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To me this is proof that infinity is something only present in our math and not in the universe. Infinity is a nice approximation but it feels like wishful thi
by desperate 5y ago
To me this is proof that infinity is something only present in our math and not in the universe.
Infinity is a nice approximation but it feels like wishful thinking that our universe or anything in it is infinite.
Happy to hear disagreements tho.
- jhgb 5y ago> infinity is something only present in our math and not in the universe This is true of all mathematical objects. The number 7 doesn't exist in the universe either. It's not a physical object.
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- danparsonson 5y agoOP didn't argue that finite numbers are physical objects, they said that infinities are not present in the universe. For example, I could in theory hand you 7 electrons but there are not infinity electrons for me to hand to you.
- jhgb 5y agoThat sounds like a weird interpretation of "to be present in the universe" to me. Also I was under the impression that it's unknown whether the universe contains an infinite number of electrons or not.
- PeterisP 5y agoIt's certainly known that the observable universe does not contain an infinite number of electrons, as it has a finite size and finite mass. And it's rather moot to talk about the space beyond the observable universe that can never affect us or anything we can observe in any way whatsoever, so any other statements about it are inherently unfalsifiable, so all the science of physics is relevant only w.r.t. the (finite) observable universe.
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- danparsonson 5y agoWeirder than 'numbers are physical objects'? Can you suggest a more suitable interpretation of the OPs intent?
- hprotagonist 5y agoit's OK. electrons don't "exist" discretely, either. At best, when you "hand me 7 electrons", you're directing me towards the fat part of 7 probability distributions, so we're back to math again...
- danparsonson 5y agoWell that's a bold assertion about a theory with whose implications we are still grappling; electrons may not be point-like entities but they are nonetheless quantifiable 'packets' of energy, are they not?
- robertlagrant 5y agoBut is that not the locations that are inexact, not the quantity of electrons?
- layer8 5y agoBut the electron field has different values at different points in spacetime, and we have no evidence that either the number of points (locations) or the number of different possible values at those points is finite. Unless we posit that they are finite in number, infinity is quite present in the universe.
- danparsonson 5y agoWould not an infinite electron field in a finite (observable) universe result in an infinite energy density and therefore the entire universe would collapse into a black hole?
- layer8 5y agoIntegrals over a finite interval can have (and often do have) a finite size even though the interval contains an infinite number of points, with an infinite number of different values at those point.
- danparsonson 5y agoRight, because the integral of a function is not a straight sum of values of that function evaluated for every number in the interval; the integral of y=x dx for 0<=x<=1 is not 0+0.1+0.11+0.111+0.1111+...+1. Electrons have a fixed energy, so cramming an infinite number of them into a finite space necessarily requires infinite energy.
- wizzwizz4 5y agoI'd argue you can't cram any electrons into any finite space without infinite energy. But we're not really talking quantum physics, here.
- danparsonson 5y agoI'm not sure what you mean - any battery you have would seem to contradict you - would you elaborate?
- snet0 5y agoTell that to Plato. Honestly I think that's a continuous claim, and comes down to differences in understanding. I can certainly have 7 of some object, does the 7-ness exist in the collection? Not really, but what about another phenomenon: colour? An object appears blue, and we say it is blue, and the blueness is due to physics, but it's a subjective delineation. A table is a delineation too, the leg is part of the table and the White House is not. In some sense, the table-ness category is just as real as the 7-ness category. Of course you could just say that all that actually exists is some collection of particles/fields, but then you've abused all the words we're using until they stop being useful.
- dlkmp 5y agoWhat's your concept of time and its extension then?
- tsimionescu 5y agoWell, infinity is inherently unscientific, as there is no way to scientifically differentiate between an infinite quantity and a really huge quantity (same for infinitesimals), in finite time. What this means is that a universe that contains infinities is, even in theory, entirely indistinguishable (in finite time) from an universe that contains really large/small but finite quantities.
- turminal 5y ago> there is no way to scientifically differentiate between an infinite quantity and a really huge quantity (same for infinitesimals), in finite time That depends on the model of computation you pick, doesn't it?
- tsimionescu 5y agoOnly if you want to think about models of computation that allow performing infinite operations in finite amounts of time, which I don't think are that interesting.
- auggierose 5y agoI'd say if our universe makes such computations possible, then that would be very interesting.
- tsimionescu 5y agoAbsolutely! Similarly, if our universe allowed instantaneous travel and free energy, that would also be very interesting. Not holding my breath for either.
- auggierose 5y agoThe fact that you can breath at all is quite a miracle. Not sure why you are so pessimistic about the rest.
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- robot_no_419 5y agoMathematics doesn't really "exist" in the first place. It's more of a language that's rich enough and with enough logic to describe/approximate the laws of physics that actually do exist.
- bobthechef 5y agoSo quantity, structure, formal necessity don't exist? Mathematics has nothing to do with laws of physics. Even if the laws of physics[0] were different, these mathematical[1] truths would remain the same. [0] Laws of physics don't actually exist. They're shorthand generalizations about features of particulars. The notion of some kind of abstract disembodied "laws" that somehow "govern" everything is absurd. [1] For clarify: mathematics is a field that studies such things.
- snet0 5y agoLaws in the physics sense don't govern, though, they describe. It's akin to saying moral laws don't decide what's immoral, they simply describe it. Given that, "laws of physics" are certainly describable. We simply write the formulae that tell us what the next state of the dynamical system is. They are ways of delimiting what is physically possible, given the current state of the art.
- throwawaygal7 5y agoI have never understood the opposition to the law of physics you seem to hold. What is the alternative? That we merely observe rigid patterns that are baked into physical reality? Isn't whatever is 'baked in' more or less a 'law of physics'? If these are just 'brute facts' are they not then 'laws'? Maybe governance is too strong an word for the correspondence but what is the alternative?
- Michaelfonzolo 5y agoI've always adhered to the idea that "infinity" encodes "allness". For instance, to say that the sum of 1/2^n for all natural numbers n converges to 1 is not to say that we're actually adding up infinitely many numbers, but rather that I can always win a certain game: you give me an arbitrarily small epsilon > 0, I can give you enough terms in the sequence such that their sum (a finite sum) is within epsilon of 1. No, I can't actually add up infinitely many numbers, but you can never win my game, so certainly "infinity" exists in that sense. So, while I can't "point" to an infinite number of things like I can point to 9 things or 3.62 things, I still think it exists. I'm not sure how well this generalizes to all infinite cardinals, ordinals, or to transfinite induction/construction. It is certainly strange that Cantor's theorem (the cardinality of a set is strictly smaller than that of its power set) implies there are different sizes of "all" implicit in my usage of the word.