Jul 052012
 

The number of galaxies in the observable universe = 10^12

10000000000000

The number of grains of sand to fill an average office = 5×10^13

50000000000000

Meters from the earth to the edge of the observable universe = 4.3×10^26  (46 billion light years )

4300000000000000000000000000

Meters in the observable universe = 8.8×10^26  (92 billion light years)

8800000000000000000000000000

The number of particles (baryons) in the observable universe = 10^80

10000000000000000000000000000000000000000000000000000000
00000000000000000000000000

The number of grains of sand to fill the observable universe = 10^90

10000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000

A googol = 10^100

10000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000

The number of possible chess games (Shannon’s Number) = 10^123

10000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000
0000000000000

Number of plank volumes in the observable universe = 10^183

100000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000
00000

A googolplex = 10^(googol)

[there is not enough space in the universe to write this number down, even if each digit were the size of a subatomic particle]

Graham’s number = ?

(This number, the solution to a real, applied math problem, is too large for scientific notation so we need to invent a new way to write it down)

let us say that 3^^3 = 3^3^3 = 7625597484987 (a puny number in our collection)
such that 3^^^3 = 3^^3^^3 = 3^^7625597484987 = 3^3^3^3^3^….^3
where  the number of 3’s in the stack is = 7625597484987
(note: if we were to calculate this tower of powers of 3 (which is 7 trillion 3’s tall)
even the number of digits in this number would be way more than a googleplex)

and so, 3^^^^3 = 3^^^3^^^3 = 3^^^(3^^7625597484987)  = 3^^3^^3^^…^^3
where  the number of 3’s in this new stack is = 7625597484987
(remember, each 3^^3 = 7625597484987)
so now we are talking about the number:
7625597484987^7625597484987^…^7625597484987^7625597484987
where this stack of powers of 7625597484987 is 7625597484987 high

now, let us call this last number g1, such that g1 = 3^^^^3
and then let us say that g2 = 3^^^…n…^3 where (n) = g1
and that g3 = 3^^^…n…^3 where (n) = g2

and so on…

such that Graham’s Number = g64


 Posted by at 2:57 pm

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