Let me tell you about a new game that we’ve been playing in our family, the rule-making game. It is a talking game, requiring no pieces or objects of any kind, and it can easily be played whilst walking or traveling. My children and I recently played several rounds of it walking around London on a recent visit there.

The game has no rules, initially, nor even any definite procedure — it is different every time — but things usually become clear soon enough. It usually makes a better game to cooperate on the first several turns to lay the groundwork.

Let me explain how to play simply by example:

**Papa**: The first rule is that the players shall take turns making rules, and that every rule shall have a rule number, which is incremented on each turn.

**Horatio**: The second rule is that the players must state their rules in the form, “The first rule is…” or “the second rule is…” and so on, and that players are not allowed to ask what is the current rule number, or they lose.

**Hypatia**: The third rule is that the other players must say, “thank you” after another player makes a rule.

(… “thank you”…. “thank you”….)

**Papa**: The fourth rule is that the rules must not contradict each other, and no rule is allowed that abrogates an earlier rule.

(… “thank you”…. “thank you”….)

**Horatio**: The fifth rule is that after making an odd-numbered rule, the player must stomp on the ground.

(STOMP… “thank you”…. “thank you”….)

**Hypatia**: The sixth rule is that no player may win immediately after their own rule.

(… “thank you”…. “thank you”….)

**Papa**: The seventh rule is that right after a player stomps according to rule five, the other two players must hop.

(STOMP … “thank you”…. “thank you”….HOP….HOP…)

**Horatio**: The eighth rule is that if a player loses, then the game continues without that person.

(… “thank you”…. “thank you”….)

**Hypatia**: The ninth rule is that after stating a rule, the other two players must state a different color.

(STOMP … “thank you”…. “thank you”….HOP…HOP… “blue”… “green”…)

**Papa**: The tenth rule is that furthermore, those colors must never repeat, and they must be stated simultaneously, on the count of 1-2-3.

(… “thank you”…. “thank you”…. “1-2-3: neon green / violet”)

**Horatio**: The eleventh rule is that if there is only one player left, then that player wins.

(STOMP … “thank you”…. “thank you”….HOP…HOP… “1-2-3: red/orange”)

**Hypatia**: The twelfth rule is that every player must jump up and down (…jump…) while stating their rule. (….jump jump jump…)

(… “thank you”…. “thank you”…. “1-2-3: pink/turquoise”)

**Papa**: (jump jump…) The thirteenth rule is that (…jump…) in the case of dispute (…jump…), the question of whether or not someone has violated or followed a rule shall be decided by majority vote (…jump…).

(STOMP … “thank you”…. “thank you”….HOP…HOP… “1-2-3: yellow/brown”)

**Horatio**: (jump….) The fourteenth rule is that (…jump…) before stating their rule, the players must state a country, and that whoever repeats a country loses (…jump…)

(… “thank you”…. “thank you”…. “1-2-3: black/gray”)

**Hypatia**: (jump…) Germany. The fifteenth rule is that (…jump…) there can be at most twenty-five rules.

(STOMP … “thank you”…. “thank you”….HOP…HOP… “1-2-3: sky blue / peach”)

**Papa**: (jump…) United States. The sixteenth rule is that (…jump…) if all current players lose at the same time after a rule, then the player previous to that rule-maker is declared the “honorary winner”. (…jump…)

(… “thank you”…. “thank you”…. “1-2-3: white / white”)

Oh no! Since both Horatio and Hypatia said “white”, they both lose. And then Papa also loses in light of rule six. So we’ve all lost! But then, in light of rule sixteen, Hypatia is declared the honorary winner! Hooray for Hypatia!

I hope you all get the idea. Please enjoy! And report your crazy or interesting rules in the comments below.

See also the game of Nomic, which I heard about and played a few times as a child; probably I read about it in Hofstadter’s Scientific American column, June 1982. The rule-making game, of course, follows a similar spirit. As we play it, however, I find our game to be more light-hearted and playful than Nomic, and more suitable for kids.

Meanwhile, players who would win the rule-making game in a crude way, by making rules transparently to that effect, would lose their dignity in our eyes, like compromised lawmakers who attempt similar games in Congress.

But OK, here I am talking about dignity, after having played a game that required me to jump up and down while stating my rules.

And there is the similar-in-spirit game of Questions, played by Rosencrantz and Guildenstern in Tom Stoppard’s play, Rosencrantz and Guildenstern are Dead.

And also the at-first mystifying card game Mao, which inspired our rule-making game, after my kids and I recently saw their cousins playing it and shared in a few rounds.

You can go all “Fight Club” on this game:

“The first rule of the game is that you do not talk about the game.”

And also, if you’re a sore loser, just go first and declare that the first rule is that you must be the winner. After all, there are no rules that you can’t do that! 🙂

But, regarding the sore loser, would one want also to lose one’s remaining dignity?

You’re right. Let me alter my sore winning strategy:

“The first rule of the game is that the game must end where I am the sole winner, and that this does not sully my dignity.”

Now I can win without losing any shred of remaining dignity!

What would be a formal form of this interesting game?

Let’s think as a logician. We start from an arbitrary (empty) set of axioms (rules) given by $T$. But this set of rules is not solid. It may change by some parameters (time, space, players, society, weather, etc.). Thus let’s denote it as $T(t)$ (or $T(t,x,y,z)$,…). The basic questions are:

1- In a particular moment, what are the precise set of rules? ($\frac{dT}{dt}$)

2- In a particular moment, what are the precise set of valid theorems of $T$? ($\frac{dDed(T)}{dt}$)

3- In a particular moment, what are the precise set of independent statements from $T$? ($\frac{dInd(T)}{dt}$)

4- What happens if not only the theory $T$ but also “the set of rules of deduction” change during the game?

5- Can one find any interaction of this type between logic as a part of discrete maths and continuous parts of mathematics like calculus, differential equations? What would be the applications of this “Theory of Variable Theories”?

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