# Googol, googolplex

Lately in reading about modern physics and watching video interviews on contemporary cosmology, the number 10^100 (ten to the power of 100) kept coming up. Well, I found out probably why.

Googol (not Google) is a large number: “In decimal notation, it is written as the digit 1 followed by one hundred 0s.”

A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. … To give a sense of how big a googol really is, the mass of an electron, just under 10^−30 kg, can be compared to the mass of the visible universe, estimated at between 10^50 and 10^60 kg. It is a ratio in the order of about 10^80 to 10^90, or only about one ten-billionth of a googol (0.00000001% of a googol).

Here’s the key reference: “The decay time for a supermassive black hole of roughly 1 galaxy-mass (10^11 solar masses) due to Hawking radiation is on the order of 10^100 years. Therefore, the heat death of the universe is lower-bounded to occur a googol years in the future.”

And then there’s the googolpex, an even larger number: “A googolplex is the number 10^googol, or equivalently, 10^(10^100). Written out in ordinary decimal notation, it is 1 followed by 10^100 zeroes, that is, a 1 followed by a googol of zeroes.”

One googol is presumed to be greater than the number of atoms in the observable universe, which has been estimated to be approximately 10^78. Thus, in the physical world, it is difficult to give examples of numbers that compare to the vastly greater googolplex. However, in analyzing quantum states and black holes, physicist Don Page writes that “determining experimentally whether or not information is lost down black holes of solar mass … would require more than 10^(10^76.96) measurements to give a rough determination of the final density matrix after a black hole evaporates”. The end of the Universe via Big Freeze without proton decay is expected to be around 10^(10^75) years into the future.

So, “physics says what?” — incomprehensible numbers, practically infinite times. Yikes!

See, for example, the “Closer To Truth” video interview “The Physics of Eternity.”