email - May 2001

Eigen's Glass Bead Games

Last month we ran out of space before we could address Claudio's question about Manfred Eigen's theories. Eigen's ideas are basically computer simulations of evolutionary processes. Before we address his specific simulation, let's go back to the late 60's.

The Game of Life

When I first learned to program computers, the common input/output device was an ASR 33 teletype. It could print 80 characters on a line. The number of lines it could print was limited only by the length of the paper remaining on the roll. Crude pictures could be produced by printing various characters (X's, periods, blanks, dashes, etc.) that put more or less ink on the paper. From a distance (where the individual letters were difficult to distinguish) the pattern of characters produced the required areas of dark and light shading which made the image visible.

The ASR 33 was soon replaced by "glass teletype" video terminals with 34 lines of 80 characters. But graphics were still limited to images that could be presented by characters. Naturally, the computer games of this era were severely crippled by the limited output capability of the glass teletype.

One such program was the Game of Life. I don't remember exactly what the rules were, but they went something like this: You start out by entering a few clusters of X characters on the screen. Character locations were considered to be cells. A cell was alive if it had an X in it, and dead if it was blank.

Then you pressed the start button and let the computer do its thing. The computer evaluated every cell on the 34x80 terminal screen. If a dead cell was adjacent to two or more living cells, it was "born" and became a living cell. If a living cell was completely surrounded by living cells, it died from suffocation and became a blank. After the computer had evaluated all the cells, it redrew the screen. Then it evaluated every cell again.

In general, the clusters of cells would grow bigger and bigger, until most of the screen was filled with living cells. But then cells would start to suffocate. Sometimes the pattern continually changed. Sometimes it got into a stable cycle where several patterns would repeat in a sequence.

It was just a novelty. It was fun to watch. It impressed visitors who came to your office who had never seen a computer before. Nobody believed that this was an accurate simulation of life in a petri dish.

The only thing it really taught was that if you have a fixed set of rules, the eventual outcome is determined by the initial conditions. If you started out with a cluster of four X's in the top left corner, the computer would always generate the same sequence of patterns. If you started with a column of five X's starting at the third row of the seventh column, you would get a different sequence.

You could, of course, change the rules to get different patterns, too. You might say that if a living cell is adjacent to just six living cells, it suffocates. You might require a dead cell to be adjacent to three cells to be born.

The sequence of patterns you get depends entirely upon the rules and the input conditions. Given a particular initial input, and fixed rules, you always get the same pattern.

Eigen's Contribution

Eigen's contribution to these games is the introduction of random processes. He explains his ideas in terms of glass beads on a very large checkerboard, but one can play his games much more easily on a computer. One could write a program that fills the screen with different colored squares, then "rolls the dice" to see which square will change color. Eigen's game has rules about how the color will change, based on the color of some (or all) of the other squares. The game shows that (at least in some cases) the rules and initial conditions determine the final pattern, even if randomly selected squares are changed to colors that are selected by random variables.

If you have taken a course in statistics you know that "random variables" are absolutely predictable in the long run. No matter who bets on the roulette wheel, you can determine how much the house is going to win every month if you know the total amount of money that was wagered. Therefore, Eigen's results aren't surprising.

The supposed application to evolution is that despite the fact that mutations are random, the rules and environmental conditions will determine the outcome.

The question you have to ask is, "Is this computer simulation representative of what happens in the biological world?"

His games might give us some insight into how populations might change. Years ago, the Game of Life showed us that when there is lots of space available, populations grow. When conditions get crowded, things such as starvation and suffocation keep the population in check. Eigenís games show us the same general trends. In that respect, they are marginally useful.

They donít, however, give us accurate predictions of how fast the population distribution will change--unless we use the right rules and probabilities. The only way we can determine the right rules and probabilities is to play the game with different rules and probabilities until the game produces the answer we expect. That doesnít teach us much, however, because we expected that answer in advance. The simulation merely confirms what we already believed.

It is easy to make a computer tell you anything you want to hear. I have a friend who, in high school, wrote a computer dating program. All the kids in his class filled out questionnaires and he entered them into the computer. The computer then determined who should go to the school dance together. The computer paired him with Tina, who later became his wife. She didnít know that he rigged the program to decide that they were the most compatible. From his point of view, he merely wrote the program so that it would produce the ďcorrectĒ pairing.

Although Eigenís games may mimic populations trends, they certainly donít tell us how new kinds of creatures arise. It is easy to write a program in which a green bead turns into an orange bead at random. That doesnít mean a lizard can turn into a mammal at random. There is a world of difference between a glass bead changing color at random and a reptile growing a breast by chance.

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