Wild Turkeys and Things

Cruise ships in the harbour.

It seems strange posting pictures of the warm tropics while eight wild turkeys walk through the fallen autumn leaves, pecking away at a half-dead, frost-killed lawn. It is ironic that they are wild turkeys, because I am thinking of my observant turkey concept. (more to come).

Everything is a bit surreal. I am using remote desktop to log into Nassau. I am writing code that resides on a server 1,400 miles away. It is cold and sunny today in the foothills of the Laurentians. I see the fir-clad hills with the fractal geometries of the hilltops, and the outlier trees every once in a while, growing much taller than its neighbours, silhouetted against the cobalt blue sky.

And the words "fractal" and "outlier" seem strange to me, yet it is quite descriptive of what I am seeing. They are somehow the perfect level of abstraction, as I think about the concept of an observant turkey who knows that something weird is up. (Note, this is my next book idea, that I am developing). To reiterate the idea of an observant turkey, I use the example of a bunch of turkeys who for 1001 days have been fed and nurtured by human beings. However they are about to have their beliefs about the "nice" humans, built on past observations, shattered on the Wednesday before Thanksgiving. Only the observant turkey notices that something is strange of late. What it is, he has no clue, but he feels that the strange events might be a precursor to some unpredictable event.

Taleb, in his book The Black Swan, says that these unpredictable events are black swans, and it is the mathematics of Mandelbrot that describes them, rather than the mathematics of the Gaussian curves and averages. For example, if a turkey builds a model of events based on history, there is no way that he can predict the killing event. The average of his existence says that he will be fed as normal.

My contention is that highly unpredictable events are not Mandelbrotian, but rather Ulamian, named after the Polish American Ulam who first described cellular automata (Click on the Cellular Automata label to get an explanation). Mandelbrot's equations have a large degree of perceived randomness and uncertainty, but they do not have the capacity for extreme chaos that some of Ulam's cellular automatons do.

And this got me thinking deeper into the problem of chaotic events in any system. Mandelbrotian events can arise from Ulamian events but the obverse is not true. The ordered fractal geometries and topologies can be generated by cellular automatons, but fractal geometries cannot be true cellular automata in all cases because certain classes of cellular automata break down into chaos.

Mathematics is a symbolic language for many things, and while I talk about geometries, these equations can be applied to many things in life, or things and events can be modeled with these concepts.

I don't expect you to understand or even follow, and I will forgive you if you think that I have been smoking some organic substances or require a tin foil hat, however I am thinking out loud in a stream of consciousness that seems to make sense to me. I will let you know if this is a bona fide hallucination.

I will also try to find a better way to explain it without all of the arcane and esoteric language.