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stoutfellowLast week, after getting my algorithm working, I used it to trawl for data. There were two things I could fiddle with: which polyhedron I'm looking at, and what "primitive generator" (sorry, technical term, which I'm not going to define) I'm using. I set up a neat little table to organize the results - polyhedra down the side, generators across the top. Lots and lots of nice data....
Up in one corner, though, something unusual was happening. All across that row - corresponding to the ordinary tetrahedron - I had results of one kind ("order 2, simple"), except there at the end ("order 2, not simple"). Anomaly. Gotta figure it out....
During the snow day on Monday, I tried to work out why the anomaly was there. I eventually worked my way around to an argument that it ought to be not just there, but all over the place. This I knew to be wrong, but I couldn't see the hole in the argument. This left me badly confused, and I think I may have frightened W with my raving when I saw him this morning.
When I finally got to the office, I began checking my argument, and soon saw the flaw in it... at which point it became clear that the anomaly should not be there, or indeed anywhere. The entire flaming row ought to be "order 2, simple". I reluctantly concluded that there was still something wrong with my algorithm.
I spent two bloody hours trying to track it down. I finally focused in on two formulas, embedded in the code, which I had worked out by hand, at home. I tried tweaking them. The anomaly exploded all over the place. Wrong tweak. Try again. The anomaly's gone - at least, it's not there; now it's over here.
Crap.
I finally worked out the formulas again, this time using Mathematica. I also spent some time staring at the geometry. ("Which way does that arrow go?") Finally, I adjusted the code and ran the data again. No anomaly.
Whew.
All of the results I'd gathered, except that one, turned out to be correct. I spent all that work to, basically, get back where I'd started from (but with that one blemish removed).
Who says a mathematician's life can't be exciting?
Up in one corner, though, something unusual was happening. All across that row - corresponding to the ordinary tetrahedron - I had results of one kind ("order 2, simple"), except there at the end ("order 2, not simple"). Anomaly. Gotta figure it out....
During the snow day on Monday, I tried to work out why the anomaly was there. I eventually worked my way around to an argument that it ought to be not just there, but all over the place. This I knew to be wrong, but I couldn't see the hole in the argument. This left me badly confused, and I think I may have frightened W with my raving when I saw him this morning.
When I finally got to the office, I began checking my argument, and soon saw the flaw in it... at which point it became clear that the anomaly should not be there, or indeed anywhere. The entire flaming row ought to be "order 2, simple". I reluctantly concluded that there was still something wrong with my algorithm.
I spent two bloody hours trying to track it down. I finally focused in on two formulas, embedded in the code, which I had worked out by hand, at home. I tried tweaking them. The anomaly exploded all over the place. Wrong tweak. Try again. The anomaly's gone - at least, it's not there; now it's over here.
Crap.
I finally worked out the formulas again, this time using Mathematica. I also spent some time staring at the geometry. ("Which way does that arrow go?") Finally, I adjusted the code and ran the data again. No anomaly.
Whew.
All of the results I'd gathered, except that one, turned out to be correct. I spent all that work to, basically, get back where I'd started from (but with that one blemish removed).
Who says a mathematician's life can't be exciting?
