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Who’ll win, Al Gore or George W. Bush? Let me explain why my statistical model proves Al Gore is gonna be Mr. 43. Oh, wait– the election was a decade ago, argh. So much for my 10,000 word essay! When it comes to politics, the longer you hold off, the better the return you get [...]

Skills are specific things we know how to do, like how to make origami, how to weave, how to paint, and so on. They are generally things you learn by doing, rather than by reading about in abstract. Sure, you can gain knowledge about them by reading general theory, but you have to actually get [...]

“If it turns out P=NP, cryptography will break, and all kinds of practical problems will become easy” I can see why people like to speculate this sort of thing: it makes a compelling narrative. It’s just not accurate. If somebody proves P=NP, then maybe cryptography will break and computation power will jump by a few [...]

Casa Blanca was a boring movie without a lot of action, but Star Wars, man did that have some great light saber fights. I’m speaking here, of course, as a kid: to see how children understand language, you need look no further than your own memory, specifically, your memory of movies and video games from [...]

I was never a big swimmer when I went to the gym, but this Summer, my girlfriend and I moved to an apartment with a pool, and I’ve fallen in love. How did I go this many years without realizing what an amazing workout swimming is? It’s like a machine which hits every muscle equally, [...]

Zorn’s Lemma is one of the most beautiful and subtle axioms of mathematics. It is equivalent to its better-known sister, the Axiom of Choice, but in a certain sense, Zorn is the stronger statement– it’s certainly the more “mystical”. A mathematical joke goes: “The Axiom of Choice is obviously true, the Well-Ordering Theorem is obviously [...]

Truth, no matter how inconvenient, is more beautiful than fiction. An Echo Chamber is a community based around a subjective set of assumptions, which never questions those assumptions, and twists everything into supporting those assumptions. It can be useful and profitable to spend some time in such a community, because of the unique lens they [...]

René-Louis Baire His “Baire space” and “Baire Category Theorem” help us understand topological spaces whose complements are very bare. George Cantor Taught us how to count infinite sets. Carl Friedrich Gauss Made a pretty good guess at how many primes there are below x. Also, some stuff about statistics. Kurt Gödel Played God by applying [...]

A subtle distinction in math is that between infinitely large things and arbitrarily large things. Suppose we have a set of elements, and each element has some “size”, where the sizes are allowed to range over the nonnegative numbers along with “infinity”. If one of the elements does happen to be infinite, then that implies [...]

Lately I’ve been studying a multi-parent analog of trees. A mathematical tree can be thought of as the family tree for an asexual species where each node (except the root) has exactly one parent. In the “trees” I’m looking at, instead of a root, there’s a finite set of “xatriarchs” (e.g. matriarchs and patriarchs but [...]