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Not sure if it was in the article or not but I think the Hairy Ball theorem from Topology would be important. Since earth is a sphere the wind can't blow all in
by johnwatson11218 13y ago
Not sure if it was in the article or not but I think the Hairy Ball theorem from Topology would be important. Since earth is a sphere the wind can't blow all in the same direction. Some currents must oppose others. In a torus the wind could start blowing in one direction and stay that way forever.
- rtkwe 13y agoThat's not what the Hairy Ball Theorem (HBT) says, the HBT says that there must be a point on a sphere where a continuous vector field is zero. It doesn't say they can't be pointing in the same direction except that point.
- johnwatson11218 13y agothis link http://uncyclopedia.wikia.com/wiki/Hairy_ball_theorem http://uncyclopedia.wikia.com/wiki/Hairy_ball_theorem talks about the application to the torus. It states that it is possible to completely comb the hair on a doughnut. That is the point I was trying to make earlier. I think it does imply that the wind could start blowing in the same direction if we lived on a torus. I think it would be the same if we lived inside like in science fiction movies or if we lived on the surface with a normal atmosphere.
- valtron 13y agoI can't tell if you're being sarcastic... but if not, this is the first legitimate use of uncyclopedia as a source I've seen.
- pndmnm 13y agoIn fact, it does -- to demonstrate, assume otherwise and use the definition of continuity.
- rtkwe 13y agosigh To quote because topology is a pain: > "there is no nonvanishing continuous tangent vector field on even dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0" Which means they can all blow in a continuous path except for at least one point, so the wind at every point but 2 could be blowing east on a sphere. http://en.wikipedia.org/wiki/Hairy_ball_theorem http://en.wikipedia.org/wiki/Hairy_ball_theorem
- lutorm 13y agoYes, but the velocity must go to zero as you approach the poles. I took the OP to mean "with the same velocity", not "in closed loops". Obviously wind must blow in closed loops, since there are no sources or sinks of air.
- dogecoinbase 13y agoSo to you, "pointing in the same direction" includes "pointing in exact opposite directions within an epsilon-ball for any epsilon"?
- xyzzyz 13y agoThere's a whole continuum between "pointing in the same direction" and "pointing in exactly opposite directions".
- rcthompson 13y agoWind currents would be determined by convection and Coriolis effects, so it would always be going in different directions at different locations.