Facts for September 23-25, 2008 – cleaning out the noggin’

Damn I’m busy these days.  Guess that’s what I get for teaching an overload (in a different department, no less).  Anyway, here’s a couple days worth of useless trivia from my overstuffed head:

– The famous mathematician Georg Cantor noticed that there, in fact, are different “sizes” of infinity.  Take, for example, all the natural numbers, N.  They are, of course, 1, 2, 3, 4, 5, 6, 7, 8, … and so on.  We intuitively know that there are an infinite number of them.  Now consider all the even numbers, 2, 4, 6, 8, 10, … and so on.  Clearly these are also infinite.  But notice that we’ve plucked out every other member of our first set, so it seems as if the first set ought to be bigger than the second.  This is what Cantor noticed and then formalized.

– Antarctica is technically the world’s largest desert.  It is the world’s driest place, receiving an annual average of less than two inches of precipitation, and is a whopping 5.5 million square miles (well, it is a continent, after all).  Outside the polar regions, the largest desert is the Sahara in Africa which is 3.5 million square miles.

– The Greek philosopher Socrates, unlike Plato and Aristotle who were landowners (and thus gentlemen farmers), was a stonemason and likely contributed to the building of the Parthenon.

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