Idle Time

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.

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