Scale

2009-04-29 10:25:27 UTC

264 doesn’t sound much bigger than 232, does it?

264 is 232 × 232, but this relation is hard to put into perspective. Even saying that 264 is more than four billion times as big as 232 doesn’t adequately convey how much larger it really is.

Let me do that for you now.

I wrote a program that counts from 0 to 232. It takes about 11 seconds to run:

% ./count-up
2009-04-29 09:52:55.387 count-up[57932:10b] Time to count up to 4294967295: 11.313282

Now, as I said, 264 is 232 × 232, so the time to count to 264 is likewise the time to count to 232 (11.313282 seconds) multiplied by 232. That works out to:

  • About 48,590,176,200 seconds
  • About 13,497,271 hours
  • About 562,386 days
  • About 1540 years

Simply by doubling the exponent, we increase the time it would take my late-2006 four-core Mac Pro to count up to the number from 11 seconds to a millenium and a half.

One Response to “Scale”

  1. Jordy/Jediknil Says:

    ++ A very good way to make that size difference accessible. Reminds me of Grace Hopper’s “nanoseconds”.

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