January 6th, 2012

eyes black and white

"It can jump to one hundred times its size!"

Endlessly repeated as an echo from Mount Stupid, the invitation to consider with amazement how fleas can jump to one hundred times their height, or how other small animals are capable of similar jumps to whatever multiple of their size.

Now, given some cellular technology, some animal muscle can store and release a kinetic energy proportional to its mass in one extension of the muscles. Various animals will also have the same order of magnitude in muscle to non-muscle ratio, and in muscles usable in a maximal extension, for too great a disbalance would probably be a waste of muscle, or the unability to escape predators. Therefore, the kinetic energy that any animal can release in single action is roughly proportional to its weight by a factor Em = E/m. Any animal that jumps upward may thus jump to roughly the same height z=Em/g, independently from its size.

Of course, some species tend to do better than others, and within species there will be plenty of individual discrepancy; but the performance varies with metabolic efficiency, muscle to non-muscle ratio, and specialization to the task of jumping, not with size. Common excited remarks from documentaries that "this (tiny) animal can jump up to one hundred times its height" are thus particularly misleading, and odiously insulting to the listener's intelligence. They are misdirections making people more ignorant rather than more knowledgeable, by smuggling in the implicit assumption that how high an organism jumps should be roughly proportional to its size, and that animals for which this doesn't hold are somehow notable.

A better documentary would instead explain how the alleged "feat" fits in a better informed set of expectations. A measure of height jumping performance would be in terms of absolute height reached, not in height relative to animal size. That fleas jump much lower than humans or cats show that they are not that good at jumping after all. What does that say about the other factors in jumping performance? It might be notable that fleas be specialized towards jumping at all; what does that tell us about their life cycle and the evolutionary pressures that shapes it? We may expect metabolic performance of muscles (plus supporting infrastructure) to have been optimized long ago by harsh evolutionary pressures and to not vary wildly across species; or does it? Between the flea and other jumpers, the muscle ratio is probably what varies most, and is obviously lower for fleas than for cats. But is this muscle ratio in the expected range for other animals their size, or is it not? Interestingly, how much does this ratio vary across animals of a same species, across unrelated species of similar size, or across related species of varying sizes?

The laws of nature are not scale-independent. Stories based on size-changing rays may make for pleasant fantasy, they are anti-science fiction rather than science fiction. Stories explaining how things work at each scale, how these scales feel different and mutually weird, and how phenomena at one scale are related to phenomena at other scales, are more enlightening. Anthropomorphizing phenomena is often but the failure to even try to understand.

"A common man marvels at uncommon things; a wise man marvels at the commonplace." — Confucius