Saturday, November 1, 2014

Computation

Is computational ability limited?

If the universe has a finite amount of matter and computation requires matter than it would appear that computational ability is finite. Even if the universe has infinite matter, it would take an infinite time to collect. Therefore computational ability is limited.

If computational ability is limited, what can be computed? How about a simulation of our universe?
A simulation of the universe would require at least the amount of matter in the universe to be accurate. Using approximations would result in significant changes over time.

Could a somewhat isolated system such as our solar system or perhaps our galaxy be simulated? Would the simulation be able to predict the future?

Quantum physics is based on the idea of inherent uncertainty at sub-atomic levels. The presence of randomness in physical laws would disallow an accurate simulation of the universe. This does not mean simulations of the universe cannot be useful. Methods used to obtain approximate models of various systems has already been demonstrated.

Besides physical simulations, what else could be computed? What about the answer to mathematical questions? Assuming a general formula is not found, prime numbers of what magnitude can be found?

Does N=NP?

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