This is inspired by Charlotte Brontë’s Villette. After reading this 1853 novel a second time in the summer of 2018, I put some passages I liked into a LaTeX file. I added some commentary and came up with a document more than 90 A5 pages long. I recently reread it and was reminded how much I had enjoyed the novel. I thought some of my commentary could be adapted to stand alone as a blog post – this one.
“The Sower,” 1850
Jean-François Millet (French, 1814–1875)
Museum of Fine Arts, Boston
We are still in the latter part of Book VI of Plato’s Republic, where Socrates undertakes to explain the education of the philosopher-kings (502c–d). They are not literally so called, as we noted last time. They are going to need to “be able to bear the greatest studies” (503e), and “the idea of the good is the greatest study” (505a). People are confused about what the good is:
It rather the case that
We looked at that much last time.
Dünya Barış Parkı 2021.10.30
This post is based on recent readings, often on or through Twitter, of the following writers.
Having originally posted this essay on January 9, 2021, I edited and augmented it, on January 19 and December 19 of that year. I return to it now, on June 22, 2023, having posted “On Dialectic,” two days ago; this one is another post that quotes lots of people, and I want to check how it reads. It reads fine, to me, although I did have to correct occurrences of “behavior” spelled as “behavor.” Moreover, although I had forgotten what was here, I recognized it instantly as I read; another reader would not experience this recognition.
What stands out most to me now is Christa Peterson’s suggestion,
A representation of our own gender … could … be a means of picking out people as who we are co-gendered with …
As the essay already suggests, if you replaced “gender” with “race,” then the resulting speculation could get you called a racist, and that is supposed to be something bad. However, if we replace “gender” with “sex,” we obtain a proposition that is fundamental to contemporary biology, as I understand it, because evolution is
I think this is why Nina Paley can say, in a blog post called “Why I Don’t Use ‘Preferred Pronouns’,” which I referred to also in “Imagination,”
Like most mammals, I can’t help but identify someone’s sex with +99% accuracy. (… Women, I think, are better at identifying sex than men, either due to instinct or conditioning for survival …)
We know that there are two sexes, and we know who is of which sex, the way we know that some foods are good to eat. However, Peterson seems to think of this knowledge a bit differently:
Trans people’s dignity and legitimacy does not depend on the success of any one attempt to conceptualize their experience. But the most common way, in terms of “gender identity,” is perfectly functional. The commitments of the popular notion are minimal: people have an internal sense of their own gender that can come apart from their knowledge of their assigned sex, and is generally fixed, and certainly not revisable in the way ordinary beliefs are.
What is the word “assigned” doing here? Does whether you are trans depend on whether somebody made a mistake when checking one of the boxes marked “male” and “female” at your birth?
A lot of old PSA’s about drugs are on YouTube and the Web Archive, and sometimes they are linked to by articles that ridicule them. There is one that I have not been able to find, perhaps from around 1970, in which parents confront their teenager with the drug paraphernalia that they have found in his room. The boy storms out of the house, saying, “You don’t understand!”
There’s a lot that I don’t understand. I must not, since it seems childish, but is coming from adults. Some of these adults stormed the US Capitol the other day; others encourage them; still others are professors of philosophy.
“Human egg and sperm cells.”
Asimov’s New Guide to Science (1984), page 600
Pacifism is properly pacificism, the making of peace: not a belief or an attitude, but a practice. Mathematics then is pacifist, because learning it means learning that you cannot fight your way to the truth. Might does not make right. If others are going to agree with you, they will have to do it freely. Moreover, you cannot rest until they do agree with you, if you’ve got a piece of mathematics that you think is right; for you could be wrong, if others don’t agree.
To ease the strain of pandemic restrictions, I was recently called on to recommend a poem. I chose “The Undertaking” of John Donne. I want to say here why. Briefly:
Diotima’s ladder, or stairway, is recounted by Socrates in Plato’s Symposium (211c, in the translation of Jowett, with my bullets):
And the true order of going, or being led by another, to the things of love (τὰ ἐρωτικά), is to begin from the beauties of earth and mount upwards for the sake of that other beauty, using these as steps (οἳ ἐπαναβαθμοί) only, and from
- one going on to
- two, and from two to
- all fair forms (τὰ καλὰ σώματα), and from fair forms to
- fair practices (τὰ καλὰ ἐπιτηδεύματα), and from fair practices to
- fair notions (τὰ καλὰ μαθήματα), until from fair notions he arrives at
- the notion of absolute beauty, and at last knows what the essence of beauty is (ὃ ἔστι καλόν).
Two books that were my mother’s
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
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.
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.
Kuzguncuk, 2017.11.05
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. On this subject, old books on my shelves are not much help; my own experience is not much more help, 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
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.
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
Polytropy 