“Show me who your friends are, and I will show you who you are.”
(Russian saying, in Karen Ehman’s Keep it Shut)
What is this dreaded thing called continuity, forcing a poor student like you to learn about infinity, limits and all sorts of wacky symbols?
Continuity is like peer pressure. If your neighbourhood is badness and you succumb to peer pressure, you’re no good either unless you’re a measure zero discontinuity way above your neighborhood. I recall a secondary school Chinese text 《愛蓮說》(Ode to the Lotus, literally, ”love-lotus-speak“)。 The line 「出淤泥而不染」means “[the lotus is] born of the grimy dirt yet is untainted”. In writing this, the author and philosopher Zhou Dunyi (周敦頤) praised the lotus for being unspotted from the world around it, that it is a singleton of beauty in an ugly pond. If I too have such force of character that my relational point-set topology is a singleton, I’m still continuous – trivially. 🙂
I have just lent the idea of “continuity being like peer pressure” to a mainland Chinese scholar (Qun, LIN 林群), who is passing by my university [for his mathematical talk 微積分動漫版†] and posited that calculus be taught in terms of ratios of measurement to reality being 0.9, 0.99, 0.999 approximating 1. “So, every day we work, we add a 9 to the end of our work, and we improve.”
I didn’t know that the mainland Chinese academia, like my English-speaking Twitter audience, also values math education and popularisation, and the importance of STEM. Whatever conveniences we enjoy today, such as procrastinating on F.T.I, come from the blood, sweat, toil and tears of scientists and engineers who made the day we call “today” possible. It is thus exceeding treachery to teach horribly our STEM knowledge to our next generation, so horribly that they’d rather skip the meaningless calculations and leap into more down-to-earth subjects like law* and the arts and humanities, drowning STEM in a sea of irrelevance, ignorance and romanticism. More on these ideas later, for if I ramble on, I’d sound like a page from an 18th century book…
† I think you may translate the title of Professor Lin’s talk as “Calculus in action”, but we Chinese could also interpret it as “The Anime Version of Calculus”. However it turns out to have nothing to do with the cutesy and shocking motion picture called Japanese anime! No wonder I spotted students falling asleep. They probably wanted to know about this book instead! Thanks Murray Bourne for reviewing the Linear Algebra version though.
* Math Forum has two excellent articles on why lawyers need math. In fact the Math Doctors could add that Pierre de Fermat, of his Last Theorem’s fame until Andrew Wiles shared it, was a lawyer. In Hong Kong, if you have great grades, you’d prefer to study law, business or medicine instead of mathematics in university – the two exceptions I know are Martin Li, a new math professor at my university specialising in geometric analysis, and my classmate Peter Chan, who got 5 A’s in the very last A-Level examination in Hong Kong in 2012 and is now investigating mathematical physics. It’s intimidating, yes, but sometimes it feels cool to be a contemporary of great people, and both of them are friendly.