Randomness Kills Simplicity, But Hey, That's Reality

“Things Should Be Made As Simple As Possible, But Not Any Simpler”

I was actually feeling quite content as I boarded a bus to New York City today regarding some of the concluding thoughts in the last post about schema theory, and the ebb and flow from complexity to simplicity. As usual of course I brought with me my pseudo-bible, “Fooled By Randomness,” to re-read it... again. As has always been the case, it definitely put me in my place, so I thought I’d temper some of the optimism of the last post with a dose of what Taleb knows best—randomness. Thoughts are again welcome.

Inductive Reasoning
Schema Theory and inductive reasoning have a lot in common. Inductive reasoning involves observing empirical data and searching for patterns of behavior which form the basis for hypotheses about the nature of reality. In other words, it wades through large amounts of data and attempts to make sense of it all through causal links and unifying properties. This is somewhat similar to how a financial analyst gathers a lot of information which at the start seems independent and distinct, but which over time (hopefully) comes together under some line of logic to form a complete understanding of the company and the nature of its business and dynamics.

Taleb’s Issue With Inductive Reasoning
Taleb took more than a few shots at inductive reasoning, and rightfully so. Inductive reasoning’s conclusions are very sensitive to the properties of the process whose observations we analyze. If some process we see is very well behaved, for example is normally distributed, then the information gain we receive with each additional observation is a quantifiable amount which we know a priori. But how can we know in reality with no ability to see the future that a process will continue to behave in a normal fashion going forward? And when the distribution underlying the process becomes increasingly non-normal, we start to run into serious information gain problems.

Taleb characterized this as playing Russian roulette using a gun with 1,000 chambers. If I were to play this Russian roulette with no knowledge of the number of chambers or the number of bullets in the gun, and it just so happened that after 500 trials I was still standing, I would probably start believing there were no bullets in the gun in the first place—induction might lead to a conclusion like this given my knowledge of guns and the number of trials, but this would obviously be wrong.

The main point I’d like to drive home then is the fact that induction naturally and unavoidably simplifies the world. Drawing positive conclusions from an incomplete data set is to some extent what we have to do if we want to do anything, and yet it naturally leads to error. Knowing that such error is always possible and will probably lead to mis-evaluation requires an acceptance and appreciation of randomness. And randomness is the bane of the simplification process I mentioned earlier. The company no longer occupies one mental slot in my brain. All those facts relating to the company which cannot be logically connected to my paradigm of “the company” must sit uncomfortably in other mental slots. It’s inefficient, but it’s also how things are, so what can you do but accept that.

Conclusion
So when Einstein said “things should be made as simple as possible, but not any simpler,” what I think he’s acknowledging is the fact that there is a natural limit to the amount of simplification which can occur. Because of randomness, many things cannot and should not be connected if ones goal is to obtain a rational view of reality for the purposes of forecasting.

It’s a bit sad to believe that we can only truly know that which is false, and can never really know that which is true (Popper). We can only make our best guesses, over and over again, and hope that through personal risk management, the randomness which plagues the decisions we make based on those guesses aren’t so correlated that we suffer terribly. This was Taleb's conclusion, to the best of my understanding. It's not as if he ceased to make decisions. He used statistical inference for all that it was worth to make investment decisions, but then made sure to separate that process from his weighting methodology to tailor his risk profile to his liking.

Not too happy a blog post, sorry guys.
-Danny