I used to waste hours of my life playing The Batte of Wesnoth, a strategy conquest game. Some of the maps in the game are hidden: you start with a tiny part of the terrain open and visible, the rest covered in dense fog. Enemies jump out of the fog where you least expect them. As you move your troops, the explored terrain grows, more of the map becomes visible. Yet there are still too many unknowns to predict the flow and the position of new enemies. And then at some point - while a sizable part of the map is still covered in fog - you just know it all, and the enemy does not stand a chance. For practical purposes, a clear view of maybe three fourths of the terrain is as good as the complete view.
And that reminds me of the famous complexity theory thought experiment - imagine a thousand beads on the floor. They are disconnected. You take a piece of string, randomly select any two and connect them. Then you repeat the procedure again and again, until small clusters start forming - 2 beads here, 3 here, 4 over there... And then you reach a point when almost every bead is in a cluster, big or small; but there are still dozens of clusters. And finally with just a few more iterations everything coagulates into one giant cluster. You have not at all exhausted all the possible connections between the beads, far from it; yet everything is connected, albeit not necessarily directly, to everything else. That transition is not unlike the Eureka moment of playing the game and all of a sudden "knowing" the whole map.
So what kind of "knowing" are we talking about? What does it mean to say that somebody knows their stuff? Well, we only make knowledge claims about patterned phenomena. Nobody in their right mind would claim knowing a sandpile, a primarily chaotic system. Up in the Bezengi area of the Caucusus mountains is the 18 kilometer long Bezengi glacier, the longest in the Caucasus. To get to the base camps for many of the climbs, you have to walk up the glacier for about ten kilometers. It is very monotonous; everything looks the same the whole time, especially to a new comer. There is no discernible pattern. Part of the glacier may collapse overnight, shifting the optimal path a hundred yards to the left. It is hard to "know" the glacier.
But even there you can get to a point that you run up and down the glacier in dense fog without a compass and know exactly where you are going. You have learned to recognize the subtle patterns of the system, same as you would "know" a big city. You don't really "know" every street, every house, every station; but with enough knowledge about some of them (like the beads connections reaching a transition) you can predict the rest of them and find them with an almost 100% accuracy. It is almost like you have latent knowledge of every node in the system, based on the positions of some of the nodes and the overall structural principles of the system. This is what Confucius was talking about it when he said, only those who can imagine the three other corners of a quadrant when shown one corner are worthy of being a student.
For years and years and years I have been pushing myself to learn more about information technology. It always seemed like a giant map covered in fog, with me standing in some corner of it blabbering about PHP and CSS. Yet yesterday I realized how far I have come already. I had my "beads-in-a-cluster" / "this glacier has a pattern" moment.
I don't need to see the whole map. I feel (=know) the rest of it already, without having ever seen every element of it.
Published on the old blog on May 13, 2009