Subj : Incomputable (was: some other thread) To : comp.programming,comp.object From : Chris Sonnack Date : Tue Aug 16 2005 03:20 pm Dmitry A. Kazakov writes: >> Are we possibly talking about two different things here? Yes, >> Goedel showed we can't fully analyse any non-trivial system, >> but I believe Shannon hasn't been superceded in the sense that >> anything that *can* be expressed or computed can be expressed >> or computed in binary. > > Which contains a hidden tautology, of course. Everything = anything > computable in 1s and 0s? (:-)) [grin] I suppose you could see it that way. >>> And even if there were one, neither fuzziness nor randomness >>> can be expressed in a deterministic system without some >>> incomputable elements. >> >> But they are incomputable by *any* means, right? > > That's an interesting question. Agreed! > It depends on the hardware. We don't know if the Universe can offer us > anything beyond Turing machine. In particular, can our biological > "hardware" compute incomputable? It can certainly imagine the unimaginable ("sound of one hand clapping"). One starting question in my mind involves comparing human (or other!) mentation to hardware computation. Are they even comparable? I really, really hope I'm still alive when technology reachest the point where we can fully simulate the human brain--the hardware--and we will reach that point eventually. The burning question is, what will happen when we turn it on? Will we have a *mind* or just a big neural net. > Nobody knows it for sure. Right. 'Swhy I hope to be there! > Then there is quantum computing. So far people are busy trying to > make 1/0s computing out of it. But let's look in another direction. > What if quantum computing is more than that? We had a similar discussion here recently. One point of view was that Q/C would *only* allow us to solve problems that were "incomputable" due to lack of resource (time, space, energy, etc.)--that is, that it would just be a MUCH faster version of current machines. The other point of view was that it would open new vistas in computation not even dreamed of now. Another one where we'll just have to wait until we can throw the switch! > Purely fictitious, let you can compute random distributions, rather > than their realizations (the only thing we can do now), then this > class of computing will be incomputable for any Turing machine. Couldn't you do that now by using a true random (hardware) source? Such as semi-conductor thermal junction noise? In both cases you'd be leveraging the randomness of Q/M. -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| .