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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 p

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 https://ibb.co/P1KwLDm

pkulak 3y ago
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.
- waffletower 3y ago
  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.
  - namru1620 3y ago
    You wouldn't happen to have a link handy about that vertical axis perception thing would you, I l'm super curious about it.
    - waffletower 3y ago
      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/S0042698900000924 https://www.sciencedirect.com/science/article/pii/S004269890...
A_D_E_P_T 3y ago
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.
- reilly3000 3y ago
  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.
  - deleted 3y ago
    [deleted]
  - TeMPOraL 3y ago
    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.
  - chipsa 3y ago
    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.

pkulak 3y ago

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.

waffletower 3y ago
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.
- namru1620 3y ago
  You wouldn't happen to have a link handy about that vertical axis perception thing would you, I l'm super curious about it.
  - waffletower 3y ago
    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/S0042698900000924 https://www.sciencedirect.com/science/article/pii/S004269890...

A_D_E_P_T 3y ago

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.

reilly3000 3y ago
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.
- deleted 3y ago
  [deleted]
- TeMPOraL 3y ago
  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.
- chipsa 3y ago
  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.