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> those fantasies… in the guise of string theory obtained a death grip on fundamental physics What? The real numbers, with all the uncomputable reals included,

• TheOtherHobbes 6y ago
  Nothing in physics has infinite precision. Math is an abstraction - which is to say a stylised representation - and while you can imagine processes and representations with infinite precision, that level of precision is metaphysical. 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.
  • dcow 6y ago
    I don't know why you’re being downvoted. This is a rather good analogy. And it doesn't mean the initial comment of this thread is not presumptuous. In other words, the why should the expectation be that general authors assume universe be computational in nature, is sorely missing. But it doesn't invalidate an explanation of how analytical and discrete systems are yet unreconciled (and may never be).
  • creata 6y ago
    I'm not disagreeing that the real numbers have no physical basis; that would be silly. I'm disagreeing with the absurd claim that "uncomputable numbers … in the guise of string theory obtained a death grip on fundamental physics". The real numbers are used in every single part of physics, and physicists do not care to distinguish between computable and non-computable reals, because that makes the theory much more complex with no known practical benefit. 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.
• btilly 6y ago
  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. 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.
  • creata 6y ago
    > Unpopular treatments of Calculus that only deal with computable numbers exist and produce the same results for physics. 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.
    • btilly 6y ago
      I was thinking intuitionistic math, such as smooth infinitesmal analysis. And yes, they are less developed than classical analysis, and harder to work with. But should not produce different results.
      • Jweb_Guru 6y ago