What kind of evidence should we use to know which structures are real?
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Replying to @ObjectOfObjects @CurlOfGradient
If by "real" you mean "corresponding to something observable," then none of these systems are real.
#Ultrafinitism (Or perhaps more specifically,#Actualism)2 replies 0 retweets 1 like -
Replying to @davidmanheim @ObjectOfObjects
Even if our universe were finite, the real numbers are a perfectly coherent system that one can make true or false statements about. I don’t get ultrafinitists
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Replying to @CurlOfGradient @ObjectOfObjects
It's not that it's an incoherent system, it's that there is nothing that it maps to in reality. And making the mistake of thinking that it is meaningful in practice leads to lots of problems. So we should be careful not to claim that the "real" numbers are more than a toy.
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Replying to @davidmanheim @ObjectOfObjects
As a physicist I use the real numbers to describe reality all the time. You can't do physics without them.
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Replying to @CurlOfGradient @ObjectOfObjects
Yes, you use a convenient mapping of states to the real number system. But accepted physics implies there literally cannot be evidence that there are arbitrary precision numbers for position/velocity, much less infinite information density, as the real numbers would imply.
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Replying to @davidmanheim @ObjectOfObjects
Just because our measurements of reality can't be real numbers doesn't mean the state of the universe can't involve them. And even if we discover the universe is a complicated cellular automaton, current physics is so accurate we'll go on using it for most purposes anyway.
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Replying to @CurlOfGradient @ObjectOfObjects
I'm not arguing they are not useful, I'm arguing that they are unnecessary, and that, AFAICT, reality cannot contain them.
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Replying to @davidmanheim @ObjectOfObjects
I'm confused about your assertion that they are unnecessary. Has someone invented a fully discrete version of physics that I don't know about?
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Replying to @CurlOfGradient @ObjectOfObjects
You're arguing that the absence of knowledg of a perfect model, is evidence for the correctness *untestable* implicit assumptions in your admittedly incomplete current model? That's certainly not Popperian or Bayesian reasoning.
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You seem to be arguing that because we can never make a measurement of a real number, there can't *be* any real numbers. I think the fact that physics does so well by assuming space and time are continuous is evidence that space and time are, in fact, continuous.
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