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Puzzling complexity

| Wednesday, June 16, 2010

Imagine a jigsaw puzzle of 1 billion pieces. They are scattered randomly across a pasture that is 1 million miles square. If someone assigns you the task of finding all these pieces, how would you do so?

One option is to search for each of these billion pieces by yourself. If you choose this option, you'd likely die before you complete the task. Even if you lived for 95 years and began nonstop searching for the pieces the moment you were born, you'd have to find one piece every three seconds to find them all before you die.

But suppose you enlist the help of 999 friends to fan out with you across the pasture, searching for the pieces. The task is now much easier. Even if each of you finds one piece only every 30 seconds, you and your friends together will complete the task in a little less than one year.

Of course, this task can be made even easier by enlisting the help of 1 million people or (better still) 100 million people. With 100 million people scouring the pasture for puzzle pieces, each person would have to find an average of only 10 pieces. And so, if each of these 100 million searchers finds a piece every 30 seconds, the task will be completed in a mere five minutes.

Human cooperation is powerfully productive. Still, in this example, simply collecting all the pieces of a jigsaw puzzle is not by itself a very valuable achievement. The puzzle must eventually be put together properly to justify the effort spent on finding all the scattered pieces.

Think of each jigsaw-puzzle piece as a unit of information that is potentially useful for making the economy work successfully. One piece might be information that deposits of iron ore exist in a certain location in Australia. Another piece might be information about which mining engineers are especially skilled at designing an operation for extracting this ore from the ground.

A third piece is information about how best to transport the ore to a smelting plant. A fourth piece is information on how to make a crucial part for the engine of the truck that will transport the iron ore. A fifth piece is how to design the roads on which that truck will be driven.

Clearly, the number of pieces of information that must be found and used for iron ore to become, say, a steel girder in a skyscraper is mind-bogglingly immense. It is a number far larger than the mere 1 billion pieces of the jigsaw puzzle in my example.

It's beyond foolish to expect any one person (or small group of persons) to find all these pieces of information necessary for the production of steel girders (and steel automobile bodies, steel sheeting for ocean-going tankers, stainless-steel dental tools ... the list is long).

Not only is the mere finding of each piece of information too difficult to entrust to a small group of persons; so, too, is the task of putting these pieces together in a way that yields useful final products.

Allow me to amend the example to make the jigsaw puzzle a better metaphor for economic reality. Suppose each piece of the puzzle can be made to fit snugly and smoothly with any other piece. In this case, merely assembling all the 1 billion puzzle pieces so they fit together neatly is easy. But note that it is possible to create an unfathomably large number of scenes with these pieces.

Trouble is, only a tiny handful of these scenes will please the human eye. Most of the scenes will be visual gibberish. The challenge is to arrange the pieces together so that the final result is a recognizable scene -- say, of a wheat field or of a bustling city street. Only if the scene is recognizable is the assembled puzzle valuable.

Now imagine yourself standing alone before a gigantic table covered with these 1 billion puzzle pieces. What are the chances that you alone can put these pieces together so that the final result is a coherent visual image -- a valuable final result?

The answer is "virtually zero." Even if the number of possible valuable scenes is 1 million, that's still only a minuscule fraction of the number of possible ways this puzzle can be assembled. For these pieces to be fitted together so that the result is valuable requires many people receiving feedback at each step of the way about whether the act of connecting, say, piece 143 with piece 56,997 is a good move -- a move that brings the puzzle closer to depicting a scene pleasing to the human eye.

In my next column I'll discuss this feedback.

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