hairy ball theorem

[dextrous]

Thought the title would get your attention.
Am in a mathsy sort of mood,

So the hairy ball theorem basically asks you to imagine that a shape (say a tennis ball) has little strands of hair sticking straight out of it. The theorem proves that it is impossible to comb it perfectly smooth - there are always going to be spirals or tufts. A highly practical application is to imagine that the hairs are gusts of wind - which if you take it to the natural conclusion, demonstrates that it is impossible for a planet (say Earth) to have a completely calm weather situation over it's whole surface.

However, it would be possible to have "global" smooth weather if you lived on a doughnut (a "torus", if you want to be exact) with a hole in it.

ZZZZZZzzzzzz

 

[conny]

Keep going!

This is interesting!

 

[dave.m]

So the hairy ball theorem basically . . . .
. . . . demonstrates that it is impossible for a planet (say Earth) to have a completely calm weather situation over it's whole surface.

However, it would be possible to have "global" smooth weather if you lived on a doughnut with a hole in it.

Hard to prove, or disprove, because I have never come across a hairy doughnut
I’ll look for a mouldy doughnut in Asda next time I‘m in and take it from there.

Signed
Hinestine.

 

[dextrous]

Easy to imagine though. The tuft or swirl at crown of your head is a perfect example of the theorem in action.

There are many ways of combing hairs on a doughnut smooth.

 

[dave.m]

Good night , Dex.

 

[wotan]

Thought the title would get your attention.
Am in a mathsy sort of mood,

So the hairy ball theorem basically asks you to imagine that a shape (say a tennis ball) has little strands of hair sticking straight out of it. The theorem proves that it is impossible to comb it perfectly smooth - there are always going to be spirals or tufts. A highly practical application is to imagine that the hairs are gusts of wind - which if you take it to the natural conclusion, demonstrates that it is impossible for a planet (say Earth) to have a completely calm weather situation over it's whole surface.

However, it would be possible to have "global" smooth weather if you lived on a doughnut (a "torus", if you want to be exact) with a hole in it.

ZZZZZZzzzzzz

And I always thought it was the heating of the earths oceans and land masses, coupled with the Coriolis effect that caused the worlds weather.

 

[dextrous]

And I always thought it was the heating of the earths oceans and land masses, coupled with the Coriolis effect that caused the worlds weather.

It is, but the theorem explains why globally the weather canoot be simultaneously settled - there always has to be eddies or anticyclones somewhere at any given time, which occasionaly harmonise to become for example a tornado.

 

[wotan]

And I always thought it was the heating of the earths oceans and land masses, coupled with the Coriolis effect that caused the worlds weather.

It is, but the theorem explains why globally the weather canoot be simultaneously settled - there always has to be eddies or anticyclones somewhere at any given time, which occasionaly harmonise to become for example a tornado.

Is it remotely possible, that the high rise buildings and structures that we have constructed, have had any effect
on the wind patterns?

 

[conny]

Without a doubt, coupled with mans interference with the natural shoreline and making/breaking of natural breakwaters.

 

[wotan]

Without a doubt, coupled with mans interference with the natural shoreline and making/breaking of natural breakwaters.

If this is the case, then it should be possible to reverse engineer to our advantage.
If we stopped beating on about the greenhouse effect and do something positive.

Wotan

 

[dextrous]

Without a doubt, coupled with mans interference with the natural shoreline and making/breaking of natural breakwaters.

If this is the case, then it should be possible to reverse engineer to our advantage.
If we stopped beating on about the greenhouse effect and do something positive.

Wotan

There is a slight problem however. We all know that energy cannot be created nor destroyed, and that the human species has spent a great deal of time and effort converting energy in solid form to energy in kinetic form. We are not so adept, however, at converting kinetic energy back into solid form. In short, some things just aren't reversible.

 

[ColJack]

that theorem is wrong, or at least in respect to the earths weather..

it is theoretically possible to have globally calm weather..
if there was no wind movement at all, there would be no cyclones or anticyclones.. think of it as a scared tennis ball.. all the hairs just sticking straight up and not moving one way or another..

practical and probable though are another thing entirely..
for this to work, the earth would have to be in total darkness for a long period to attain a global surface and air temperature and prevent pressure differentials.. as well as the magma core having to solidify and cool to prevent localised heating of the crust where it is thinner..

 

[WDIK]

use of fuzzy logic required

 

[tim west]

Sounds like a load of old b******s to me

 

[dextrous]

that theorem is wrong, or at least in respect to the earths weather..

it is theoretically possible to have globally calm weather..
if there was no wind movement at all, there would be no cyclones or anticyclones.. think of it as a scared tennis ball.. all the hairs just sticking straight up and not moving one way or another..

A valid argument Although your description of the criteria required misses the other slight detail that, since no air movement is permitted, no one (and nothing) is moving, nor breathing, nor the earth rotating (there is some friction between gaseous particles, especially in the stratoshphere which would cause turbulance which would, from the chaos "butterfly effect" have an effect on the rest of the planet. Also, all gases would have to be in a state of total stillness, which may prove difficult at atomic or quantum levels.