Greg Egan on Nostr: I spent today immersed in an 8-dimensional moduli space of 3-dimensional Lissajous ...
I spent today immersed in an 8-dimensional moduli space of 3-dimensional Lissajous curves, looking for a curve with just the right properties.
That sounds like a highly visual thing … but because the properties were very computationally expensive to quantify, and because 8 parameters makes the space of possibilities so large, it was really more like being a blind mole sniffing around in the soil, following promising trails but sometimes hitting dead ends and backtracking.
It would be wonderful if we could visualise every mathematical problem with a glorious bird’s-eye view that showed the whole structure of the solution space at a glance. But for anything complicated, you usually can’t do that unless you pretty much already know the answer.
Anyway, I think I found a nice curve (though almost certainly not the nicest possible one, globally), and in a couple of weeks I’ll post something about the reasons that I think it’s so nice.
That sounds like a highly visual thing … but because the properties were very computationally expensive to quantify, and because 8 parameters makes the space of possibilities so large, it was really more like being a blind mole sniffing around in the soil, following promising trails but sometimes hitting dead ends and backtracking.
It would be wonderful if we could visualise every mathematical problem with a glorious bird’s-eye view that showed the whole structure of the solution space at a glance. But for anything complicated, you usually can’t do that unless you pretty much already know the answer.
Anyway, I think I found a nice curve (though almost certainly not the nicest possible one, globally), and in a couple of weeks I’ll post something about the reasons that I think it’s so nice.