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Computational Irreducibility

Much of theoretical physics has traditionally been concerned with trying to find "shortcuts" to nature. That is to say, with trying to find methods that are able to reproduce a final state of a system by knowing the initial state but without having to meticulously trace out each step from the initial to final states. The fact that we can write down a simple parabola as a path a thrown object makes in a gravitational field is an example of an instance where this might be possible. Clearly such shortcuts ought to be possible in principle if the calculation is more sophisticated than the computations the physical system itself is able to make. But consider a computer. Because a computer is itself physical system, it can determine the outcome of its evolution only by explicitly following it through. No shortcut is possible. Such computational irreducibility occurs whenever a physical system can act as a computer. In such cases, no general predictive ability is possible. Computational irreducibility implies that there is a highest level at which abstract models of physical systems can be made. Above that level, one can model only by explicit simulation.

Web Resources On Computational Irreducibility

http://www.cna.org/isaac/Glossb.htm

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