Darwin's Dangerous Idea (31 page)

tool to several more uses, as we go along. This game does an excellent job of ON in the next instant whatever its current state. Under all other conditions, the cell is OFF.

taking in a complicated issue and reflecting back only the dead-simple essence or skeleton of the issue, ready to be understood and appreciated.) That's it—that's the only rule of the game. You now know all there is to Life is played on a two-dimensional grid, such as a checkerboard, using know about how to play Life.
The entire physics of the Life world is captured
simple counters, such as pebbles or pennies—or one could go high-tech and
in that single, unexceptioned law.
Although this is the fundamental law of play it on a computer screen. It is not a game one plays to win; if it is a game the "physics" of the Life world, it helps at first to conceive this curious at all, it is solitaire.4 The grid divides space into square cells, and each cell physics in biological terms: think of cells going ON as births, cells going OFF

as deaths, and succeeding instants as generations. Either overcrowding (more than three inhabited neighbors) or isolation (fewer than two inhabited
4.
This description of Life is adapted from an eariier exposition of mine (1991b). Martin neighbors) leads to death. Consider a few simple cases.

Gardner introduced the Game of Life to a wide audience in two of his "Mathematical In the configuration in figure 7.3, only cells
d
and / each have exactly Games" columns in
Scientific American,
in October 1970 and February 1971. Pound-three neighbors

stone 1985 is an excellent exploration of the game and its philosophical implications.

ON, so they will be the only birth cells in the next generation.

Cells
b
and
h
each have only one neighbor ON, SO they die in the next generation. Cell
e
has two neighbors ON, SO it stays on. Thus the next

"instant" will be the configuration shown in figure 7.4.

168 PRIMING DARWIN'S PUMP

The Laws of the Game of Life
169

FIGURE 7.3

application of our one law of physics. Or, in the terms I have developed in earlier writings (1971, 1978, 1987b), when we
adopt the physical stance
towards a configuration in the Life world, our powers of prediction are perfect: there is no noise, no uncertainty, no probability less than one.

Moreover, it follows from the two-dimensionality of the Life world that nothing is hidden from view. There is no backstage; there are no hidden variables; the unfolding of the physics of objects in the Life world is directly and completely visible.

If you find following the simple rule a tedious exercise, there are computer simulations of the Life world in which you can set up configurations on the screen and let the computer execute the algorithm for you, changing the configuration again and again according to the single rule. In the best simulations, one can change the scale of both time and space, alternating between close-up and bird's-eye view. A nice touch added to some color versions is that ON cells (often just called
pixels)
are color-coded by their age; Obviously, the configuration will revert back in the next instant, and this they are born blue, let us say, and then change color each generation, moving little pattern will flip-flop back and forth indefinitely, unless some new through green to yellow to orange to red to brown to black and then staying ON

cells are brought into the picture somehow. It is called a
flasher
or traffic black unless they die. This permits one to see at a glance how old certain light. What will happen to the configuration in figure 7.5?

patterns are, which cells are co-generational, where the birth action is, and so Nothing. Each

forth.5

ON cell has three neighbors ON, SO it is reborn just as it is.

No

One soon discovers that some simple configurations are more interesting OFF cell has three neighbors ON, SO no other births happen. This configuration is called a
still life.
By the scrupulous application of our single law, than others. Consider a diagonal line segment, such as the one in figure 7.6.

one can predict with perfect accuracy the next instant of any configuration of ON and OFF cells, and the instant after that, and so forth. In other words, the Life world is a toy world that perfectly instantiates the determinism made famous 5. Poundstone 1985 provides simple BASIC and IBM-PC assembly language simulations by Laplace: if we are given the state description of this world at an instant, you can copy for your own home computer, and describes some of the interesting we observers can perfectly predict the future instants by the simple variations.

170 PRIMING DARWIN'S PUMP

The Laws of the Game of Life
171

prey usually cannot. If the remainder of the prey dies out as with the glider, the prey is consumed. [Poundstone 1985, p. 38.]

Notice that something curious happens to our "ontology"—our catalogue of what exists—as we move between levels. At the physical level there is no motion, just ON and OFF, and the only individual things that exist, cells, are defined by their fixed spatial location. At the design level we suddenly have the motion of persisting objects; it is one and the same glider (though composed each generation of different cells) that has moved southeast in figure 7.6, changing shape as it moves; and there is one less glider in the world after the eater has eaten it in figure 7.8.

FIGURE 7.6

It is
not
a flasher; each generation, its two end ON cells die of isolation, and there are no birth cells. The whole segment soon evaporates. In addition to the configurations that never change—the still lifes—and those that evaporate entirely—such as the diagonal line segment—there are configurations with all manner of periodicity. The flasher, we saw, has a two-generation period that continues
ad infinitum,
unless some other configuration en-Notice, too, that, whereas at the physical level there are absolutely no croaches. Encroachment is what makes Life interesting: among the periodic exceptions to the general law, at this level our generalizations have to be configurations are some that swim, amoebalike, across the plane. The sim-hedged: they require "usually" or "provided nothing encroaches" clauses.

plest is the
glider,
the five-pixel configuration shown taking a single stroke Stray bits of debris from earlier events can "break" or "kill" one of the to the southeast in figure 7.7.

objects in the ontology at this level. Their
salience as real things
is considerable, but not guaranteed. To say that their salience is considerable is to say that one can, with some small risk, ascend to this design level, adopt its ontology, and proceed to predict—sketchily and riskily—the behavior of larger configurations or systems of configurations, without bothering to compute the physical level. For instance, one can set oneself the task of designing some interesting supersystem out of the "parts" that the design level makes available.

This is just what Conway and his students set out to do, and they suc-Then there are the
eaters, puffer trains, space rakes,
and a host of other aptly ceeded majestically. They designed, and proved the viability of the design named denizens of the Life world that emerge as recognizable objects at a of, a self-reproducing entity composed entirely of Life cells that was also new level. (This level is analogous to what in earlier work I have called the (for good measure) a Universal Turing machine—it was a two-dimensional
design level.
) This level has its own language, a transparent foreshortening of computer that in principle can compute any computable function! What on the tedious descriptions one could give at the physical level. For instance: Earth inspired Conway and his students to create first this world and then An eater can eat a glider in four generations. Whatever is being consumed, this amazing denizen of that world? They were trying to answer at a very the basic process is the same. A bridge forms between the eater and its abstract level one of the central questions we have been considering in this prey. In the next generation, the bridge region dies from overpopulation, chapter: what is the minimal complexity required for a self-reproducing taking a bite out of both eater and prey. The eater then repairs itself. The thing? They were following up the brilliant early speculations of John von Neumann, who had been working on the question at the time of his death 172 PRIMING DARWIN'S PUMP

The Laws of the Game of Life
173

in 1957. Francis Crick and James Watson had discovered DNA in 1953, but Displaying a 1013-pixel pattern would require a video screen about 3

how it worked was a mystery for many years. Von Neumann had imagined million pixels across at least. Assume the pixels are 1 millimeter square in some detail a sort of floating robot that picked up pieces of flotsam and (which is very high resolution by the standards of home computers ). Then jetsam that could be used to build a duplicate of itself that would then be the screen would have to be 3 kilometers (about two miles) across. It able to repeat the process. His description (posthumously published, 1966) would have an area about six times that of Monaco.

of how an automaton would read its own blueprint and then copy it into its Perspective would shrink the pixels of a self-reproducing pattern to new creation anticipated in impressive detail many of the later discoveries invisibility. If you got far enough away from the screen so that the entire about the mechanisms of DNA expression and replication, but in order to pattern was comfortably in view, the pixels (and even the gliders, eaters make his proof of die possibility of a self-reproducing automaton mathe-and guns) would be too tiny to make out. A self-reproducing pattern matically rigorous and tractable, von Neumann had switched to simple, two-would be a hazy glow, like a galaxy. [Poundstone 1985, pp. 227-28.]

dimensional abstractions, now known as
cellular automata.
Conway's Life-world cells are a particularly agreeable example of cellular automata.

In other words, by the time you have built up enough pieces into some-Conway and his students wanted to confirm von Neumann's proof in thing that can reproduce itself (in a two-dimensional world), it is roughly as detail by actually constructing a two-dimensional world with a simple phys-much larger than its smallest bits as an organism is larger than its atoms. You ics in which such a self-replicating construction would be a stable,
working
probably can't do it with anything much less complicated, though this has not structure. Like von Neumann, they wanted their answer to be as general as been strictly proven. The hunch with which we began this chapter gets possible, and hence as independent as possible of actual (Earthly? local?) dramatic support: it takes a
lot
of design work (the work done by Conway physics and chemistry. They wanted something dead simple, easy to visu-and his students) to turn available bits and pieces into a self-replicating alize and easy to calculate, so they not only dropped from three dimensions thing; self-replicators don't just fall together in cosmic coincidences; they are to two; they also "digitized" both space and time—all times and distances, too large and expensive.

as we saw, are in whole numbers of "instants" and "cells." It was von The Game of Life illustrates many important principles, and can be used to Neumann who had taken Alan Turing's abstract conception of a mechanical construct many different arguments or thought experiments, but I will computer (now called a "Turing machine") and engineered it into the content myself here with just two points that are particularly relevant to this specification for a general-purpose stored-program serial-processing stage in our argument, before turning to my main point. (For further computer (now called a "von Neumann machine"); in his brilliant reflections on Life and its implications, see Dennett 1991b.) explorations of the spatial and structural requirements for such a computer, First, notice how the distinction between Order and Design gets blurred he had realized—and proved—that a Universal Turing machine (a Turing here, just as it did for Hume. Conway
designed
the whole Life world—that is, machine that can compute any computable function at all) could in principle he set out to articulate an Order that would
function
in a certain way. But do be "built" in a two-dimensional world.6 Conway and his students also set out gliders, for instance, count as designed things, or as just natural objects—

to confirm this with their own exercise in two-dimensional engineering.7

like atoms or molecules? Surely the tape-reader Conway and his students cob-It was far from easy, but they showed how they could "build" a working bled together out of gliders and the like is a designed object, but the simplest computer out of simpler Life forms. Glider streams can provide the input-glider would seem just to fall out of the basic physics of the Life world "au-output "tape," for instance, and the tape-reader can be some huge assembly tomatically"—nobody had to design or invent the glider; it just was
discov-of eaters, gliders, and other bits and pieces. What does this machine look
ered
to be implied by the physics of the Life world. But that, of course, is like? Poundstone calculates that the whole construction would be on the actually true of
everything
in the Life world. Nothing happens in the Life order of 1013 cells or pads.