Effectiveness

Preface

First posted 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.

Papers on a table with a view of trees and a distant hill between stone columns

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Boolean Arithmetic

Mathematics can be highly abstract, even when it remains applicable to daily life. I want to show this with the mathematics behind logic puzzles, such as how to derive a conclusion using all of the following premisses:

  1. Babies are illogical.
  2. Nobody is despised who can manage a crocodile.
  3. Illogical persons are despised.

The example, from Terence Tao’s blog, is attributed to Lewis Carroll. By the first and third premisses, babies are despised; by the second premiss then, babies cannot manage crocodiles.

George Boole, The Laws of Thought (1854), Open Court, 1940

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On Knowing Ourselves

In a 2012 post in this blog, I criticized a 2009 essay called “50 Years of Stupid Grammar Advice.” The putative advice was that of Strunk and White. However, what these two had written was not the elements of grammar, but The Elements of Style. They gave style advice by precept and example. The advice is good, if well understood. The critic should recognize that, as I wrote, “Rules of style are supposed to induce thinking, not obedience.”

View between two hotel buildings from one mountainside to another, with a bit of the sea beyond
All photos taken in Delphi, July 12–14, 2017

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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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Şirince January 2018

In the Nesin Mathematics Village recently, I was joined at breakfast one morning by a journalist called Jérémie Berlioux. He knew Clément Girardot, the journalist whom I had met in the Village in the summer of 2016. This was before the coup attempt of July 15, but after the terror attack at Atatürk Airport on June 28. I wrote about this attack the next day in “Life in Wartime” on this blog. Then I headed off to Şirince to join a “research group.” My wife and colleague came along, though not to be part of the group; afterwards we headed up the coast for a beach holiday. We were at the beach when the coup attempt happened, as I wrote in my next blog article, “War Continues.” I contrasted politics with mathematics, which was an inherently nonviolent struggle. This was the kind of struggle engaged in by the research group in the Math Village.

Large clay pot against dark vines

Outside the Nişanyan Library

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What Philosophy Is

With my presumptuous title, I imitate Arthur Danto’s What Art Is (2013), mentioned in my last post, “Some Say Poetry.” The book is fine, and I have learned from it; but Danto could have learned from Collingwood’s Principles of Art.

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Some Say Poetry

In a poetry review, a remark on being a student has 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.

This is from the second half of a “New Books” column by Christine Smallwood, in the Reviews section of Harper’s, July 2017. After quoting Smallwood’s review, I want to say something about learning and creating, in poetry and also in mathematics.

Potted palms with plaster farm animals on hillside behind
Kuzguncuk, 2017.11.05

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Women and Men

This began as an update to “Confessions,” which concerns the man called G. H. Hardy and the woman called Sylvia Plath. I had originally included a photograph of the subjects’ respective books. On Hardy’s, the author poses reluctantly; on Plath’s, a woman applies powder in a compact mirror.

Plath’s book was the 2013 Faber and Faber 50th Anniversary Edition of The Bell Jar, and the cover is controversial. See Alexandra Topping, “The Bell Jar’s new cover derided for branding Sylvia Plath novel as chick lit” (The Guardian, Friday 1 February 2013). I learned of the controversy from Emily Van Duyne, “Sylvia Plath Looked Good in a Bikini—Deal With It,” in Electric Literature, hosted by Medium (October 9, 2017). Medium had promoted the essay to me when I read Brian E. Denton, “The World Will Not Quarrel: Day 282 of A Year of War and Peace.

Yesterday I happened upon a tweet juxtaposing the real cover of the British edition of Volume I of The Letters of Sylvia Plath with a fake cover of The Letters of Ted Hughes. Each cover shows the letter-writer posing in revealing swimwear on a beach, though the head of Plath’s husband seems to have been imposed on another man’s topless body. The text reads:

If male writers were marketed in the same way as female writers. Via Christopher Hamilton-Emery. pic.twitter.com/1IwN8MfckZ

— Jane Harris (@blablafishcakes) October 4, 2017

(I saw the tweet as retweeted by Jennifer Williams, but Twitter seems not to preserve this valuable information.)

The three real and one fake book cover shown above are all somehow undignified. More precisely, I would feel undignified to be seen reading such books. Hardy did not like having his picture taken, and it shows on the cover of A Mathematician’s Apology. On the cover of The Bell Jar, the compact mirror and powder puff suggest superficiality. But then Hardy’s image does reflect the uptightness that I see in his book. And Sylvia Plath did wear lipstick.

Her favored color was Cherries in the Snow, by Revlon. A devotee of Plath called Patricia Grifasi learned this only after buying the lipstick for herself. She wrote (in “The Rise And Fall Of Sylvia Plath’s Favorite Lipstick,” The Gloss, June 16, 2015),

Forget that Plath’s poetry is terrifyingly intimate, crowded with speakers who say things like, “I eat men like air” (“Lady Lazarus”). Forget that her journal entries describe how satisfying it is to scoop out a pesky glob of snot. In a weird way, wearing Cherries in the Snow allowed me to be even closer to a writer I admired than reading all those very personal things.

Thus the 50th anniversary cover of The Bell Jar may not be inappropriate. As for the bikini on the Letters, says Emily Van Duyne in the aforementioned Electric Lit article,

The reality, and it’s astounding to me that I have to write this sentence down, is that we can take a writer who wears a bikini seriously. I have three in my closet, the most recent of which is a vintage-inspired red-halter. I bought it because I love red; I love red partly because I love Sylvia Plath. I wear “Cherries In The Snow” lipstick to the classes I teach, to parties, to intimidating meetings with condescending men, and when I do, I invoke her, just a little bit—for inspiration. For luck. For permission, which she gave me, which she gives me—to be brave. To try and astound. To say the things no one wants to say, or hear. To be beautiful, and to be smart, and sexual, and to never, ever fall into the foolish trap that these cannot coexist.

I have read The Bell Jar just the once so far. Looking back at my copy with the garish cover, I see that I marked several passages, noting their page numbers at the back. The later passages are uses of the term bell jar, and for now I have nothing more to say about this term than I did at the end of my earlier article. Many essays have no doubt been written about the meaning of the title, and some of these will be available on line, perhaps for a price, so that you can turn them in to your teacher as if they were your own (perhaps after making enough changes to fool automatic plagiarism detectors).

The earlier passages that I marked may perhaps illustrate what Plath meant by the bell jar. In any case, since I found an electronic text on a New York high school English course web page, I am able to quote the passages at length with no trouble.

I hadn’t the heart to tell Jay Cee there wasn’t one scrap of space on my senior year schedule to learn languages in. I was taking one of those honors programs that teach you to think independently, and except for a course in Tolstoy and Dostoevsky and a seminar in advanced poetry composition, I would spend my whole time writing on some obscure theme in the works of James Joyce. I hadn’t picked out my theme yet, because I hadn’t got round to reading Finnegans Wake, but my professor was very excited about my thesis and had promised to give me some leads on images about twins.

When I read this, I had not yet heard about and joined the project of Brian Denton (mentioned above) to read War and Peace over the calendar year, one chapter a day. Plath seems to make an ironical acknowledgment of what Robert Pirsig would write, in a passage of Zen and the Art of Motorcycle Maintenance that I considered also in “One and Many”:

Schools teach you to imitate. If you don’t imitate what the teacher wants you get a bad grade. Here, in college, it was more sophisticated, of course; you were supposed to imitate the teacher in such a way as to convince the teacher you were not imitating, but taking the essence of the instruction and going ahead with it on your own.

Plath either understands this or betrays it. Her first person Esther later looks at herself: the emboldened clause is specifically what I had marked.

I started adding up all the things I couldn’t do.

I began with cooking.

My grandmother and my mother were such good cooks that I left everything to them. They were always trying to teach me one dish or another, but I would just look on and say, “Yes, yes, I see,” while the instructions slid through my head like water, and then I’d always spoil what I did so nobody would ask me to do it again.

I remember Jody, my best and only girlfriend at college in my freshman year, making me scrambled eggs at her house one morning. They tasted unusual, and when I asked her if she had put in anything extra, she said cheese and garlic salt. I asked who told her to do that, and she said nobody, she just thought it up. But then, she was practical and a sociology major.

I didn’t know shorthand either.

This meant I couldn’t get a good job after college. My mother kept telling me nobody wanted a plain English major. But an English major who knew shorthand was something else again. Everybody would want her. She would be in demand among all the up-and-coming young men and she would transcribe letter after thrilling letter.

The trouble was, I hated the idea of serving men in any way. I wanted to dictate my own thrilling letters. Besides, those little shorthand symbols in the book my mother showed me seemed just as bad as let t equal time and let s equal the total distance.

Would somebody call Plath’s Esther a snowflake? “Look, Honey, none of us like the idea of serving men, but we all gotta do it.” This could be said by another woman or by a man. That doesn’t make it fair. Plath is writing the truth, as a confession.

Finally Esther meets a psychiatrist and reveals her fantasy of what such a man might be like.

I hated him the minute I walked in through the door.

I had imagined a kind, ugly, intuitive man looking up and saying “Ah!” in an encouraging way, as if he could see something I couldn’t, and then I would find words to tell him how I was so scared, as if I were being stuffed farther and farther into a black, airless sack with no way out.

Then he would lean back in his chair and match the tips of his fingers together in a little steeple and tell me why I couldn’t sleep and why I couldn’t read and why I couldn’t eat and why everything people did seemed so silly, because they only died in the end.

And then, I thought, he would help me, step by step, to be myself again.

But Doctor Gordon wasn’t like that at all. He was young and good-looking, and I could see right away he was conceited.

I would have to read the novel again, to think about how much irony is here.

Recently I was alerted (again by a tweet, as retweeted by Nicholas Christakis) to a theory described in a 2015 article in The Scholar’s Stage blog called “Honor, Dignity, and Victimhood: A Tour Through Three Centuries of American Political Culture.” The Iliad portrays an honor culture, but America passed from such a culture to a culture of dignity. Honor is given us by others; dignity, we can have on our own. Now that many Americans are sensitive to so-called micro-aggressions, the country may have passed to a culture of victimhood.

I confess to being insufficiently interested to read all of the sociology. I know what is happening in America, only from a distance. Plath’s Esther seems to have been hoping for help from a man. In recent tweets, I see women asking men to help fight abuse at the hands of Harvey Weinstein and the like. This is not victimhood, if victimhood is something to be perversely proud of, the way one might be proud of one’s honor or one’s dignity. The requests for help are recognition that we are all connected, and life might be better if we did not have to defend ourselves from attack, all of the time.

This sounds like the sort of thing that I have tried to work out, as in the article “All You Need Is Love,” where the topic is education—as it often is for me, and as it is in a good part of The Bell Jar. For Pirsig, rather than being imposed on you, education is something you ought to demand for yourself. But there is a middle way. Quoting my own email, I wrote,

Perhaps it is best to learn because one understands it as one’s role in the community that one is happy to be a part of. Here again is something that Pirsig may miss. Pirsig is the individualist, the lone wolf, and this is a reason why I like him. But education is not just something one achieves for oneself. It means joining an educated community; it means helping others join that community.

Life can be cooperative and not just adversarial. There are things you can learn on your own, or demand to learn, like a prosecutor examining a witness for the defense. If you can learn them, you may well be smart. Let me then end with one bit of tweeted wisdom:

History of full of stories of catastrophe brought about by people who are smart only in only a narrow domain, and lack humility and remorse.

— Zeynep Tufekci (@zeynep) October 6, 2017

Fascism As Abetted by Realism

Fascism is class warfare waged on behalf of the capitalists. This should be realized by anybody who is attracted to accidental features of Fascism such as nationalism, racism, or militarism. The Fascists are not on your side, even if they share your nationality or “race” or fascination with weaponry and military discipline.

The illustrations are explained near the end of the text. This one, the cover of Cruisin’ 1964, shows a young bearded man, holding Report of the Warren Commission against a law dictionary, saying to another, “Luthor … how come you never make it to the free speech rallies anymore?” Luthor has a cigarette, closed eyes, and a guitar

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Romance

At the end of Shakespeare’s romance called The Tempest, Prospero plans to retire to Milan, where “Every third thought shall be my grave.” I remember these words from reading the play in school and college. I also have thoughts of my grave, and their frequency may increase as the years pass. However, for each of those thoughts, I seem to have more thoughts that are based on memories of youth and childhood.


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