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/sci/ - Science & Math

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7442521 No.7442521 [Reply] [Original]

it's said that pi is a completely theoretical concept because "there are no perfect circles in nature." but can this really be said for certain? what exactly in nature prevents there being a perfect circle somewhere in our universe?

>> No.7442524

>>7442521
> what exactly in nature prevents there being a perfect circle somewhere in our universe?

The rest of the universe

>> No.7442531

>>7442521
The problem is that a circle requires an infinite amount of points and most "things" that people can point to are made of a finite amount of particles. The solution is of course to find a perfect circle in space and not in matter. How about the event horizon of a black hole? Or the electron shell of a hydrogen atom?

>> No.7442537
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7442537

>>7442521
pi is not rational and irrational numbers are nothing be chimeras

reminder that only predicativists constructive are doing sensible mathematics, perhaps even only the finitists

>> No.7442541

aren't any "common" shapes impossible in nature

>> No.7442585

>>7442541
what the fuck?

ab ebby bobun bups butteeble ib bubber

>> No.7442652
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7442652

>>7442541
I don't know, you tell me.

>> No.7442657

>>7442652
I don't think that's the definition of nature OP meant

>> No.7442660

>>7442531
>electron shell
>circle
summer

>> No.7442693

>>7442660
If a sphere exists then a circle exists.

>> No.7442710

>>7442521
All math is completely theoretical

>> No.7442732

>>7442693
>electron shell
>sphere
This is only true as a limit. Any finite # of observations will not produce a perfectly spherical distribution. Limits, being a mathematical abstraction, are not a part of nature.

>> No.7442738

>>7442732
We're not talking about observations of an electron shell, we're talking about the electron shell itself. That is what exists.

>> No.7442757

Because math isn't something that exists in nature that we discovered one day. Science is based on observation, while Mathematics is a completely made up system to help us explain other made up shit

>> No.7442812

>>7442738
So you are saying there is this thing in nature that's not observable by any means, but it must be a precise sphere.

What test could you run to show that the electron shell isn't a polyhedron with ~10^99 sides?

>> No.7442831

>>7442812
I'm pretty sure that since it's summer, 10^99 is close enough

>> No.7442833

>>7442660
>thinks the electron shell breaks parity conservation
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

>> No.7442846

>>7442531
>How about the event horizon of a black hole?
Gets very close over time (to a circle, not a sphere -- there's angular momentum), as long as you're not throwing new stuff in. But not theoretically perfect.

>Or the electron shell of a hydrogen atom?
An abstraction. For any given real atom, you're not going to have a perfect 100% chance the electron is in an s orbital.

>> No.7442884

>>7442738
Just to clarify the electron shell isn't really a "thing" in nature. It's a probability distribution of finding the electron if observed and therefore much more theoretical than real. That being said, the shell is not so much of a "shell" as it is a cloud that is radially distributed from nucleus of the atom. What people refer to as the shell just happens to be the band/surface of highest probability density. But even then, this she'll would only be perfectly symmetrical if there were no other particles in the universe other than those contained in the hydrogen atom itself, because any variations to the potential well or any interference from other particles (no mater how negligible) will change the distrubution to not be a perfectly spherically symmetric.

>> No.7442896

>>7442884
>But even then, this she'll would only be perfectly symmetrical if there were no other particles in the universe other than those contained in the hydrogen atom itself,
yes, perfection exists only as an idea that nobody has ever perceived.

do not dwell on delirium like these, nobody knows what one atom is in a empty universe [to say that it is just like when there is no other potential assumes that our model thus far is correct [and that the idea of modelizing is relevant at all]]

>> No.7442913

Even if an electron is orbiting in the ground state, there is a very small potential field (from the rest of the universe). Although that potential becomes very close to zero, it will have some effect.

So the orbital can never be truly a perfect sphere.

>> No.7442916

>>7442521
Circles are just an abstraction encoded by neurons in human heads.

>> No.7442963

>>7442521
The granularity of matter.

Even at the subatomic level, it's extremely unlikely that quarks are perfectly round. Anything higher than that, and you're running into the issue that matter can be subdivided, so your "circle" is lumpy, with some points just slightly closer to the center and some points just slightly further away.

>> No.7443131

my bollocks are perfect spheres

>> No.7443152

>>7442521
That's why PI is an irrational number.
Nature isn't irrational. (at least on the macro-scale.)

>> No.7443157

>>7443152
>Nature isn't irrational. (at least on the macro-scale.)
Why are you separating the macro and mirco? Why are you claiming nature is rational , when it is only rational because that's all you've known and are used to?

>> No.7443161

>>7443157
Because at the very small, quantum effects take place. I suppose you could argue that this is a highly rational thing. But with our current limited knowledge, things really do look irrational.

>> No.7443191

>>7442531
>The problem is that a circle requires an infinite amount of points and most "things" that people can point to are made of a finite amount of particles
You're thinking of circles with the euclidean metric over the reals.

With the discrete metric, there's lot's of circles in reality.

>> No.7443193

Electric field generated by a point charge.

>> No.7443194

>>7443161
You're confusing linguistic definitions of "rational" and "irrational" with mathematical definitions of "rational" and "irrational".

"Rational" in mathematics means "expressible as a ratio of whole numbers", which is not at all what the everyday meaning is.

>> No.7443196

>>7443193
No such thing as a point charge, though. Electrons do have radius. It may be a very, very small one, but it's a radius nonetheless.

>> No.7443204

>>7443196
So, are electrons perfect spheres?.

>> No.7443221

>>7443193
The observed electric field of the electron includes that of transient virtual particles, and is therefore never completely spherically symmetric.

>> No.7443245

>>7443221
What if you look at the electric field at a point very close to the "border" of the electron?
Would it still be affected by that?

>> No.7443339

>>7442812
Again, we are not talking about whether you can "observe" the electron shell as a perfect sphere, we are talking about whether or not perfect spheres exist. According to physics, which is based on empirical data of the atom and reasoning, the electron shell is in actuality a perfect sphere. Your solipsism is irrelevant to the topic of discussion.

>> No.7443372

>>7442846
>For any given real atom, you're not going to have a perfect 100% chance the electron is in an s orbital.
An isolated atom will have perfect spherical symmetry.

>> No.7443384

>>7442524
>>7442531
>>7442732

You are retarded

The distribution of a electron's charge is proven to be a perfect sphere. Take a threshold value and that sphere has a border, divide that sphere in half and the flat surface is a circle. There is your perfect circle from nature.

>> No.7443439

>>7443372
Your perfectly isolated atom doesn't exist. There will always be some probability it's been kicked into an excited state by a passing photon.

>> No.7443483

>>7442521
Cows are perfectly spherical.

>> No.7443485
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7443485

>>7443339
>the electron shell is in actuality a perfect sphere.
no it is not, the electronic wave functions are not perfect spheres in general

and the wave function is nothing but a math tool, it does not exist.

>> No.7443486

>>7443384
>Take a threshold value and that sphere has a border, divide that sphere in half and the flat surface is a circle.
tell me how to ''divide that sphere ''

>> No.7443553

>>7443439
And there will always be some probability it's not, so a perfect sphere exists.

>>7443485
I'm talking about s orbitals or the 3 p-orbitals combined. The waveform is as physical as a photon's.

>> No.7443557

>>7443553
>And there will always be some probability it's not, so a perfect sphere exists.
Only in the sense that perfect sine waves exist because you can do Fourier analysis.

>> No.7443573

>>7443557
>Only in the sense that perfect sine waves exist because you can do Fourier analysis.
That has nothing to do with what I'm talking about.

>> No.7443580

>>7443573
You have a wavefunction that you're decomposing into things that involve perfect spheres in order to show that perfect spheres exist in nature.

>> No.7443635

>>7443486
with a saw

>> No.7443656

>>7443635
I should not but because the asker of "how to divide a sphere" is retarded, I'd like to explain a bit better. When a perfect sphere exists, a perfect circle exists too, how would you make a perfect sphere without leaving a perfect circle in 2 of the dimension of the sphere? It does not matter whether it's just charge, or a more physical object. Everyone thinking that nature is not able to come up with perfect circles, and haven't done already is more retarded than even Satan could imagine. Pi makes sense, and you already know what I think about you when you disagree. REEEYTAARD!!!!!!!!

>> No.7443683

>>7443384
>The distribution of a electron's charge is proven to be a perfect sphere.

For the entirely unperturbed 1-electron Coulombic Hamiltonian, maybe, but that's no more physical then the perfect black hole mentioned earlier. Any real atom is going to be perturbed by its environment in a way which breaks the radial symmetry of the orbital.

>> No.7443994

>>7443683
Electrons can survive easily without a nucleus in a vacuum. Also, magnetic and electric fields can be shielded to cancel out disturbing factors to a not- measurable size. This makes it easy to measure them. Also, the field of a electron cannot be anything else than a perfect sphere because any disturbance in the shape of the charge would mean the electron to be a dipole or "multipole", which is impossible, also proven. Black holes as we know are not as perfectly spherical because they are more likely to be influenced by objects like stars or other black holes, disturbing the gravitational field, and thus the shape of a black hole to a non-insignificant proportion. It might be that black holes which are not visible due to the absence of matter in its environment are "more round" than others, like those in centers of galaxies.
The fact that those objects are hard to grasp and the earth itself has very little perfect spheres to offer, it's stupid to deny that they exist, and you're really autistic if you can't agree that a soap bubble on a tile. or a circle drawn by a compass are circular enough.

>> No.7444035

>>7443580
No, the TOTAL wavefunction is spherically symmetric.
>>7443553
>The waveform is as physical as a photon's.
More so, in fact. Photons can only be described by QFT, because they are always moving at relativistic speeds (or, speed). This means they don't actually have a particular waveform, but instead a wave functional, or propagator etc.
>>7443683
But in a quantum system, you can't really say ANY state is physical, since everything is in a superposition of states. If some eigenstate of an actual physical system is spherical, then this is as real as any other state.
We cannot treat quantum systems the same way we treat classical ones, so the very question of a perfect sphere or circle &c is not really well founded.

>> No.7444084

Aren't shapes just a measurement, and not an actual thing anyway. It's almost an optical illusion to see a shape in the world

>> No.7444131

>>7444084
In loop quantum gravity spacetime is chopped up into lots of little blocks, so in that theory I think it is safe to say shape is real. Likewise in string theory the geometry of spacetime is recovered from a coherent state of a load of strings, each of which traces out a nice smooth surface in spacetime, so it seems in the two main theories of how our universe works on a fundamental level, shapes are very "real".

>> No.7444156

>>7443994
Yeah, I totally misread the original post (to mean the anon was talking about the distribution of an electron in a hydrogen atom, rather then the charge distribution of the electron itself). Others seem to made the same mistake, but it's my bad.

I'm sure there's still an argument to be made. (If the electron is not embedded in perfectly flat space time what are the consequences?) but since you're talking about "perfect to the threshold of measurable effect" then I'll concede the point, noting I'm not sure that this is what the OP had in mind.

>>7444035
But a *real* Hamiltonian isn't going to have a perfectly spherical eigenstate (at infinite precision). To first order, sure, but the vast majority of perturbative effects are not radially symmetric and centred on the system's locus. Even if we "emptied" the universe around the system a real Hamiltonian would always be varying due to vacuum fluctuations.

>> No.7444779
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7444779

>>7443656
>When a perfect sphere exists, a perfect circle exists too, how would you make a perfect sphere without leaving a perfect circle in 2 of the dimension of the sphere?


this is what happens when undergrads take deductive mathematics to be ontologically relevant.


a circle in a plane is not like a circle on a sphere. the two constructions are proven equivalent after conceptual work

now, we talk about a concrete construction, that is to say, a constructive algorithm to check concretely whether something is a circle

good luck separating a circle from a sphere with scissors or more advanced tools

>> No.7444976

>>7442652

those squares are perfect, not geometrically, but gustatorially

>> No.7445017

>>7442521
It's just used to relate a dimension of a circle into numerical concepts.

>> No.7445075

Assume you had enough stuff in the universe to create a ring consisting of infinitely many particles. For it to be a circle, there'd have to be some point in space from which one would measure the same distance to any particle on the ring. But all the particles would have neighbourhoods in which they could be anywhere, violating the constant distance.

>> No.7445479

>>7444779
>good luck separating a circle from a sphere with scissors or more advanced tools
there are countless ways depending on material.

>> No.7445534

>>7442710
Your dick is completely theoretical

>> No.7446862

bump

>> No.7447162

>>7445534

oh shit, we're getting scientific now

>> No.7447180

>>7442521
What the fuck does the value of pi have to do with circles in our Universe. What the fuck do Math care about how the Universe is.

Jesus, /sci/.

>> No.7447191

>>7447180
Congratulations. You rephrased the OP's question. Now you're both faggots.

>> No.7447192

>>7447180

the smell of summer

>> No.7447202

>>7447192
Moot showed that there's essentially the same traffic in summer as during the rest of the year. But hey, don't worry, you're blending in just fine.

>> No.7447206

>>7447202

>omg lol i talked to the king of 4chan and he told me that everyone is special and we all matter equally to him :^) :^)

seriously kill yourself

>> No.7447241

>>7447206
You are special to me :*

>> No.7447314

>>7442757
>other made up shit
xD