Playing in the Sand Pile – Observations About Sand in Your Shoes – Part II

             I really am more organized than I sometimes seem. I had an outline of the topic I wanted to write about tonight. I started about four hours ago thinking I would be done in an hour or so. Well, it isn’t an hour later (as my previous sentence suggests) and I deviated quite a bit from the original outline. However, I feel that I need to lay this groundwork tonight. I cannot over emphasize the importance of being wary of economic and financial models or money schemes or the best investment you could ever make. Regardless of what Ben Bernanke (of the Fed) or Tim Geithner (of the Treasury Department) or leading economists (with lots of letters and abbreviations behind their names) or your neighbor (it is such a hot tip) or your best friend or a member of your religious congregation or your financial planner, tells you - be suspicious (in a nice way if you think you need to).     

             Previously we touched on the idea of the sand pile effect in nature and modeling. It includes such  concepts as nonlinearity and the critical state, is often known as complexity theory and sometimes called chaos theory. These ideas and concepts are discussed by Mark Buchanan in his book Ubiquity Why Catastrophes Happen, who we looked at briefly last blog and Nassim Nicholas Taleb in Fooled by Randomness who we have discussed several times.

             Let’s illustrate nonlinearity. Suppose we are enjoying a day at the beach with nothing better to do than build a sand tower as high as we can. As the tower increases with each bit of sand we add there comes a point that one more bit of sand causes the entire tower to collapse and slide down. This illustrates a nonlinear effect resulting from a linear force exerted on an object. Our tower suffered a disproportionate collapse from a very small additional input, namely a little bit of additional sand. It the sand pile would have reacted in a linear fashion we would have expected the small bit of sand to have a small impact. There are some idioms that incorporate this idea, the straw that broke the camel’s back or the last straw, or the drop that caused the water to spill. I can remember my father saying something like “that was the last straw” as he explained to me why I was being punished for what I thought was a fairly minor infraction and not worthy of the severity of the particular punishment I was receiving.

Taleb suggests that the nonlinear dynamics has what he calls the bookstore name of Chaos Theory. Taleb further suggests this is a misnomer because the theory has nothing to do with chaos or randomness instead, chaos theory does concern itself mainly with functions in which a small input can lead to a disproportionate response. A little bit of sand generates a massive sand slide. Buchanan suggests a slightly different but similar definition in his comment on what he calls the critical state. He says it represents “…a special kind of organization characterized by a tendency toward sudden and tumultuous changes, an organization that seems to arise naturally under diverse conditions when a system gets pushed away from equilibrium.” Buchanan says this is the first landmark discovery in the emerging science of nonequilibrium physics. Remember he is science writer and has a Ph.D. in theoretical physics.

             Look at the sand pile example again. Suppose you were to apply the nonlinearity principle to your commute home. A trip could take from a few seconds to months. Or suppose you are coming to the corner of the street. What is the likely height of the next person to come around the corner towards you. If we are in the sand pile the person could be from inches to miles high. Yet we have examples that follow this nonlinearity. Why is Bill Gates so rich. Is it because he is an intellectual giant compared to the rest of humanity. Or perhaps he is so much more intelligent than the rest of us. He may very well be of above average intelligence and superior work ethics and have high personal standards. But is he so much better as to deserve to be so wealthy. An element of nonlinearity or luck would better account for it. Economies, markets and social arenas tend to be nonlinear.  There really isn’t a mathematical model that can successfully model this type of activity. The model has to have a random element. Having said that, there are many who try to model parts and bits of things but the full, rich experience which makes up the world around us is difficult and complex. Think of weather models, how successful are we in predicting how much rain will fall on our backyard tomorrow, then one month later. If weather was linear we should be able to predict both time periods with great accuracy. Taleb suggests that one reason we get in trouble with economic and financial models is that some “…intelligent people who felt compelled to use mathematics just to tell themselves that they were being rigorous in their thinking, [and] In the great rush [to develop models] decided to introduce mathematical modeling techniques… without considering the fact that either the class of mathematics they were using was too restrictive for the class of problems they were dealing with, or that perhaps… the precision of the language of mathematics could lead people to believe that they had solutions when there were none.“  The purveyors of economic and financial models may try to convince us that their models do include enough “mathematics” to describe the particular situation but from our examples of tonight it seems very unlikely that the models will stand any test of time or uncertainty.