Monday, August 01, 2005

Thinking big

For some time my six-year-old son has been obsessed with the googolplex (the impossibly large number, not the Googleplex, the corporate HQ for Google). He had a passing interest in infinity, but it was a little too abstract to hold his attention. But for him the googolplex has the virtue of making the incomprehensible mathematically concrete. And you know something, it is a pretty friggin' big number:

A googol is greater than the number of particles in the known universe,which has been variously estimated from 10^72 up to 10^87. Since this is less than the number of zeroes in a googolplex, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, 1-point font. TeX 1pt font is .3514598mm per digit, which means it would take about 3.5 * 10^96 meters to write in one point font.

The known universe is estimated at 7.4 * 10^26 meters in diameter, which means the distance to write the digits would be about 4.7 * 10^69 times the diameter of the known universe.