Abstract Things and Cellular Automata

With my blog graphics, I am taking a real abstract tack in the past couple of days. The above shot is of a marlin fishing boat leaving Nassau harbour in the morning for a day's fishing. I was riding on the back of the Bo Hengy fast ferry to Harbour Island off Eleuthera when I snapped the shot.

I am also on a highly abstract mental tack as well. I have been devoting a lot of brain cycles to cellular automata. What the heck is cellular automata, you ask. I'll give you the first few sentences in the Wikipedia entry:

A cellular automaton is a discrete model studied in computability theory, mathematics, physics, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off". The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood (usually including the cell itself) is defined relative to the specified cell.

Still clear as mud. Here is a pic of a simple cellular automaton:

This is an incredibly simple cellular automaton. Here is a practical explanation of how it works: Divide your computer screen into say 500 grid spaces or cells. Take a set of 5 colours. Assign each grid space a random colour, but apply a few rules. For example, one rule can be that no two adjacent sides (top, bottom, left and right of the cell) can have the same colour. Another rule can be that you can't have the same colour for more than three grid spaces. Choose some arbitrary rules, and then start the program and let it run indefinitely, scrolling up and continuing on when you reach the last row.

You will be amazed. At first it will be a mumble jumble. Then out of chaos, order will form. At first you will see a small orderly geometric pattern arise. Then it will arise again and start getting more complex. Then you will start to see snowflakes and wildly complex geometries. Then you will start to get the chaos and it will break down and start over again.

Here is a complex cellular automaton caught in a particularly neat state:

I first read about cellular automata in Scientific American in the the 1980's. I was fascinated with it then, but I never had a chance to do much with it. To me, it is proof that there can be order in chaos.

I got to thinking how this applies what Taleb, in his book The Black Swan, describes as unpredictable events or black swans. Unpredictable events would become less unpredictable if you had some inkling of the coming chaos.

This sparked the genesis of my next book manuscript. In cellular automatons, when you are in a state of high complex order, the automaton signals the coming chaos with discordant random pixels. You don't know what is going to blow up, or what random event will happen. You will just know that something is coming.

This approach takes the black swan out of the mathematical realm of the Mandelbrotian (after Benoit Mandelbrot and fractals) into the realm of what I coin the Ulamian.

Stanisław Ulam while working at the Los Alamos National Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. His colleague was John von Neumann, a mathematician who made great contributions to mathematics, physics and compute dynamics. Together they came across cellular automata, although they planned to use it for a model of self-replicating robots.

So what does taking random events out of the Mandelbrotian realm and putting them into the Ulamian realm? Mandelbrot's mathematics while pseudo random, has a high degree of intrinsic order. The Ulamian realm has much more chaos in it, which is more reflective of the human condition and events driven by human action.

How am I going to tie this together? I haven't decided on a working title, but it will probably be either "The Random Pixel" or "The Observant Turkey". Taleb gives the classic problem of unpredictability of the future using the past in the Thanksgiving Turkey scenario.

Take a thanksgiving turkey. For a thousand and one days, humans feed and care for the bird. Based on the past history, the turkey gets a warm and fuzzy feeling for the humans that care for it. Because for 1001 days, it has been nurtured, it will predict that life will continue on. Then comes the Wednesday before Thanksgiving. The neck-wringing turkicide was not predicted by any of the turkeys. Taleb contends that this was a black swan for the turkeys.

I take this contention a little further. If the turkey was observant, it would have noticed the random pixel in the cellular automata of its existence. For example on that fateful morning, instead of a whistling farmer bringing corn, a big huge truck pulls up. That is the random pixel that signifies the coming chaos. The observant turkey in the bunch would have noticed that something was different. If the turkey was really observant, it would have noticed that in the last month, the food was more plentiful and its comrades were getting incredibly fat.

And that is what thoughts go through this head on a Sunday morning in November. I think that I will go out for some random pixel spotting. This is a book that could literally write itself. More to come.