h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I think you'll end up with a tuft at the North and the South pole, TiT. That'll ruffle your feathers.

Traveller in Time on top
"Nope, the fluid will flow slightly up near the 'equator' at the poles a flow to the ball will take place pressing the single hair down.

Your formulation of the hairs is they have to lay 'flat' on the surface. Not about vectors only parrallel to the surface.


I use the phrase 'slow rotating' as high speeds would make it a pump. Well, the speed is depending on the viscosity of the liquid and the stiffness of the hairs.



I guess it is indeed the angle of writing that makes an Entry for the Guide. (using pins as markers for the poles)"

I thought about this this morning, TiT, and you are right. The zero point in the function can be a tuft or a "hole" where the hair all radiates away from a point. The theorem guarantees that there will be at least one of these, but it doesn't guarantee it will be a tuft.

I'll have to reword the entry slightly.

Gnomon:

Sorry if I've missed it somewhere in this excellent entry, but is this effect related to, the same as, or the opposite of the 'hedge hog'?

Thanks, and congrats on another great idea for a topic!

What do you mean by "the hedgehog"?

Fascinating entry, Gnomon - congratulations!

A couple of minor things:

A footnote identifying Brouwer would be good - L.E.J (Luitzen Egbertus Jan) Brouwer, (1881-1966)

I'm not sure the closing sentence works particularly well, but then I can't think of anything better at the moment. I like the informal style of the article.

I've removed the second 'Of course'.

I've added a footnote about Brouwer.

In the interests of mathematical accuracy, I've rewritten the entry slightly to incorporate holes in the hair as well as tufts. This is to incorporate the evidence uncovered by TiT. I suspect that he found the only case which wasn't adequately described by the original entry.

I don't think it reads quite as well now, but I'll live with it.

Somehow this reminded me of Old Hairy... Y'know: Maths and Hairs...

Anyways, this is a great usual Gnomon style Entry.

SAUSAGE

I was thinking of Old Hairy too.

I was so worried when I clicked on this entry - it sounds vaguely [very?] obsecene, but no, it's just mathematical madness. Perhaps it could do with retitling, or at least some kind of attempting not to scare people away ness.

Brilliant though.

It's supposed to sound vaguely obscene. That's the childish humour in it! If the theorem was just called the non-zero vector field theorem, it wouldn't be half as interesting.

Childish humour?! Bah - true wit too woo!

Wonder if there's enough material for an entire GE on 'Vaguely Obscene-Sounding Scientific Theorems'?

Very enjoyable, and I do agree that the childish humor is an essential part of its charm.

Now then, what about the trivial solutions: 1) all of the head is a tuft, as when touching a Vandegraff generator, and 2) all of the head is a hole, by which I mean bald? But this would be the hairless ball solution and good news for donut eaters.

'Bout time I made a sensible contribution as well.

In the 'Wind Patterns' bit, you correctly state the assumption that the wind must be two-dimensional. But a more unrealistic assumption is that the wind follows a straight line vector, which of course it doesn't. This plunges us deep into the world of fractals and chaos, so I suggest you don't attempt a full refutation.

B

Are you suggesting the existence of turbulence, mu beta?

*ignores all talk of maths/physics and whatever*

nice entry

Love the title

Are you suggesting the non-existence of turbulence?

B

I'd actually rather suggest the non-existance of Maths/Physics and all that other stuff that confuses me

Gnomon, my friend:

Sorry it has taken me so long to get back to the thread. I hope I didn't keep you waiting.

From your question, I can't be sure if you are asking 'Which hedgehog', or 'What is a hedgehog' (in this context).

I'll presume that you may be familiar with some of the ways in which the 'hedgehog' visual cue has been used in physics, and want me to describe the one in my question.

When, in the early '70s, physicists gave up trying to describe the universe as 'numbers' at each point in space and started using the concept of 'arrows' to describe each point in space (associated with force fields describing the behavior of fundamental particles), it was a bit revolutionary. Topology began to be discussed more earnestly.

Then, in the mid '70s, Hooft and Polyakov raised the question of what if, sometimes, the arrows didn't line up, but formed a 'spiny' sphere, a hedgehog?

As the arrows closer to the center, there comes a time when there is no more room for 'arrows' and something must break down. In cooling metal, it's called a vortex, and allows superconductivity to take place; but, in the middle of the vortex, not much is certain.

The real thing is that, once a vortex (or three-dimensional hedgehog) is formed, no matter how you twist and turn it, stretch it or dent it, they cannot disappear. Their stability is guaranteed by topology.

It is thought that the underlying physics of the hedgehog handle the problem of the center by creating a region where the arrows shrink to zero, and will stay together once created.

Some versions of the GUF contains just such and arrow from which hedgehogs could be born (the Size and mass being determined by the characteristics of the GUF itself). Strangely, they turn out to be both tiny (10 to the -16 the mass of the proton) and massive (10 to the 17 times the mass of the proton).

The astonishing thing was that the theory calls for the hedgehog to emit a magnetic field. It is considered to be the previously illusive magnetic pole (actually, the magnetic monopole). All monopoles were ostensibly created at 10 to the -36 seconds after the big bang. There are gazillions around, but I don't know that any have actually been detected.

Well, that's the topology angle that reminded me of the bit about the 'tuft'; just as a childs hair must have a whorl somewhere - once combed - on some other side of the sphere there should be both a whorl and a tuft, or neither.

If all that is any clearer than mud, I must not be as ill as I've felt for the past week.

Good luck, again, with the excellent entry!