Patterns and Randomness

When we see patterns—whether in the arrangement of stars in the sky (see "Spying Pi in the Sky") or in the distribution of guests at a dinner party (see "Party Games")—we are constantly tempted to think of these patterns as existing for a purpose and being the effect of a cause. Ramsey's theorem (see "Playing Fields of Logic") suggests otherwise. Patterns can, and indeed must, arise out of pure randomness (or chance).

In mathematics, in science, and in life, we constantly face the delicate, tricky task of separating design from happenstance. We must make decisions about the meaning of apparent coincidences, whether what we have before us is medical data showing an unusual cluster of cancers in a community, a sequence of events that suggests a conspiracy, or a peculiar arrangement of stars in the sky.

Seeing patterns among the stars: Draco and Ursa Minor. Library of Congress.

We detect eight stars in a straight line and think, "That can't be an accident." Is this pattern the result of some cosmic ordering driven by gravity? Is an unknown force involved? Is it a string of deliberately placed beacons for interstellar travel?

In the absence of an obvious explanation, the human tendency has been—and still is—to invoke supernatural forces, extraterrestrial visitors, or other fantastic beings and events to make sense of what we observe.

Humans are model builders, and the human mind is very good at identifying patterns and constructing theories. We are programmed to search for patterns and to invent explanations, and we find it difficult to imagine that patterns emerge from randomness.

As builders, humans can also create edifices on a vast range of scales, from the giant pyramids of ancient times to the intricate microscopic components of a computer's microprocessor. We can manipulate individual atoms to spell out tiny words on a silicon surface, and we can orchestrate the construction of giant skyscrapers and vast malls.

To do so, we design, make plans, create blueprints, organize labor, and marshal resources to create the order that we desire. In nature, however, that order and structure arises from randomness, and we face the puzzle of how the components of life assemble themselves without blueprints as guides.

Previously: Group Thoughts