Sunday, January 26, 2014

A menace to penguins

We interrupt your weekend merry-making  with a red alert:

Let us imagine a planet covered with calm water. If you drop a large rock into the water at the North Pole, a wave will propagate out  in a circle of ever-increasing radius.  In due course, however, this circle will reach the equator, after which it will start [inexorably] to shrink,  until eventually the whole wave raches the South Pole at once, in a sudden burst of energy.
-- “Manifolds and Differential Geometry”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 44

Moral of the story:  DO NOT DROP A LARGE ROCK INTO THE WATER AT THE NORTH POLE !  It would swamp the penguins!

[Note for connoisseurs:  This effect is an analog of what S|G|NTers call "antip*dal recepti*n", one variety of the 'whispering-gallery' phenomenon.]

Incidentally -- For an example of a manifold in the form of a differentiable penguin, click here.

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