2018-11-21
Here's links to Wikipedia and a numberphile video. And you'll also need to understand the up arrow notation, so here is a link to that.
Graham's number is basically an enormous number that solves a combinatorics problem. If you've understood a) what the combinatorics problem is, and b) how Graham's number is defined, you've pretty much understood everything there is it to it.
Or atleast everything mere mortals can understand. Because it still makes no sense, a not-that-complicated problem producing sucha huge number.
So one of the things I like to do with a random person (usually someone with some interest in maths) is first try to explain the problem that Graham's number solves as best as I can in simple English, and then ask them to blindly guess how many dimensions must my hypercube have for this to work?
And then they'll be 5, I'm like nope, more than that. 500? Nope, more than that. A trillion? More than that. 10^100 (a googol)? No, more than that. 1 followed by 10^100 zeroes? Nope not enough.
At this point I gotta explain the arrow notation to them, and ask them to resume guessing ...
10 arrow arrow arrow 10? Nope. 10 followed by a thousand arrows followed by 10? Nope. 10 followed by a googol arrows followed by 10? Nope, not even close.
By now pretty much anyone would give up ... At which point I explain the g sequence and ... Graham's number.
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