Please no butterfly analogies.
In: Mathematics
In complex systems, a slight change in the system’s input can give very different results.
Take playing a game of pool as an example. The cue ball and all the other balls are ideally in the same places when you start the game. If you try to hit the triangle of balls in the same place when you start the game, you’ll probably see most of the balls move very differently each time.
This is an example of chaos theory in action. The subtle difference in how hard you hit the cue ball, how the balls in the triangle are slightly in different places each time you play, and a number of other things all snowball together to give you a very different pattern of how all the balls move around the table, even though your game’s setup was so very similar to every other time you set up a game.
Where this really builds up complexity is when the balls start bouncing off the sides of the table after the first hit sends them flying. A slight difference in speed and direction will cause balls to bounce off each other at different angles and sides, or even cause totally different balls to bounce off each other.
This means that near the start, all pool games you play are very similar. Even after you hit the cue ball and it hits the triangle of balls, you’ll still be mostly the same as every other game you’ve played. It’s the complexity of all the balls bouncing around and off each other that very quickly turns small differences into bigger and bigger ones.
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