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Comment by mjburgess | Hacker News Reader

It's not clear to me why people think perfect geometries do not exist, they occur all the time in physics.

Of composite matter, sure, because it's composite in a certain sort of way, you do not get perfect circles. But the structure of macroscopic material does not exhaust the physically.

Even here, one could define some process (eg., gravitational) which drives matter towards being a perfect circle, because perfect circularity is a property of that process. This is, as a matter of fact, true of gravity -- if it weren't we'd observe violations of lorentz invariance, which we do not.

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Perfect in a single-body universe, perhaps, but the gravity field of a particle is perturbed by other nearby particles - where "nearby" is relative to precision desired - and therefore never a perfect sphere.

Or, to put it another way, so-called "perfect circles" exist in a real, 4-D, wibbly-wobbly gravity-distorted space, and are no longer perfect Cartesian circles.

They still only exist theoretically; not in practice.

Circularity is still a property of the process. One requires perfect circles to describe it.

It is also easy enough to construct circular state spaces, and the like.

The idea that what's real is simply the geometry of macroscopic visible matter, or even of matter alone, is a nonesense.

The world is "immanently abstract", and possess primeness, circularity, etc. in itself -- not as something merely imagined. This is obvious from the physical description of its evolution.

Irregularity, of this kind, is derivative of a geometrical reality. The irregular doesn't govern the irregular, if it did, there would be no structure whatsoever.

Perfect circles just exist on probabily using 2pi for random directions and overall statistics.

When was the circle discovered? When it became essential to physics?

When it was essential to perception. Its necessary to have a model of a circle (, elipse...) in order to correctly parse (at least,) visual perception -- because space is inherently geometrical.

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