I love it. Really interesting stuff. Related:
Carl Sagan estimated that writing a googolplex in numerals (i.e., “10,000,000,000…”) would be physically impossible, since doing so would require more space than the known universe provides.
An average book of 60 cubic inches can be printed with 5 × 105 zeroes (5 characters per word, 10 words per line, 25 lines per page, 400 pages), or 8.3 × 103 ‘0’s per cubic inch. The observable (i.e. past light cone) universe contains 6 × 1083 cubic inches (1.3 × π × (14 × 109 light year in inches)3). This implies that if the universe is stuffed with paper printed with ‘0’s, it could contain only 5.3 × 1087 ‘0’s—far short of a googol of ‘0’s. In fact there are only about 2.5 × 1089elementary particles in the observable universe so even if one were to use an elementary particle to represent each digit, one still would require the universe’s volume about a trillion times larger. Therefore a googolplex cannot be written out since a googol of ‘0’s cannot fit into the observable universe.
The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around about 1.51 × 1092 years, which is 1.1 × 1082 times the age of the universe, to write a googolplex.[2]
i love theoretical physics!
