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Comment by lutorm | Hacker News Reader

Circles are not always invisible. A circle made up by a closed-loop line source of photons would be visible. (They're kind of hard to make, though.)

It's sort of the question of what is the smallest thing a human can "see". Stars, for example, are extremely small, far below the resolution of the human eye (outside of the atmosphere, of course). Yet seeing them is not a problem, you just get an unresolved image.

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Then it's the photons that are visible.

A circle is a set of points, and a point is an abstract concept. Having a photon centered on a point does not make the point visible.

Also, a circle is an infinite set of points, so even if points were visible, you couldn't have a real circle without infinite points.

By that definition, nothing is visible. You never see anything except photons.

That's true; and sometimes, that definition is useful, as it is here.

Visible means "able to be seen." You can see things that emit or reflect light. Abstract concepts don't emit or reflect light.

Real objects can only approximate a circle. The pedantic definition of a circle in this context is being used to make the point that you can't make a perfect circle with pixels.

No. If you made an abstract object that emitted light, like the "linear light source" I hypothesized, it would be a perfect circle, and visible. It doesn't exist, of course, but if it did, it would be visible... ;-)

Richard Feynman spoke well and humorously on this topic: http://http://www.youtube.com/watch?v=XpYhM4x4PmY

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