Category Archives: Harper’s

Harper’s Magazine



First published May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are
    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically—and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.
  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.
  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.
  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.
  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.
  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)

I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.
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Some Say Poetry

Potted palms with plaster farm animals on hillside behind

Kuzguncuk, 2017.11.05

I originally set out to preserve here, for future reference, a poetry review that I liked. A remark on being a student had drawn my attention:

In My Poets, a work of autobiographical criticism with occasional ventriloquial interludes, McLane recalls two “early impasses in reading,” freshman-year encounters with Charles Olson and Frank O’Hara. She writes about not “getting it” but wanting to get it, about a desire to get it that was left wanting by code-breaking and analysis and satisfied by hearing and feeling.

I shall try to say more about learning and creating, in poetry and also in mathematics, after quoting the review in its entirety. It constitutes the second half of a “New Books” column by Christine Smallwood, in the Reviews section of Harper’s, July 2017.

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Ahtamar Island

During a mathematics conference, I visit the ruins of a monastery on a remote island in an inland sea. This moves me to consider the relation between introversion and, if not mathematics, then monasticism. On the origins of Christian monasticism, I look at several sources, notably Gibbon (see the References); also Maugham, who writes of a hermit on an island of the Torres Strait. Since the monastery on the island was Armenian, in what is now Turkey, one should consider also the treatment of minority populations here. I only acknowledge the issue, suggesting Wikipedia pages (linked to presently) as a starting point for research. Old books on my shelves are not much help; my own experience, not much more, at least not in a way that lends itself to being written of here. I do know that Turkish politicians will treat imputations of their own Armenian ancestry as an insult.

We visited Ahtamar Island for a second time on Wednesday, August 23, 2017. Thus we saw again the remains of the Church of the Holy Cross. This Armenian church was consecrated in 921 and presumably desecrated in 1915, if not earlier; now, since our last visit, though officially a museum, the church would seem to have been reconsecrated, to judge by the new altarpiece, featuring an icon of the Madonna and Child.

Altarpiece, Church of the Holy Cross, Ahtamar Island

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War and Talk

This is a foray into the mystery of how things happen, based the 164th of the 361 chapters of War and Peace. This chapter contains, in a one-sentence paragraph, a summary of Tolstoy’s theory of history:

Each man lives for himself, using his freedom to attain his personal aims, and feels with his whole being that he can now do or abstain from doing this or that action; but as soon as he has done it, that action performed at a certain moment in time becomes irrevocable and belongs to history, in which it has not a free but a predestined significance.

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The Private, Unskilled One

I went into Istanbul’s Pandora Bookshop a month ago, looking for an English translation of War and Peace, since the Garnett translation I had read at college was falling apart. I was told the Oxford World’s Classics edition (with the Maude translation) was coming the next week, and it did come.

Elif Batuman, The Idiot, in Nesin Matematik Köyü, Kayser Dağı Mevkii, Şirince, Selçuk, İzmir, Turkey, 2017.05.18

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Duty to Nature

Index to this series

Summary and update (added October 14, 2018): When we do something, or propose to do something, we may explain it or justify it—give a reason for it—as being useful, right, or dutiful. Such is the theory of Collingwood, analyzed here, especially with regard to a question that has increasing urgency: have we a duty, not only to one another, but to nature?

When I originally composed this post, I had recently analyzed several relevant chapters of Collingwood’s New Leviathan:

Those chapters are the last in Part I, “Man.” Part II, “Society,” returns to the same ideas in Chapter XXVIII, “The Forms of Political Action.” I would analyze this, 18 months later; it has an example of abuse of the concept of duty, by the German political theorist Treitschke.

By one interpretation of a passage in Herodotus, the ancient Persians perceived a duty to nature, by a teaching now attributed to Zoroaster. His teachings influenced Manichaeism, and thus in turn the “Albigensian heresy,” the subject of Chapter XLIII of the New Leviathan.

We tend to explain what happens in the world the way we explain what we ourselves do. If our ethics are utilitarian, then, like the ancient Greeks, we may see things in nature too as serving purposes. If we govern, or aim to govern, our own behavior by laws, then we may also seek laws of nature, as physicists do now.

Being general in form, utility and law provide incomplete accounts of exactly what we do. Though we may not always use the word this way, duty is to be conceived as providing a complete account of what we do. Conscience tells us that we have a duty; then we have to reason out what it is. The corresponding science of the world is history, which studies us as free agents. Collingwood does not describe a corresponding science of nature as such, at least not in the New Leviathan; but at the end of his first book, Religion and Philosophy, he concluded that everything that happened must be an act of will. This was in the chapter called “Miracle,” which I looked at especially in “Effectiveness.”

It may be hard to distinguish lawful action from dutiful action. Here I look at the examples of

  • paying off a student loan;
  • smoking cigarettes, when rules restrict it;
  • collecting armaments, because, at the Last Supper, by the account in Luke, Jesus recommended buying swords;
  • Islam, as a rule-bound religion;
  • Christian denigrators of Islam, who find in it rules that they think believers must be bound by, even as some Muslims find inspiration in the teachings of Prophet Jesus.

I conclude with an Episcopal priest called Stephen Blackmer, for whom nature is a church and a member of his congregation.

This is a synthesis of some ideas from a recent spate of posts in this blog. A theme is the question of why we do what we do, and whether what we do to Nature in particular—how we think of Nature—can change.

Farhang Mehr, The Zoroastrian Tradition, cover with image of Zarathustra 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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Rock & Roll

The May 2016 Harper’s features a review of some books about the rock band called Guns N‘ Roses. I find this a bit odd, though perhaps reassuring, since I think I am too old for Guns N’ Roses, and yet Harper’s seems pitched at people who are at least as old as I. During the former editorship of Lewis Lapham, the magazine ran cigarette ads; now it runs ads for retirement communities, hearing aids, and mobile phones with large buttons.

Guns N’ Roses performing at the Los Angeles Street Scene, September 28, 1985 © Marc Canter

Guns N’ Roses performing at the Los Angeles Street Scene, September 28, 1985 © Marc Canter

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On trial for pacifism

This is about the 1918 trial of American radical political cartoonist Art Young and others for conspiracy and interfering with enlistment. Most of the article is a quotation of Young’s own words. The words provide some perspective on today’s struggle for freedom of speech.

Capitalism, Art Young, private collection (reproduced in Harper's, Jan 2016, p. 64)

Capitalism, Art Young, private collection (reproduced in Harper’s, Jan 2016, p. 64)

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Body and Mind

Does consciousness have a “physical basis” or “material basis”? I am provoked by the suggestion that it does; for the question itself is misleading, if not simply meaningless.

In the September, 2014, issue of Harper’s magazine, Edward O. Wilson begins an essay called “On Free Will” with the following paragraph. Continue reading