Wednesday, October 01, 2008

Now that's what I call quite big...

Philip kindly sent me this little link to Google's "2001 Index" part of their 10th Birthday doings. Why not visit and look up things that aren't on it? Anyhoo, all of this Google related such-n-suchery got me to thinking, and brought me round to the subject of this post, which, started out with the humble googol, and, well it ended up... well, I'm just going to have to cut and paste this in by way of the mighty Wiki...

How big is a googolplex?

One googol is presumed to be greater than the number of elementary particles in the observable universe, which has been variously estimated from 1079 up to 1081. A googol is also greater than the number of Planck times elapsed since the Big Bang which is estimated at around 8 × 1060.

Since a googolplex is one followed by a googol zeroes, 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 0's. Indeed, if you had an unlimited supply of ink and paper, you would need around 1020 times the current age of universe to fully write down a googolplex.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, one-point font. TeX one-point font is .3514598 mm per digit, which means it would take about 3.5 × 1096 meters to write in one-point font. The known universe is estimated at 7.4 × 1026 meters in diameter, which means the distance to write the digits would be about 4.7 × 1069 times the diameter of the known 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 1.1 × 1082 times the age of the universe to write down a googolplex.*


S'quite big, then...

Yours,

somehow a little afraid,

Bluecupboard


* I had literally no idea that when I cut and pasted this in from the Wiki, that all the links would stay live! Holy information fandango, Batman!! Thought I'd better mention that someone else did all of that in case you thought I'd lost my mind (and also learned a large amount about maths and physics very quickly)...

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