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Nothing in physics has infinite precision. Math is an abstraction - which is to say a stylised representation - and while you can imagine processes and represen
by 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 agoI 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 agoI'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.