Norman Samish writes:

http://arxiv.org/abs/nlin.AO/0506030 shows the following abstract,
suggesting that complex computations are not precisely repeatable.  Doesn't
Bruno's Computation Hypothesis imply that computations ARE precisely
repeatable?

"Modern computer microprocessors are composed of hundreds of millions of
transistors that interact through intricate protocols. Their performance
during program execution may be highly variable and present aperiodic
oscillations. In this paper, we apply current nonlinear time series analysis
techniques to the performances of modern microprocessors during the
execution of prototypical programs. While variability clearly stems from
stochastic variations for several of them, we present pieces of evidence
strongly supporting that performance dynamics during the execution of
several other programs display low-dimensional deterministic chaos, with
sensibility to initial conditions comparable to textbook models. Taken
together, these results confirm that program executions on modern
microprocessor architectures can be considered as complex systems and would
benefit from analysis with modern tools of nonlinear and complexity
science."

Isn't the noise in the system (with ensuing unpredictable behaviour) one of the main limits to how densely packed circuits on a chip can be? If computations are not precisely repeatable, then what is to stop my computer from garbling this email and sending it to some random destination? Now, in the case of complex analogue systems like human brains, it would be a different matter: you would expect classical chaos to have an effect, and different brain states might result even given the same inputs (or no inputs). We expect this unpredictability from people, but if our machines start behaving in a similar fashion, we assume that they're broken or incompetently designed. Is this an unfair double standard?

--Stathis Papaioannou

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