Ok, so i stumbled across a video about Graham's Number which is an upper bound to the number of dimensions a hyper cube can exist whereby if you coloured all its lines using two colours youcannpot avoid having a face all the same colour.
so it is a number that is part of a solution to a mathematical problem.
but the number is huge.
how huge? full write up
https://waitbutwhy.com/2014/11/1000000-grahams-number.htmlsome cliffs:
consider a
googol. 1 followed by 100 zeros.that is pretty big. imagine filling the universe with grains of sand. you could fill the universe with sand 10 billion times over with a googol grains of sand.a
googolplex is 1 followed by a googol zeros. imagine trying to write down the digits of a googolpex : you have the universe filled with grains of sand. you would have to write 10 billion zeros on each grain of sand to be able to fit a numerical representation of a googolplex into the observable universe. it would take two lifetimes to complete one grain of sand.grahams number dwarfs a googolplex.
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you can begin to represent it with arrow notation. let ^ = an arrowe
3^3 = 3 to the power of 3 = 27
3^^3 = 3^(3^3) = 3 to the power of 27 = about 7.6 TRILLION
so adding one arrowe moves the number from 27 to 7 trillion.
what about three arrowes
3^^^3 = 3^^(3^^)
this is 3 with a stack of threes above it 7.6 trilllion threes long.
for compassion a tower of three 3;s is 7.6 trillion. a tower with 7.6 trillion 3's yields a number that is 3.6 trillion diigits long. a googol [the niumber of grains to be able to fill the universe 10 billion times over) is 100 digits long
3^^^^3 leads to a tower of 3's that would stretch to the sun if written down. again to compare about 10 centimeters of that tower would drawf a googolplex. this tower is 150 trillion meters long.
4 arrows is not comprehensible. each arrowe makes the number more unintelligable to our brains and at four arrowes we have gone from 27 to the universe not being big enough to contain the number, literally or poetically.
but 3^^^^3 is only the start of grahams number:
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let 3^^^^3 = G1 : a terrifying number that we cannot describe
G1 = the number of ARROWS between the 3's : 3^^^^G1^^^3
and that = G2 which is the number of arrows between the 3's in G3 etc etc
grahams number = G64
we don't know how many digits are in this number. the universe could not contain the number of digits of the number which describes the number of digits in the number which describes the number of digits Grahams number. you can iterate that by the number of atoms in the universe before you get to a number that would fit into the universe.
crazy crazy number.
BUT
we know it is an odd number. and we know it ends in a 7
and the lower bound of the n dimenisions in the problem = 12
so somewhere between 12 and Graham's Number = the answer to the problem he was trying to solve
maths eh, bloody hell
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