"I claim in the free will case that all generating functions are not as likely."
<attempted steelman> Not only is there structure all around us to be studied, but that the arrival of these structures is also not random. That is, there exists some privileged generating function, and by calculating the auto-mutual information we will arrive, at the end of time, with a unique function[⌁]. In the infinite time case, we apply auto-mutual information by endlessly taking new measurements. <⎚> Of course, as Nick likes to point out, the universe may be random. This isn't to say that auto-mutual information gets us nowhere, though it does scope the usefulness. By analogy, we can consider the dimensionality problems that happen with manifold reconstruction, Taken's method say. There, we can get pretty good approximations, using delay-line methods, for some of our most aperiodic trajectories in low dimensional phase space. For anything on the order of 10 or higher, though, good luck. Over the course of last week's foray into data compression, I worked on an optimization for the Burrows-Wheeler transform. The relevant piece here is at the lexicographical sorting step where we take n copies of a tome, and where each copy (a class of tomes in Borges' library of Babel) is a periodic translation of every other[λ]. In particular, I was looking at a savings one can determine by only reading the first few characters from each tome. After all, lexicographical sorting only requires comparisons up to the first difference. Heuristically, I determined, from tomes in English lying around, that often a window size of 9 would suffice[⎌]. In a non-random world, I have some hope of determining the ultimate window size for all tomes of a given type, but the problem is already made more difficult if I take English tomes from any other time in the history of the written English language. Further, as tomes proliferate (randomly) in time, it becomes more difficult to even determine which tomes are English. All of this may just be muddying the waters, but if the world turns out to be random, then we are stuck forever approximating our generating function (and possibly not even in a reasonable way, a function performing jumps all over the function space[?]). I claim that training-style arguments regarding determinism are ill-equipped to say anything about *free-will*, though they allow us to discuss randomness. [⌁] Which again, all else accepted, I argue is a class. From that class some will argue for *the razor* and select the simplest representation. [λ] f 0 xs = xs f n (x:xs) = f (n-1) (xs ++ [x]) [⎌] It is fairly clear that if a tome has any significant repetitions, whose paragraphs repeated say, that the window size would need to be larger. This would take me, I think, away from my main point. [?] Very quickly we are moving into a space that would have been cool to have been acculturated into, but alas I wasn't. -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
