Namsan question for people into math

Why does it always-- and I mean always-- seem that, when I'm walking uphill on Namsan, I encounter fewer people going downhill when I'm near the foot of the mountain than when I'm near its summit? Generally speaking, that's how it works: as I start up the mountain proper, there's almost no one. But as I get near the top, I encounter more and more people on their way down my path.

If this were a simple matter of dispersion and concentration, I wouldn't be bothered by this problem. If, say, Namsan were a perfect cone shape with no distinct paths, then it's obvious that, as you approach the top of the cone, you'll encounter a higher concentration of people. But Namsan isn't a perfect cone, and the number of paths up the mountain is finite. As soon as you step off the summit, you're on a particular path.

This phenomenon seems to occur no matter what time of day I hit the mountain-- whether it's 6am or 9pm or 2am, the result is always the same: there's almost no one when I'm at the bottom, but there is a significant number of people going downhill (usually in groups) when I'm near the top. Why do I never encounter these "downhillers" near the bottom?

My theory, based on a complete ignorance of mathematical principles, is that, no matter what time I go to Namsan, everyone else has gotten there before me and has decided to come down only as I approach the mountaintop.

Heh.


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