71–80 of 226 posts
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Can you name a physical thing that is a circle even to the baseline precision level of a 64 bit float?
A black hole.
Any rotating/spinning black hole will no longer be a perfect sphere.
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As in why bother using real numbers in physics? Mostly because you need them to make the maths rigorous. You can't do rigorous calculus (i.e. real analysis) on rationals alone.
You don't need the full set of real numbers to do physics, only the computable subset of the real numbers. Using the full reals is mostly done out of simplicity.
Is sqrt(2) computable?
Is BB(777) computable?
Is [the integer that happens to be equal to BB(777), not that I can prove it, written out in normal decimal notation] computable?
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You don't need the full set of real numbers to do physics, only the computable subset of the real numbers. Using the full reals is mostly done out of simplicity.
What do you mean by "the computable subset of the reals" formally? Is sqrt(2) computable? Is BB(777) computable? Is [the integer that happens to be equal to BB(777), not that I can prove it, written out in normal decimal notation] computable?
So yes sqrt(2) is computable.
Every BB(n) is computable since every every natutal number can be computed. It's the BB function itself that is not computable in general, not the specific output of that function for a given input.
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> But the Cantor vision of the real numbers is just wrong and completely unphysical. They're unphysical, and yet the very physical human mind can work with them just fine. They're a perfectly logical construction from perfectly reasonable axioms. There are lots of objects in math which aren't physically realizable. Plato would have said that those sorts of objects are more real than anything which actually exists in…
> They're unphysical, and yet the very physical human mind can work with them just fine Nah, you're likely thinking of the rationals, which are basically just two integers in a halloween costume. Ooh a third, big deal. The overwhelming majority of the reals are completely batshit and you're not working with them "just fine" except in some very hand wavy sense.
the first 2 naturals form an integer.
that integer and a 3rd natural constitute a real (but this 3rd natural best be bigger than zero, else we're in trouble)
what I choose to focus after observing the "unphysical" nature of numbers. is the sense of natural opposition (bordering on alternation) between "mathematical true" and "physical true". both are claiming to be really real Reality.
in the mathematical realm, finite things are "impossible", they become "zero", negible in the presence of infinities. it's impossible for the primes to be finite (by contradiction). it's impossible for things (numbers or functions of mathematical objects) to be finite.
but in the physical reality, it's the "infinite things" which become impossible.
the "decimal point" (i.e. scientific notation i.e. positional numeral systems) is truly THE wonder of the world. for some reason I want something better than such a system... so I'm still learning about categories
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> Nature and the universe is all about continuous quantities One could argue that nature always deals in discrete quantities and we have models that accurately predict these quantities. Then we use math that humans clearly created (limits) to produce similar models, except they imagine continuous inputs.
The quantity of matter and the quantity of electricity are discrete, but work, time and space are continuous, like also any quantities derived from them. There have been attempts to create discrete models of time and space, but nothing useful has resulted from those attempts. Most quantities encountered in nature include some dependency on work/energy, time or space, so nature deals mostly in continuous quantities, o…
I'm under the impression that all our theories of time and space (and thus work) break down at the scale of 1 plank unit and smaller. Which isn't proof that they aren't continuous, but I don't see how you could assert that they are either.
> the principle that there is more reality in a cause than in its effect What a weird idea. Why would that be?
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I don't think time and measurement precision are necessarily related in that way. You can measure weight with increased precision by using a more precise scale, without increasing the time it takes to do the measurement.
The real point is that it takes infinite energy to get infinite precision. Let me add that we have no clue how to do a measurement that doesn't involve a photon somewhere, which means that it's pure science fiction to think of infinite precision for anything small enough to be disturbed by a low-energy photon.
All math is just a system of ideas, specifically rules that people made up and follow because it's useful. I'm so used to thinking this way that I don't understand what all the fuss is about, mathematical objects being "real". Ideas are real but they're not real in the way that rocks are. Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But…
then maths is really THE absolute best description available of language and nature.
but non-mathematical minds will simply wonder and be amazed at how "maths explains the world", a clear indication that somebody is not thinking like a mathematician.
> Whenever there's a mysterious pattern in nature, people have felt the need to assert that some immaterial "thing" makes it so. But this just creates another mystery: what is the relationship between the material and the immaterial realm?
the relationship between the material and the immaterial pattern beholden by some mind can only be governed by the brain (hardware) wherein said mind stores its knowledge. is that conscious agency "God"? the answer depends on your personally held theological beliefs. I call that agent "me" and understand that "me" is variable, replaceable by "you" or "them" or whomever...
oh, and I love (this kind of figurative) digging. but I use my hands no shovels.
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A black hole.
There is no black hole that is a perfect sphere. That would, at a minimum, require a body with absolutely no angular momentum which isn't in anyway feasible. Any rotating/spinning black hole will no longer be a perfect sphere.