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

What you are describing sounds like the 3-d analogue of the Hairy Ball. It sounds fascinating, but I don't think I need to cover it in this entry. It might be something for a future entry.

Absolutely correct! I did not mean for this to be considered as a point for inclusion in your current entry; I just wondered if this was, in your estimation, related to the 'Hairy Ball' concept.

I admit that 'hedgehog' is also not as eye-catching for a subject title as 'Hairy Ball', in any case. But, now you've got me curious; I thought that the Hairy Ball was a 3-d phenomena! Did I miss something?

It is really restricted to the surface of the sphere. The sphere itself is a 3-d object, but the surface is 2-dimensional.

I see, and I understand. Topologically, the sphere is the same, but you are just discussing an aspect of its 'skin'. Only the most exterior arrows (hairs) are involved.

I am (somehow) reminded of a discussion on gravity that suggested thinking of a planetary body as layers, and imagining oneself on one of the 'interior spheres' to calculate the effects of gravity from all layers of the planet. If we take the hairy ball, and imagine another ball inside of it (also hairy), we see that we may not need to limit ourselves to the one outer layer with the hair, but that the same hairy ball effect will be seen at every interior level as well.

In fact, topologically, it shouldn't matter whether the shape was spherical, oblong, square, pyramid, conical, octoganal, etc. In each case, would have to be a tuft.

Interesting! This, then, should be a universal phenomena of any closed, single surface, 3-d, hairy object!

I think that's right, and wouldn't it even predict sunspots?

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