On the Rubbing of Hands

[stoutfellow]

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:

Comments

[toraks.livejournal.com]

Wow, that's really cool! Hope it went well!

[stoutfellow.livejournal.com]

It did, mostly. I came up with proofs for a couple of my conjectures, and knowing they're true should give me some leverage on the others.

Basically, I've nailed down one tiny corner of the problem I'm interested in; extending my methods to the rest of the problem looks promising, but rather difficult.

Prof. W and I have a longstanding friendly dispute over the meaning of the words "the same", and that came up again today. (Some geometric objects that I think ought to be considered different, he thinks should be thought of as the same. He has a good argument, but I think I gave a solid justification for my interpretation. Prof. T is on my side.)

[toraks.livejournal.com]

Slow progress in fits and starts. Finding something out that takes a long time, but which is actually just getting you to the point where you wanted to be and then you can get to the real interesting stuff.

Sounds like good research fun. :-)

Press on!