Tag Archives: T. S. Eliot



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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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 VII: “Appetite”

Index to this series

How can we compare two states of mind? This is the question of Chapter VII of The New Leviathan. The answer is contained in the chapter’s title. “Appetite” is a name, both for the chapter and for the fundamental instance of comparing a here-and-now feeling with a “there-and-then” feeling. We compare these two feelings because we are unsatisfied with the former, but prefer the latter.

It would seem then that appetite is at the root of memory. Thus we are among the ideas of the opening verses of The Waste Land of T. S. Eliot, who attended Collingwood’s lectures on Aristotle’s De Anima at Oxford (and was just a year older):

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Below is a provocative passage (transcribed by me) from the conclusion (p. 325) of R.G. Collingwood, The Principles of Art. This book was first published by Oxford in 1938, and its 1958 paperback edition is still in print, presumably without a copyright (my own paperback, bought about 20 years ago, has no copyright notice).

I typed up the passage below and put it on my website years ago. I want to promote it here because of the article that I chanced upon recently (because it was promoted on the Arts & Letters Daily site). The article itself is on the Poetry Foundation website, is by Ruth Graham, and is called Word Theft: Why did 2013 become the year of the plagiarists? I gather from the article that some contemporary poets have been found to have plagiarized from other contemporary poets; and what is especially annoying about the plagiarism is that the plagiarists are not actually improving what they are appropriating. In this case, they are not following Collingwood’s recommendation, though possibly they are ineptly trying:

To begin by developing a general point already made in the preceding chapter: we must get rid of the conception of artistic ownership. In this sphere, whatever may be true of others, la propriété c’est le vol. We try to secure a livelihood for our artists (and God knows they need it) by copyright laws protecting them against plagiarism; but the reason why our artists are in such a poor way is because of that very individualism which these laws enforce. If an artist may say nothing except what he has invented by his own sole efforts, it stands to reason he will be poor in ideas. If he could take what he wants wherever he could find it, as Euripides and Dante and Michelangelo and Shakespeare and Bach were free, his larder would always be full, and his cookery might be worth tasting.

This is a simple matter, and one in which artists can act for themselves without asking help (which I am afraid they would ask in vain) from lawyers and legislators. Let every artist make a vow, and here among artists I include all such as write or speak on scientific or learned subjects, never to prosecute or lend himself to a prosecution under the law of copyright. Let any artist who appeals to that law be cut by his friends, asked to resign from his clubs, and cold-shouldered by any society in which right-thinking artists have influence. It would not be many years before the law was a dead letter, and the strangle-hold of artistic individualism in this one respect a thing of the past.

This, however, will not be enough unless the freedom so won is used. Let all such artists as understand one another, therefore, plagiarize each other’s work like men. Let each borrow his friends’ best ideas, and try to improve on them. If A thinks himself a better poet than B, let him stop hinting it in the pages of an essay; let him re-write B’s poems and publish his own improved version. If X is dissatisfied with Y’s this-year Academy picture, let him paint one caricaturing it; not a sketch in Punch, but a full-sized picture for next year’s Academy. I will not rely upon the hanging committee’s sense of humour to the extent of guaranteeing that they would exhibit it; but if they did, we should get brighter Academy exhibitions. Or if he cannot improve on his friends’ ideas, at least let him borrow them; it will do him good to try fitting them into works of his own, and it will be an advertisement for the creditor. An absurd suggestion? Well, I am only proposing that modern artists should treat each other as Greek dramatists or Renaissance painters or Elizabethan poets did. If any one thinks that the law of copyright has fostered better art than those barbarous times could produce, I will not try to convert them.

Collingwood’s book suggests the author’s admiration for T.S. Eliot, and the two contemporary thinkers seem to share an opinion about copying. Eliot’s verbalization of the idea is apparently the more memorable one and is quoted by Ms Graham in the article on the Poetry Foundation website:

T.S. Eliot, who relied on other sources for much of “The Waste Land” (plagiarism or allusion?), famously wrote, “Immature poets imitate; mature poets steal.” Less often quoted is the next line, “Bad poets deface what they take.” This is what seems to gall many victims of plagiarists: to see their poems reprinted in weaker versions than the original.