Art and Algorithm

An algorithm is fundamentally the product of human enterprise. No matter how complex we design a computer, we can never hope to emulate nature.
Nature is spontaneous order and unplanned coincidence. Even though algorithms can incorporate many elements of a natural process, they can never get more complex than their designer. Like nature, a computer can randomly choose from a set of outcomes. But in its very nature, an algorithm is a discrete set of instructions for a machine to follow.

It is possible to simulate the complexity of the process of natural selection to any degree of detail desired. In modeling nature, one can break the natural process down into any number of discrete events or operations. For example, if one wishes to model how a genotype is mapped into a phenotype and then a phenotype is mapped into fitness, then one can write a complex set of commands that define phenotypes for all genotypes, and a fitness landscape that incorporates all phenotypes in its domain. But even while it is possible to make an algorithmic model of natural selection to any degree of detail, evolutionary algorithms face a limitation that is implicit in the very fact that we measure them in terms of detail.

We understand natural selection in terms of discrete events in which species win and lose in some sort of extremely complex competition. But our understanding of the process can never capture it in full. The mapping from genotype to phenotype to fitness is one example of how evolution in nature must differ from any algorithm. The constructor of an algorithm must specify how this mapping occurs and must decide phenotypes can be ranked into fitness. An algorithm might have a sophisticated mechanism to make a mapping, but that sophistication will always be a part of the algorithm itself. Yet in nature, the very instructions that make these types of choices are themselves a product of evolution. Those very instructions that make up the ‘algorithm’ of natural selection, in its full nature, the very products of the process itself.

More generally, natural selection is not an algorithm because it is impossible to create a perfect model of nature. Science is an ever-advancing set of hypotheses that will always face new tests, modifications and rejections. But precisely because there are always more details, and just because there will never be a time when a scientist can say “science is finished, there is nothing more to be known,” an algorithm can never be nature, and nature. As our comrade Charles Darwin put it once, “natural selection is a power incessantly ready for action, and is as immeasurably superior to man’s feeble efforts as the works of nature are to those of art.”
Indeed science itself is as much art as algorithm. Following Popper, science is the falsification of hypotheses. Testing theoretical statements against empirical facts, this is an algorithm. One can conceive of a computer that tests hypotheses and a function that maps a statement as true or false.

We can ask an algorithm “is our theory true?” Any yet we can never ask an algorithm to wonder for us “what is that which we do not know?” To Popper, science is an algorithmic test of hypotheses. But an algorithm will never answer what we have not asked. That glorious intuition which guides us to questions we did know exist, that insatiable imagination that drives us to develop those new theories we never think possible, these are art in science.