View from the Pennines: a Cosmic Indian Rope Trick

This year we have had both frogspawn and toadspawn in the pond. The tadpoles emerged first and very quickly started to eat the toadspawn. Since the toad tadpoles are poisonous to many creatures it is not clear whether the tadpoles were eating the developing toad tadpoles or just the jelly, but whichever combination they were eating, the carefully roped toadspawn was rapidly destroyed. It is possible that the frog tadpoles were getting their retaliation in early, and that if they fail to destroy the toad tadpoles before they leave the spawn they might become food for the toads-to-be in their turn. To preserve a few toad tadpoles we removed them from the pond and kept them in a jar. One characteristic I had not appreciated is that whilst frog tadpoles rest horizontally on the bottom of the pond, young toad tadpoles rest vertically with their heads up; a position which would be very unstable in the absence of the supporting relatively high density water. Indeed, I have not discovered the source of the stability of this pose, which should be closer to an inverted pendulum than anything else I can think of, but I suppose that a light inverted pendulum could be stable in treacle, though had I been thinking about it at the time I would have looked to see whether there was any periodic oscillation in the tadpoles’ tails. My thoughts turn to small oscillations because of recent work on stabilizing an inverted pendulum, and even highly articulated multiple pendula such as the bicycle chain, using periodic or random perturbations [1, 2, 6]. Experimentalists and applied mathematicians produced a series of wonderful experiments and applications in the mid 1990s which reproduce the effect of the classic Indian rope trick – a flexible wire can be stabilized in the upwards direction by the right sort of oscillation at the base [5, 7]. This provides a great example of the power of applied mathematics to explain surprises (it took no new physics to understand what was going on, just the time and expertise required to analyze the equations).