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The more sensible question, IMO, is "Is the universe fundamentally quantized?". Can you concretely say where the boundary between an apple and the surrounding a
by pphysch 8y ago
The more sensible question, IMO, is "Is the universe fundamentally quantized?". Can you concretely say where the boundary between an apple and the surrounding air is? Is a particular electron on the boundary part of the apple or the air?
If the universe is not truly quantized, then there is nothing to count. By extension, mathematics is not related to physical reality, and it makes no sense to apply mathematical notions of infinity to the universe in such speculative ways.
- CompelTechnic 8y agoEven if the universe is not discretized, there is no reason to completely discount the value of mathematics. Continuous probability distributions of particle locations still have meaning, individual entities can still be disambiguated as local maxima of density gradients, counting can still be built up from raw axioms and set theory. Even for people don't accept the "monism" (to use a metaphor to the monism/ dualism debate of the human mind and body) of physics and mathematics, these same people cannot avoid accepting that correctly applied theoretical manipulations of mathematical symbols jive perfectly well with the predicted, physical outcome they represent. Does claiming that the numbers don't mean anything mean anything?
- swerveonem 8y agoWell said, I wish I knew you in real life.
- pphysch 8y agoI don't know where you read that I "completely discount the value of mathematics". >"...cannot avoid accepting that correctly applied theoretical manipulations of mathematical symbols jive perfectly well with the predicted, physical outcome they represent." Close, except for "perfectly". Mathematics and other scientific models are approximations of reality and nothing more. They are fantastic tools but don't be misled into thinking they give a "perfect" picture.
- throwaway37585 8y ago> If the universe is not truly quantized... mathematics is not related to physical reality How does that follow? Mathematics is perfectly capable of modeling continuous quantities.
- pphysch 8y agoYes, math can model "continuous quantities", but is the idea of "quantity" anything more than a human abstraction? How do you define quantity, and can you do it without the notion of counting and discrete objects?
- throwaway37585 8y ago> is the idea of "quantity" anything more than a human abstraction? What, to you, would not qualify as a human abstraction? > How do you define quantity, and can you do it without the notion of counting and discrete objects? Absolutely. See Tarski's axiomatization of the real numbers, for instance.
- pphysch 8y ago> What, to you, would not qualify as a human abstraction? Nothing insofar as "what" implies a load of human abstractions. But it's clear that there is a lot of "stuff" out there that no human has ever experienced. It is extremely improbable that humans exist at a "Goldilock's scale" wherein we are even physically capable of experiencing "everything" and of finding boundaries on the universe. > Absolutely. See Tarski's axiomatization of the real numbers, for instance. I meant counting in the broadest sense, which is where numbers themselves emerge from. It seems plausible that there are alien modes of cognition that don't rely on the notion of object and can approach continuous "stuff" more directly. Maybe even some terrestrial organisms work this way.
- throwaway37585 8y ago> I meant counting in the broadest sense, which is where numbers themselves emerge from. Are you asking how define quantity without quantity? Also, I think it's fair to say there are quantities that no human has ever "experienced".