The Deviation of Randomness: Unexpected Results

Recommendations from the article: The Black Swan (Amazon), Three Body Problem (Wikipedia), Nobel Prize Nominations for Henri Poincaré (NobelPrize.org)

Time To Read: 5 – 7 minutes

Highlights and Quotations: 1 – 2 minutes

Before the advent of the Nobel Prize there was a competition to celebrate the 60th Birthday of King Oscar of Sweden and Norway. The King was a charitable supporter of the sciences. The competition was framed around what is now known as the three body problem and constructed by mathematician Gosta Mittag Leffer. Henri Poincaré, the studious renaissance man often described as a polymath because of his strides in mathematics, physics, engineering and science, won the prize. Then seen as the highest scientific honor, for his memoir on the stability of the solar system. Prior to its planned publication the following year in 1890 a major calculation error was discovered. The error actually proved the exact opposite of the initial theory, the unpredictability of the solar system or aptly titled mathematical chaos.

“Poincarés reasoning was simple: as you project into the future you may need an increasing amount of precision about the dynamics of the process that you are modeling, since your error rate grows very rapidly. The problem is that near precision is not possible since the degradation of your forecast compounds abruptly – you would eventually need to figure out the past with infinite precision. Poincaré showed this in a very simple case, famously known as the three body problem.” – Nassim Taleb author of the Black Swan

The three body problems is designed to show the explosive effects of multiple interactive bodies within our solar system. But more applicable to our individual lives it shows the endless diverging possibilities from prediction. Specifically the possible resulting trajectories to our personal decisions and actions.

One of the readers of Taleb’s book, David Cowan, drew the picture of scattering, which depicts at the second bounce, variations in the initial path can lead to massive diverging resultant paths. As the first imprecision or reaction is multiplied throughout the following or additional reactions it becomes magnified exponentially. The error rate or more impartially labeled, the resulting paths, grow disproportionately. My addition was the text giving a corresponding label not in celestial example but in our daily decision making. We have the power to control our individual actions and “project” what the outcomes of those actions will be. But we must realize consciously that we do not have the power to predict exact results or even a reasonable estimation of the resulting paths.

“Explosive forecasting difficulty comes from complicating the mechanics, ever so slightly. Our world, unfortunately, is far more complicated than the three body problems; it contains far more than three objects. We are dealing with what is now called a dynamical system – and the world, we will see, is a little too much of a dynamical system.” – Nassim Taleb author of the Black Swan

Where celestial travel and planetary motion are not accessible as examples to most, Taleb briefly covers something that is, Earth, or more precisely the world that we each live in it. The unpredictability that Poincaré ended up with was grounded in vast distances of space and immense amounts of time. Where only three distinct bodies or “actions”  cause the inability to calculate their linear movement. Taleb says, “Our world, is far more complicated than the three body problems”. The count of interacting “bodies” in our day to day lives is never ending only leading to an exponential amount of more outcomes and distance between the paths of those outcomes.

This may seem like a meek outlook on the course of our lives. Just as Poincarés initial theory the opposite is actually true. Where, true, we do not have control of our lives to the extent of the direction our actions take after interacting with the outside world. But, also true, we do not have the capacity to calculate the potential of those outcomes either. The “potential” of the results is far greater than we can ever imagine. Since we often think in terms of our actions and their trajectory as a [often linear] path of our control we limit the reach of the result. Knowing that we and our decisions interact with far more than “three bodies” each reaction causes a slight deviation in course only being magnified further from each corresponding reaction after. Simply, our actions are pin balled constantly as they interact with the outside world. Each time moving forward in a slight, but also compounding, difference with each interaction. Where this makes it hard to predict, or forecast in the financial world of Taleb, it also allows for resultant paths to far exceed the limit of our expectations as well.

Delving deeper into the human application of the three body problem, the initial argument made against its application of having a resulting “positive” path far greater than personally imaginable would be its “negative” counterpart. The initial action could exponentially result in a “negative” path far “worse” than you can fathom. On an inhuman level of mathematical equations that would be true. But the argument in a human world, full of emotion and intention, would be that the “value” placed in that individual action before any resulting deviation has far greater impact than any pinball bumpers it hits along the way. If we act in a positive harmoniously manner its results have a far greater potential, although immeasurable, to be “positive”. If we act in a malicious inharmoniously manner its results also have a likelihood to be “negative” with exponential potentials.

This becomes the groundwork for aligning with the notion of action. Where Taleb is deeply critical in his writings is the deep pocketed industries of forecasting. The future outlook is proposed often without an impartial eye to the projections of the past. Because those projections are excusatory when they find themselves on immeasurably different paths than what the reality was.  As an individual in an imperfect model the choice must always be to move forward with amicable intentions.  With a foundation of thought that what you may reap is unimaginably bountiful.