211–220 of 226 posts
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The number 2 simply exists independent of human intervention.
I am not convinced. There are no two equal things in nature. Numbering things, say apples, is a completely human abstraction over two different things.
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Proof by contradiction. Heard mathematicians like that.
Ironically, finitists and constructivists don't like proof by contradiction... I agree though, that you have come up with a contradiction. Specifically, because you seem to believe these two statements: There are finitely many natural numbers. Given any finite list of natural numbers, we can always produce another natural number not on that list.
It “exists” just like magic in Harry Potter exists. Not really.
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By “things get weird” I meant “our current theories/models predict things to get weird”. So, like, I’m saying that if Einstein’s model of gravity is applicable at very tiny scales, and if the [p,x] relation continues to hold at those scales, then stuff gets weird (either by “measurement of any position to within that amount of precision results in black-hole-ish stuff”, OR “the models we have don’t correctly predict…
I get what you mean, but one thing about which we are certain is that you cannot apply Einstein"s model of gravity at these scales, because his theory is only an approximation that determines the metric of space from an averaged density of the energy and momentum of matter, not from the energy-momentum 4-vectors of the particles that compose matter. So Einstein's theory depends in an essential way on matter being con…
I don’t expect this to work. For one thing, we already know the conditions under which the spin precesses. That’s how they measure g-2 .
Also, orbital angular momentum is already quantized. So, I don’t know why you say that the “precession” is responsible for the quantized values for the spin.
the representations of SU(2) for composite particles, combine in understood ways, where for a combination of an even number of fermions, the possible total spin values match up with the possible values for orbital angular momentum.
Could you give an explanation for how you think precession could cause this difference? Because without a mathematical explanation showing otherwise, or at least suggesting otherwise, my expectation is going to be that that doesn’t work.
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I get what you mean, but one thing about which we are certain is that you cannot apply Einstein"s model of gravity at these scales, because his theory is only an approximation that determines the metric of space from an averaged density of the energy and momentum of matter, not from the energy-momentum 4-vectors of the particles that compose matter. So Einstein's theory depends in an essential way on matter being con…
> The offset of the spin is likely to be caused by the fact that for particles of non-null spin their movement is not a simple spinning, but one affected by some kind of precession, and the "spin" is actually the ratio between the frequencies of the 2 rotation movements, which is why it is quantized. I don’t expect this to work. For one thing, we already know the conditions under which the spin precesses. That’s how…
I have used "precession" for lack of a better term for suggesting its appearance, because while there is little doubt about the existence of 2 separate kinds of rotations in the particles with non-null spin, there exists no complete model of how they are combined.
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Ironically, finitists and constructivists don't like proof by contradiction... I agree though, that you have come up with a contradiction. Specifically, because you seem to believe these two statements: There are finitely many natural numbers. Given any finite list of natural numbers, we can always produce another natural number not on that list.
Leading to yet another finite list. You will never actually end up with an infinity. You’ll run out of space, you’ll run out of time. It “exists” just like magic in Harry Potter exists. Not really.
What it means for there to be infinitely many natural numbers is that for any finite list, there are natural numbers not on that list (something you appear to agree with). If there were finitely many natural numbers this wouldn't be true
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Leading to yet another finite list. You will never actually end up with an infinity. You’ll run out of space, you’ll run out of time. It “exists” just like magic in Harry Potter exists. Not really.
No one thinks you can actually write an infinite list. What it means for there to be infinitely many natural numbers is that for any finite list, there are natural numbers not on that list (something you appear to agree with). If there were finitely many natural numbers this wouldn't be true
Let’s not even begin about the axiom of choice. Or transcendental numbers.
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No one thinks you can actually write an infinite list. What it means for there to be infinitely many natural numbers is that for any finite list, there are natural numbers not on that list (something you appear to agree with). If there were finitely many natural numbers this wouldn't be true
Sure they do. Cantors argument, infinite sums, mathematicians keep using infinite lists as if they do exist. Let’s not even begin about the axiom of choice. Or transcendental numbers.
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Why are rationals special? They represent an exactness in a similarly unphysical way as the integers. The rationals are infinitely precise. 1/3 is not the same as 0.33333 or 0.33333333 or 0.3. The real numbers exist and are approximable, either by rationals or by decimal expansion. The idea of approximability and computability are the critical things, not the specific representation.
I am confused why you think the exactness of integers and rationals is unphysical. "This egg carton has 12 eggs" is a (boring) physical statement. "You can make 1/3rd of a carton of eggs without cutting an egg" also seems perfectly physical to me. Your problem with zero-point-three-repeating is a quirk of decimal representation, not a mystical property of 1/3. Egg cartons might sound contrived but the reals don't nec…
Some eggs are smaller than others; some are more dense, etc. Yes, the "count" is maybe sort of interesting in some very specific contexts, but certainly not in any reductive physical context. It only works in an economic context because we have standards like what constitutes a "chicken egg large white grade AAA".
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There are two things being talked about here, and worth teasing them out. On the one hand, this article is talking about the hierarchy of "physicality" of various mathematical concepts, and they put Cantor's real numbers at the floor. I disagree with that specifically; two quantities are interestingly "unequal" only at the precision where an underlying process can distinguish them. Turing tells us that any underlying…
> For example, the idea that there are the same number of integers as even integers is a stupid one that in the end does not lead anywhere useful. I am not sure what you are arguing here. We’ve been teaching this to all undergraduate mathematicians for the last century; are you trying to make the point that this part of the curriculum is unnecessary, or that mathematics has not contributed to the wellbeing of society…
Otherwise it's pretty much a dead end unless you're in the weeds. You just mutter "almost everywhere" as a caveat once in a while and move on with your life. Nobody really cares about the immensely large group of numbers that by definition we cannot calculate or define or name except to kowtow to what is in retrospect a pretty bad theoretical underpinning for formal analysis.
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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.
Yeah but if you look down the axis of rotation you will have a perfect (to many decimal places anyways) circle... which was the demand.
> > The idea of arbitrary precision is intrinsically broken in physical reality.
There is no contradiction here.