[FRIAM] Free Will in the Atlantic

[jon zingale]

"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.




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