On 24 Dec 2009, at 02:13, Nick Prince wrote: > Thanks Bruno > > I want to have a good think about your answers and also the eighth > step in your paper. I think it is the most difficult for me and yet I > sense its somehow. Schmidhuber assumes a great programmer runs the UD > but you effectively dispense with him. If a universal turing machine > necessarilly exists platonically which is capable of running UD's that > can simulate our minds then our experience of reality follows. Yet I > still feel that somehow this will be confusing the map of the > territory with the "reality", the equations of physics with the > physically real.
And here there is a famous difficulty, which is that physicists and logicians use very different if not opposite vocabulary. Logicians distinguish a theory (-usually a finite or recursive (mechanically decidable) thing, and its interpretation (usually an infinite mathematical structure. In the comp frame, it is even more difficult, given that we are going through a metatheory, where both the theory and its interpretations are studied at the theory level, and then we have to consider the fixed point of the interpretation function. Intuitively, you can understand that with comp, we do confuse, purposefully, the map and the territory. You can see a brain as a theory of reality. But that reality contains a brain. So, at some point the brain will accept (or bet) that it is itself an object in that theory, and the computationalist practicers will have to bet that is "brain-theory" is well described (relatively to his neighborhood) by a finite thing (its own backup in such or that machine). It is not stranger that Brouwer fixed point in geometry or topology. After all, we know that if the map of a territory is continuously embedded in the territory, a point of the map will be confused with a point in the territory. It is the indexical "You are here" point of the map. Likewise, in computer science, the meaning of a program can be described by a fixed point of some universal transformation (like in Scott denotational semantics, for example). To understand this well, it is necessary to NOT confuse a theory, with his mathematical interpretation, and to NOT confuse a mathematical interpretation with an interpretation in some reality. Physicists have not yet this level of sophistication. They usually confuse a theory (the SWE for example) with the mathematical (standard) interpretation (the wave function). This can lead to many misunderstanding of what the logicians are doing, especially in applied logic. Concerning the existence of platonic Turing Universal Machine, it is equivalent with the platonic existence of the prime numbers, or the even numbers, etc. With Church thesis you can eliminate the "Turing" label. 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.
