Another way to say that is symmetry and compressibility are essentially synonymous. Any redundancy in a system can be compressed, leading to a reduction in size

Another way to say that is symmetry and compressibility are essentially synonymous. Any redundancy in a system can be compressed, leading to a reduction in size. Thus, the ability to compress a system is essentially finding what symmetries you can exploit in the system to reduce the representation. In my opinion, the reason why we see so much symmetry in nature is because living things are always trying to balance an economy of "source code" size (DNA) with expressibility and/or versatility. I think compression is kind of the overarching generalization but another type of symmetry commonly run into is composeability ( f(g(h(...(x)))) ).