Hi everybody, My name is Travis - I'm currently working as a postdoc at the Perimeter Institute. I got an email from Richard Gordon and Evgenii Rudnyi pointing out that my recent paper: http://arxiv.org/abs/1101.2198 is being discussed here, so yeah, I'm happy to join the conversation. I'll respond to some specific points in the discussion thread, but what the heck, I'll give an overview of my idea here...

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The idea flows from the assumption that one can do an arbitrarily good simulation of arbitrarily large regions of the universe inside a sufficiently powerful computer -- more formally I assume the physical version of the Church Turing Thesis. Everything that exists can then be viewed as different types of information. The Observer Class Hypothesis then proposes that observers collectively form by far the largest set of information, due to the combinatorics that arise from absorbing information from many different sources (the observers thereby roughly resemble the power set of the set of all information). One thus exists as an observer because it is by far the most probable form of existence. A couple caveats are of crucial importance: when I say information, I mean non-trivial, gauge-invariant, "real" information, i.e. information that has a large amount of effective complexity (Gell-Mann and Lloyd) or logical depth (Bennett). I focus on "gauge-invariant" because I can then borrow the Faddeev-Popov procedure from quantum field theory: in essence, one does not count over redundant descriptions. I also borrow the idea of regularization from quantum field theory: when considering systems where infinities occur, it can be useful to introduce a finite cutoff, and then study the limiting behavior as the cutoff goes to infinity. For instance, regulating the integers shows that the density of primes goes like 1/log(N) - without the cutoff one can only say that there are a countable number of primes and composites. These ideas are well known in theoretical physics, but perhaps not outside, and I am also using them in a new setting... Let me give a simple example of the use of gauge invariance from the paper - consider the mathematical factoid: {3 is a prime number}. This can be re-expressed in an infinite number of different ways: {2+1 is a prime number}, {27^(1/3) is not composite}, etc, etc... Thus, at first it seems that just this simple factoid will be counted an infinite number of times! But no, follow Faddeev and Popov, and pick one particular representation (it's fine to use, say, {27^(1/3) is not composite}, but later we will want to use the most compact representations when we regularize), and just count this small piece of information once, which removes all of the redundant descriptions. To reiterate, we only count over the gauge-invariant information. Consider a more complex example, say the Einstein equations: G_ab = T_ab. Like "3 is a prime number", they can be expressed in an infinite number of different ways, but let's pick the most compact binary representation x_EE (an undecidable problem in general, but say we get lucky). Say the most compact encoding takes one million bits. Basic Kolmogorov complexity would then say that x_EE contains the same amount of information as a random sequence r_i one million bits long - both are not compressible. But x_EE contains a large amount of nontrivial, gauge invariant information that would have to be preserved in alternative representations, while the random sequence has no internal patterns that must be preserved in different representations: x_EE has a large amount of effective complexity, and r_i has none. Focusing on the gauge-invariant structures thus not only removes the redundant descriptions, but also removes all of the random noise, leaving only the "real" information behind. For instance, I posit that the uncomputable reals are nothing more than infinitely long random sequences, which also get removed (along with the finite random sequences) by the selection of a gauge. In some computational representation, the real information structures will thus form a sparse subset among all binary strings. In the paper I consider 3 cases - 1) there are a finite number of finitely complex real information structures (which could be viewed as the null assumption), 2) there are a infinite number of finitely complex structures, and 3) there are irreducibly infinitely complex information structures. I focus on 1) and 2), with the assumption that 3) isn't meaningful (i.e. that hypercomputers do not exist). Even case 2) is extremely large, and it leads to the prediction of universal observers: observers that continuously evolve in time, so that they can eventually process arbitrarily complex forms of information. The striking fact that a technological singularity may only be a few decades away lends support to this extravagant idea... Well anyways, that's probably enough for now. I am interested in seeing what people think of the idea :-), and I am going through previous threads to see what other sorts of things are being discussed. Sincerely, Travis -- 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.