| abstract | - Promaxima, short for "probability maximum", is a physical constant approximately equal to \(10^{10^{245}}\). It is an upper bound on the number of different possible parallel universes taking only into account our observable universe. The term was coined by Sbiis Saibian in 2004, in response to an anonymous contributor, who wrote: So I was thinking about large number which actually could possibly somehow correspond to actual real physical world phenomena. Like this. So take the entire space of the universe, and imagine that it was filled *solid* with atoms or subatomic particles. The number of those particles would be huge, I wonder what it'd be. But, now, what about all possible permutations of those particles in space. I guess that'd be N! [referring to the factorial] where N is the number of particles. Someone figure out the number! It's gotta approach or exceed Googol, or even Googolplex. Yathink? Saibian solved this problem by packing the observable universe with "strings," the smallest possible physical objects. These are \(10^{-35}\) meters long, and the diameter of the observable universe is \(10^{26}\) meters. Packing the universe, then, takes \(\left(\frac{10^{26}}{10^{-35}}ight)^3 = 10^{183}\) strings. (Note that our universe is not packed with strings; therefore this number is an overestimate.) The number of arrangements of these strings is then \(10^{183}!\), approximately \(10^{10^{185}}\) (using Stirling's approximation). Saibian took this a step further by introducing time. The number calculated above is only the number of the strings in a single Planck time, or about \(10^{−43}\) seconds. Letting the universe run for 500 quadrillion years, the number of possibilities becomes \(10^{10^{245}}\). Promaxima is a good bit larger than googolplex.
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