Tag Archives: Alexandre Borovik

Be Sex Binary, We Are Not

Content warning: suicide.

The following sentence is bold in the last paragraph of an essay: “the science is clear and conclusive: sex is not binary, transgender people are real.” I don’t know what the writer means by this. As far as I can tell, as a biological concept used for explaining reproduction, sex has two kinds or parts or sides or aspects, and the essay tacitly affirms this; at the same time, obviously persons called transgender exist.

☾ ♂ ☿ ♃ ♀ ♄ ☉

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NL I: “Body and Mind” Again

Index to this series

“We are beginning an inquiry into civilization,” writes Collingwood, “and the revolt against it which is the most conspicuous thing going on at the present time.” The time is the early 1940s.

Human tourists photographing sculptured supine blue ape with chrome testicles outside the Intercontinental Hotel, Prague Continue reading

Logic of Elliptic Curves

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. Continue reading

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.)

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All You Need Is Love

Here are some meditations on education from the summer of 2016, when Donald Trump was threatening to become President of the United States. Education cannot be forced on unwilling students. Neither need students know just what they are accepting; they may be enticed or beguiled into learning. Whether they have learned cannot be directly tested. I include some memories of racism (as an observer, not a victim) and of my own liberal education. (Note added May 31, 2018)

Would education solve the world’s problems? A meaningfully positive answer would imply that the appropriate education could actually be supplied to us, or enough of us; and yet education is not a drug that can be administered willy-nilly.

Tables for art entrance exam, MSGSÜ, 2016.08.02

Tables for art entrance exam, MSGSÜ, 2016.08.02

My thoughts here are occasioned by a friend’s remark yesterday (Istanbul time, August 1, 2016), to the effect that the current presidential election cycle in the United States shows the need of liberal education, of learning to think: and this learning should start in grade school. I responded as follows (this was on that social medium that I loathe):

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Limits

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