Math’s ‘bushy ball theorem’ exhibits why there’s all the time not less than one place on Earth the place no wind blows

You could be stunned to study 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 bushy ball theorem,” is a proud discovery from a department of math known as topology. Juvenile humor apart, the concept 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 seek advice from 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, usually depicted as an arrow, is simply one thing with a magnitude (or size) and a course. Combing the hair flat towards the edges of the coconut would kind the equal of tangent vectors—people who contact the sphere at precisely one level alongside their size. Additionally, we wish a easy comb, so we do not permit the hair to be parted wherever. In different phrases, the association of vectors on the sphere have to be steady, which means that close by hairs ought to change course solely steadily, not sharply. If we sew these standards collectively, the concept says that any method you attempt to assign vectors to every level on a sphere, one thing ugly is sure to occur: there will likely 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 area on a sphere cannot exist.

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