The Universe of Discourse

Fri, 29 May 2020

An optical illusion?

A couple of years ago I wrote an article about a topological counterexample, which included this illustration:

A circle, with the
center marked.  A shortest-distance path is drawn in blue between two
blue points on the same radius, and in red between two red points on different
radii.  The blue path goes straight from one blue point to the other.
The red path goes from one point straight to the origin,
then straight to the other point.

Since then, every time I have looked at this illustration, I have noticed that the blue segment is drawn wrong. It is intended to be a portion of a radius, so if I extend it toward the center of the circle it ought to intersect the center point. But clearly, the slope is too high and the extension passes significantly below the center.

Or so it appears. I have checked the original SVG, using Inkscape to extend the blue segment: the extension passes through the center of the circle. I have also checked the rendered version of the illustration, by holding a straightedge up to the screen. The segment is pointing in the correct direction.

So I know it's right, but still I'm jarred every time I see it, because to me it looks so clearly wrong.

[ Addendum 20200530: John Gleeson has pointed out the similarity to the Poggendorff illusion. ]

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