Game Theory 2: It's the SIMple things in Life
or how very simple rules in Life and The Sims
become very complex patterns.
There is an interesting branch of mathematics called Chaos Theory which explains how slight imperfections in accuracy of measuring an initial state can cause radically different outcomes of a final state. I have discussed it a little in the past here.
A similar phenomenon can be found while playing games. There are many games that follow very simple rules, but result in very complex games of strategy. Chess is the most obvious example, but other games like Go and Reversi fit this description as well.
What I want to discuss are two computer solitaire games that have this property. Both games have very simple rules, both were created to simulate biological behavior, neither have a real objective or a way to win. Both start with very simple easy to follow rules which result in very complex hard to control outcomes. The first is a fairly old game called "Life" created by John Conway in 1968. The second is a fairly new game called "The Sims" created by Will Wright and Electronic Arts in 2000.
The Computer Game of "Life"
"Life" is not the popular game from Milton Bradley, it is rather an example of a "cellular automata". "Life" is played on an infinite grid of square "cells", like a checkerboard that goes on forever. A cell can be live or dead. A live cell is shown by putting a marker on its square. A dead cell is shown by leaving the square empty. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals. The super easy rules of the game are:
- A live cell will remain alive if there are two or three neighboring cells that are also alive. Less than two and the cell "dies" of starvation, more than three and the cell "dies" of overcrowding.
- A dead cell becomes alive if exactly three neighboring cells surround it.
- Cells do not change until after all cells that change have been determined.
The game is played via computer, the rules being very easy to program. From these very simple rules comes an almost magical world of cells living and dying. The best way to experience life is to actually play it. A great java version can be found here.
To demonstrate the complexity of the game,
try just drawing a straight line of dots and click go. Two dots in a row will
disappear instantly. Three dots in a row will turn into what is commonly called
a "blinker" or a "traffic light".
Four dots in a row will turn into a
"beehive" (see the picture on the left) in two moves. Five will turn
into four blinkers, six will disappear in 12 moves, and seven will turn into
four "beehives" in 14 moves.
Eight dots in a row will not go stable for
48 moves, when it ends up as four "beehives" and four
"blocks" (pictured on left). Nine dots turns into eight blinkers in 23
moves.
Finally, ten dots in a row
will, after two steps, fall into this 15 step repeating cycle.
Most any pattern of cells you use as your starting pattern will behave similarly. Either they will all die out, or they will reach a stable pattern, or they will get stuck in a cycle that repeats forever. There is a fourth possibility: the number of live cells grow forever. This is a very rare outcome, so rare that "Life" players get excited discovering new ways to accomplish this goal.
For further details about this game, I recommend either this beginners page, or this more advanced site. Whole books have been written about the study of this game. One entertaining book is The Recursive Universe by William Poundstone. It is not currently in print, but it is available in many public libraries.
The basic lesson of "Life" is that complex patterns can emerge from a seemingly simple foundation. It is even possible to create a pattern in "Life" to simulate the operations of a computer. It is therefore possible (in fact it has already been done) to create a pattern in "Life" which simulates the playing of "Life". This gives it the distinction of being the first game smart enough to play itself.
The Sims
"Life" may be an interesting diversion from reality, but it is easy to lose interest after a while. Two years ago this month, the makers of Sim City released a game which takes cellular automata to a whole new level. "The Sims" has become one of the most popular and addictive video games ever released.
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Cells in "Life" can do two things, live and die. Sims can be born, grow up, go to school, make friends, date, get a job, get married, have children, and of course die. Along the way they engage in all sorts of typical human behavior, such as eating, sleeping, cleaning, bathing, swimming, dancing, kissing, and dozens of other activities (yes, even sex). |
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And yet, underlying all this human like behavior, is a very simple routine. Each "Sim" is defined by five personality traits which cannot be changed, six basic skills which can be developed, and eight "moods" -- hunger, energy, comfort, fun, hygiene, social, bladder, and room -- which vary constantly. There are also relationship levels between Sims. When the Sim is not doing anything, all of these moods slowly decrease, making the Sim more miserable. Engaging in activities will cause one or more of the moods, skills, or relations to improve, thus making the Sim happier. The central algorithm is very simple:
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For example, if the Sim is hungry, they will go to a refrigerator, grab some food, cook it and eat it. If the Sim lacks energy, they go to bed and sleep. That is pretty much all there is to the game. Sounds simple enough, but with up to eight Sims in a household and eighty in a neighborhood all acting autonomously (when you are not controlling their behavior), the game will constantly surprise you. It is easy to waste hours of your real life trying to get your Sims to be happy in their simulated life. As a simulation of real human behavior, the game fails miserably. For example, the happiest Sims are polygamous bisexuals, which is nearly non-existent among the real human population. Yet, The Sims do simulate complex, near "human like" behavior. Thus, it succeeds to demonstrate the same pattern as "Life" -- complex behavior described with simple rules. |
More info about The Sims can be found at the official home page.
Complexity
These "games" demonstrates a basic principle found in all sciences that search for simple explanations for complicated patterns. For example, in Biology, we know exactly how cells work, and how they divide and grow. Cells follow easy to understand rules. What we still do not understand is how cells become multi-cell organisms such as plants or animals.
We know the basic laws of physics governing matter in the universe, whether it be sub atomic matter or the motion of planets. Yet, the universe which does nothing but behave in accordance to these rules still constantly surprises us. Some scientists have even coined the term "emergent complexity" to describe this phenomena.
The real advantage to studying how simple things become complex is to consider the reverse: We see complicated and seemingly unpredictable behavior all around us from weather patterns to stock market prices. Are these complex systems simply following uncomplicated rules we have not discovered, yet?
Complex outcomes may be a result of simple causes, or they may just be complex by nature. Those complexities that turn out to have simple causes can be simulated and studied, thus increasing our knowledge without needing direct observation.
Do you know why most countries have banned nuclear weapons tests? It is not because they one day hope to ban nuclear weapons, it is because the physics of nuclear weapons are so well understood that new weapons can be designed and tested via computer simulation, thus eliminating the need for live testing.
Computers can compute and simulate phenomenon that are really difficult to understand, all we need to know are the rules.
Games can teach us that complex situations can have simple causes. Knowing this is the beginning of understanding everything from Physics to Politics.
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