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Speaking as a physicist I think its very far from obvious that digital physics (or anything else) is the correct approach from a philosophical perspective. Rea
by eigenket 3y ago
Speaking as a physicist I think its very far from obvious that digital physics (or anything else) is the correct approach from a philosophical perspective.
Real numbers are so ubiquitous in physics because space-time (and other quantities) look really continuous.
- consilient 3y agoAgreed that digital physics is far from obvious, but the use of real numbers as our default model of the continuum is at least in part historical accident. We could have for instance easily ended up with locale-theoretic foundations instead, though I doubt the finitist crowd would find that any more satisfying.
- CuriouslyC 3y agoRational numbers can produce "continuous" values to a precision way beyond what any equipment you could get your hands on could differentiate without physically ludicrous postulates.
- eigenket 3y agoThat is certainly true. In fact you don't even need rational numbers, it is entirely possible that there are a finite number of positions on the universe, for example. Nevertheless physics seems to work very nicely when expressed in the language of calculus. Everything from Schrödinger's equation to the Einstein field equations, and from classical mechanics to the standard model of particle physics are expressed in the language of calculus. This all looks like a wild and strange coincidence if fundamentally we are living in a relm like the rationals, where calculus doesn't really make sense.