It's pi day, a day to remember that the ratio of a circle's circumference to its diameter cannot be expressed as the root of any polynomial
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Replying to @arthur_affect
It's one small way in which what seem to be basic facts about the world we live in don't make sense according to our intuitions
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Replying to @arthur_affect
The Pythagoreans were driven mad by the discovery that something as simple as the diagonal of a square couldn't be expressed as a ratio
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Replying to @arthur_affect
And pi is a transcendental number which means it makes even less sense than the square root of 2
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Replying to @arthur_affect
In Carl Sagan's Contact he said the decimal representation of pi contains hidden in it a message for the human race in binary code
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Replying to @arthur_affect
This conceit seems absurd and yet if pi is a "normal" real number then that message does exist somewhere in it as do all strings of digits
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Replying to @arthur_affect
Proving whether pi is "normal" - or any computable real number is - is a great unsolved mathematical problem
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Replying to @arthur_affect
But it would be more weird if pi didn't contain the message than if it did
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Replying to @arthur_affect
At the same time the odds that we would find the message within the lifespan of the entire universe are infinitesimal
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Because if the decimal representation of pi is truly infinite that means knowing a quadrillion digits is the same as knowing zero digits
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