In the last episode I talked a bit about Richard Dawkins’s book “Climbing Mount Improbable”, explaining how arguments about the mathematical impossibility of evolution tend to overlook some details of how it actually works. Today we’re going to talk about another interesting mathematical aspect of evolution that Dawkins discusses in that book, the rise of symmetry. We all know that most modern animals seem to mostly exhibit symmetry along at least one axis. Some have argued that this is evidence of intelligent planning, similar to a computer-based CAD design done with attention to appearance, beauty, or other subjective standards. But actually, if you think about how evolution works, there are several natural selection pressures which would inherently push multicellular creatures towards symmetry as they evolve.
One of the most basic observations is that if you’re a creature that simply floats in the water, is anchored to a point on the ground, or doesn’t move much, you have a natural notion of “up” and “down”, but most other directions are equivalent. Up is the place where sunlight comes from, while Down is the direction where gravity pulls you. Aside from this distinction, you don’t want to favor particular other directions, since you don’t know where your food will happen to come from. So if you evolve some useful new feature, like a starfish’s arms, the most efficient design will equally space them around you, enabling their use in all directions. A natural form of mutation is to duplicate a body part. These simple observations result in the radial symmetry we see in creatures like jellyfish and starfish.
In the case of creatures that intentionally move for a while in a consistent direction, new factors come into play. You still have the natural concepts of up and down, since the sun and gravity are almost always going to be critical factors. But now whenever you are moving, you also have a definite direction of motion, usually towards your food. Thus you want to have a mouth at one end, and your waste disposal method at the other, so you leave your waste behind rather than wasting energy uselessly re-eating it. But the directions perpendicular to your motion, the left and right, are still essentially equivalent, so biasing your body in favor of one side would be disadvantageous, or even lead to pulling you around in circles if it affects your method of movement.
I think the most interesting examples of evolution are the rare exceptions to the above rules, where a formerly symmetric animal finds benefits in breaking that symmetry. For example, flatfish like flounders and sole look pretty bizarre to us, as they lie on the bottom of the water with both eyes facing upward, one in the “proper” location and the other oddly misplaced on the fish’s face. They evolved from typical symmetric, nice-looking fish that swam vertically in the water, and in fact are born in a similar form. But when some of them developed a behavioral mutation and discovered they could feed efficiently by laying on the bottom, selection pressure gradually created mechanisms that moved the now useless bottom eye around to the top as the fish grows. The resulting arrangement is bizarre-looking due to its asymmetry, but of course quite functional for the fish. And remembering our discussion in the last episode, how evolution must proceed from very small, not-too-improbable steps: a series of mutations that gradually move the existing eye to an awkward but functional position is much more likely than a lucky, almost impossible mutation that would rearrange the eyes to symmetrical positions on top of the fish.
And of course, we can’t forget the many cases where a useful body feature doesn’t directly affect a creature’s interaction with the outside world, so can evolve asymmetrically with no problem. How many medical comedies have you seen on TV with a cliche situation where someone starts to cut on the wrong side to remove someone’s appendix? We actually have many internal organs in asymmetric positions— in fact, to a designer who valued the beauty of symmetry, human (and most animal) internal organ arrangements are a total mess. Maybe in a few years we’ll understand DNA well enough to redesign ourselves in a nice, truly symmetric, pattern.
And this has been your math mutation for today.