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> Sure, just hard code them. That would be super lucky if possible - almost all reals are not computable. How would we initialize or specify this Turing machin
by lanstin 2y ago
> Sure, just hard code them.
That would be super lucky if possible - almost all reals are not computable. How would we initialize or specify this Turing machine? Going to use non-constructive methods?
Given how quickly reality unfolds, it's a bit of a stretch to assume that "simulate it to arbitrary precision" means "computable in a digital representation in real time." I mean, if we have Turing machines that did each computation step n in 2^{-n} time.
- eru 2y ago> That would be super lucky if possible - almost all reals are not computable. How would we initialize or specify this Turing machine? Going to use non-constructive methods? The standard model doesn't use arbitrary reals. All the parameters are rational numbers with finite precision. Obviously, your Turing machine can only hard code a finite amount of information about the parameters, eg whatever finite prefix of their decimal expansion is known. Btw, the speed of light is one of those parameters that's 'known' with absolute precision thanks to some clever definitions. We can do similar tricks with many of the other parameters, too.
- lanstin 2y agoI don’t think that’s true, there are parameters that must be measured experimentally: https://spinor.info/weblog/?p=6355 https://spinor.info/weblog/?p=6355 (I am not a physicist, so I welcome education to clarify this).