Maths in Freedom Struggle, and Love

In his book, The Joy of x, Steven Strogatz points out every field of maths has “one notoriously difficult topic”:

“In algebra, it’s word problems. And in geometry, it’s proofs.”

The reason why proofs are so hard is because it’s usually the first time in their life a student has to prove something. Everything until then was always “because I said so”, be it from the teacher or the parents…

 

With hindsight, with the benefit of life and experience, (some) adults look back at proofs in a different way, as something relevant to areas of life far beyond “triangles, circles, and parallel lines”:

“It trains you to think clearly and logically… What’s important is the axiomatic method, the process of building a rigorous argument, step by step, until a desired conclusion has been established.”

 

Half tongue-in-cheek, he cites the American Declaration of Independence as an example. Thomas Jefferson wrote, “We hold these truths to be self-evident”, and listed the basic things all people are entitled to. And from those, he “derived” the conclusion that the (British) colony of America had the right to govern itself, “as inevitable as a fact of geometry”!

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In another part of the book, he talks of love. Yes, in a book on maths! Based on the “tumultuous ups and downs” part of love, he takes a slightly contrived scenario where one person’s love increases and decreases in proportion to his partner’s responsiveness. His partner, weirdly though, reacts in the opposite way: she’s increasingly put off the more he loves her, and attracted when he shuns here. Such scenarios are perfectly expressed by differential equations, he jokes, which can then be solved.

 

Problem solved? Not entirely. In our author’s case, it turned out:

“There was an important variable that I’d left out of the equations – her old boyfriend wanted her book.”

To the author, problematic though it was, the situation now reminded him of an un-solve’able problem in maths: the three-body problem! What’s that? Newton ran into this problem soon after he formulated his famous theory of gravity, using which he could explain why planets move in slightly elliptical orbits. But add the moon into the equation, and you have three bodies (sun, earth, and moon):

“He couldn’t solve it, and neither could anyone else.”

Nobody knew it at the time, but the three-body problem “contained the seeds of chaos, rendering its behavior unpredictable in the long run”.

 

Just like love, our author reminds us.