I didn’t do any blog writing this week, because of reasons. The good news is I’ve got a growing list of blog posts to get around to, the bad news is a decreasing amount of free time. Probably no post next week either. Anyway, here’s the obligatory list of some things I think are cool.

This calculus teacher got his students excited about math in a clever way. Yay math! And yay educators! They calculated the size of the dating pool as a function of age to find when it’s largest. Apparently the answer is 42. Also he links to Hyperbole and a Half, which automatically makes him cooler.

I bragged about this on Facebook and Twitter, so I should probably post it.

All even perfect numbers are of the form p(p+1)/2, where p is a Mersenne prime. So p=2^k-1 for some k. Therefore, for any even perfect number there is a positive integer k such that

n=(2^k-1)(2^k-1+1)/2=(2^k-1)*2^(k-1)

=2^(2k-1)-2^(k-1)

That implies that each even perfect number is more than twice the size of the previous one.

Replace k with k+1, you get 2^(2k+1)-2^k. That’s the smallest possible size of the next biggest perfect number.

Doubling a perfect number gives 2^(2k)-2^k, which is smaller than that. So every even perfect number is more than double the previous one. The sum of two numbers must be less than double the larger one, so perfect plus perfect equals not perfect. I call it Galinda’s Theorem. (This proof might not work in the unlikely event that odd perfect numbers exist, but Galinda would deny being odd anyway.)

The puns over here are much less forced than that. This is a chart of what words mean to non-philosophers and philosophers. It’s only funny if you’ve heard some of the words, but you’re probably familiar with “logic” and “utilitarianism” and some of the others.

Cleverness is fun to read about, so click here and read a fairy tale in which the protagonist wins through application of knowledge of economics.

Paul Ebert was, by all the hilariously one-sided accounts I’ve read, a pretty sucky dude. Little things like threatening to have witnesses killed unless they testify falsely to convict someone else of murder. But the other, much funnier, thing I want to mention is that he once won an election against a ham sandwich.

Good news: Using the word “whom” is apparently considered attractive. As a part of the pro-”whom” lobby, I hope this leads to more people using it correctly. Bad news: It’s considered attractive even if it isn’t used correctly.

The linked post is uncomfortably misogynist and its statistics are subpar. They say it doesn’t matter if the pronoun is used correctly or not, but I’d bet the effect is larger if it’s used correctly. I doubt there are people who actively prefer the word to be misused, and I know there are people who prefer it being used correctly.

”Human” is an incredibly specific word that narrows down the space of all possible people by a lot. It always annoyed me how a typical human uses “everybody” to mean “a typical human.” So I enjoyed this tumblr conversation about how humans are totally terrifying from points of view that don’t start from the assumption that humans are normal. The third text block is especially good.

And, best for last, someone needs to call in the Magratheans. I’ve always wondered if this was possible, and apparently it is not only possible but awesome…. You can have habitable Earthlike planets in the shape of a donut! Differing strengths of gravity based on where on the surface you are. Incredibly high mountains and awesome moons. This person even calculated the seasons and weather, and yes; those are cool too. Sunrises and sunsets happen much faster and more often. And the effect that we call the Northern Lights happens over a much wider area. I want to move there.

Roxolan“I doubt there are people who actively prefer the word to be misused, and I know there are people who prefer it being used correctly.”

Throwing hypotheses at the wall: maybe there are some exceptionally sexy uses of “whom” that happen to be grammatically incorrect, which the average recipient doesn’t notice. Also, there must be some people who’ve learned incorrect “whom” rules, though they’re almost certainly a minority. (This doesn’t make Slate any less wrong.)