Life after Life
What a simple game reveals about a complex world
In October 1970 the mathematical games column in Scientific American magazine described a kind of game created by the British mathematician John Conway. The game was called Life and it was intended as a stylized simulation of cellular reproduction. Life unfolds on a grid (usually on a computer screen) of discrete cells that can be either empty or full, and a set of rules governing the successive configurations of empty and full cells. The empty cells are thought of as dead (or never having lived); the full cells as alive. Although the rules of evolution can vary, a typical set dictates that any cell that is alive in the present generation and is bordered by two or three living cells (of the eight possible: above, below, to the sides, and on the corners) survives into the next generation; a living cell that is bordered by fewer than two living cells dies (of loneliness); a living cell bordered by more than three living cells dies (of overcrowding). Any currently dead cell that has exactly three living neighbors will be replaced in the next generation by a living cell (their progeny: ménage à trois is the practice here); any currently dead cell with fewer than three or more than three living neighbors will stay dead.
Population biologists have utilized versions of Life to study aspects of the evolution of colonies of plants and animals; the fit has been more or less realistic depending on the species. For historians and social scientists, the interesting thing about the game is that it is both deterministic and unpredictable. For any given initial configuration of living and dead cells, the future of that colony is entirely determined, to the ten-thousandth generation and beyond. The rules allow no room whatsoever for ambiguity. Needless to say, free will and other real or imagined artifacts of human consciousness play no part.
At the same time, for all but the simplest initial configurations (which tend to die out after a few generations or enter a stable state of a small number of repeating patterns), the future is unpredictable in any meaningful sense. As simple as the rules of the game are, there appears to be no way, even in theory, to tell what the ten-thousandth generation of any given initial configuration will look like—without actually working through all the generations leading up to the ten-thousandth.1
Broadly speaking, works of history can be categorized as analytical or narrative (or, obviously, a combination of the two). Analytical history strives to explain why things happened; implicitly or explicitly, it creates models of human behavior that have—the analytical historians hope—predictive value. Narrative history contents itself with describing what happened.
Especially in the academic world, but also among people who consider themselves serious thinkers, analytical history is more highly valued than narrative history. Analytical history looks more like science; analytical history affords guidance for policy.
Yet the guidance given by analytical history has often been disappointing. This is partly because though events in the present moment might be similar to events at some past moment, they are never identical to those past events. And one can’t know ahead of time whether the similarities or the differences will be more important.
John Conway’s game of Life puts this inability to know on a formal footing. Real life is at least as complex as Conway’s Life, and if we can’t predict the future in Life, we certainly can’t predict it in life.
Which leaves narrative history as the alternative. The purpose of narrative history, beyond telling good stories, is not to build theories of human behavior but to probe human nature. Analytic historians put humans into conceptual categories; narrative historians highlight the singularity of each human.
Ask an analytical historian what history teaches, and you'll get a list of lessons more or less applicable to whatever prompted the question. Ask a narrative historian, and if you get an answer at all it will probably be a riff on the fascinating idiosyncrasy of our species. Analytical historians have one foot in the social sciences and often wish for two. Narrative historians feel greater kinship with philosophers and poets.
Narrative historians would be the last to imagine that information theory would confirm the sophistication of their approach to the past. But they might not be surprised. The world is full of unexpected things. That's life, they’d say. Or Life.
The unpredictability of Life follows from results in results in a branch of information theory dealing with “computational complexity.” An accessible introduction to computational complexity can be found in Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford, 1989), 140-45. Stephen Wolfram, “Cellular Automata as Models of Complexity,” Nature, October 4, 1984, 419-424, provides more detail.