Mar 15 2022

## Why Is Life Symmetrical There is an inordinance of symmetry in living structures. Perhaps this is why humans have an aesthetic predilection for symmetry – but why does life have a probabilistic predilection for symmetry? Of all the possible forms that exist, symmetrical ones are a minority, and yet evolution seems to prefer them. We might hypothesize that there is a functional advantage to symmetry, but this is not obvious, at least not as a general principle. Specific forms likely function better when symmetrical. For example, forces need to balance, when walking or flying, and symmetry achieves that. Imagine a bird with one wing much bigger than the other, or with the wings placed at different positions along the body.

There appears, however, to be symmetry in excess of function, and this symmetry exists as all levels of biology, down to the molecular level. There are exceptions, of course, but symmetry is the rule. Further, some symmetry is baked into evolutionary designs long before any adaptive use. Therefore we need another, non-adaptive, hypothesis to fully explain symmetry. I have long felt that there is probably a mathematical reason, although could not state it in rigorous terms.  The DNA genetic code for a living organism is not a detailed blueprint. Rather it is a set of instructions to be followed. Think of it like a honeycomb beehive. There is no blueprint for the beehive, and no bee knows what it is supposed to look like. The bees follow simple rules over and over again, and the complex honeycomb pattern emerges. That is where the answer must lie.

Researchers have already put a lot of flesh on this skeleton of an idea, and a recent paper adds some further mathematical rigor. The key does lie in the use of simple algorithms to produce the complexity of life. Imagine having to describe to someone else how to create a pattern, such as with tiling a floor. You are not going to tell them where each tile exactly goes. Rather you will explain a technique or pattern that then gets repeated over and over until the space is filled. That, of course, only works if there is a simple pattern. If the ties are laid out in a mosaic creating a complex landscape, then yeah, you may need to describe where each tile goes.

The core concept here is that symmetry is algorithmically efficient. There is even a term for this branch of math – algorithmic information theory. This is a subset of information theory, which deals with the mathematics of information. This has come up in evolutionary discussions before, primarily because creationists tend to completely misunderstand and abuse information theory to make bogus arguments. Information theorists ask questions such as – how compressible is information? This is exactly the same as computer programs that compress files, storing them in a smaller form. One core concept here is that entirely random information is not compressible, because by definition there is no pattern. At the other end of the spectrum, if you had a series of 1,000 1s you could compress that down to “1000 1s”. A simple pattern is highly compressible.

Remember what I said about DNA – it’s a list of instructions, not a blueprint. In a sense DNA is a compressed version of the information that describes a fully developed organism. If that organism has a lot of asymmetry, that would require more DNA to describe than if the organism has a lot of repeated patterns, which tends to produce symmetry. Symmetrical creatures, therefore, are more algorithmically efficient, there information is more compressible, and the DNA that codes for them would be more efficient.

But is that enough to explain why symmetry dominates over asymmetry in nature, despite the fact that there are many more asymmetrical designs than symmetrical ones? The authors argue that it is, and they invoke another concept to do so – the arrival of the frequent. Here is the original paper from 2014 going over the math. Essentially simpler algorithms are easier and would occur more frequently by chance, and this increase in frequency would make them much more likely to be evolutionarily set in place.

The authors use the old infinite monkeys on infinite typewriters analogy. Let’s say there are lots of monkeys typing randomly on lots of typewriters, but we are not waiting for one of them to produce Shakespeare. Rather, we simply look at what they are typing for usable patterns, following rules that could act as a formula. Simple formulas would be much more likely to occur through this random typing than complex formulas. If we had to create stuff out of the formulas created randomly by the monkeys, we would therefore be relying much more on short simple formulas. If you use simple formulas (or algorithms) as your building blocks, then symmetry will spontaneously emerge out of the results, like the pattern of tiles on the floor.

Therefore, while there is an adaptive explanation for some symmetry in nature (specifically when balancing forces) there is a non-adaptive explanation that emerges spontaneously from the probabilistic advantage of following simple algorithms.