4 ms·

Because I don’t think infinite amounts of information, and uncomputable numbers, exist. They are fantasies, and relatively recent ones at that. Unfortunately th

Because I don’t think infinite amounts of information, and uncomputable numbers, exist. They are fantasies, and relatively recent ones at that. Unfortunately those fantasies came to dominate 20th century mathematics, and in the guise of string theory obtained a death grip on fundamental physics. Fortunately a new generation of smart people, with intuitions honed on computers, is well placed to capitalize on this arbitrage opportunity.

taliesinb 6y ago
Heartening to see that unusual perspectives and opinions are rewarded with downvotes.
- krastanov 6y ago
  I suspect the downvotes are due to (1) the lack of intellectual humility and (2) misrepresentation in your comments. Plenty of physicists agree that uncomputable numbers are unphysical and the idea that infinite information density can not exist is in no way new or controversial (it is pretty much the starting point for the holographic principle, one of our main paths to a theory of everything). They are beautiful ideas worth discussing, but you used your knowledge of them to disparage people and fields which it seems you only have passing familiarity with.
  - dcow 6y ago
    Yes. It is dogmatic, not scientific, to suggest that a paper is worthless because the authors didn’t frame their argument under some set of axioms you just really identify with, conceptually.
creata 6y ago
> 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, 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.
- 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.
btilly 6y ago
Thank you for answering. My apologies for not engaging previously with your answer. 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 https://www.scottaaronson.com/blog/?p=3827 and https://www.scottaaronson.com/blog/?p=4372 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.

taliesinb 6y ago

Heartening to see that unusual perspectives and opinions are rewarded with downvotes.

krastanov 6y ago
I suspect the downvotes are due to (1) the lack of intellectual humility and (2) misrepresentation in your comments. Plenty of physicists agree that uncomputable numbers are unphysical and the idea that infinite information density can not exist is in no way new or controversial (it is pretty much the starting point for the holographic principle, one of our main paths to a theory of everything). They are beautiful ideas worth discussing, but you used your knowledge of them to disparage people and fields which it seems you only have passing familiarity with.
- dcow 6y ago
  Yes. It is dogmatic, not scientific, to suggest that a paper is worthless because the authors didn’t frame their argument under some set of axioms you just really identify with, conceptually.

creata 6y ago

> 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, 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.

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.

btilly 6y ago

Thank you for answering. My apologies for not engaging previously with your answer. 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 https://www.scottaaronson.com/blog/?p=3827 and https://www.scottaaronson.com/blog/?p=4372 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.