Since writing my book "Irreligion" and some of my recent Who's Counting columns, I've received a large number of e-mails from subscribers to creation science (who have recently christened themselves intelligent design theorists). Some of the notes have been polite, some vituperative, but almost all question "how order and complexity can arise out of nothing."
Since they can imagine no way for this to happen, they conclude there must be an intelligent designer, a God. (They leave aside the prior question of how He arose.)
My canned answer to them about biological order talks a bit about evolution, but they often dismiss that source of order for religious reasons or because of a misunderstanding of the second law of thermodynamics.
(See Complexity and Intelligent Design for my Who's Counting discussion of biological and economic order and complexity arising out of very simple programs.)
Because the seemingly inexplicable arising of order seems to be so critical to so many, however, I've decided to list here a few other sources for naturally occurring order in physics, math, and biology. Of course, order, complexity, entropy, randomness and related notions are clearly and utterly impossible to describe and disentangle in a column like this, but the examples below from "Irreligion" hint at some of the abstract ideas relevant to the arising of what has been called "order for free."
Let me begin by noting that even about the seemingly completely disordered, we can always say something. No universe could be completely random at all levels of analysis.
In physics, this idea is illustrated by the kinetic theory of gases. There an assumption of disorder on one formal level of analysis, the random movement of gas molecules, leads to a kind of order on a higher level, the relations among variables such as temperature, pressure and volume known as the gas laws. The law-like relations follow from the lower-level randomness and a few other minimal assumptions. (This bit of physics does not mean that life has evolved simply by chance, a common mischaracterization of evolution.)
In addition to the various laws of large numbers studied in statistics, a notion that manifests a different aspect of this idea is statistician Persi Diaconis' remark that if you look at a big enough population long enough, then "almost any damn thing will happen."
A more profound version of this line of thought can be traced back to British mathematician Frank Ramsey, who proved a strange theorem. It stated that if you have a sufficiently large set of geometric points and every pair of them is connected by either a red line or a green line (but not by both), then no matter how you color the lines, there will always be a large subset of the original set with a special property. Either every pair of the subset's members will be connected by a red line or every pair of the subset's members will be connected by a green line.
If, for example, you want to be certain of having at least three points all connected by red lines or at least three points all connected by green lines, you will need at least six points. (The answer is not as obvious as it may seem, but the proof isn't difficult.)