…literally.

In his

*Meditations on First Philosophy*, Descartes distinguished between imagination and conception, or between mental images and concepts. Thus he supposed that one can conceive of a chiliagon, a polygon of a thousand sides, although one cannot form a mental image that represents it—none, at any rate, that wouldn’t represent a circle equally well. This shows that imagination has its limits, and that one can conceive of things that one cannot (adequately) imagine.In order to discern what these limits are, I invite my readers to test the limits of their own imaginations in an experiment based on Descartes’ example. Since it concerns only what you can imagine, you don’t have to resort to a lab—in this case a “thought experiment” and a real experiment coincide!

Now, I’m sure you can imagine a polygon with the least possible number of sides—a triangle. I’d wager that you can also imagine a square, a pentagon, a hexagon… but not a chiliagon. It would thus seem that there is some number

*n*such that you can imagine an*n*-sided polygon but not an*n*+1-sided polygon. (Note: For the purposes of this experiment you only count as imagining a polygon if you can imagine the whole thing at once.) Let’s call this*n*-sided polygon your*limit polygon*. I have two questions: First, what is the number of sides of your limit polygon? Second, do you notice anything about the phenomenology of your limit polygon? If so, what?