Huh? My quality of life hasn't gone down any. In fact, I've been working on this problem:

http://xkcd.com/356/

I can't quite figure out how to get past infinite resistors in one dimension and move on to two... sorry, that's a bit off-topic. Anyway, the point is that I still appreciate me some maths.

I was caught and the truck ran over me. I may count as 5 points to you Duckling because I'm a physicist and a mathematician.

My first approach at solving it is:

Compute for each path j the electric intensity,

I

_{j} = V / n

_{j},

where n

_{j} is the number of one ohm resistors in the path j.

Then sum the intensity for all paths (an infinite sum, of course)

I

_{tot} = sum

_{j=1 to ininity} I

_{j}.

And finally compute R

_{eq} = V / I

_{tot}.

Of course, the hardest part is to organize the sums in a way that allows us to compute somehow that sum, for instance, a way to compute how many paths of size n exist, for all n

I have a feeling that there may exist near sqrt(n) paths of length n, thereby making R

_{eq} = 0. I'll think about it a bit more if you, Duckling, or anyone else is interested in this thread. Or if Craig shuts down the forums in pure horror when he looks at this thread. Whatever happens first.