Wednesday, November 26


A Few Million Orders of Magnitude

Dear Dan,

When you say "there are 16.8 million to the power of 307,200 possible images that can be displayed on a 640 by 480, 24 bit screen", you are of course correct, but when you continue "and to display all of them, you'd need 2400 televisions showing 25 frames per second for eight billion years", you are off by a very considerable margin.

Those 2400 televisions, in that time, could display 15,147,648,000,000,000,000,000 frames - a 23-digit number, a little over 15 sextillion.*

But 16.8 million raised to the power of 307,200 is... Well, bc ain't gonna calculate that one for me in a hurry.** Let's call it ten million (7 zeroes) raised to the power of 300,000. That's a 1 followed by 2.1 million zeroes. We're talking big big big numbers here. If every subatomic particle in the Universe was a TV, showing one frame every Planck Time... You wouldn't even be started by the time the entire Universe had dissociated into electron/positron pairs (or collapsed into the Big Crunch, depending on the value of the Cosmological Constant).

But what's a few million orders of magnitude between friends?

*That's an American sextillion, 1021. The old-fashioned British sextillion is 1036, a very much larger number.
** bc just came back with the answer. Of course, this involved a lot of scrolling of the screen - after all, it's just an 80x60 terminal session - but it's pretty impressive.

(I emailed this to Dan, but I thought it would make a nice blog entry as well. Dan's Data is one of the best geek sites around. Dan knows his stuff, knows what's cool (Giant magnets! Tiny tanks! Backyard trebuchets!), and doesn't talk down to the non-geeks.)

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