I agree that computation is likely a better model than string theory. However I have the humility to not insist that reality must match any set of concepts that I have.
In particular in this case results like the ones discussed at https://www.scottaaronson.com/blog/?p=3827 and https://www.scottaaronson.com/blog/?p=4372 say that quantum mechanical systems can perform operations in ways that are different from and fundamentally impossible for classical computers. Therefore it seems likely to me that classical computing is going to break down pretty hard as a model for how things really work.
What? The real numbers, with all the uncomputable reals included, are used in every corner of physics, not just in string theory. There is no treatment of calculus (with any semblance of popularity) that does not feature the usual real line.
This confuses Platonists who seem to believe that differential equations really exist - somewhere.
But that's like arguing that you will clock up air miles by zooming around Google Maps.
The set of operations you can perform on representations of reality is in no sense identical to the set of operations you can perform on reality itself.
If this still isn't obvious, try to differentiate a rock.
I also wish that the person I initially replied to would expand on their vague claim that
> Fortunately a new generation of smart people, with intuitions honed on computers, is well placed to capitalize on this arbitrage opportunity.
First of all, there is no application of physics where uncomputable reals make one bit of difference. Unpopular treatments of Calculus that only deal with computable numbers exist and produce the same results for physics.
Secondly, physicists have a well-known disregard for whether official mathematical constructions support how they are using them. To name but two examples, both the Dirac delta and renormalization were in wide use long before any formalization existed that could justify them.
Given that, there is no way in which the use of mathematics by physics serves as justification for the reality of the obscure mathematical notions that mathematicians have developed.
I'd really appreciate if you named them. I've seen synthetic differential geometry, which isn't nearly well-developed enough for use in all of physics, and I've seen nonstandard analysis, which obviously doesn't do away with the uncomputable reals at all.
> there is no way in which the use of mathematics by physics serves as justification for the reality
I am not saying the standard reals are real. I am saying that they are more convenient than any existing alternative, and fulfil the current needs of all of physics. I am also saying that the parent's claim that "uncomputable numbers … in the guise of string theory obtained a death grip on fundamental physics" is absurd, since string theory and uncomputable reals are pretty much unrelated.
And yes, they are less developed than classical analysis, and harder to work with. But should not produce different results.
(a) you're either wrong or incredibly optimistic regarding our ability to carefully rephrase the statements of classical analysis in a way that works constructively.
(b) what would be the point of a harder-to-use system that offers exactly the same results, anyway? The whole reason I find SDG interesting is that it will eventually be simpler to use, and because it provides an entirely fresh of the number line.