"There are none so blind as those who will not see." --

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Friday, September 28, 2012

Testing the limits of your imagination: Part 2

In this post I invite my readers to test the limits of their imagination. As I said in Part 1,
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 Part 1 I tried to determine the maximum number of sides that you can visualize a polygon as having. This time, I want you to test something different: imagined motion.

Experiment 1:
Visualize a disc (or a square; whichever proves to be easier). To help you to keep track of the motion, imagine it as half white and half black, or as having black and white stripes or dots. Now imagine the figure rotating about its center, at a relatively slow pace--say about half a rotation per second. After a few seconds, imagine it rotating once per second. Now repeat his process, gradually increasing the number of rotations  per second. I predict that at some point you will no longer be able to "keep track" of the motion. What I would like to know is how many rotations per second you can  visualize before you lose track of the motion.

Experiment 2:
Now, I want you to imagine a system consisting of two discs, one about two to three times as big as the other, with the larger one at the center.  Now visualize the smaller disc orbiting the larger one, much like planet orbiting a star (as the system would be viewed from "above", i.e., not "edge on"). Start by imagining the smaller disc orbiting at one half a revolution per second. As in Experiment 1, gradually increase the number of revolutions per second step by step: How many orbits per second you can  visualize before you lose track of the motion?

Thanks for your cooperation!

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