This is closing out a busy week’s worth of comic strips mentioning some mathematics theme. Three of these are of extremely slight mathematical content, but I’ll carry on anyway.
Reza Farazmand’s Poorly Drawn Lines for the 8th has a bear admit the one thing which frightens him still is mathematics. It adds to it a joke showing that he’s not very good at mathematics, by making a mistake with percentages.
Will Henry’s Wallace the Brave for the 8th has Wallace working out an arithmetic problem in class.
Dana Simpson’s Ozy and Millie rerun for the 9th is part of a sequence of Ozy being home-schooled. The joke puts the transient nature of knowledge up against the apparent permanent of arithmetic. The joke does get at one of those fundamental questions in the philosophy of mathematics: is mathematics created or discovered? The expression of mathematics is unmistakably created. There is nothing universal in declaring “six times eight is forty-eight” and if you wish to say there is, then ask someone who speaks only Tamil and not a word of English whether they agree with exactly that proposition.
But, grant that while we may have different representations of the concept, it is the case that “eight” exists, right? We get right back into trouble if we follow up by asking, all right, will “eight” fit in my hand? Is “eight” larger than the weather? Is “eight” more or less red than nominalism? I chose nouns that made those questions obviously ridiculous. But if we want to talk about a mathematical construct existing, someone’s going to ask what traits that existence implies. It’s convenient for mathematicians, and good publicity, for us to think that we work on things that exist independently of the accidental facts of the universe. But then we’re stuck when we’re asked how we, stuck in the universe, can have anything to do with a thing that’s not part of it.
Not mentioned in this particular Ozy and Millie strip is that the characters are Buddhist. The (American) pop culture interpretation of Buddhism includes an emphasis on understanding the transient nature of … everything … which would seem to include mathematical knowledge. Still, there is a long history of great mathematical work done by Buddhist scholars; the oldest known manuscript of Indian mathematics is written in a Buddhist Hybrid Sanskrit. The author of that manuscript is unknown, but it’s not as if that were the lone piece of mathematical writing.
My limited understanding is that Indian mathematics used an interesting twist on the problem of the excluded middle. This is a question important to proofs. Can we take every logical proposition as being either true or false? If we can, then we are able to prove statements by contradiction: suppose the reverse of what we want to prove and show that implies nonsense. This is common in western mathematics. But there is a school of thought that we should not do this, and only allow as true statements we have directly proven to be true. My understanding is that at least one school of Indian mathematics allowed proof by contradiction if it proved that a thing did not exist. It would not be used to show that a thing existed. So, for example, it would allow the ordinary proof that the square root of two can’t be a rational number; it would not allow an indirect proof that, say, a kind of mapping must have a fixed point. (It would allow a proof that showed you how to find that point, though.) It’s an interesting division, and a reminder that even what counts as a logical derivation is a matter of custom.
Peter Maresca’s Origins of the Sunday Comics for the 9th reprints The Troubles of Noah, a comic strip drawn by James Swinnerton and originally printed the 21st of July, 1901. And this is really included just because it depicts a monkey at a typewriter, a dozen years before Émile Borel created the perfect image of endless random processes. (Look to the lower right corner, taking dictation from Noah.) There’s also a bonus monkey setting type in the lower left.
That’s finally taken care of a week. Time to take care of another week! When I have some of last week’s comic strips written up I will post the essay at this link. Thanks for reading.