Suppose you have a ball covered entirely with
hair and you’re trying to comb the hair so that it lies flat everywhere along the surface.
If the ball were a donut, or it existed in two dimensions, this would be easy! But in
three dimensions? Well, you’re going to run into trouble. A lot of trouble. A big hairy
ball of trouble. That’s because of a theorem in algebraic topology
called the “Hairy Ball Theorem” (and yes, that’s it’s real name) which unequivocally
proves that at some point, the hair must stick up. Now don’t go wasting your time playing
around with a hairy ball trying to prove the theorem wrong – this is math we’re talking
about. It’s proven – done – QED! Technically speaking, what the Hairy Ball
theorem says is that a continuous vector field tangent to a sphere must have at least one
point where the vector is zero. So what does this have to do with reality
apart from uncombable hairy balls? Well, the velocity of wind along the surface of the
earth is a vector field, so the Hairy Ball Theorem guarantees that there’s always at
least one point on earth where the wind isn’t blowing. And it doesn’t really matter that the object
in question is ball-shaped. As long as it can be smoothly deformed into a ball without
cutting or sewing edges together, the theorem still holds. So the next time a mathematician
gives you trouble, ask them if they can comb a hairy banana.

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Dennis Veasley

100 thoughts on “The Hairy Ball Theorem”

  1. There are only 2 types of comments on this video:-
    1. The ones joking about hairy balls
    2. The ones pissed after reading those

  2. I wanted to make a joke about how I play with hairy balls all day long….but I see that too many people have already!

  3. that doesn't relate to earth's wind, you're completely wrong. The earth's wind in't all going in 1 direction like the ball, so it doesn't have to have no wind

  4. just make all the hairs point toward the center of the object

    like if the hair was on the very top of the ball make it point (0.0, -1.0, 0.0)

  5. Whew! That's a relief! I have been trying to comb hairy balls so they look perfect for ages now!
    Everyone, please watch my tiny nature videos. There is no talking in them. Shhh!

  6. I love comedy. Like the… Science of comedy I guess? That there is short silence from both the narrator and the music after he says balls at 0:42 and that pushed me over the edge into a huff of laughter. Without that delivery I dunno if I would have laughed out loud or even realized HOW humorous this was but… The pause, the… Disorientation??? something. Comedy science 101 😭😭😭👌👌👌👌👌

  7. In German, that phenomenon is called "Das Gesetz des gekämmten Igels" or translated "The law of the combed hedgehog".

  8. Wow, the only time in the last two years when I laughed at "hairy banana" or joke of that sort is when minutephysics combined maths with it.

  9. this theorem cant be applied to human balls…
    unless you cut them off.

    technically we are equivalent to a torus, because theres a hole that connects your mouth with your butt

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