These remarks are inspired by a review in TLS (Times Literary Supplement) by Martin Kemp of Philip Ball's trilogy on Nature's Patterns. Kemp is the prolific Oxford art historian who appears frequently in Nature on the subject of art and science. Ball is an equally prolific Oxford-educated science writer. The subject of Ball's trilogy and Kemp's review is the oldest problem in science: How does order arise in nature? The problem is made more urgent in modern times by the discovery of the Second Law of Thermodynamics, the entropic imperative toward disorder.
In general, solutions to the problem have fallen into two categories.
The first category involves solutions from the top down. These might invoke a supernatural designing agency. Or they might look for similar patterns across ranges of scale or experience, such as the medieval idea of microcosm and macrocosm, D'Arcy Thompson's 1917 classic On Growth and Form, or contemporary chaos theory.
The second category is bottom up, reductionistic -- looking for casual laws that operate at the level of assembling fundamental particles, atoms, or molecules. By these accounts, similar patterns encountered in different areas or scales of experience may or may not be related.
I think it is fair to say that as a matter of practical utility the reductionistic approach has been overwhelmingly more successful. Of course, bottom-up explanations are less satisfying aesthetically, and emotionally. The human brain seems to want unity across the full spectrum of experience -- holistic explanations. We like to think that existence is more than just impersonal mechanical laws nibbling their way into an unspecified future.
Is science necessarily reductionistic? Of course not. What works works. But we are still waiting for top-down explanations that provide fruitful paradigms for research. Just look at any weekly edition of Science or Nature: reductionism reigns unchallenged.
Consider one example of order in nature: the honey bee's hexagonal comb. Kepler sought an explanation four centuries ago (in The Six-Cornered Snowflake) and showed that hexagonal cells are the way to compartmentalize a volume with the least amount of wax. Aha! The bee knows. The bee shares the human (or divine) talent for top-down design.
But does the bee know? How does it know? Surely its propensity for a certain collective architecture is genetically encoded, contrived by the trial and error of natural selection. At least this is the only explanation that at the moment offers a program for research. The human mind may love the fact that the bee employs an optimal -- and beautiful -- architecture, but saying so takes us nowhere new. To say "the genes do it" leaves us languishing in the same vale of mystery -- but it is a vale whose hidden paths and tangled undergrowth invite specific exploration.