Comment by TechBro8615 | Hacker News Reader

Comment by TechBro8615 | Hacker News Reader

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I'm neither a mathematician nor a physicist, so I'm not nearly informed enough to elaborate on the subject properly, but I would note that the axiom of choice is not proven, and while you can mathematically divide a continuum into infinitesimally small sets, you cannot do the same to physical matter. From my understanding, many of the contradictions between classical and quantum physics arise at this boundary between the discrete and the continuous, where classical physics generally assumes continuity while quantum physics is constructed around discrete quantization mostly independent of time.

Again, I'm not a physicist, but I think it's telling that the validity of continuum mechanics [0] depends on a model and multiple assumptions. I have no trouble agreeing with your original statement, "with enough marbles, the discrete distribution behaves like a continuous distribution," when speaking mathematically, but mathematics by its nature is an idealized model of the world - I'm not willing to accept that it's objectively representative of physical reality. The discussion we're having here is one of metaphysics, so it feels a bit like the height of hubris to use mathematics as the tool for describing objective reality, because metaphysically, we cannot say that mathematics is anything other than a tool we've constructed for approximating the model of the world as we understand it. Considering the subject of this post is about retrocausality, we're already throwing out some pretty wild ideas, so I think it's a bit hubristic to dismiss them by citing a branch of mathematics that assumes the existence of countably infinite sets [1].

[0] https://en.wikipedia.org/wiki/Continuum_mechanics#Validity

[1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...

This whole thread hinges on your not giving credence to the word "practically" , as in "approximately". No countably infinity needed, and Continuum Hypothesis isn't relevant at all in any way, as it is aboit uncountable infinity. Until you explain what you are trying to say, you aren't saying anything meaningful. The one showing hubris here is you, tossing around technical terms don't admit you don't understand.

> The one showing hubris here is you, tossing around technical terms don't admit you don't understand.

Hence the disclaimer. I just think this stuff is fascinating. If you're interested, this is the article that originally got me thinking about these ideas as they relate to the flow of time: "Does Time Really Flow? New Clues Come From a Century-Old Approach to Math" [0]. It's effectively an appeal to intuitionist mathematics and a rejection of constructivism, where - simplified - every particle since the big bang can be assigned some "number" that describes its position on its world line, with a precision that is finite, but always increasing - and it's this increase in precision from which emerges the "flow" of time. If you ctrl+f the article for "continuum," you'll see some better constructed arguments for what I'm trying to argue, e.g.:

> Moreover, the continuum can’t be cleanly divided into two parts consisting of all numbers less than ½ and all those greater than or equal to ½. “If you try to cut the continuum in half, this number x is going to stick to the knife, and it won’t be on the left or on the right,” said Posy. “The continuum is viscous; it’s sticky.”

The impression I'm left with is that the difference between constructivist vs. intuitionist mathematics (which rejects the law of the excluded middle) has some parallels to the difference between eternalism (there is a past, present and future) vs. presentism (there is only the present).

As a layman, I just can't help but notice the same patterns come up again and again when looking at unresolved problems between classical and quantum mechanics, namely those that lie at the boundary between the continuous and discrete. FWIW, I asked ChatGPT for some unresolved mathematical problems that might relate to this, and it came up with: The Continuum Hypothesis, The Axiom of Choice, and The Riemann Hypothesis, all of which it admitted are possibly impossible to prove because they're effectively unfalsifiable. (I also showed it this entire thread, and it agreed with your critique of my arguments, but also that every argument in the thread is unfalsifiable - and then it pointed me to the Boltzmann Brain paradox).

[0] https://www.quantamagazine.org/does-time-really-flow-new-clu...

Indeed, the original claim treats mathematics as a modeling tool, not philosophy. Nevertheless, it is my belief that untestable hypotheses about True Reality (should it even exist) are not debatable without causing migraines of epic proportions. There's no physics without mathematics -- as physicists say, shut up and calculate.

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