Dr. Ard Louis (University of Oxford)

In the famous trope of monkey's typing at random on keyboards, the probability of typing a specific sequence of length L on a keyboard of N keys, is simply 1/N^L.  If, however, the monkeys are typing into a computer programme, they might accidentally type, with probability 1/N^20,  the 20 character code "print "01" 500 times" which will output an ordered sequence of length 1000 of the form 0101010....    In the first scenario, all outputs of length L are equally likely,  but in this second algorithmic scenario, certain outputs with short codes are much more likely to appear than others.  This intuition has been formalised in the coding theorem of algorithmic information theory (which should be much more widely taught to physicists).   Outputs with short codes are called "simple" ones, and the coding theorem suggests that many processes in nature may be highly biased towards simple outputs.   Evolution proceeds by random genetic mutations which then affect developmental processes which generate biological outputs called phenotypes.   So evolution proceeds by the second algorithmic scenario above.   In this talk we will show that the coding theorem predicts that random mutations in evolution are exponentially more likely to  generate simpler, more compressible outputs.    This algorithmic picture implies, for example, a bias towards higher symmetry, since more symmetric structures can be described in more compact ways by repeating a simple unit.   Evidence for this  strong bias towards simplicity and symmetry has been found in protein clusters, the structure of RNA, and in gene regulatory structures.   Interestingly, these same principles predict an Occam's razor like bias in machine learning methods such as deep neural networks as well, suggesting an intriguing link between theories of learning and biological evolution.