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Comment by waffletower | Hacker News Reader

I thought the article would go further and posit that Circles do not exist in reality as they are approximations of a mathematical ideal. But the author does present the raster image as a bonafide circle, rather than the approximation that it truly is -- more resolved than others or not. A zoomed in excerpt of the author's rasterized circle approximation clearly shows that scale is key in perception of reified ideals: https://ibb.co/P1KwLDm

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That's true in a sense, but you've got to go way down. At a fine enough level --- say, at the level of atoms --- all material things are granular, and circular or spherical things are built stepwise from material building blocks, as though from pixels. Thus even very "smooth" things are rough and granular.

Further: There are no circular (2D) molecules; nature prefers hexagons and other polygons for that. Even the proton isn't perfectly spherical. Whether the electron and other subatomic particles are perfectly spherical cannot, as yet, be determined. (The electron seemingly has a diameter far below the Planck Length.)

There are no very large circles or spheres, either. All astronomical bodies are somewhat flattened.

So I dare say perfect circles and spheres do not really exist, save as idealized mathematical objects.

I wouldn’t have believed you until I started looking into how spheres are made with various materials. All of them require immense amounts of iterations from rough cutting to polishing. Generally they are formed by reducing from a larger piece of material, sometimes inflated. It is never a cheap process to make a sphere and against nature is to achieve it. In the collection of gravities the earth and its inhabitants are subject to, straight lines are rare. A perfect sphere demands infinite straight lines of equal length from one point in space and for those to persist over time. A tall order for mere matter. Buckyballs are good enough for me.

But isn't the nature of attractive forces, like gravity, to squish everything into perfect spheres? The matter wants to resist, but that's another topic. The main issue is that pesky rotation - angular momentum is a blemish on the otherwise perfect equations of the cosmos.

Lead shot is typically spherical without any trimming from a larger piece. The traditional method is called a shot tower, and involves dropping molten lead so it forms small drops that cool as they fall, until they impact into a water bath. This works because drops of liquid are spherical below a certain size dependent on the material. The classic depiction of a rain drop is entirely false.

Is similar not also true of Lines, and Points?

That is: every real, non-theoretical Point must have a size, a resolution; and every non-theoretical straight Line is surely not a true straight line if we zoom far enough down into sub-atomics.

What about orbits?

What, precessing ellipses with major and minor axes?

What about them?

Don't we wish, orbits are only ellipses via the simplified model provided by newtonian physics.

Large black holes are the most spherical things in the relative sense, not in an absolute sense; although more so than pico-black holes, which are not very spherical.

Light cones/the 4d-radii of causality are* perfectly spherical.

Aren't they warped by the curvature of space/time that they are spreading over?

How big a factor is the rotation of the black hole? Maybe look for a large black hole not rotating too much if you want to be sure. :-)

>The electron seemingly has a diameter far below the Planck Length

According to what? We have nothing that can measure anything close to that. The standard model doesn't predict any radius on the electron, just defining it as point-like.

> Whether the electron and other subatomic particles are perfectly spherical cannot, as yet, be determined.

How can we ever determine something to be perfectly spherical? Any measurement comes with finite precision, and maybe the thing is actually not a sphere if we measured with more precision?

All measurements we have done on the electric dipole moment of the electron suggests that it could be zero. (The standard model predicts it to be non-zero, but very very very small.) This suggests that the charge distribution of the electron is spherical (or very very very close to).

That statement is just one of a million in the "calculus does not exist" realm, and is not nearly as interesting as this article was.

EDIT: apologies for the tone; came off very snide on second read.

I don't think the statement attempted to invalidate the article, there are many gems inside, such as the idea that human perception elongates the vertical axis, etc.

You wouldn't happen to have a link handy about that vertical axis perception thing would you, I l'm super curious about it.

I haven't been able to find anything corroborating the claim. But I, perhaps gullibly, shared the perception. Did find this somewhat related white paper during my short search: https://www.sciencedirect.com/science/article/pii/S004269890...

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