Somewhere back towards the beginnings of this strange little game company, Kadon, in about 1982, I was driving to Chicago for the wedding of some very special friends. I had met them the year before at the World Science Fiction Convention held that year in Chicago, where I was selling Quintillions, our first and only game, since its inspiration came from a sci-fi novel by Arthur C. Clarke.

At Chicon I first met Michael Waitsman in person, after having had many exchanges with him by mail. Within a few months we had published two of his games that he first showed me at Chicon: Void and Proteus. Proteus is a meta-game, where the rules change when tiles are flipped. It's sort of a 27-dimensional tic-tac-toe with chess moves. I was going to Michael's wedding. He was marrying the lovely and immensely talented artist, Liane Sebastian, his partner in their graphic arts business.

The long drive from Maryland gave much time for thought.

I began reflecting that most board games I knew fell into very few categories:

• Direct combat and conquest, such as chess, checkers, go, Alquerques, Othello.
  
  

• A race to the finish, generally ruled by the luck of dice and including being the firstest and having the mostest, such as parcheesi, backgammon, and all their descendants, Candyland, Sorry, Chutes and Ladders, and even the acquisition-minded Monopoly.
  
  

• Abstract, positional, strategy games, such as Scrabble, dominoes, mah jongg, Chinese checkers, halma, and of course Michael's Void and Proteus.

Even in these categories there were some overlaps:  Chinese checkers is a speed race, Scrabble collects points, backgammon has (temporary) captures, dominoes and Scrabble depend on the luck of drawing the right tile. Surely, I thought, there must be more to games than these simple elements of symbolic wars, acquisitions and beating others to a finish through better luck. My natural inclination was always towards games of strategy without those hostile or predatory elements. That's what I had loved about Michael's games and why I leaped to produce them.

Mind you, this was before the fantastic explosion of new game genres of the past quarter century: role-playing, fantasy, war games, party games, trivia, and the sophisticated European board games that have put slick new wrappings on the same old conquer-and-acquire themes. In today's multimedia world, anything is subject to becoming a board game, from movies to novels to quiz shows.

But I digress. Speeding along on I-80 toward Chicago, I pondered whether there could not be a game theme outside the big three. Maybe the players themselves could decide the theme as the game was played? What if the players themselves could make up the rules, so each time it's played, it will be a different game? Aha! Within two seconds my brain had seized the idea and worked it out in full.

I recalled that a boardless rule-making game had been proposed a while back, Nomic, which became something of a cult thing after Douglas Hofstadter wrote about it in Scientific American. And Michael had told me Nomic inspired his creation of Proteus. But Proteus had fixed rules, a limited menu. I wanted an unlimited menu but not a boardless game.

It should be a game that paralleled the evolution of ideas, ideas that build on each other... just the way human civilization developed. I wanted a game that would symbolize society not as a brute-force historical process but as the future evolution of the mind, with maximum freedom of innovation.

At first I was going to call the new game Evolution, but that name was already in use elsewhere. Searching for another word to express the building or hierarchy of ideas, I hit upon Lemma, meaning a supporting proposition.

What didn't come so instantly was the design of the board itself. I doodled on that for a year. Michael had an unused gameboard design he offered, but it didn't quite fit. Then, one day, one of my doodles struck paydirt. A nest of lines, points, cells would enable players to define their playing field in any number of ways. Three colors plus black and white would allow relationships of similarly colored checker-like playing pieces. And it was unlike any gameboard I had ever seen, with its nested squares and floating multi-dimensionality. Done!

Its prime directive is:  Let there be rules. And from that come only 6 groundrules. All else is up to the players to choose and decide and invent. The 6 groundrules:

1. On each turn, players create a new rule and illustrate it by some action on the board. (A rule you can't show can't be made.)
   
   

2. Only one new rule may be introduced at a time, no compound rules.
   
   

3. Only the gameboard and pieces are used as elements in the rules and actions. No outside elements may be included.
   
   

4. A player unable to fulfill both parts of a turn is eliminated.
   
   

5. All new rules and actions are subject to all previous rules, and no new rule may contradict any previous rule.
   
   

6. No new rule may invalidate any groundrule.
   
   

Basically, then, anything not prohibited is allowed. A most satisfying maximum freedom of choice. Any action or event on the board, other than "placing" from outside the board, has to be introduced by a new rule. All rules get written down, of course.

Rule No. 3 became necessary when, during a playtesting session with friends using improvised equipment, one player wadded up the paper napkin serving as the board and declared, shoving it into his mouth, "The gameboard may be eaten!"

To assure that groundrules and previous rules are adhered to, players may challenge a new rule and discuss how it has to be changed to be acceptable. It is at this intellectual level that the true meta-game is being played.

Among some guidelines provided in the rule book is the provision that it is not necessary to play until only one player remains. Players may choose to adjourn the game at any time because "in this microcosm of survival dynamics, all survivors are winners."

One of the amazing aspects of watching people play Lemma is the personal transformation that comes over them when it's their turn to make the rule. A moment of omnipotence seizes many, and strange things come of it. People you thought you knew well become something else altogether. Inventiveness in the game tends to build.

A few people are not comfortable with an infinite game that doesn't end with defeating someone. But, hey, this is the new paradigm.

Besides Lemma, the board serves for several other, more regular games, including two medieval ones: Alquerques and Hounds and Hares, played on the intersections of the inner field (colored area below). Two other games play on the intersections of the full board. The hefty instruction book also includes a few hundred puzzle challenges. Here are two for you to try:
 

SEVEN ROWS — Place 7 disks on the intersections of the board so that no two of them lie on the same line or row, in any direction. For this puzzle, all points are considered to be in the same row if they can be connected with a ruler that is then parallel to any other line on the board. There are 7 vertical and horizontal rows. There are 9 diagonal rows. For example, look at the upper left yellow area. If you joined the two midpoints on its left and top edges, they'd be part of a diagonal row parallel to the edge of the largest square. They are, therefore, in the same row, even though you can't see a line on the board connecting them. You may use the whole board, even the outermost black corners, to solve this challenge.

FOUR BLOCKERS — Place 4 disks on the intersections of the board so that no more can be placed anywhere on the whole board without being in the same row with any of these four. "Rows" are defined as for the preceding puzzle.