On the Rubbing of Hands

This morning, picking up around the house, I rediscovered the manual for Geometers SketchPad. Leafing through it, I learned of several things the program is capable of, that I hadn't been aware of, ranging from the mundane - how to attach explanatory text to your sketches - to the unexpected but useful - how to create a point which is restricted to move along the perimeter of a given polygon.

Armed with this new knowledge, when I arrived at work I quickly sketched out several examples of the phenomena I've been studying - quick, but detailed and accurate. (I could do these by hand, but slowly and with much computation that the sketches make superfluous. I spent a good bit of yesterday doing just that.) I was then easily able to read off the data I want to understand.

Without data, you can't make conjectures, and without conjectures, you can't construct proofs. (How can you, when you don't know what you're trying to prove?)

Now I have data.

Now I have conjectures. Boy, do I have conjectures. (I don't yet see how to prove them, but the way the data fits together makes them plausible.)

The seminar will be meeting, unusually, tomorrow morning. I will have things to say.

:rubs hands gleefully: