On 17 Nov 2008, at 04:41, Brent Meeker wrote: > But all possible implementations is a logical concept that exists only > in platonia -
Any program for the universal dovetailer like this one GEN & DU implements all computations in our (apparently) material world we are sharing now. > so what is the distinction between implemented and > un-implemented computations. Suppose I am inviting you on the planet mars. We have to take a digital teleporter though (I can afford a two place tickets for a conventional rocket, sorry). So we are read and cut on the planet earth, and the information read is send on mars. There, I am reconstituted, and you, well, bad luck but the reconstitution-machine just break down. In that case, I am implemented on the planet mars, and you are not. Implementation is a relative notion. A program P is implemented on a universal machine M when P is translated in the language of the machine M, and when M is trigged so that it evaluates or executes the program P, on earth or in platonia. Implementation is a purely mathematical notion for the theoretical computer scientist. For the physicist, or the business man, it is true that the word is sometimes used in the sense of concretely implemented in a real machine in front of us. But note that the UD has been implemented and executed, for a few days, concretely on a Macintosh Computer in 1991. That is the key of the whole construction. The deployment of the UD is a precise concretisable object. This is made possible by the "Godel's miracle", or "Church's thesis". It is the only place in math were an epistemological notion (computation) admit a universal definition. Godel did not believe in Chuch thesis for a long time, and after he begin to accept it, he called it a miracle, because it is indeed hard to believe in it, when you are aware of Cantor's proof and the power of diagonalisation. As said Godel, it is amazing that Church thesis can survive to diagonalization. This is the hidden difficulty of the step seven. I thionk Tom Caylor grasped it through his redaing of the Cutland book. The notion of computation is highly non trivial. Computer (universal computing machine) are highly non trivial mathematical object (implemented or not here or there). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
