There is no fact about reality that can ever threaten facts about mathematics. Mathematic definitions exist independent of reality.
Irrational
Submitted 10 months ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/df5d1747-d1af-491f-bf21-686708dc2fef.jpeg
Comments
Leate_Wonceslace@lemmy.dbzer0.com 10 months ago
rockerface@lemm.ee 10 months ago
In fact, you can build a system of definitions that very clearly doesn’t exist in real world, like hyperbolic geometry.
tate@lemmy.sdf.org 10 months ago
Sometimes we find that obscure pure mathematics does describe reality when no one expected it to. Riemannian geometry is one such example.
Zehzin@lemmy.world 10 months ago
sir_pronoun@lemmy.world 10 months ago
But irrational numbers aren’t the same as imaginary numbers. Also, there are irrational imaginary numbers. And quantum physics loves using imaginary numbers. So that sentence in the image is nonsense, right?
pantyhosewimp@lemmynsfw.com 10 months ago
“Imaginary” was merely poor word choice from long ago.
bstix@feddit.dk 10 months ago
The definition of irrational numbers is that they are the real numbers that are not rationel. So we need to look at the definition of real numbers. A real number is a number that can be used to measure a continuous dimensional quantity.
Quantum physics says that reality is not continuous. Particles make “discrete” jumps instead of moving continuously. So irrational numbers can’t exist.
kogasa@programming.dev 10 months ago
That is not a definition of the real numbers, quantum physics says no such thing, and even if it did the conclusion is wrong
wholookshere@lemmy.blahaj.zone 10 months ago
They don’t make “discrete jumps” as in teleportation. They exist stable in discrete energy levels, but that doesn’t imply things don’t move continuously.
CodexArcanum@lemmy.world 10 months ago
What? You use these words, but I do not think they mean what you think they mean.
Ziglin@lemmy.world 10 months ago
This sounds really interesting but I’m afraid it’s a bit high level for me. Can you explain how vibrations would cause quantisation? I’d also be happy with a link to the correct Wikipedia article or a paper which explains it. :)
CodexArcanum@lemmy.world 10 months ago
This text book seems to cover the idea. phys.libretexts.org/…/30.06%3A_The_Wave_Nature_of… I guess I’m drawing my ideas mainly from the Bohr model.
observantTrapezium@lemmy.ca 10 months ago
The premise here is completely wrong.
Kaput@lemmy.world 10 months ago
I know those words, Someone please explain .
Dagwood222@lemm.ee 10 months ago
Blue_Morpho@lemmy.world 10 months ago
Imaginary numbers are a rotational operator.
You don’t need quantum mechanics to observe rotation in the real world.
i_love_FFT@lemmy.ml 10 months ago
Yes please!
Dagwood222@lemm.ee 10 months ago
sciencenews.org/…/quantum-physics-imaginary-numbe…
Nontechnical article explaining the concept.
bstix@feddit.dk 10 months ago
But that’s imaginary numbers, not irrational numbers.
The issue between quantum physics and irrational numbers is different than the use of imaginary numbers: Irrational numbers have infinite decimals, while quantum physics is quantized.
aberrate_junior_beatnik@midwest.social 10 months ago
So because quantum mechanics is well modeled by imaginary numbers, the existence of quantum particles threatens the definition of irrational numbers? That doesn’t make any sense.
Blue_Morpho@lemmy.world 10 months ago
Yes, it does not make any sense. If the link above is what it appears from the summary, some students unknowingly attempted to square the circle.
aberrate_junior_beatnik@midwest.social 10 months ago
My only guess as to what this could mean is that since quantum mechanics is quantum, i.e. discrete, the universe therefore cannot be continuous as the reals are. But this is a category error. Just because you could never find an object that is, say, exactly pi meters long, does not mean that the definition of pi is threatened. There’s nothing infinite that we can observe, but infinity is still a useful concept. And it works both ways; just because quantum mechanics is our best model of the universe doesn’t mean the universe is therefore quantum. 150 years ago everyone believed the universe was like a big clockwork mechanism, perfectly deterministic, because Newtonian physics are deterministic. And who knows, maybe they were right, and we just don’t have the framework to understand it so we have a nondeterministic approximation!
themeatbridge@lemmy.world 10 months ago
We could make an object that is exactly pi meters long. Make a circle of 1 meter in diameter, and then straighten it out. We would not be able to measure the length more accurately than we can calculate it (that might be the larges understatement ever) but to the tolerance with which we could make a 1 meter dismeter circle, you should have the same tolerance to the circumference being pi.
Donkter@lemmy.world 10 months ago
I mean, you only need 39 digits of pi to calculate the circumference of a circle with a diameter the size of the universe to the width of a hydrogen atom. So no matter how detailed you get it’s impossible to determine if a circles circumference is anywhere close to exactly pi.
To ops point, you could set up your thing theoretically and we can math out that it should be pi. But we could not make that object.
aberrate_junior_beatnik@midwest.social 10 months ago
No, by our current understanding there is no length smaller than a Planck length, and any distance must therefore be divisible by an integer. That is, the length is made up of discrete quanta. Pi, or any other irrational number, is by definition not divisible by an integer, or it would be a ratio, making it rational. This has nothing to do with the accuracy or precision of our measures.
Ziglin@lemmy.world 10 months ago
Two issues: