Medium Dependent Intelligence, Uncopyable Intelligence, and Transhumanism

[sir_pudding]

Originally Posted by Anthony

It's not too hard to estimate to within 1%, though. The factorial can be rewritten as e^(∑(n=1-1e11)ln(n)), which can be reasonably approximated as the integral for large values of n, and the integral of the natural logarithm has a known solution.

Of course, a computer's solution to that interegral isn't different from the identical solution that a person could arrive at by hand.

[Anthony]

Originally Posted by sir_pudding

Of course, a computer's solution to that interegral isn't different from the identical solution that a person could arrive at by hand.

Right, and stirling's approximation appears to be a refinement of that (not surprised there's a refinement). Really, inventing sufficient calculus to do this efficiently is a big task that current computers would be bad at doing, but applying known formulas is just lookup and grunt work.

[sir_pudding]

Originally Posted by Anthony

Right, and stirling's approximation appears to be a refinement of that (not surprised there's a refinement). Really, inventing sufficient calculus to do this efficiently is a big task that current computers would be bad at doing, but applying known formulas is just lookup and grunt work.

Although I would be surprised if it could be demonstrated that inventing sufficient calculus is a task that requires infinite (or finite but impossible) resources.