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>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
by Grue3 10y ago
>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_.CE.A3_and_S https://en.wikipedia.org/wiki/Busy_beaver#Known_values_for_....
[2] https://en.wikipedia.org/wiki/Rule_110 https://en.wikipedia.org/wiki/Rule_110
- andrewflnr 10y agoSee also the turing machines whose halting behavior is independent of ZFC. http://www.scottaaronson.com/blog/?p=2725 http://www.scottaaronson.com/blog/?p=2725