The Lovers (1923; National Gallery of Art, Washington)
Pablo Picasso, “The Lovers,” 1923
National Gallery of Art, Washington

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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. After I finished reading it next day in Espresso Lab on İstiklâl, a woman who had earlier been speaking Turkish asked in English to look at the book. She pondered the front and the back before handing the book back to me. When I asked whether she knew of it, she simply said yes. She may not have understood my meaning; but I did not put her English (or my Turkish) to the test. Had she been made curious by the cover, showing a woman applying powder with the aid of a compact mirror? Did that cover accurately reflect the novel?

On an airplane once I was reading a paperback whose cover displayed a painting of ruins beneath the Acropolis of Athens. “I love historical fiction!” gushed a flight attendant. The term might be stretched to cover what I was reading; but it was the Oxford World’s Classics edition of Plato’s Republic.

Plato’s Republic

I had first read Hardy’s Apology in high school, thanks to the suggested reading at the end of Spivak’s Calculus. A couple of weeks ago, I somehow found a blog that took its title from the end of Hardy’s opening paragraph. That paragraph reads:

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

The blog was called just that: Second Rate Minds. “We quote Hardy with irony,” says one of the two creators,

because we do not agree with him.

I believe there is great importance in communicating mathematics as widely as possible. I think it is important that children are encouraged to enjoy mathematics so that they might take further interest in the subject. Equally important is the view of mathematics held by the general public. Despite Hardy’s disdain for applications, mathematics nevertheless pervades the modern world and benefits from society valuing its role.

This is all fine; except I wonder if the writer has been corrupted by the same culture that made Hardy into somebody he found himself in disagreement with. This is the culture of judging people against one another, in order to rank them. Hardy gives a hint of this culture in the closing section of his essay:

I cannot remember ever having wanted to be anything but a mathematician. I suppose that it was always clear that my specific abilities lay that way, and it never occurred to me to question the verdict of my elders. I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively.

I do not remember just what I thought of Hardy’s Apology in high school. I was at a school for boys, where I won prizes for mathematics and other subjects. I did not wish to emulate Hardy, either in pursuing just one thing, or in trying to beat others at it. Nonetheless, at the end of my freshman year at St John’s College in Annapolis, I bought my own copy of Hardy’s Apology in the College bookshop. The manager remarked that the book had decided her against pursuing mathematics. She had had dreams of doing good for the world; by Hardy’s account, mathematics was about personal glory.

I did want to do mathematics, as I ultimately understood. But this final understanding came after four more years: three in college, and one at large. I was working at a farm when I understood in a dream that I must learn modern mathematics. I cannot say that Hardy had any role in this, one way or other. Still, I would suggest now that, if Hardy does discourage you from pursuing mathematics, this may be just as well. You will have to focus like a laser if you want to do mathematics; you will be judged mercilessly, as mathematical truth is merciless; and you will suffer self-doubt, when it seems that the hardest you can work is still not good enough.

I am sorry that Hardy continued to be preoccupied with comparing himself to others:

I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one the thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.’

At least Hardy can accept that he was not quite at the level of his two collaborators. The mathematician must guard against all illusions.

In the end, I say, think what you like about Hardy; but give him credit for giving us a window into his life. Reading his essay yet again, I am impressed by the clarity and rhythm of the language, and by the frankness of the writer.

Sylvia Plath reminds me of Hardy. This is not because she ultimately gives up her virginity to a mathematician, at least in her novel. Like Hardy, she appears early on as an unpleasant person.

Plath’s character Esther proposes to Doreen that they ditch a party and have drinks with a man who wears cowboy boots and a lumber shirt. Doreen agrees to go up to Lenny’s apartment, as long as Esther will go. In the apartment, Doreen asks Esther to stick around. Still, Esther slips out; and back at the hotel, when a drunken Doreen pounds on her door, Esther won’t let her in. She allows Doreen to pass out in the corridor, since she won’t remember the incident anyway.

Maybe this was all part of the Girls’ Code, though it would seem to be a violation. Esther did not seem very nice to me. But then, trying to kill yourself is not very nice either, and Esther will do this repeatedly. There is a lot to investigate and contemplate here, including an academic system that squeezed both Plath and Hardy. It is odd that a bell jar is a place where the pressure is taken off. Now I want just to appreciate both Plath and Hardy, for laying themselves bare.

Written January, 2017. Revisited August 27, 2022. Later in 2017, I wrote more about Plath (and a little more about Hardy) in “Women and Men.”

How to Learn about People

A chance encounter with a Medieval definition of God, used as the title of a sculpture, leads to an ancient plane tree and to more consideration of what can go wrong with public opinion polls.

Ancient plane tree of Bayır, Marmaris Peninsula, September 9, 2010

Ancient plane tree of Bayır, Marmaris Peninsula, September 9, 2010

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One & Many


This essay – these notes for an essay, this draft of an essay – is inspired by Robert Pirsig’s first book. I have made sectional divisions where they seemed to occur naturally.


While we who work at universities may be employed by the state, our true work is to serve not the state as such, but what may be called knowledge, or science, or reason. This is a theme of Pirsig, which I take up here.

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The Facebook Algorithm

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


This is about getting used to things, and things one should not get used to.

There is a free-speech crisis in Turkey now, brought on in part, but not exclusively, by the murders at the Charlie Hebdo offices in Paris. See an editorial of the Platform for Independent Journalism (P24) for a list of issues.

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