> "Hal Finney" wrote:
> The first is that numbers are really far more complex than they seem.
> When we think of numbers, we tend to think of simple ones, like 2, or 7.
> But they are not really typical of numbers.  Even restricting ourselves to
> the integers, the information content of the "average" number is enormous;
> by some reasoning, infinite.  Most numbers are a lot bigger than 2 or 7!
> They are big enough to hold all of the information in our whole universe;
> indeed, all of the information in virtually every possible variant of our
> universe.  A single number can (in some sense) hold this much information.

How ? Surely this claim needs justification!
The single number can be of infinite length, with infinite digits, and can therefore contain unlimited information.  One could compare the single number to a tape to a Universal Turing Machine.  Granted, the UTM needs a head and a program to read the tape, so the tape by itself is not sufficient to hold information.

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