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Zendo and scientific thinking
blaisepascal
On one of the Looney Labs-based mailing lists I subscribe to, a question about Zendo came up. Zendo is a game invented about 10 years ago by Kory Heath originally for use with the pyramid-shaped playing pieces designed by Andrew Looney. The question concerned a strategy suggested in the published rules for the game.

First, let me explain the game (Wikipedia has a description of it, with rules, but I want to simplify even further).

The game is played with several players, one of which is deemed the "Master", the others deemed "Students". The Master begin the game by secretly deciding a rule which will separate "koans" into two groups, koans which "have the Buddha-nature" and koans which don't. The Master presents to the Students two koans, one which has the Buddha-nature, and one which doesn't. The koan with the Buddha-nature is marked with a white marking stone, the koan without is marked with a black marking stone.

The Students take turns presenting koans of their own to the Master to judge. There are two procedures the Student can use to get the Master to judge a koan: First, she can just ask the Master if the presented koan has the Buddha-nature, and the Master places the appropriate colored marking stone next to it.

Second, she can call "Mondo", and all the Students (including the one who called Mondo) present simultaneously their beliefs about the Buddha-nature-hood of the current koan (usually by opening their fist with the appropriate marking stone. The students who successfully judge if the koan has the Buddha-nature get a "guessing stone" as a reward.

At the end of a Student's turn, she has an opportunity to spend guessing stones guessing the secret rule. She gives a guessing stone to the Master, explains her proposed rule, and if she's wrong, the Master proves it by building a koan that her rule gets wrong. She can spend more guessing stones on more guesses if she chooses. If she's right, she wins.

That's the game. The official rules go on much more, defining what sort of secret rules are legal (basically, the rule must (a) be able to divide any presented koan into Buddha-nature or non-Buddha-nature, and (b) depend only on features intrinsic to the koan. A rule like "a koan has the Buddha-nature if it's on my left" is an illegal rule), and a lot of strategy-discussion, definitions of things which apply to pyramids, etc.

I didn't define what a "koan" was because it's immaterial to the basic nature of the game. Koans could be (as in the original game) arrangements of colored stackable plastic pyramids, or they could be things put together out of Legos, or they could be English sentences.

The question on the list concerned advice given in the rules about calling Mondo. The strategy listed in the rules was
When to Call Mondo: Don't call mondo unless you have at least one whole-pattern that works for everything on the table. The best time to call mondo is when you're about to spend a stone on a guess, because if the mondo supports your guess you will win a stone to pay for it. If you have no guessing stones and are desperate to take a guess, you should still perform an intelligent mondo that attempts to test your theory. If your theory is correct, you will win the stone that you need. If you don't win the stone, that means that your theory was incorrect, so you no longer have a desperate need for the stone. If you choose to do an "easy" mondo which guarantees you a stone, you'll be providing free stones for everyone else as well, and you'll be forced to state your theory out loud (since you've made no attempt to test it with your play). If your theory is correct, this won't matter, but if it's not correct, this is the worst possible outcome of a mondo.
and the question was why would calling Mondo force you to state your theory out loud? Why not call Mondo every turn?

My answer pointed out that they has misread the strategy. One is forced to state your theory aloud when guessing, giving the other Student's ideas as to your thinking. If, before you guess, you Mondo with a koan which attempts to falsify your guess, testing it in a way which isn't clear from existing koans, you win two ways: If you get the Mondo wrong, you won't make an incorrect guess and no one will be able to tell how you are thinking. Many of the other Students will likely have judged the Mondo incorrectly as well, so won't get guessing stones they would have with an "easy" Mondo. Plus, you still have a counter-example which can help formulate your next guess.

It's here that geeky/sciency folks looking at Zendo go "hey, look, scientific method". You advance in the game by looking for patterns, forming hypotheses, and testing them by experimentation. A good experiment is one which has a reasonable chance of proving your hypotheses wrong, and so forth.

Others answering the query pointed out that the strategy of not mondo-ing except to prepare for a guess is important when one is playing competitively, trying to win first, but not when the Students play cooperatively, trying to find the solution regardless of who wins. Then the fact that incorrect guesses help all the students isn't a flawed strategy, but a benefit. Of course, it's possible to play it somewhere in between purely cooperative and purely competitive. I've played many a "competitive" game where there was plenty of table-talk about what various theories were. But every koan played, every guess made, is usable by all, so there's always a bit of cooperative nature to it.

In fact, with some minor variation -- eliminate guessing to win, and allow the results to be more nuanced than black/white -- one could easily say science is Zendo where the scientists are students playing mostly cooperatively with Nature as the Master.

I'm not the first to wonder of Zendo would be suitable for science classroom use. The obvious objection -- the terminology (master, student, zendo, koan, Buddha-nature, etc) comes from Zen Buddhism -- can easily be overcome by rebranding: the rule becomes a Theory, guesses become Hypotheses, koans become Experiments, etc. I see it very much in line with the type of creativity exercises my high-school CS teacher would have us do, things that weren't directly part of the curriculum, but he felt it important for us to keep our minds limber.

I can see multiple versions/levels of the game. First, rebranded, but otherwise as-is. Second, eliminate guessing but award points for being the first to suggest a particular "whole-pattern" (theory which discriminates all white from black koans), and points for suggesting a koan which successfully breaks a previously suggested "whole-pattern". Then show them a bunch of marked "koans" (say, simple chemical reactions they haven't learned yet, some possible and some not) and ask them for theories as to the rule.

I know there are science educators on my Friends list. I'm interested in hearing what you think of the idea.
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I'm a (future) math educator, who's already been thinking about ways to use Zendo in my glassrooms --patterns of numbers especially come into play.

But this? This is totally cool!

~Sor

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