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Comment by michaelfeathers | Hacker News Reader

> Circles are invisible. When we say we want to draw a circle on the screen, we want to set pixels (light up equally sized rectangular bits of the screen) at integer coordinates to represent an approximation of the circle.

Priceless.

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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.

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

Ceci n'est pas un cercle?

I don't think that paragraph is of much value, and I think all the replies you got kind of address a non existent discussion.

I don't think it makes sense to discuss if a mathematical concept is 'visible' just because it happens to be something that is often represented on a 2d plot.

This discussion is not visible, what's visible is the group of pixels that form the text on the display device you're using to read this webpage.

Honestly, is this kind of observation of any value?

When I spend all day hopping up and down through different levels of abstraction in the service of building some particular program, it's all too easy to start confusing the map with the territory. If I'm writing some code to draw a circle, I might also have the circle stored on disk in a file that lists a (center, radius) pair, and I might be passing it around in memory as an IDrawable object for someone else's code to consume and I'm putting it on the screen wit pixels and so on and so on and at a certain point it does become useful to have someone remind me that none of those things are really the same circle, or really circles at all, but all representations of some Platonic circle that doesn't actually exist in my code. This problem gets worse when more than one programmer is involved. How many arguments have we seen between two people who agree with each other, but can't tell because they're stuck arguing over whether (center, radius) or a pixel group is "the real circle"?

So no, it's not of much value in that it doesn't tell us anything that we don't already know. But it can be of value to frame our understanding or discussion of the problem.

I think it is valuable because it is funny.

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