Which is Bigger – The Number of Atoms in Universe or Complexity of Go?

go-game

The board of Go Game has 19×19 lines. Players place stone on the line intersections. Therefore the complexity of all state space is 3^³⁶¹ because each intersection could have three 3 possibilities: black, white or nothing.

Researchers have estimated the number of Atoms in universe is somewhat between 10^⁷⁸ to 10^⁸² [Ref] let’s assume it is 10^⁸⁰.

So, which is bigger?
Of course, with the help of computers, these two numbers can be calculated first and then compared. But we human don’t (and can’t) calculate the actual values of both. Instead, we do a little math here.

Let’s denote N is the number of atoms in universe i.e. 3^³⁶¹ and M, the all state space complexity of Go i.e. 10^⁸⁰. We know which is bigger if we compare the value of M/N with one.

Let’s take lg(M/N), we know that equals lg(M)-lg(N) so

  lg(3^361) - lg(10^80)
= 361*lg(3) - 80*lg(10)
= 172.24 - 80
= 92.24 

Therefore, M/N = 10^92.24 that means M is a lot larger than N! The Go State complexity is way more huge than the number of atoms in universe. Even the computers cann’t bruteforce all the possibilities!

Feature Comment

Interesting. Consider the other side though. If judging the size of complexity, it’s not simply how many options there are. You can create a model that would allow you to “find” any particular version of the game without needing to store each one. It would be a much much smaller and simpler model than one that allowed you to find each atom of the universe.

I guess though… we’re judging complexity against the number of atoms, not complexity of atoms! Even the smallest amount of complexity is bigger than any definable number, so Go still wins!

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