Tuesday, July 18, 2017

A Disinclination for Mathematics

I have always had my doubts about writers who boasted, or seemed to boast, of their incompetence in mathematics. Henry James, Ford Madox Ford, and Robertson Davies come to mind. A passage in the first section of James's Notes of a Son and Brother runs for example
 I so feared and abhorred mathematics that the simplest arithmetical operation had always found and kept me helpless and blank--the dire discipline of the years bringing no relief whatever to my state...
Ford I recall as putting it more whimsically, Davies more plainly. But the message is the same. I was therefore struck by a passage noticed the other day in The World as Will and Representation, Third Book, Section 36:
The disinclination of men of genius to direct their attention to the content of the principle of sufficient reason will show itself first in regard to the ground of being, as a disinclination for mathematics. The consideration of mathematics proceeds on the most universal forms of the phenomenon, space and time, which are themselves only modes or aspects of the principle of sufficient reason: and it is therefore the very opposite of that consideration which seeks only the content of the phenomenon, namely the Idea expressing itself in the phenomenon apart from all relations. Moreover, the logical procedure of mathematics will be repugnant to genius, for it obscures real insight and does not satisfy it; it presents a mere concatenation  of conclusion according to the principle of the ground of knowing. Of all the mental powers, it makes the greatest claim on memory, so that one may have before oneself all the earlier propositions to which reference is made. experience has also confirmed that men of great artistic genius have no aptitude for mathematics; no man was ever very distinguished in both at the same time. Alfieri relates that he was never able to understand even the fourth proposition of Euclid.
Well, perhaps. On the other hand, in the first book, section 15, Schopenhauer writes that
In our view, however, this method of Euclid in mathematics can appear only as a very brilliant piece of perversity.... We see that such a method is like that of a wanderer who, mistaking at night a bright firm road for water, refrains from walking on it and goes over the rough ground beside it, content to keep from point to point along the edge of the supposed water.
Would Alfieri have made more progress with a better text?

There are writers I prefer to Ford and Davies, if not necessarily to James, who were competent in mathematics. Stendhal was briefly fond of mathematics in his youth. Novalis wrote some pages in praise of mathematics that might or might not reflect considerable knowledge. I suspect that Tolstoy, as artillerist, and Chekhov, as physician, must have picked up at least the rudiments, and likewise Eliot and Stevens as businessmen. Still, perhaps I should not roll my eyes the next time I encounter the anti-mathematical writer.


  1. Schools have taken to teaching something called consumer math rather than more demanding math courses. Not everyone can grapple with anything more complicated than consumer math. For example, I struggled with algebra and barely passed those courses. I believe some people have no aptitude for the subject.

    1. It seems to me that consumer math might properly be taught by middle school, being--if I understand what it means--simply arithmetic.

      A college friend insists that I helped her with the algebra she needed to pass then. I guess I could have done so, but I have no recollection if so. I suspect that more people could understand algebra than do; but good math teachers are uncommonly rare.

  2. Postscript: BTW, I tried algebra again in college with similar disappointment.

  3. Perhaps such people have a helpful splash of autism (that is, we're all on a spectrum, and maybe they're a teeny bit more toward the Aspie/autism place on the line) to make them want to do only what they want to do and also to have a complete lack of interest in those things that are alien to what they want to do. If strongly obsessive about one area, a person tends to be uninterested in pursuits that have nothing to do with that area.

    On the other hand, my father was an analytical chemist who published in his field but also wrote poems and novels for pleasure. I did not have a similar combination of interests....

    1. They clearly have an ability to focus that most of us have only intermittently and in short bursts. I don't think that it much resembles autism, but I'm not a psychiatrist, and have met few enough artists.