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AI’s new type of knowledge

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If you know how to play chess, then you know how to set up the board, how each of the pieces move, how to capture a piece, and how to tell if you’ve won or lost. In short, you know the rules and how to apply them to any state of the board.

That paradigm of knowledge— knowing the rules and the starting state of the domain to which they apply— works for everything, from astrophysics to cooking. For example, we know the laws of gravity and motion, we know the mass of the moon, and the mass of a golf ball. We can know the height from the surface of the moon that a golf ball is dropped, thus we can know how long it will take to land.

This way of knowing works pragmatically for some very complex systems of the sort we find in the real world. But, oddly, it seems not to work so well in some artificially simple systems.

Betting on the craps table

For example, the craps table at a casino is designed to be as simple as possible in every way: It’s flat, uniformly felted, level, padded, and symmetrically shaped. The only major variables are how the human shakes and releases the dice. Yet, even knowing all that, we still can’t predict any specific result.

Let’s make things simpler still. You can’t get much simpler than cellular automata. Invented in the 1940s with credit usually going to John von Neumann, they’re probably most familiar from John Conway’s 1970 Game of Life (playgameolife.com). But let’s look at an even simpler example: Stephen Wolfram’s use of them in his 2002 book A New Kind of Science.

Imagine a row of empty squares except for one black square in the middle. That’s the ultra-simple starting state. Now, write rules for how the square to the left and to the right of any square will determine its color in the next step. These rules will say things like this: A black square with white squares on either side will turn white in the next move, but a white square in the same state will stay white, and so on. There are four possible conditions for any black square and four for any white square.

Now, pick any of the 256 possible rule sets and apply it to that initial row. Then apply the rule set to the result, and stack it right below the first rule set. Do this a hundred times, or a thousand times, or a billion times. Then start again and do the same thing for each of the 256 rule sets. In some cases, you’ll get simple, complex, or fractal patterns that repeat forever. Other rule sets don’t yield anything except noise, randomness, and chaos.

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