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Introducing Enigma – The Little Black Box

I have spent the last few week-ends designing a little computer game about decision-making. You can play it yourself, and observe how you need to change your methods once you leave the ordered world and enter a complex environment. Here’s its story.

I once read a book where complexity was described with the help of an imagined game. It is a black box with four buttons, four signals and a simple little mechanism inside. If you press a button, it shows a signal. Your task is to predict what signal will be shown when you press a specific button. And the book said that without looking into the black box, without knowing how the mechanism works, just by playing around with the buttons until you get it, you would be completely at a loss. And that would be what you experience in complexity.

Some years later I searched again for that passage, but to this day I have been unable to find it. I did however remember the game well enough to build a simulation. One player would impersonate the machine, and read the answers from a sheet of paper. The others would have to “press the buttons” by asking the person. I’ve played that game with about sixty teams of two to five players, and this is my conclusion:

All the teams get very frustrated, and most of them give up. But their behaviour is interesting. Most teams press buttons about 10 times, and then turn around and create their big theory of everything, being very hesitant to press more buttons. They also hesitate to test their theory before it is complete. If they do test it and the test fails, they again press very few buttons and start building their next theory. I even designed some cards with hints about methods to use, and gave them to the players. Many teams ignored them.

Some teams however did find the solution and were able to predict the signals correctly. Interestingly, they still had no idea how the machine works inside. So the method that produced correct predictions was independent of the understanding of the causal workings of the machine.

Overall, the game served its purpose. Once they saw the mechanism, people understood that this is probably the smallest possible step into complexity. And your known habits of problem solving all go down the drains.

But there was a downside to the whole game. Of the sixty teams, only three found the solution, usually after forty-five minutes and two flip-charts full of letters and numbers. This is why I decided to cut the number of buttons and signals down to three each, making it easier. Some tests revealed that more than half the players were now able to solve it in about ten minutes. That is when I decided to translate it into a beautiful little computer game. You can find it here and on the bottom of the homepage.

But this is where the story gets interesting. By chance, I bought a collection of essays by some of the founders of Cybernetics and Constructivism. And it contained an essay by Heinz von Foerster, which introduces this game as a non-trivial machine. But his conclusion is different from the passage I remember reading. He says that in order to solve the puzzle, you need to check it against 102466 possible versions of the machine. Just to give you an order of magnitude, the number of atoms contained in the universe is guessed to be less than 1082. While I am unable to give you the number for three instead of four buttons, it still remains so high that von Foerster’s conclusion would be convincing: This is impossible for a human being to solve.

Had I known this, I would not have tried the simulation in class, yet alone built the computer game. Only the incomplete transmission of this knowledge made me plough on, and come to a different conclusion.

So why was von Foerster wrong? At the moment, I can only offer some guesses. First, there is a graduation of difficulty. There are some more devilish ways I could set the machine, and yes, they would be impossible to solve. But I see something else at the core of it. If you were to create a theory of the machine, form a number of assumptions, and then exclude them one after the other, you would be choosing a very systematic, linear, computational way, but it would be the hard way. By comparison, the teams that solve the puzzle create a large number of data and are able to sustain very incomplete, sometimes contradictory assumptions about it for a long time, searching for more fragments of insight, before at some point more and more fall into place. It is like solving a 1000 piece puzzle. If you search for the bottom left corner piece and then for those that come next to it, you go about the task very systematically, but it will take ages. What most people do, however, is group colours, and maybe connect fragments of a few pieces each, undisturbed by the fact that for the moment there could be several places where this collection of pieces could fit in the final picture. It is a very non-linear, approximative approach to problem solving.

And that is probably a cornerstone in why humans are surprisingly good at dealing with complexity.

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