Hypothetical CS type question...

[madnak]

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The one caveat is that the computer has finite space

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I completely forgot about this! This changes things because it means the set of programs that can run on the computer is finite. But I'm also thinking that the distinction of "meaningful" is too imprecise. There is really no program at all that I can't see someone reasonably wanting to program under the right circumstances. Ah, barring redundancy and bugs.

By any standard I think the numbers are extremely large. But I have to agree that 3 will represent the biggest group. Generally the number of specific operations being performed (roughly speaking - different "classes" of operations will have different speeds, and some operations may be performed concurrently, but that doesn't change the basic fact) will determine the speed. As a result, the number of possible permutations of programs will tend to increase as the running time increases. And that will exceed 1 year quickly.

Also basically any process that describes a "simple" program will be a necessary subroutine in a large number of "complex" programs, so (given finite memory) there is a many-to-one relationship between the long programs and the short programs. There have got to be more long programs, and I'd say by orders of magnitude.