Tuesday, November 24, 2020

Numbers with personality

I think Ramanujan's friendliness with the natural numbers is a different sort of friendliness from that described in Major's paper. Ramanujan was so well acquainted with numbers that he knew their mathematical properties and quirks in the same way that people know their friends, but the essence of this knowledge was mathematical. What Major describes is something else: an association of non-mathematical properties to numbers for non-mathematical reasons, such as the sound of the word, the shape of the symbol, or synesthesia. It's possible that Ramanujan made these sorts of associations too (perhaps as a mnemonic), but the anecdote about 1729 isn't an example of this.

I don't think this is the sort of thing I would introduce very much in my classroom, because I don't find myself focusing on individual numbers very much. I tend to look at the relationships between numbers rather than the numbers themselves (and the curriculum seems to as well). On the other hand, I do sometimes make offhand remarks about, for example, 24 being a "nice" number because it has a lot of factors, or 51 being a strange number because it seems like it should be prime but isn't. I don't think I'll make this a focus of my class though.

Another exception for me could be the famous constants: pi, Euler's number, the square root of two, etc. I can't think of personalities or qualities that I associate with these, but because of their distinct uses I could see myself associating more things with them, and using that in the classroom. 

In general, though, I'm not much for personification. The few associations I do make for numbers, days, and months are based on the mathematical properties of numbers, the things which usually happen on those days, and the weather of the months. I don't have the type of creativity that associates personalities to concepts willy-nilly, but I appreciate the people who do!

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