> This is not true. Air can flow out of a zero point - just heat it up, and air will flow out of it.
I'm having a lot of trouble visualising this. There is no air at a point. A point, by definition, has no volume. Are you manufacturing air?
I think you are using some definitions that are completely at odds with what everyone else, including me, are using. No doubt if we stood in front of a whiteboard you could make yourself clear quickly, but almost everything you have said is, according to my model of how the world works, wrong.
I'd like to understand you, but I suspect that's never going to happen.
I know the theorem - I proved a generalised version of it as a base case for a much bigger result. I haven't bothered to read most of the comments because usually the whole thing is mis-quoted or mis-interpreted, but I just had to say something to try to understand you.
It's true that the theorem does not require a cyclone. The theorem can imply a zero point with the vector field radiating from it, but in a conservative 2D fluid flow that can't happen. In a 3D flow you can get that effect on the surface as the fluid descends to that point and then spreads, but that's different.
Perhaps you're responding to incorrect "interpretations", perhaps you're right and I just don't understand you, but you're really not making yourself clear. Either that, or you're wrong.
"There is no air at a point. A point, by definition, has no volume. Are you manufacturing air?"
Sorry. Assume an area, heat it up and wind flows out of it. However the air in the area itself is moving, so conceptually all the air is moving out of the point in the center of it. (It's not really, it's moving out of the area, but all the vectors point away from the point, so that's what it looks like.)
"It's true that the theorem does not require a cyclone."
Thanks. That's really all I was arguing about.
The thing with continuous and cyclone: I was assuming, that people were saying, that the wind _always_ has to move - even if in a circle. And I was saying, no, it doesn't have to move, you can have a still area, and wind radiating out of it (or into it).
If I am correct about that, then please edit the wikipedia article to remove mention of cyclones.
Why do you say that can't happen in a 2d fluid flow? Why does it have to be a cyclone? My understanding of weather is you have a large area, you heat it up, and wind flows out of it - but there is no cyclone. (I guess with fluid flow you are assuming there is no way to manufacture fluid, but with wind you can since heat will "create" more of it.)
Tell me if I'm wrong here:
The hairy ball theorem assumes there is hair everywhere, so you have to have a cyclone at the poles. But with wind there are spots without hair, so the theorem just doesn't apply to wind.
I'm having a lot of trouble visualising this. There is no air at a point. A point, by definition, has no volume. Are you manufacturing air?
I think you are using some definitions that are completely at odds with what everyone else, including me, are using. No doubt if we stood in front of a whiteboard you could make yourself clear quickly, but almost everything you have said is, according to my model of how the world works, wrong.
I'd like to understand you, but I suspect that's never going to happen.
I know the theorem - I proved a generalised version of it as a base case for a much bigger result. I haven't bothered to read most of the comments because usually the whole thing is mis-quoted or mis-interpreted, but I just had to say something to try to understand you.
It's true that the theorem does not require a cyclone. The theorem can imply a zero point with the vector field radiating from it, but in a conservative 2D fluid flow that can't happen. In a 3D flow you can get that effect on the surface as the fluid descends to that point and then spreads, but that's different.
Perhaps you're responding to incorrect "interpretations", perhaps you're right and I just don't understand you, but you're really not making yourself clear. Either that, or you're wrong.