Frustrated Geek

[lederhosen]

I've just spent more than two weeks trying to solve a mathematical problem that looked simple but wasn't. (Basically, "smooth an arbitrary region so it matches the bits around it"). I sat down and tried to solve it myself, no luck. Then I asked friends, some promising leads, but nothing worked out. Then I went looking on the Internet, and again no luck.

So I pulled out the big guns and asked my father. He gave me a solution and... well, theoretically it's valid. But in practice, it doesn't work, because it ends up being smooth only in the same way that the tip of a needle is rounded when you look at it with an electron microscope. And it's slow, too.

So yesterday I sat down again, and mucked around with ideas like "eigenfunction" and "damping high-order terms" and whatnot. I thought to myself: "If there *was* a solution, it would have to look something like this... and it would have to do certain things, so let's build one that does those things and try it."

And, what do you know? I came up with a filtering method that works. It's not quite perfect - there are ways to breka it - but it's more than sufficient for what I'm doing; it creates a nice smooth function, and it does it in a reasonable timeframe.

But, big 'but', I don't actually understand *how* it works. I have a fuzzy notion of the basic principles, but no real grasp of the detail of it. I designed it by intuition, and I can't rigorously show _why_ it does what it's supposed to do.

All of which is immensely frustrating to this mathematician.

Comments

[panacea1.livejournal.com]

Just write a comment in the code about how the proof for this is absolutely brillliant but you don't have time to write it down now... ;-)

[tyggerjai.livejournal.com]

"You are not expected to understand this".

sol.
.

[malada.livejournal.com]

I think our brains are far more complex then we give them credit for. Somewhere in the back of your mind you *know* how it works... but it hasn't quite filtered through to the front.

Or since you worked it out backwards, you have the answer but one of the steps is alluding you because you don't fully know it yet. Show your stuff around. I'll bet someone can fill in the blanks.

-m

[thorfinn]

I'm not certain, but it sounds to me like the original problem isn't actually a particularly tractable one. And it further sounds to me like your filtering method is probably a heuristic, rather than an algorithm. And the problem with heuristics is that you can't really "prove" that they work... because, well, they don't "work", for all values of inputs.

[lederhosen.livejournal.com]

It's not a heuristic (at least, not by definition #3 here, which I presume is what you mean?)

Will post more detailed writeup of the problem and the filtering method later. And no, it doesn't seem to work for absolutely all inputs, but it still seems to work on 'nice' inputs, and I ought to be able to quantify why.

[thorfinn]

Ah, no, I meant a combination of senses 1 and 3. That is, the algorithm you have isn't a "true solution", it's a guide in the direction thereof, plus the results of it are an approximation of a "correct solution". Recursivity isn't really required to be a heuristic... I think sense 3 as written there isn't really accurate.