[FRIAM] alternative response

[Jon Zingale]

Ok, so what I think I like about Gisin's model is that he is presenting
a constructivist physics. Important to the model Gisin constructs is
that his alternative physics preserves the integrable dynamics of
standard dynamics. There are still a number of points I am unclear on:

Gisin commits to the holographic principle for his model, from which
it follows that a finite volume of space contains at most finite
information. He summarizes the Bekenstein bound:

"In brief, any storage of a bit of information requires some energy and
large enough energy densities trigger black holes".

He further summarizes by requiring units of information densities to be
limited by Landauer’s *Information is physical* assumption.

He continues: "Consequently, assuming that information has always to be
encoded in some physical stuff, a finite volume of space cannot contain
more than a finite amount of information. At least, this is a very
reasonable assumption".

Here I am not sure how the underlying topos that follows from the
Bekenstein bound liberates position from the clutches of arbitrary
assignment along the real line. Does anyone on the list know what
underlying topos will suffice, a Fotini topos
<https://arxiv.org/pdf/gr-qc/9811053.pdf> perhaps? To what extent
does this unnamed topos allow Gisin to further assert:

"One may object that this view is arbitrary as there is no natural bit
number where the transition from determined to random bits takes place.
This is correct, though not important in practice as long as this
transition is *far away *down the bit series."

In the case of discrete dynamical systems, there is a natural topos
where we can speak meaningfully about the distance some propositional
state is from being true, and those states which are *far from true*
is sent to false. It seems that in whatever topos he imagines, there is
a *far from true*, but I am not sure whether it is treated the same as
I have stated above. Somehow, I suspect there is a connection to
automata theory through *observability* and *realizability*.

If simply it is the case that we construct a physics without the reals,
this is probably reasonably untestable. I can't help but notice, though,
that Gisin's model appears to make no room for non-algebraic numbers,
such as those that arise when solving for the roots of larger than 4th
degree polynomials, a la Galois theory. What then are the implications
for computing arbitrary Fourier transforms? Does the validation of such
a theory explain *the unreasonable effectiveness of Pade approximates*?
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