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Assuming all other things being equal, for how long can the Counter of Babel count?

Assuming babel counter
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Assuming all other things being equal, for how long can the Counter of Babel count?

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The Counter of Babel stores numbers into exponential units of billions. So, the first unit maxes out at 1 billion. The second unit maxes out at 1 billion billion. The third at 1 billion billion billion and so forth. If one computer was running the counter, it would take 6 years to max out the first unit and 6 billion years to max out the second. If everyone in the world were running the program, it would only take about a year to max out the first two units, but another billion years to max out the third. Since the storage capacity allows for literally millions of units, it’s conceivable to say that the Sun is scheduled to burn out before the Counter of Babel stops counting.

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