Yay, More Graphs; More Graphs, Yay!

july 9th, 2008 at 11:44 pm

These graphs have been making the rounds lately, so I thought I'd share. Sam Harris made them, and he writes books. So there.

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Thanks, Wikipedia!

july 6th, 2008 at 12:30 am

So I was reading about set theory today on Wikipedia and I thought I'd share.

First of all, reading about math on Wikipedia is generally a terrible idea because, like the science articles, the subject matter tends to be written by people who assume two things: familiarity with mathematical jargon and a certain amount of prior knowledge that only mathematicians usually have. I mean, just look at the list of set theory topics Wikipedia has articles on. Most of those articles are a couple pages long, too. I ended up reading a lot about this guy Georg Cantor, who pretty much invented set theory. My favorite theory of his is Cantor's First Uncountability Proof, so that's what I'll focus on. The basic gist of the theorem is that the real numbers outnumber the natural numbers, i.e., more than infinity real numbers exist. Or, if you prefer math-speak:

• There is no injective function from X to the set of natural numbers.
• X is nonempty and any ω-sequence of elements of X fails to include at least one element of X. That is, X is nonempty and there is no surjective function from the natural numbers to X.
• The cardinality of X is neither finite nor equal to א₀ (aleph-null, the cardinality of the natural numbers).
• The set X has cardinality strictly greater than א₀.

They way he proved this is really clever, but Wikipedia does a really poor job of explaining it. Observe:

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Wow

june 20th, 2008 at 10:59 pm

So I was playing around with SensibleUnits.com, and came to some startling conclusions:

YouTube moves 322 PB (petabytes) per month — that's 3,870 PB/year

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