
Mathematical languages shape our understanding of time in physics - etqwzutewzu
https://www.unige.ch/communication/communiques/en/2020/une-physique-indeterministe-pour-un-monde-plus-ouvert/
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AlEinstein
This article apparently goes from “most reals are non-algebraic and therefore
contain an infinite amount of information” to “so if I use reals to describe a
physical system then my mathematical model is infinite even if my physical
system is not”.

There are so many problems with both of those statements that it’s hard to
know where to start.

How about this: if you represent finite information with reals, your reals
will be finite and there’s no problem.

Let’s say my physical system is a rocket launching into space to deploy a
satellite into orbit. There are lots of numbers and many equations involved.
Exactly none of those numbers we be of the “infinite information” kind. All of
the numbers are either measured or derived. Measurements don’t produce an
infinitely precise real number.

And of course there’s the whole quantum limit on the amount of information in
a given volume of space. So we don’t even need real numbers really.

Even Pi, the example given, doesn’t “contain” an infinite amount of
information. It can be represented as the limit of a series using a finite
amount of information. In terms of Kolmogorov complexity it contains very
little information.

You know, “most” of the reals are uncomputable too. That doesn’t mean the ones
we use are all uncomputable.

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etqwzutewzu
Nature article (paywall):
[https://www.nature.com/articles/s41567-019-0748-5](https://www.nature.com/articles/s41567-019-0748-5)

