Math’s ‘hairy ball theorem’ shows why there’s always at least one place on Earth where no wind blows

You is likely to be stunned to study which you can’t comb the hairs flat on a coconut with out making a cowlick. Maybe much more shocking, this foolish declare with an excellent sillier identify, “the furry ball theorem,” is a proud discovery from a department of math known as topology. Juvenile humor apart, the theory has far-reaching penalties in meteorology, radio transmission and nuclear energy.

Right here, “cowlick” can imply both a bald spot or a tuft of hair sticking straight up, just like the one the character Alfalfa sports activities in “The Little Rascals.” In fact, mathematicians do not confer with coconuts or cowlicks of their framing of the issue. In additional technical language, consider the coconut as a sphere and the hairs as vectors. A vector, typically depicted as an arrow, is simply one thing with a magnitude (or size) and a path. Combing the hair flat towards the edges of the coconut would type the equal of tangent vectors—those who contact the sphere at precisely one level alongside their size. Additionally, we wish a easy comb, so we do not enable the hair to be parted anyplace. In different phrases, the association of vectors on the sphere have to be steady, that means that close by hairs ought to change path solely regularly, not sharply. If we sew these standards collectively, the theory says that any approach you attempt to assign vectors to every level on a sphere, one thing ugly is sure to occur: there might be a discontinuity (an element), a vector with zero size (a bald spot) or a vector that fails to be tangent to the sphere (Alfalfa). In full jargon: a steady nonvanishing tangent vector discipline on a sphere cannot exist.