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But computing machines aren't unpredictable. They are very predictable. They appear to pull complex structure out of the aether.

Perhaps the interesting thing is that the set of n-bit programs expands to only 2^n possible outputs. Why are some finite number of infinite-length outputs accessible, but not others? Why does nature favor those sequences?




>But computing machines aren't unpredictable. They are very predictable.

Are they though? A 5-state Turing machine might seem trivial, but there exist programs in it, that we don't know if they ever halt or not [1]. Their behavior is totally non-deterministic for our understanding. There are also minimalistic cellular automata that produce completely unpredictable patterns. [2]

[1] https://en.wikipedia.org/wiki/Busy_beaver#Known_values_for_....

[2] https://en.wikipedia.org/wiki/Rule_110


See also the turing machines whose halting behavior is independent of ZFC. http://www.scottaaronson.com/blog/?p=2725




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