Polytropy

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.

The title of the essay is a command: “Stop Using Phony Science to Justify Transphobia.” I can support that. I don’t even need the qualifier “phony.” If transphobia is the kind of morbid fear suggested by the suffix “-phobia,” then science ought to help dispel this, not promote it.

One might also just say, Stop using phony science.

The writer of the essay in question (dated June 13, 2019) is called Simón(e) D Sun. I imagine the parenthetical letter is meant to suggest alternation between masculinity and femininity. I shall therefore use the epicene, formerly plural “they,” with a singular verb, when I want a pronoun for the writer. Their essay being only a blog post like this one, I might have passed it by; but it is on the website of Scientific American.

I have respected that magazine since childhood, when my godfather gave me a subscription, and I became a devoted reader of Martin Gardner’s “Mathematical Games” column.

I saw the blog post recommended on Twitter to somebody who was trying to understand the slogan, “Trans women are women.”

Trans, intersex, or neither

In an earlier post, “Sex and Gender,” I suggested (though not in these terms) that Scientific American had engaged in phony science by publishing “Beyond XX and XY: The Extraordinary Complexity of Sex Determination” (September 1, 2017). The explicit information about intersex conditions is presumably correct; however, as far as I can tell, the pictorial suggestion that those conditions lie on a spectrum is phony, in the sense of being given neither a justification nor even a meaning that could be justified. For example, there is no clear sense in which a person with Turner syndrome is closer to being a “typical biological female” than is a person with congenital adrenal hyperplasia.

Those are intersex conditions. Being trans is different. The essay under review has a concluding remark,

The trans experience provides essential insights into the science of sex and scientifically demonstrates that uncommon and atypical phenomena are vital for a successful living system.

The essay has hardly mentioned trans persons, nor said what the “trans experience” is (I can imagine several possibilities).

I have no idea how anything could show “that uncommon and atypical phenomena are vital for a successful living system.” Every living system that we can observe is successful; otherwise it would not be there in the first place. Be that living system an organism or a species, there must be something atypical, something not only uncommon, but unique, that distinguishes it from others. I don’t know how this would be understood as a scientific conclusion. I don’t know, and the author makes no appearance of trying to let the reader know.

“Transgender people are real,” says Simón(e) D Sun, in the passage already quoted. I didn’t think there could be any question of this. Some persons do in fact disagree with the sex they were assigned at birth; and as far as I know, this is what it means to be transgender, or simply trans.

It’s not actually so simple. Some trans persons don’t disagree with their assigned sex; they are made dysphoric by it. They affirm that they always will be of the sex they were assigned as birth; they still prefer, or are led by an inner compulsion, to live as if they were of the other sex. These persons may take hormones, and undergo surgery, to make their bodies mimic the opposite sex, without actually becoming it. Debbie Hayton seems to be a notorious example of such a trans person.

As far as I can tell, some trans persons only adopt clothing and mannerisms associated with the other sex. Some persons do the same, while not considering themselves trans. Such persons may be called trans, posthumously; Marsha P. Johnson and Stormé DeLarverie would seem to be examples.

Biology

This whole discussion assumes that sex is binary, and there are two sexes, male and female. These are only ideals or concepts, and how they are to be applied is not always clear. Simón(e) D Sun may mean something like that. Nonetheless, the way they brings in science, I have to ask: who gets to decide? Some activists seem to assert that the individual gets to decide their sex—or their gender, which is independent of sex, though referred to with the same or similar vocabulary.

If the individual decides their sex, then biology would seem to be irrelevant. Nonetheless, Sun says the following:

A newly fertilized embryo initially develops without any indication of its sex. At around five weeks, a group of cells clump together to form the bipotential primordium. These cells are neither male nor female but have the potential to turn into testes, ovaries or neither. After the primordium forms, SRY – a gene on the Y chromosome discovered in 1990, thanks to the participation of intersex XX males and XY females – might be activated.

Intersex XX males and XY females exist, although, as the writer has told us,

Nearly everyone in middle school biology learned that if you’ve got XX chromosomes, you’re a female; if you’ve got XY, you’re a male … The popular belief that your sex arises only from your chromosomal makeup is wrong.

Before college, I myself had no biology course; instead, those of us who were interested in science were advised to satisfy other requirements, and then take chemistry and physics as our sciences. (This was at St Albans School for Boys, in Washington, DC. The “other requirements” were courses in ancient Greek history and the Bible.)

As for the writer’s words above, apparently they originally referred to XX males and XY females as being transgender. This would have been phony science, and it was corrected. The correction was properly noted (on 6/18/19), and this is how I can know it happened.

Humanity

Members of a group may not agree with the activists who campaign in their name. Not all African Americans will agree with everything that is done under a banner that reads, “Black lives matter.” Activists may also make a poor case for a worthy cause; examples may include some of the white people who preach against racism.

Simón(e) D Sun does say why their cause is important:

… “intellectual” assertions are used by nonscientists to claim a scientific basis for the dehumanization of trans people. The real world consequences are stacking up: [1] the trans military ban, [2] bathroom bills, and removal of [3] workplace and [4] medical discrimination protections, [5] a 41-51 percent suicide attempt rate and [6] targeted fatal violence. It’s not just internet trolling anymore.

The “‘intellectual’ assertions” referred to here are attributed vaguely to the Intellectual Dark Web, though the writer cites only Bari Weiss’s New York Times opinion piece of May, 2018, as a reference for this entity.

I am not sure what Sun means by dehumanization. The Louisiana diner scene in Easy Rider (1969) might be an example; here local white men talk about the three male freaks who have arrived on two motorcycles.

—Check that one with the long hair. —I checked him. Might have to bring him up to the Hilton before it’s over with. —I think she’s cute. —Isn’t she though? Guess we’ll put ’em in a woman’s cell, don’t you reckon? —I think we oughta put ’em in a cage and charge admission to see ’em.

—You know, I thought at first that bunch over there … their mothers may have been frightened by a bunch of gorillas … but now I think they’re a cult. —One of ’em is Alley Oop, I think, from the beads on him. —One of ’em, darn sure, is not Oola. —Look like a bunch of refugees from a gorilla love-in. —A gorilla couldn’t love that. —Nor could a mother. —I wouldn’t even mate him up with one of those black wenches out there. —Oh, now, I don’t know about that. —That’s about as low as they come, I’ll tell you.

—Man, they’re green. —No, they’re not green. They’re white. —White? You’re color-blind. I just got to say that. —I thought most jails were built for humanity … and that won’t quite qualify. —Wonder where they got those wigs from? —They probably grew ‘em. Look like they’re standin’ in fertilizer. —Nothin’ else would grow on ‘em. —I saw two of ’em one time. They were just kissin’ away. Two males! Just think of it.

The girls in the diner adore the visitors. The men’s discussion ends ominously:

—What you think we oughta do with ’em? —I don’t know, but I don’t think they’ll make the parish line.

About ten years after that movie, my grandmother told me that my long hair made me look like a girl. I didn’t cut it.

Suicide

As for the consequences of dehumanizing trans people, I have no detailed knowledge. I would say that one of the consequences, in the numbering that I supplied, is not like the others. All but number 5 may be addressed with laws that, properly framed, ought to be unobjectionable. Suicide can be addressed with law too: it can be made illegal. However, I don’t think this is what the writer has in mind.

Suicide attempt rates are disputed, as for example in another blog post, called “The Theatre of the Body: A detransitioned epidemiologist examines suicidality, affirmation, and transgender identity.” Here is just one of the epidemiologist’s remarks:

… clinicians in the earlier days of proper gatekeeping often reported that their male trans patients commonly used manipulative suicide threats to get more rapid approval for hormone drugs and genital de-masculinization surgery.

Journal articles from 1965 and 1979 are cited. The post is not on the site of a well-known magazine, but of 4thWaveNow, “A community of people who question the medicalization of gender-atypical youth.” The post itself is by Hacsi Horváth, who says,

For about 13 years, I also masqueraded “as a woman,” taking medical measures which suggest, shall we say, that I was completely committed to that lifestyle. Most men would have recoiled from this, but in my estrogen-drug-soaked stupor it seemed like a good idea. In 2013 I stopped taking estrogen for health reasons and very rapidly came back to my senses. I ceased all effort to convey the impression that I was a woman and carried on with life.

Such detransitioners are examples of persons who cannot always be trusted to know their own sex or gender, or what they want in general. Maybe you can usually trust people, but you have to allow for exceptions. This is a basic point made in the first book of Plato’s Republic, after Polemarchus says, quoting Simonides, “it is just to render to each his due,” in Shorey’s translation; in Jowett’s, “the repayment of a debt is just” (ὀφειλόμενα ἑκάστῳ ἀποδιδόναι δίκαιόν ἐστι 331e).

Justice is not actually so simple. Only the letter of the rule of Simonides, but not the spirit, would be observed in returning weapons to the hands of somebody who has gone mad. Such, at least, is Socrates’s observation.

You cannot always trust Socrates to say what he believes. He is also only a character in a dialogue of Plato. In any case, somebody’s believing something doesn’t make it true. If one needs an argument, the dialogue of the Republic makes clear enough that there is no foolproof formula for justice.

Besides the one by Sun, another Scientific American blog post is an interview of a trans woman scientist who says she would commit suicide if she could not obtain the hormones she takes.

If suicide can be a side effect of anti-depressant medication, maybe it can be a side-effect of not taking certain medications. Such, at least, would seem to be the claim.

Nobody should use suicide as a threat, and nobody else should be manipulated by such a threat. Though your lover may say they will kill themself when you propose to break up, you should still go through with it, according to a WikiHow article (with a number of references), “How to Break Up With Someone Who Is Threatening Suicide.”

Perhaps the trans scientist in the Scientific American blog post is not making a threat, but simply stating the facts as she sees them. In that case, she needs help. I do not know how that help can best be given; perhaps indeed with hormones. However, the judgment of any suicidal person is ipso facto questionable. Survivors of suicide attempts from the Golden Gate Bridge say they regretted their decision the moment they jumped. (I first learned of this regret from a recorded lecture of Nicholas Christakis, “The Sociological Science Behind Social Networks and Social Influence.”)

Purpose

I return to the science of sex, the nominal subject of the essay under review. As far as I understand, the binary distinction between female and male is useful for explaining what is called sexual reproduction, which is the kind of reproduction that human beings engage in. Among us, an egg from a woman (or call her what you will) combines with a sperm from a man (or call him what you will) to produce a zygote, which can be nourished in the woman’s womb (or suitable replacement, such as another woman’s womb) so as to develop into a new human being.

The zygote has a sex, or is going to have a sex, but the expression of this sex may be ambiguous. It still seems reasonable to say that nature tries to make a zygote into a girl or boy. This is the purpose of nature, although this purpose may not be realized in individual cases.

Whatever the purpose of nature may be, it imposes no moral obligation on us. For instance, we need not try to “help” nature by performing genital surgery on intersex infants. I addressed the general issue in “A New Kind of Science,” noting that while a fever may be nature’s way of fighting an infection, it may not be our best way in any particular case.

In a book that I happen to have on hand, Tinbergen makes some useful remarks about nature’s purposes (the bold emphasis is mine):

Whereas the physicist or the chemist is not intent on studying the purpose of the phenomena he studies, the biologist has to consider it. ‘Purpose’ of course is meant here in a restricted sense. I do not mean that the biologist is more concerned with the problem of why there should be life at all, than the physicist with the problem of why there should be matter and movement at all. But the very nature of living things, their unstable state, leads us to ask: how is it possible that living things do not succumb to the omnipresent destructive influences of the environment? How do living things manage to survive, to maintain and to reproduce themselves? The purpose, end, or goal of life processes in this restricted sense is maintenance, of the individual, of the group, and of the species. A community of individuals has to be kept going, has to be protected against disintegration just as much as an organism, which, as its name implies, is a community of parts—of organs, of parts of organs, of parts of parts of organs.

That is from page 2 of Social Behavior in Animals (1953/1964). A bit later (page 8), Tinbergen mentions a mated pair of herring gulls in which the male had no “brooding urge.” The female alone sat on the couple’s eggs for twenty days, then gave up. Her personal purpose was defeated, though not the species’s:

However disastrous this was for the young, it was a blessing for the species, for what if the offspring inherited this defect from the father and supplied the species with three instead of one of these degenerates?

Such eugenic considerations are irrelevant to our own moral concerns. More precisely, you may use them in making your own reproductive decisions, but not impose them on others.

Natural law

Nature attempts to make each of us male or female, but is not always successful. In the same way, gasses try to obey the gas laws, combined ultimately as

The attempt cannot be entirely successful, if only because gasses comprise discrete individuals, namely molecules, while pressure, volume, and temperature vary continuously, as far as the given equation is concerned.

I make no judgment of what this all means, ontologically.

In his book, Mathematics Under the Microscope (2007), as well as in his blog, Alexandre Borovik remarks on the challenge of taking a finitistic course of calculus, while working out the subject independently in the usual way: “I learned to love actual infinity – it makes life so much easier.” There may be no actual infinite or infinitesimal quantities in nature; we still find it convenient to study nature as if there were.

Brains

Simón(e) D Sun refers to research whereby the brain of a trans woman (for example) is in some ways like a cis woman’s, in other ways like a cis man’s, and in yet other ways in between. Studies were made “both before and after transitioning”; indeed, the title of one cited article explains: “Grey and white matter volumes either in treatment-naïve or hormone-treated transgender women: a voxel-based morphometry study.”

Is Sun really hoping for a way to use physiology to decide whether a person is trans? If so, there is a long way to go. The cited studies seem not to involve the testing of hypotheses arising from a theory of the gendered brain.

One of Sun’s references mentions such a theory. The article is called “Regional Grey Matter Structure Differences between Transsexuals and Healthy Controls—A Voxel Based Morphometry Study,” and it says,

According to a recent review about the sexual differentiation of the human brain, transsexualism might be the result of the fact that the development of the sexual organs in the fetal life occurs well before the sexual differentiation of the brain. Thus, if something disturbs the sexual differentiation of the brain, the fetus already has sexual organs according to his/her assigned sex, while his/her brain might develop differently.

So there is a potential theory, but I don’t see a proposal for testing it. It’s somebody else’s theory, anyway. The authors themselves have an hypothesis of sorts:

Our hypothesis was that the regional structural parameters of the brain of transsexual subjects will be different from that of control subjects with the same biological gender.

The verification of such an hypothesis would seem to be practically inevitable, since the transsexual subjects are few (n = 17), and the “regional structural parameters of the brain” are (apparently) numerous.

Science

As a mathematician, I cannot normally write a paper that says, “My hypothesis is that such-and-such is true, and I have attempted to prove it in this way, but the proof fails.” I may be able to salvage something out of my work; but in mathematics we haven’t the custom that Feynman urges for natural science, whereby we must publish whatever we come up with. As he says in “Cargo Cult Science,”

If you’ve made up your mind to test a theory, or you want to explain some idea, you should always decide to publish it whichever way it comes out. If we only publish results of a certain kind, we can make the argument look good. We must publish both kinds of result.

However, it seems the publishing should also be part of such a project as Feynman describes:

When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition.

Thus Mendeleev’s hypothesis of the periodic table had to be confirmed by discovery of the elements whose existence it predicted; and Ventris’s hypothetical interpretation of Linear B had to be confirmed by its successful application to newly discovered documents.

Above was a quoted suggestion of a possible theory of the gendered brain. In describing the theory, the authors continue (emphasis mine):

These authors suggest that the disturbance of the testosterone surge that masculinize[s] the fetal brain might be at the background of GID [Gender Identity Disorder] in certain cases. Furthermore, they emphasize that there is no compelling evidence that postnatal environmental factors play a crucial role in sexual orientation and gender identity.

This theory is contradicted by the references cited in another of the papers that Sun themself links to, namely “A Review of the Status of Brain Structure Research in Transsexualism” (emphasis mine again, and I have removed the references):

In regard to environmental variables, parental and family factors have been reviewed; parental influences seem to be a contributing factor to the development of GID and play a role in social gender transitioning.

Something is fishy here. What should the lay reader conclude? Here is Feynman again:

I would like to add something that’s not essential to the science, but something I kind of believe, which is that you should not fool the layman when you’re talking as a scientist … I’m talking about a specific, extra type of integrity that is not lying, but bending over backwards to show how you’re maybe wrong, that you ought to do when acting as a scientist. And this is our responsibility as scientists, certainly to other scientists, and I think to laymen.

“Thanks to the participation of trans people in research,” says Sun, “we have expanded our understanding of how brain structure, sex and gender interact.” And yet if we actually look up Sun’s references, they do not seem to share a common understanding.

Feelings

According to the article that Sun cites called “Neuroimaging studies in people with gender incongruence,”

Causal mechanisms for feelings of gender incongruence are unknown, but biological factors are suggested to play a role. Men and women have been shown to differ in several characteristics, but the largest difference may be found in gender identity: most women feel that they are women, and most men feel that they are men.

Has there really been a scientific study, showing that most men and women feel that they are men and women?

I wonder how such a study would proceed. It might mean asking people on the street two questions:

1. What is your gender?

2. Do you feel that you are of that gender?

I don’t think answers could be of much use, if they were even forthcoming. Perhaps the first question would be replaced with a request for consent to examine the subject’s genitals.

The reference in question cites no study of gender identity, though it does give citations for such claims as, “Boys and girls show differences in the development of grey and white matter volume over the course of puberty.”

Do trans people, do any of us, want to leave the question of who we are to a physiologist of some kind?

Speaking for myself, I don’t feel that I am a man. I may then differ from my fellow man Charlie Rich, who sang in 1973,

And when we get behind closed doors
Then she lets her hair hang down
And she makes me glad that I’m a man
Oh, no one knows what goes on behind closed doors.

I used to hear this on the AM radio in my father’s Pontiac. When behind closed doors as Rich describes, I am glad to be who I am, where I am, with whom I am with; being a man as such has nothing to do with it.

Before Charlie Rich, though I heard them only later on my friend’s cassette player, the Grateful Dead were singing the lyrics of Robert Hunter and Bob Weir:

She can dance a Cajun rhythm,
Jump like a Willys in four wheel drive,
She’s a summer love in the spring, fall, and winter,
She can make happy any man alive.

“Sugar Magnolia” may be the Dead’s most joyful song, but I reject the idea of a generic way of making me happy as a man.

I acknowledge responsibility for being a man, in the sense that, when men are boorish, even by writing that last verse above, this somehow reflects on me. There may not be much I can do about it, beyond not being that way myself.

When men fight on the street in Istanbul, I witness from a distance, counting on the intervention of men who know the belligerence better; and the intervention always happens. I suspect that some men try to fight, knowing others will restrain them.

I have once or twice approached a quarrelling, (sexually) mixed couple, to see that no violence would be done.

After participating in the March for Women’s Lives in April, 1989, in Washington, I was a member of the National Organization for Women for some years, until I started thinking that I could afford to give money to such organizations, only because I lived the kind of frugal lifestyle that the leadership of those organizations did not adopt. One of my five roommates worked as an assistant to the NOW president, Patricia Ireland, whom I had met when she spoke at the University of Maryland. After her talk, another man shook her hand when I did, but he turned out to be an anti-abortion activist. He didn’t get to ask whatever clever question he had in mind; a handler took Ireland off to an interview.

Abortion

The trans debate, and what it is even about, remain in question; but the abortion debate can perhaps be informed by science, and more precisely ethology. Here is Angela Saini, from Inferior: The True Power of Women and the Science that Shows It (2017), reporting from the San Diego Zoo.

I’m transfixed by a fluffy two-year-old bonobo. She’s cheerfully hanging on to her mother’s fur as the ape leaps from branch to floor, letting go of her to playfully roll on the ground for a few seconds before quickly returning. I have a two-year-old as well. And the bonobos’ behavior reminds me of my own close relationship with my son. In the little bonobo I see a similar mischievousness and even the hint in her of his cheeky smile. They watch each other the same way that we do. The similarities between us are uncanny.

At close quarters like this, I start to understand why humans are sometimes regarded as another great ape, alongside bonobos, chimpanzees, gorillas, and orangutans. But as much as we have in common, there’s one important contrast between me and the bonobo mother. In the entire time I’m looking into the glass enclosure, I never see her lose contact with her infant. At no point does the little one fall out of her mother’s protectively tight orbit. My son, on the other hand, is already at the other end of the enormous zoo with his father.

Many primate species are like bonobos. Humans and tamarins are different; our females do not raise their young exclusively, and mothers who have no help are known to abandon their offspring. Primatologist Sarah Hrdy is reported to use such observations to argue for the availability of abortion and childcare.

I think the argument can go as follows. A priori, a woman might be expected to regret an abortion. She may also regret keeping the child, while letting others look after it. However, there seems to no “biological” reason why this should be so, because:

• in some primate species (Hrdy observed the langur; Dawn Starin, the red colobus), mothers will carry around the corpses of their dead infants;
• in other primate species, mothers will abandon even living children they cannot care for;
• in those species, children do not cling so tightly to their mothers as, say, bonobos do;
• neither do human children so cling.

That is all fine; but still we have to ask whether we want to be like tamarin monkeys. We probably do not wish any infants to be exposed in the manner intended for Oedipus.

Ethological studies only broaden the range of moral examples that we can consider, as we decide what to do.

Facts

After the bolded sentence from their last paragraph that I quoted in the beginning, Simón(e) D Sun says,

Defining a person’s sex identity using decontextualized “facts” is unscientific and dehumanizing.

I think defining a person’s sex using biological facts is simply what is done, scientifically.

Defining a person’s identity by any kind of classification is, if not dehumanizing, depersonalizing. I have written something about this in “On Knowing Ourselves.” It may be more or less accurate to call me a cis het white male, but if that tells you all you need to know about me, then perhaps that tells me all I need to know about you.

We have seen Sun’s conclusion,

The trans experience provides essential insights into the science of sex and scientifically demonstrates that uncommon and atypical phenomena are vital for a successful living system.

We have seen Tinbergen’s account of the kind of success studied by biology: “maintenance, of the individual, of the group, and of the species.” This is reproductive success, in a broad sense. For success in human reproduction, much more is needed than the joining of male and female gametes. Evolutionarily speaking, infertile persons, such as women past menopause, who can help care for the young may be an essential component of successful human reproduction; but Sun makes no suggestion that trans persons as such are a component of this reproduction.

There would be no need for such a suggestion. Trans persons are members of our species and deserving of respect as such.

Models

Again, Sun had originally tried to say that trans persons had led to the discovery of the SRY gene; but it was intersex persons. I have so far skipped the section of the essay about hormones; but it does not mention trans persons at all. It says,

The binary sex model not only insufficiently predicts the presence of hormones but is useless in describing factors that influence them.

It seems to me such a sentence ought to be followed by an account of a better model than the binary sex model. Instead there is a brief elaboration on how

Environmental, social and behavioral factors also influence hormones in both males and females.

This itself would seem to show tacit acceptance of the binary sex model.

There are other models. I heard of the five-sex model in the 1990s, but apparently Anne Fausto-Sterling was proposing this “with tongue firmly in cheek,” by the account she gave later in “The Five Sexes, Revisited” (2000; available from the Wayback Machine). The main focus here is on intersex persons, rather than on those whom Fausto-Sterling calls “Transsexuals, people who have an emotional gender at odds with their physical sex.”

Simón(e) D Sun alludes to no such work as Fausto-Sterling’s, nor to any other alternative to the binary model of sexual reproduction. Neither does they make any suggestion of what an alternative model would be modeling.

“Stop Using Phony Science to Justify Transphobia,” says the title. I think I have looked at all of the examples: the ideas that (1) males by definition differ from females by having a Y chromosome in place of an X; (2) males and females have different brains; (3) males and females have different hormones. Sex is assigned on a more complicated basis, because being intersex is possible; and there’s a lot more to us anyway than sex.

Sources

I have said what I have to say about “Stop Using Phony Science to Justify Transphobia.” Now I would say more about science and how I come to it.

When writing “Sex and Gender,” I bought Saini’s Inferior, because the bookshop had this, but not Superior. I cited Audra J. Wolfe for the observation that the latter book was not really science, but journalism; the same is true for the former book.

Tinbergen’s Social Behavior in Animals (1953) was read in the freshman laboratory at St John’s College in Annapolis.

I have written about St John’s for the De Morgan Gazette, as well as on this blog in “The Tradition of Western Philosophy.”

In my freshman year at St John’s, my language tutor, Chaninah Maschler, noted the paradox of the gas laws (that they provide a continuous model for collections of discrete objects, namely gas molecules).

This was in a conference with me about a paper I had written, but I don’t recall the connection. Mrs Maschler must have been thinking independently about the freshman laboratory, where we studied the development of the gas laws and of the notion of the cell. In a recent essay called “When ‘Academic Solidarity’ Is Sophistry,” College alumna and current tutor Zena Hitz lauds the possibility of having such conferences between student and tutor:

I expected small liberal-arts college teaching to be more fulfilling, but I was not prepared for the magnitude of its superiority over the teaching I had done earlier. With only 50 students a semester, in three classes, I knew whom I was teaching. I could meet with each student one on one and calibrate feedback according to the needs and the character of each.

More importantly, the small scale of teaching meant I could give students the freedom to set their own educational agenda, rather than raining PowerPoint bullet points down over a large lecture hall – the regurgitation of which too often stood as a standard of achievement. In my new role, students set their own paper topics. Their questions drive the discussion, not my research program.

At St John’s, one may select one’s own paper topics; but the books that are read collectively are selected by the College. I read recently that American students do not choose colleges for academic reasons; they figure the academic aspects are pretty much the same everywhere, so what they look for is social life and reputation. Not me; I chose St John’s College precisely for the academics (though it probably helped that the students in the promotional literature looked serious as they read their books).

In the College music tutorial, which took the place of laboratory in sophomore year, we read (among other things) the Gradus ad Parnassum of Johann Joseph Fux. In the summer after my graduation, I met a piano teacher who thought Fux’s was an odd book to study. Maybe somebody would say that of the Tinbergen that I quoted above. Readings at the College may be chosen more for the discussion they can provoke than their continued significance. In Fads and Fallacies in the Name of Science (1957), Martin Gardner (he of “Mathematical Games” in Scientific American) wrote of the College,

so heavy is the emphasis on highlights in the past history of science, that little time is left for acquiring a solid grasp of current scientific opinion.

Indeed, the point is not to learn the opinions of others, but to develop one’s own knowledge. This happens, not by looking at mere “highlights,” but by spending months studying Ptolemy’s obsolete geocentric theory of astronomy. This could be one of the most distinctive and valuable features of the College.

I recently encountered a critical allusion to Ptolemy by one of my fellow mathematicians:

This is the problem with physics. Contrivances that fit the observed data but are fundamentally wrong. In the ancient world think of the theory that the sun orbited the earth in a circle. To explain why the solstices and equinoxes are not quite evenly spaced through the year they offset the centre of this circle from the earth. Aristotle had averred that all cyclic motion must be based on circles, so ellipses were not acceptable. This idea led to the absurd contrivance of circles whose centres moved on other circles (epicycles) to explain the motion of the planets around the earth.

Thus “Dark Matters” (The Critic, 22 June, 2020), by Mark Ronan, whom I recall meeting at Antalya Algebra Days in 2001. It seems to me that contrivances fitting the observed data are precisely what physics wants to find. The contrivance of epicycles fit the data well enough for some centuries.

If ancient astronomers had thought elliptical orbits for planets “acceptable,” they still would have had to determine the planets’ rate of motion along those ellipses. “Obvious” choices might have been constant linear speed, or constant angular velocity about the center of the ellipse, or constant angular velocity about a focus of the ellipse. The last might have been most natural, since we can draw an ellipse with a loop of string and pins at the two foci.

A law of planetary motion along ellipses needed a second law about rate of motion; and by the law that ended up best fitting the data, angular velocity about a focus is inversely proportional to distance from the focus. Placing the sun at the relevant focus, Kepler was able to work out this law from observations taken from the earth. He thus needed the hypothesis of Copernicus, that the sun is not a planet or “wanderer” (πλανήτης), one of the seven heavenly bodies whose symbols I put near the head of this essay; but the earth is.

I don’t see a basis for ridiculing the generations of astronomers who did not hypothesize Kepler’s laws. Or if there is a basis, it might serve also for ridiculing Kepler’s earlier hypothesis, that the planets moved along spheres nested in Platonic solids. We may also note that Copernicus had still explained the heavenly motions in terms of circles.

We are all living in the same world, be we in the second century or the twenty-first, in Africa or Europe. There is no reason to think any one of us understands the world any better than anybody else. Each of us is going to have their opinions; but there is no test – no universal test – for whose ideas are better, other than dialogue.

So-called IQ tests have been administered to people of different countries, and “national” IQ scores inferred. This was the subject of a good recent thread of tweets. Some countries get very low IQ scores. You can conclude that the people of those countries must be intellectually disabled, whether from their genes or from environmental conditions; or you can question the idea that your IQ test measures something in the first place. I would go with the latter. The test is certainly meaningless unless the subject cooperates; this makes it not objective in the way that a test for body temperature is.

I would propose similar considerations when people in the past turn out not to have seen things that are obvious to us. Like Newton, we may stand on their shoulders. If we cannot literally have a dialogue with them, we can read them, preferably in a college, a collegivm, that takes them seriously.

In the senior laboratory of St John’s College, after trying to learn something of quantization from original papers, and performing such demonstrations as the Millikan Oil-drop Experiment, we read, as I recall, a Scientific American article on the EPR paradox. Somehow I heard, perhaps not directly from him, that one of our tutors thought an aim of our laboratory was to enable us to understand articles in Scientific American. This then is another personal reason of mine to worry if that magazine publishes phony science. I would however give a more serious account of the St John’s laboratory. It is a study of science as a human endeavor.