Hi Jacques, Thank you for your commentary on my (old) UDA argument. I must say you have a curious style for asking me to refresh the key definitions. You should not excite so much my teacher professional deformation :)
The tricky term is the term "survive". The point is that we don't need a definition of it in UDA although it helps using grandma definition for the first few steps. No doubt at later steps grandma is more and more astonished living the gap between what she feels to be herself (1-person) and her doubles (3-person). But ok, the 1-person and the 3-person is what you ask me definitions of. If you read my posts you will see that I have given more than one definition of the 1-person. The simple one is enough for both Everett's justification of the appearance of probability with pure QM (SE + comp) and enough for my (ok, sorry) justification of the appearance of probability in "pure comp" (through the grandma UDA. You can say I borrow it from Everett if you want. [BTW thanks for your "grandma" expression I love it. I recall for the others that in the cognitive/mind science the grandmother or folk psychology is what you need for following a Mickey comics (american definition) or a "Tintin and Milou" (Belgium definition). Grandma psychology accept explanation like "John postponed the operation because he was afraid by anesthesia", etc. In the second part of my thesis I substitute grandma for an arithmetical grandma driven by the Godel Lob modal logic G and G*. It makes possible the translation of UDA in arithmetic through Kleene's arithmetical Metamathematics. I say a little more below]. 1-person (simple definition working for UDA and Everett): I suppose an observer has a memory. A way to record result of experiment. Let us symbolize it by a diary (but the observer's brain works aswell). In the frame of duplication experiments (resp. the quantum superposition). The 1-person discourse is defined by the content of the diary *<which is supposed to accompany the candidate of the duplication>*, i. e. the diary is duplicated too. And then the 3-person discourse is defined to be the content of the diary of an external observer of the duplication experiment. He is just an observer NOT entering the duplication machine, but still trying to describe the experiment. (In QM the 3-person is given by the SE). Illustrations: Look at the following experiences. There are two rooms quite identical except that one has a zero painted on the wall, and the other has a one painted on the wall. In the experience A I duplicate the candidate, that is I *cut* him and *paste* him, with his diary, in both rooms. I ask the candidate to write in his diary the number painted on the wall in front of him). I repeat that experience 64 times, staying outside of the duplication machine (I play the role of the scientist here, accepting only 3-descriptions). Now here is my 3-description of the 1-discourses: About 18 thousand billions of billions of diaries, in most of which, by simple arithmetic it is just incompressible noise. A typical diary content is not unlike 1100100100001111110110101010001000100001011010001100001000110100 (except this one is compressible! Do you recognize or guess?). In experience B I have a Stern Gerlach Device and I send silver atom. You are asleep (with you diary in your pocket). We use like above two rooms with 1 and 0 painted on the wall. If the atom goes up I put you in the first room, then wait you wake up and you are here also supposed to write the number on the wall in your diary. I repeat the experience 64 times. The 3-description, i.e. SE gives a superposition of about 18 thousand billions of billions of diaries. But here SE entails the observer duplicate too, and SE applied to me and the candidate gives, for a typical observer a typical diary content: noise. In QM the observer cannot stay outside the duplication machine, but the UDA shows that it is the same with comp, we cannot stay outside the universal dovetailing, and that is why 3-person sharable discourse comes first from 1-person *plural* sharing histories. (But I anticipate perhaps too much ... on my preceding post!). Although the definition of the 1-3 difference presented here is enough for the UDA (the main and key point being that the diaries does not contains comments on *delays* of reconstitution so that the search of the measure must be done on the whole UD* (the whole platonistic work of the UD), I cannot resist giving more elaborate definition useful for the understanding of the ultimate description of the 1-person in arithmetical term. A nice one, using more deeply grandma psychology though, is based on the following fact: I cannot prove to you that I am conscious. Or, if you prefer, if you decide to believe I am a zombie, there is no way for me (if comp is true) to refute your assertion. Still I bet most people like you and me are NOT zombie. Now the first person is everything you know about you but that you cannot prove to others, and which makes yourself NOT being a zombie. I let you the exercice of showing that this definition is stronger than the simple one. Hoping that can help you. The last definition (in my thesis) of the 1-person is the one given by Thaetetus in Plato. It is the knower. I say a honest machine communicates p, if the machine gives me a proof of p. And I say, with Thaetetus that the machine knows p, if it communicates p and p is true. Unfortunately "p is true" cannot be translated in the language of the machine (by Tarski theorem). But then I use a trick (found independently by Boolos, Goldblatt, and Kusnestsov and Muravitskii) which leads to identify somehow the 1-person with sort of intuitionist Brouwerian creative subject. Here we got a theory of antisymmetrical time. But that subject collapses into just propositional logic in UD*, but then the miracle is that a minimal weakening of Thaethetus trick makes possible to marry the antisymmetrical knower with its quasi completely symmetrical surroundings in UD*. Well this need G and G* ... (see "modalities" in the archive). Hoping that can open your appetite :) And the term "survive"? Forget it if you don't like it. A computationalist is just someone saying "yes" to its surgeon for an artificial digital brain/body/"universe" transplant, He/She or the doctor he/she trusts (unfortunately perhaps), is *betting* on a level of functional substitution relatively to the more probable consistent extensions. The real question is not the question of comp being true or false, but the (relative) measure on the possible diaries content. To sum up the main point, the absence of account of the UD delays in the first person (classical memories of UTM's diaries) forces us to search the measure on the computational continuations on the *whole* UD*. The key of the translation of the UDA in arithmetic is that the nuance between the person point of views is literaly forced on us by the necessary nuance between provability, truth, and consistency forced by the incompleteness phenomenon on the self referentially correct machine. Adding consistency to provability throughout UD* gives rise to (arithmetical) sort of quantum probabilities (to describe the mathematical content of my thesis in a nutshell). Bruno http://iridia.ulb.ac.be/~marchal
