I am currently reading Yuri Manin’s book of essays, Mathematics as Metaphor, a translation published by the American Mathematical Society.
I may have more to say about this lovely book later. But my first impression is that it has not been well served by either the copy-editor or the typesetter. Here is one example.
On page 13, Manin quotes K. Chemla on the Chinese mathematics book The Nine Chapters on Mathematical Procedures (the title is sometimes translated differently), published during the Han dynasty. He says that one of the duties of the bureaucracy at that time was “renumerating civil servants”. I supposed at first that he simply meant “remunerating”. But perhaps “enumerating” also makes sense, in a large but very widely dispersed bureaucracy. (Even the problem of enumerating civil servants in modern Britain seems to cause some controversy, due in part to the blurring of the line between public and private enterprise.)
However, let’s take it at face value. Suppose that you have counted some collection of objects, and you want to re-count to check your result. My guess is that you probably don’t do the count in the same way, but count in a different order, or group the objects differently.
There is a potentially interesting problem here: how should you renumerate so as to maximise the chance of correcting an error if one occurred? Counting in the same way is not the answer, but the reason is not mathematical. Our thought processes get into grooves, and counting the same way has a fairly high probability of reproducing the same error that occurred first time round. So the problem is not just mathematical or statistical but has elements of neuropsychology in it as well.
This ties in with another book I have just finished reading, Sasha Borovik’s Mathematics under the Microscope, which I may also say something about later . . .