Chris J Cowan

A recent xkcd comic brought to my attention the Collatz conjecture. It goes like this. Take any number, like 5. If the number you pick is even, divide by 2. If it’s odd multiply by 3 and add 1. For our number 5, since 5 is odd we get 3 * 5 + 1 = 16. Now apply the rule to the the number we got, and keep doing this. Starting with 5 we’d get 5, 16, 8, 4, 2, 1, etc. The conjecture is, and by conjecture we mean there’s no proof, if you apply this process to any number you’ll reach 1.

Now you might say, “What’s the big deal?” Yeah, it’s not impressive at first. The math involved is simple. But there’s no proof that you’ll always reach 1. And what’s more, the mathematician Paul Erdős, who published more papers than any other mathematician in history, said “mathematics is not yet ready for such problems”. Wow. Just wow.

Anyway, wrote some Haskell code to play around with the conjecture. It’s online here.

What follows is an old essay I wrote for an college math class.

Alan Turing was born 23 June 1912 in England. He did not see much of his parents though because they lived in India; his father was in the Indian Civil Service. There was not much time for personal attention from adults, so Turing was an independent character. He was a bright boy, he taught himself to read at the age of three, but he never liked the rigor of school as he only did well in what he was interested in. His learning abilities did not help him for he scored poorly in his school work. He was very withdrawn, anti-social, clumsy, and disorderly. As Andrew Hodges, Turing’s biographer, put it

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