On Sun, May 31, 2015 Bruno Marchal <[email protected]> wrote: >> Other than randomness nobody has ever seen anything in the physical >> world that was not computable. > > > > Physics uses real and complex numbers, and use analysis (which is second > order arithmetic). >
That's nice, but other than randomness (an event without a cause) nobody has ever seen anything in the physical world that was not computable. But computable does not necessarily mean predictable, sometimes the computation will take as long to perform as it takes the system to evolve, it's as if even nature doesn't have a shortcut and it must perform the same calculations you do to figure out what it's going to do next. > > There are no standard defifinition of computability for the class of > analytical function and sets. > That's nice, but I'm not talking about the class of analytical function and sets, I'm talking about computing what a physical system will do, or in the case of Quantum Mechanics what it will probably do. > > Church thesis only equate a notion of intuitive computability, an > ability to get a result following discrete well determined elementary > digital steps, with computability in some formal system > Only?! > > (lambda calculus, etc.) > And one of the "etc" is a Turing Machine, a device made of matter that obeys the laws of physics. > > It does not require the assumption that there is a physical universe. > A Turing Machine does assume matter that obeys the laws of physics, and a Turing Machine is equivalent to Lambda Calculus. And in fact all Lambda Calculus calculations need to be performed on something, and the only something that anyone has ever found that works is matter that obeys the laws of physics, like a computer or a biological brain. > > A priori quantum computation could have been more powerful (in term of > the size of computable functions) than the function computable with lambda > calculus, and this would not have violated Church thesis, > Even a quantum computer can't produce one of Turing's non-computable numbers. A conventional computer can solve any problem that a quantum computer can just somewhat slower. A lot slower actually, for some problems a mid sized quantum computer could give you an answer in a few minutes but a conventional supercomputer would not even be close to finishing when the sun goes off the main sequence and turns into a red giant and vaporizes the Earth 10^9 years from now; it would not even be finished when matter as we know it ceases to exist because of proton decay 10^40 years from now. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
