One of the best ways to explore questions starting with "what if" without doing damage to the real world is to play games. It's also a way of spending an evening without watching TV (although some people whom I've played board games with had to tape their favorite shows to catch up with them later). Here. I want to introduce you to two games you can't buy in stores or online.
This is a game I designed when I read Douglas Hofstadters "Gödel, Escher, Bach: an Eternal Golden Braid". Somewhere in the book, Hofstadter suggests a game played on a series of chess boards. The first board is where the actual game is played. The rules of the first board are determined by the positions of pieces on the second board, who are moved according to rules on the third board, and so on. The players decide if they want to make actual moves on the first board, or moves that will change rules on the other boards. He gives a general description of this game, but does not give an example of a specific game. Then he suggests "simplifying" the game having a single board with pieces whose position determine the rules with which these pieces are allowed to move.
Hofstadter uses this game to illustrate what happens when a complex system makes statements about itself, an idea that is one of the red threads of his book. If you're interested in this idea, I suggest you read his book (or read in it, its a pretty big book). When I came to this part of the book, I wanted to get a feel for the type of game he suggested, so I came up with Mutabor.
In Mutabor, each player has 8 cards, one with a big "X" on it, and 7 with rules on it. The basic idea is that the "X" card can move around as well as move and turn other cards around according to these 7 rules. If a rule card gets turned around or gets covered, the rule is not in place anymore. At the beginning, all cards are placed facing up on a board (a chess board or anything else with squares like kitchen tiles etc.) Players take turns and apply one of the rules available to them. This continues until on player has no valid move left, either because his "X" card has been flipped, or he has no more moves, or the moves he has can't be applied for some reason,
Here are the seven rules (from left to right and top to bottom):
Recently, I added two twists to the game to make it more playable (the original game tends to result in stalemates). First, I doubled the number of cards to make the game more complex. The expanded version has two "X" cards for each player, and rules 1-3 occur twice, with slight variations (almost like different alleles of the same gene). In addition, there are four completely new rules that require the two "X" cards in close proximity, bringing the total up to 14 rules. If you are interested in the new cards, email me. Second, there is no fixed starting position. The first player sets up the cards in whatever way she wants, and the second player gets to choose colors. In effect, the first player asks which color has the advantage, and the second player may use this advantage if he can figure out on which side it lays.
Here are some comments on the game. Because the rules are limited to those on the rule cards, the game can't change completely. Also, there are some super-rules that are constant, like who wins, that only visible rules apply, and that players take turns. This is like biology, where different cells might have different rules. To give an example, an bacterial cell might have the rule "If there are calcium ions in the cell, dinner is ready", whereas a human nerve cell might have the rule "If there are calcium ions in the cell, call your superiors". As in Mutabor, there are common ground rules though, like "Proteins are made by Ribosomes" or "Water and Oil don't mix" that the cells can't change. There are games out there where this restriction is lifted. The danger of these games is that one of the players might come up with the rule "no matter what the circumstances and even if it is unfair, I win". And another player might come up with the rule "the other players don't exist but in my dreams". This pretty much takes the fun and competition out of the game.
The name "Mutabor" was taken from a fairy tale in which a Kalif has a magic spell that turns him into an animal. The secret word, "Mutabor", is actually not secret at all, but is Latin for "I shall be transformed". In the fairy tale, the Kalif and his assistant use this spell to learn what animals think. Unfortunately they forget the magic word before they can transform themselves back. The story ends happily nevertheless, with the Kalif marrying a beautiful princess. If your kids ever ask for a reason to study latin in school, just tell them the story of Kalif stork.
This game has been lying in my box of assorted treasures without being played since 1983, or so I thought. In 2005, I stumbled across a web site that mentions Mutabor and credits me with its invention. Mario Hilgemeier came across Mutabor in 1994 and designed the computer-based game rulerule. He learned about it from Markus Fix, who in turn was introduced to it by Klaus-Peter Zauner, maybe around 1990. I'm not sure what happened between 1984 (when I handed out about 20 copies of the game at a meeting of math contest winner) and 1990, when a copy of a copy (I imagine) surface in a physics lecture at the University of Tuebingen, Germany. If anybody knows, send me an email (google "Karsten Theis DNA repair" for the address).
This game was designed by a group of people I played games with in Stony Brook. It's really not a totally new game, but a combination of various rules taken from commercial games we enjoyed playing. The game plan looks like this:
It's supposed to resemble the Stony Brook campus. We gave it to a departing graduate who was part of our gaming group as a good-bye present. If you want to learn more about the game, visit Michiel's homepage and click on games.