[applfanboysbgon]

> the sentence "a monad is a monoid in the category of endofunctors" is pretty much impossible to represent in a script like egyptian heiroglyphics or this one

单子是自函子范畴中的幺半群

It bears remembering that spoken language existed long before written language, and written language developed as a form of encoding spoken language. Purely pictorial communication utilises a small number of large symbols that make it clear what is being conveyed from pictures alone, but the language depicted is too complex and abstracted to be purely pictorial; it uses a great number of small symbols, and you cannot understand what it is trying to convey merely by looking at it as a series of pictures. For a reader to understand what is written there would require understanding the relation of symbols to spoken language.

[jeltz]

> and written language developed as a form of encoding spoken language.

Do we know that it did? As far as I gather early scripts seems to have first been used only (or primarily) for accounting and then that system for accounting was adapted to also be able to express spoken language. But I agree with your main point. This language looks too complex to just be for accounting and likely can express everything the spoken language could and likely was closely connected to the spoken language.

[thaumasiotes]

Somehow it bothers me that mon- has been translated as "alone" in 单子 ("monad") but as "one" in 幺半群 ("monoid").

[eszed]

There's a relationship between the concepts: if you are alone, you are necessarily the only one there.

[thaumasiotes]

The Greek word meant "alone". Thus an oligarch rules in company with a small group of other people, but a monarch rules alone.

Internal to Greek, mon- was the conventional prefix for a meaning of "one", despite the word for "one" being different. This didn't happen in Latin, where the numeric prefix uni- ["one"] derives from unus ["one"] and not from solus ["alone"].

The Chinese terms have preserved a robust distinction between "one", the number, and "alone", the state of being. It's a strange choice, though, to offer different translations for the same concept in two closely related words. That distinction isn't in place in the original words.

[eszed]

I was aware of the Greek - but (sadly) didn't study Latin, so thanks.

I may not have understood your point, though. Do you object to this particular translation (which seems fine to me? Basically, "[thing] is singular [in this set]"), or just that English is a cursed bastard of a language - which, you know, means dragging in the Latin-derived "singular" along with the Greek mon- words might have been the simplest, albeit even more impure, route to clarity. (I'm reminded of AE Houseman's sniffy distaste for the word "homosexual": "half-Latin, half-Greek? That'll never do.")