[FRIAM] alternative response

[Jon Zingale]

The paper makes a commitment to the idea that physical information is
finite and thus is poorly modeled by real numbers, there will be
assumptions we make in our calculations with real numbers that are
ultimately unphysical when we treat the world as if it were our model.

Gisin writes: "Note that these numbers contain all computable numbers,
but are not restricted to them: they also contain “numbers” whose far
away digits are undetermined, i.e. not yet determined..."

This seems to be in harmony with Glen's scoping criterion. Gisin then
continues by importing the Bekenstein bound, the holographic principle,
and minimum/maximum energy densities required for information storage.
While I love what is going on so far, Gisin oversteps a little when he
claims:

"Furthermore, today all predictions can be—and most of the time
are—encoded in computers, computers that obviously hold at most a finite
amount of bits, as emphasized in the next section. Consequently, physics
is actually done using only finite-information numbers..."

To some extent, I wonder if he is pulling a sleight of hand here. Because
simple dynamics are dominated by their leading digit, he argues, the
latter digits do not matter. Fine, but also in the spirit of Chaitin,
we can reason about a machine language whose primitives are
incommensurable with whatever language we otherwise agree to fix.
>From the little bit of Chaitin I have read directly (thanks Ed!), he
seems to emphasize a language dependence. While I admit I have only
partially thought this through, it seems to me that representations
base Euler's number will finitely describe some numbers that are
non-finite base 2. Does this matter for Gisin's argument? Even if it
doesn't, I am happy to live in a world where I can continue to go about
my business thinking whatever non-physical thing. Thanks, Marcus for the
enjoyable read!



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