[FRIAM] Thanks again Marcus

[Jon Zingale]

The numbers most physicists use are finitely specifiable. π, for instance,
has an infinite and non-repeating representation and yet there exist
algorithms to get whatever nth digit you desire. Numbers like π are said to
be computable and so are expressible in a finite way. Physicists get to keep
π. There are other numbers, like Chaitin's constant, which have no such
algorithm. What is worse, there are so many more of these numbers that the
numbers physicists use may as well not exist, they are so few. The paper
goes on to speak of these non-computable numbers as being, in essence, what
we mean by a random number. To my mind, this is akin to Peirce's statement
that nearly everything is random. Gisin continues by pointing out that these
numbers, as they would take an infinite amount of energy to store in a
finite space, are decidedly non-physical. Chaitin points out that we cannot
even really get to know them as there is nothing we can say about them. It
seems, if Pierce excepted such a thing that he might too consider them to be
non-meaningful.

So now, left with only those numbers which behave nicely in that they are
finitely storable and can be computed, we are left with numbers that can be
compared or related. Because everywhere the word number appeared above you
can substitute some physical thing (energy-matter), we have a situation
where we can speak about what is real through relations even though anything
that can be considered real is vanishingly small wrt what is random.

The last detail, which seems relevant is that some dynamics (really most
dynamics) are notoriously badly behaved. That is, long term prediction in
classical physics is notoriously sensitive to initial conditions. The fact
that information in our model universe is finite, as understood above, those
initial conditions will march towards randomness despite the fact that the
dynamics are determined. I don't know Pierce's work outside of things you
have told me, but it seems that there might be similarities worth persuing.



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