Hi Russell, No problem at all - I myself confess to having skimmed papers in the past, perhaps even in the last 5 minutes... That I took a bit of umbrage just shows that I haven't yet transcended into a being of pure thought :-)
Let me address your 3rd paragraph first. Consider the statements: "3 is a prime number" and "4 is a prime number". Both of these are well formed (as opposed to, say, "=3==prime4!=!"), but the first is true and the second is false. To be slightly pedantic, I would count over the first statement (that is, in the process of counting all information structures) and not the second. Note that the first statement can be rephrased in an infinite number of different ways, "2+1 is a prime number", "the square root of 9 is not composite" and so forth. However, we should not count over all of these individually, but rather just the invariant information that is preserved from translation to translation (This is the meta-lesson borrowed from Faddeev and Popov). Consider then "4 is a prime number" - which we can perhaps rephrase as "the square root of 16 is a prime number". In this case we are now carefully translating a false statement - but as it is false there is no longer any invariant core that must be preserved - it would be fine to also say "the square root of 17 is a prime number" or any other random nonsense... "There is no there there", so to speak. The same goes for all of the completely random sequences - there seems to be a huge number of them at first, but none of them actually encode anything nontrivial. When I choose to only count over the nontrivial structures - that which is invariant upon translation - they all disappear in a puff of smoke. Or rather (being a bit more careful), there really never was anything there in the first place: the appearance that the random structures carry a lot of information (due to their incompressibility) was always an illusion. Thus, when I propose only counting over the gauge invariant stuff, it is not that I am skipping over "a bunch of other stuff" because "I don't want to deal with it right now" - I really am only counting over the real stuff. Let me give an example that I thought about including in the paper. Say ETs show up one day - the solution to the Fermi paradox is just that they like to take long naps. As a present they offer us the choice of 2 USB drives. USB A) contains a large number of mathematical theorems - some that we have derived, others that we haven't (perhaps including an amazing solution of the Collatz conjecture). For concreteness say that all the thereoms are less than N bits long as the USB drive has some finite capacity. In contrast, USB B) contains all possible statements that are N bits long or less. One should therefore choose B) because it has everything on A), plus a lot more stuff! But of course by "filling in the gaps" we have not only not added any more information, but have also erased the information that was on A): the entire content of B) can be compactified to the program: "print all sequences N bits long or less". The nontrivial information thus forms a sparse subset of all sequences. The sparseness can be seen through combinatorics. Take some very complex nontrivial structure which is composed of many interacting parts: say, a long mathematical theorem, or a biological creature like a frog. Go in and corrupt one of the many interacting parts - now the whole thing doesn't work. Go and randomly change something else instead, and again the structure no longer works: there are many more ways to be wrong than to be right (with complete randomness emerging in the limit of everything being scrambled). Note that it is a bit more subtle than this however - for instance in the case of the frog, small changes in its genotype (and thus in its phenotype) can slightly improve or decrease its fitness (depending on the environment). There is thus still a degree of randomness remaining, as there must be for entities created through iterative trial and error: the boundary between the sparse subset of nontrivial structures and the rest of sequence space is therefore somewhat blurry. However, even if we add a very fat "blurry buffer zone" the nontrivial structures still comprise a tiny subset of statement space - although they dominate the counting after a gauge choice is made (which removes the redundant and random). Does that make sense? > > Sorry about that, but its a sad fact of life that if I don't get the > general gist of a paper by the time the introduction is over, or get > it wrong, I am unlikely to delve into the technical details unless a) > I'm especially interested (as in I need the results for something I'm > doing), or b) I'm reviewing the paper. > > I guess I don't see why there's a problem to solve in why we observe > ourselves as being observers. It kind of follows as a truism. However, > there is a problem of why we observe ourselves at all, as opposed to > disorganised random information (the white rabbit problem) or simple > uninteresting information (the occam catastrophe problem). > > I'm not sure you really address either of the latter two issues - you > seem to be assuming away white rabbits in restricting yourself to > "gauge invariant" information (which I assume can be formalised as the > set of programs of a universal machine). I would be interested to know > if your proposal could address the occam catastrophe issue though. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
