

Ask HN: Does Unpredictability Exist? - cj

Is it possible to have a program whose output is completely unpredictable, even if the <i>complete</i> list of initial conditions is known (all of the program's input, code, algorithms, random number list, etc)?
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jimrandomh
Strictly speaking, no. However, that "no" comes with caveats.

First, it's easy to accidentally have some inputs you haven't accounted for,
which can be turned into pseudorandom number generators. For example, if the
program is multithreaded, then the exact relative timings of instructions on
each thread matter.

And second, the thing you care about might not actually be the output, but
only a subset of the output. For example, under the many-worlds interpretation
of quantum mechanics, the laws of physics are implemented by a computer
program that computes every possible final state, but only one of those final
states is observed; and the selection of which final state gets observed
depends on which observer you are, which is "random" but in a philosophically
tricky way, since every result has a corresponding observer.

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limmeau
If by "program", you mean something computable in the usual Turing-equivalent
sense, and without access to a physical random number generator, then the
output is always trivially predictable by recreating the initial conditions
somewhere and running the program.

However, the prediction may take as long to compute as the real output. There
is no general faster way to predict the result (see halting problem).

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cj
I ask this question for how it relates to
<http://en.wikipedia.org/wiki/Digital_physics> ..and how it would be possible
for a universe, if wholly deterministic, to be practically and theoretically
unpredictable.

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memetichazard
First define unpredictable. From your comment below, it seems to me you're
saying that deterministic != predictable.

Also, the halting theorem may apply.

