Balliol Croft, Cambridge
27. ii. 06
My dear Bowley,
I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you: and I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have forgotten even how to integrate a good many things.
But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules---(1) Use mathematics as a short-hand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in 4, burn 3. This last I did often.
I believe in Newton's Principia Methods, because they carry so much of the ordinary mind with them. Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature---and I have come across a good deal of that---seems to me an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English language is as short as the Mathematical. ....
I find mathematicians almost invariably follow what I regard as Jevons' one great analytical mistake, his eulogy of the Geometric mean in general: and do not see that, according to his use, erroneous weighting may do far more mischiefwith the Geometric Mean than with the Arithmetic Mean. I always have to spend some time in convincing them of the danger.
Another trouble is that mathematicians insist on assuming that, if p be the price which may vary to pr or p/r, then the two variations are prima facie to be assumed to be equally probable. Whereas, of course, if r is a considerable quantity, that is not true: Jevons has overlooked this also, I think, as a result of not thinking in English. But of course you know far more about these things than I do: and again I say I am an unprofitable Servant.