2009-02-22

Order vs. Chaos

12: 45 Restate my assumptions.
  1. Mathematics is the language of nature.
  2. Everything around us can be represented and understood through numbers.
  3. If you graph the numbers of any system, patterns emerge.
Therefore, there are patterns everywhere in nature.

- Max Cohen, in Darren Aronofsky's Pi

It all started with a simple observation


My friend Daniel enjoys abstract strategy games, but this is one of the few types of game I just can't seem to enjoy very much.

Next came an exception which clarified the rule


Mike and Elly introduced me to Zendo. This very interesting game is a pure distillation of an inductive logic puzzle, in a multi-player format. I enjoyed it very much, even though it was an abstract strategy game.

In Zendo, the master decides on a rule which distinguishes between "koans" (sculptures built of the plastic pieces shown here) which have the buddha nature, and those which do not. An example rule: "Only koans which contain an orange piece have the buddha nature." The students (other players) try to discover the rule, by observing previous examples and constructing koans to test their hypotheses. Technically, the first student to induce the correct rule "wins;" but as in most good games, "winning" provides a convenient stopping place more than a reward for good performance.

Reconciling my enjoyment of Zendo with my general distaste for abstract strategy games ended up being a bit of a realization. The games I don't like tend to have simple rules which result in complex gameplay (if you're lucky). The games I enjoy tend to have a larger, more chaotic system, and part of the fun for me is to find the order behind that chaos.

Zendo is a crossover. It has simple rules with interesting emergent properties, which I don't tend to lke. But the game creates a chaotic-looking system with the goal of discovering the rule which generates those seemingly chaotic results: exactly matching my preference.

Trying to find a rule which explains a set of observations is called "inductive logic." In contrast, "deductive logic" starts with the rules, and generates outcomes consistent with the rules. To me, the difference between inductive and deductive logic seems to mirror the sort of games I enjoy.

The problem with inductive logic in practice, is that it is easy to get stuck on a false rule which is consistent only because not enough observations have been made. Inductive logic can be applied with a greater degree of success, in cases where you know there is a simple rule which explains the chaos, such as in Zendo.

To be useful, inductive logic must be combined with a strict process to weed out the false rules. The game rules of Zendo define the process used for this during the game. In real life, the process typically used is something like this:
  • Make as many observations as possible
  • Hypothesize a rule which explains and is consistent with all observations
  • Test the hypothesis by trying to find counterexamples
  • Revise the hypothesis to match new observations
When applied to observations made about "The Real World," this process has a name: The Scientific Method.

Finally, a pattern started to emerge


Once I settled on this explanation for my preferences within the realm of board games, it became evident to me that not only do these preferences match my abilities, but they also apply to many other aspects of my life. I'm relatively good at finding the patterns behind chaos, and I also enjoy it.

As I said before, there are problems with getting stuck on invalid rules (superstitions and myths), or finding patterns where there are none (paranoia). The movie A Beautiful Mind tells the true story of mathematician John Nash, who was both a mathematical genius and a paranoid schizophrenic. This correlation between madness and genius has become almost stereotypical, but most normal people end up with the problem of superstitions, instead. Without thinking much about it, they attach themselves to simple explanations for their observations which do not hold up to tighter scrutiny.

I tend towards paranoia, and constantly questioning other peoples' explanations, rather than settling on inconsistent rules. I'm no genius, but at least I don't have the madness which goes with it.

I'll write more in the future, indirectly related to these concepts, but I wanted to describe my general thoughts first so I could refer to them later.

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