Polytropy

A human being was once a man. A female of the species was a wife; a male, a were. The word “were” was used in werewolf, but also were-eld, which became our “world.” Our word "woman" comes from wife-man.

That is roughly the history, which I shall review later in a bit more detail. It would be a fallacy to think the history told us how we must use the words “woman” and “man” today. The history does suggest what may happen again: in a world dominated by men, a word like “person,” intended for any human being, may come to have its own meaning dominated by men. Yet again, this is no reason not to try to make our language better.

There is bitter debate, even within feminism, over whether you can be a woman, just by declaring yourself to be one, regardless of your history and anatomy. As an outsider in either case, I would propose to compare womanhood and Judaism. There are ways to become Jewish. They may not be easy, since being Jewish is a big responsibility. If you are going to take it on, your understanding should be clear, and your motives good.

Regarding the question of who is a woman, both sides would seem to think there is a meaningful distinction between women and men; they just disagree over where to make it. I just want to point out that the distinction need not be made with pronouns. In Turkish, for example, you cannot choose your personal pronoun, since the language has only one of them on offer.

Returning to the noun “man” and derivatives, I do declare a certain affinity for the adjective “freshman,” as being descriptive and as beginning the series that continues with “sophomore, junior, senior.” The series is more interesting than “first-year, second-year,” and so forth. It is likewise interesting that our fingers are not named with ordinal numbers, but in order are pinkie, ring-finger, middle finger, and index finger. A passage in the Republic (523c–d) refers simply to

three fingers, the little finger, the second, and the middle (τρεῖς … δάκτυλοι, ὅ τε σμικρότατος καὶ ὁ δεύτερος καὶ ὁ μέσος) … Each one of them appears to be equally a finger (δάκτυλος μέν που αὐτῶν φαίνεται ὁμοίως ἕκαστος) …

None of this is any reason not to beware using “man” for women.

I did some of the etymological research here while keeping notes on the progress of an upper-level course in the fall of 2015. In that course, I had my students reading Pappus of Alexandria about the “Hexagon Theorem” named for him. In my notes, I recalled how my students had read Euclid in the first semester of their freshman year.

I had developed the idea of the course of reading Pappus after finding that the Wikipedia article on Pappus’s Hexagon Theorem had no discussion of Pappus’s original work. Now the article has a section called “Origins,” because I added it.

The Hexagon Theorem solves a problem that has interested me since I began reading Euclid with first-year students here in Istanbul in 2011. The general problem is to develop a theory of proportion from Book i alone of the Elements. The specific problem is to prove that, if AD, BE, and CF have a common point, and AB and AC are parallel to DE and DF respectively, then BC is parallel to EF. This is Desargues’s Theorem, in what I would call the “pyramidal” case. If, like Euclid in Books v and vi, you have a theory of proportion that yields Thales’s Theorem, whereby a line cuts two sides of a triangle proportionally if and only if the line is parallel to the base of the triangle,—if you have this theorem, then Desargues’s Theorem follows immediately; conversely, Desargues’s Theorem implies that the statement of Thales’s Theorem will serve as a definition of proportion.

Euclid’s theory of proportion relies the “Archimedean” hypothesis that of two lengths, some multiple of the less exceeds the greater. In The Foundations of Geometry (based on lectures of 1898–9), David Hilbert shows that the hypothesis is not needed. Robin Hartshorne provides an exposition in Euclid and Beyond (2000). The key is a “segment arithmetic”: a theory of taking sums and products of pairs of lengths. I propose the alternative of a “polygon arithmetic.” This involves only sums, not products; but it allows us to prove Desargues’s Theorem in stages, once we have Pappus’s Hexagon Theorem in the “parallel” case: if AB and AC are parallel to DE and DF respectively, and D and A lie on BC and EF respectively, then BF is parallel to CE. The hexagon here is ABFDEC. The theorem follows, as Pappus shows, from a theorem in Book I of the Elements, that triangles on the same base are equal if and only if the line joining their apices is parallel to the common base.

Apollonius uses polygon arithmetic in the proof I wrote about in “Elliptical Affinity” last spring. Since then, I have talked about these matters in Prague and elsewhere.

Again, when keeping a record for myself about a course of reading Pappus, I noted the results of some research in the etymology of “woman” and “man.” I return to that research now, because I have had reason to think of my own first year at college. I think of it as the freshman year of myself and all of my classmates, female and male, even though, in my last post here, I expressed the intention of avoiding “man” in an epicene sense.

I am thinking of my freshman year, because I read Herodotus then, and Somerset Maugham mentions Herodotus in the first section of The Razor’s Edge:

I have taken the liberty that historians have taken from the time of Herodotus to put into the mouths of the persons of my narrative speeches that I did not myself hear and could not possibly have heard. I have done this for the same reasons as the historians have, to give liveliness and verisimilitude to scenes that would have been ineffective if they had been merely recounted. I want to be read and I think I am justified in doing what I can to make my book readable.

I first read The Razor’s Edge, for my own pleasure, while I was a student, probably after reading Herodotus on assignment. I have lost count of how many times I have read Maugham’s novel since then. Now I have read it once more, since writing in my last post, “To read a composition properly is to compose it again for ourselves.”

A passage of Maugham’s composition is relevant to the question of whether we ought to use “he” when the referent may be a woman:

… she looked at me reflectively. “Do you think any the worse of me for what I did?”

“Would you care?”

“Strange as it may seem to you, I would. I want you to think well of me.”

I grinned.

“My dear, I’m a very immoral person,” I answered. “When I’m really fond of anyone, though I deplore his wrongdoing it doesn’t make me less fond of him. You’re not a bad woman in your way and you have every grace and every charm. I don’t enjoy your beauty any the less because I know how much it owes to the happy combination of perfect taste and ruthless determination. You only lack one thing to make you completely enchanting.”

She smiled and waited.

“Tenderness.”

The smile died on her lips and she gave me a glance that was totally lacking in amenity …

Maugham is addressing a woman of whom he has told us,

… from the pretty girl whose glowing health, high spirits and brilliant colour had given her attractiveness she was become a beautiful woman. That she owed her beauty in some degree to art, discipline and mortification of the flesh did not seem to matter.

Isabel’s beauty is unnatural. I questioned the possibility of writing naturally, in an essay “On Knowing Ourselves.” Maugham appears to write naturally; but how much of this is due to art, discipline, and mortification of the flesh? As we have seen, he admits to “doing what I can to make my book readable.” He says of Isabel’s uncle,

He was still unwilling to accept such painters as Picasso and Braque—“horrors, my dear fellow, horrors”—whom certain misguided enthusiasts were making such a fuss about, but felt himself at long last justified in extending his patronage to the Impressionists and so adorned his walls with some very pretty pictures. I remember a Monet of people rowing on a river, a Pissarro of a quay and a bridge on the Seine, a Tahitian landscape by Gauguin and a charming Renoir of a young girl in profile with long yellow hair hanging down her back. His house when finished was fresh and gay, unusual, and simple with that simplicity that you knew could only have been achieved at great expense.

At what expense is the simplicity of Maugham’s writing achieved? It may come naturally to him to refer to an unspecified person with masculine pronouns, even though the intended example is the woman whom he is addressing.

Mathematics, Maugham, and “man” are all connected here, at least by me, who never considered myself as warranting a label like ADHD, though I fancy I understand the point of a recent tweet, which at this writing has received more than 39 thousand Likes, one by me:

ADHD is not always “hey look a squirrel”

Sometimes it is “hey look a squirrel I should really stop what I’m doing and look up the etymology of the word squirrel and hey when did it become dinner time did I eat today why am I suddenly an expert in all things squirrels”

— Jennifer Lee Rossman, August 27, 2019

I am concerned not with the etymology of “squirrel” (which comes to us via French and Latin from the Greek σκίουρος, which Liddell and Scott take as a compound of σκιά “shadow” and οὐρά “tail,” although Skeat thinks this may be “popular etymology”); I am concerned with the etymology of “man,” in connection with current concerns about pronoun use and sexism in language.

The Etymological Fallacy is indeed a fallacy. There is no reason to think a word does or even should continue to mean what it once meant. Collingwood had some comments about this in Chapter XXXIV, “What Civilization Means Generically,” of The New Leviathan:

34. 26. Etymology, in fact, is a good servant to the historical study of language; but a bad master.

34. 27. It is a good servant when it helps to explain why words mean what in fact they do mean.

The traditional English term for a first-year student was “freshman.” It was also a tradition that these students would be male. Today, at Mimar Sinan Güzel Sanatlar Üniversitesi, not only are some of our mathematics students female: most of them are. In principle, any one of our first-year students may still be called a freshman, provided the second component of this term is understood to mean simply a human being. Whether “man” can be understood simply in this general way is not clear, even though the generic sense is the “prominent sense” of the word man in Old English (Hoad, “man,” p. 279), this being the language spoken in England before the Norman Invasion of 1066.

In Old English, male and female specimens of the human species were wer and wīf  respectively. Strictly, the latter word was wif ; modern scholars now mark the vowel with a macron, to show length (Smith, §6, page 4). The marking may be useful for distinguishing between words originally spelled the same, such as gōd “good” and god “god.”

The word wīf  became “wife” in Modern English. Meanwhile, wīf  also became part of the compound wīfman, which was first masculine in gender, then feminine (Hoad, “woman,” p. 544). The compound became wimman in the tenth century, with the plural wimmen. We have retained the pronunciation of the plural for today’s “women”; in the twelfth century, the singular wimman became wumman, giving us today’s pronunciation of “woman” (Skeat, “woman,” p. 614).

The Old English wer is cognate with “virile” and is seen in “werewolf.” The word “world” can be understood as compounded from wer and “eld”; the latter is an archaic noun meaning “age” in various senses, derived from the original form of the adjective “old.” The James Brown song “It’s a Man’s Man’s Man’s World” (credited also to Brown’s girlfriend Betty Jean Newsome) is wilfully redundant; but even to say “man’s world” is redundant, etymologically speaking.

I pick up the information about the James Brown song from the Web, especially Wikipedia. Information about etymologies might be considered as common knowledge, obtainable from many dictionaries; I have indicated the actual books that I used by citing the sources of specific points not found (or perhaps not found as prominently) in other sources. I have also looked at the Oxford English Dictionary (Murray), in the “compact” form that, as a freshman at St John’s College, I acquired from a graduating senior who was looking to lighten their load of personal possessions. That book remains in my physical possession in Istanbul, as do all of the other books that I list below.

References