Hi all, I suddenly feel sorry putting too much burden on just one correspondent in the list, and I would appreciate if someone else could propose answers or any remarks to the exercises.
I am also a bit anxious about Kim, who is the one who suggested me the initial explanations, but who seems to have disappear right now. There is also some sort of burden onto me, because it is hard to explain "the real thing" concerning the seventh step, without explaining or just illustrating at least some relevant portion of the mathematical reality: mainly the unexpected mathematical discovery of the universal functions, sets, numbers, systems, language, machine ... I don't mention the absence of drawing ability which does not help. Given that the list raised from a critical approach toward Tegmark and Schmidhuber, I was usually assuming some knowledge in math and physics. What was harder for me in the beginning was to motivate the use of "philosophy of mind" notions, notably the key distinction between the first and third person point of view. Then UDA should make you realize how non obvious the relation between the first person and the third person can be once we assume comp (= work in the theory comp). My original goal was to illustrate that once we assume digital mechanism, we can build a "scientific formulation" of the mind-body problem or the consciousness-reality problem. We probably depart from Tegmark and Schmidhuber, or Wolfram, by taking into account that making comp explicit entails a delocalisation of the 1-person relatively to the third person computations, and makes the identity thesis, a most complex equivalence relations. The knowledge of most people participating to the discussion is very varied, due to the extreme transdiciplinarity of the subject, and the interest it can evidently have for the layman (and indeed, for any universal machine). Marty asked me to make an attempt toward a "journalistic" description of "how physics has to become part of number theory". This is very difficult, and risky due to inevitable misunderstanding. And I feel like I have to explain in what deep sense the mathematical discovery of the "universal machine", made by Post, Turing, ... is already a quite utterly astonishing, yet subtle, discovery. Gödel himself took time to swallow it and he described Church thesis as an epistemological miracle. My intention was to derive properly Cantor theorem, and then Kleene theorem, which was the object of my old "diagonalization posts". I feel important that people understand how unbelievable Church thesis is, and why most startling propositions, including incompleteness, are easy consequences of it. Typically I am happy to share my enthusiasm about all theorems in computer science which leads to the reversal, but knowing myself I know that I could accelerate too much and makes too much burden for the correspondent especially if he is alone. So before becoming an harasser myself I invite Marty to let other people trying to answer the exercises. Marty has fully agreed to this proposal and is happy the pressure is off him to represent all those who are following anonymously. Eventually I can show the solution and proceed in addressing the post to everyone. Note that this is what I have done with the combinators, feedback were made out-of-line, then. But this lead to difficulties too. I cannot solve all the exercise out-of-line. By experience this ends up with finding myself writing too many posts with almost the same info to different people. Yet I can imagine how much it is to be the only public target of what could look like an perpetual exam, and I really want to proceed in a cooler way. Some people have encouraged me, out-of-line, to proceed, but now I think they should participate a little bit, if only to witness they are following the thread. I will probably stop to propose "easy" (a quite relative notion) exercise, but then it is important to stop me once anything is unclear. This is a problem with math, if you miss a piece, everything becomes senseless. Understanding implies some self-implication in the reasoning. So, either someone else try to participate, or I continue impersonally and eventually I will try some "non technical summary". I recall that one of the goal consists in explaining the difference between a computation and a description of a computation (beyond just doing the step 7). Any remark to improve the communication or to design a better methodology is welcome, Best regards to all of you, and thanks for letting me know your interests, 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 -~----------~----~----~----~------~----~------~--~---
