Where You Cannot Generalize from Knowledge of Parts (continuation of the Minority Rule)
By: Nassim Nicholas Taleb
Tags: Economics, Markets, Complexity, Fraud, Psychology

As we saw, complex systems are characterized by the interactions between their components, and the resulting properties of the ensemble not (easily) seen from the parts.

There is a rich apparatus to study interactions originating from what is called the Ising problem, after the physicist Ernst Ising, originally in the ferromagnetic domain, but that has been adapted to many other areas. The model consists of discrete variables that represent atoms that can be in one of two states called “spins” but are in fact representing whether the state is what is nicknamed “up” or “down” (or can be dealt with using +1 or −1). The atoms are arranged in a lattice, allowing each unit to interact with its neighbors. In low dimensions, that is that for every atom you look at an interaction on a line (one dimensional) between two neighbors one to its left and one to its right, on a grid (two dimensional), the Ising model is simple and lend itself to simple solutions.

One method in such situations called “mean field” is to generalize from the “mean”, that is average interaction and apply to the ensemble. This is possible if and only if there is no dependence between one interaction and another –the procedure appears to be the opposite of renormalization from the last chapter. And, of course, this type of averaging is not possible if there are nonlinearities in the effect of the interactions.

More generally, the Übererror is to apply the “mean field” technique, by looking at the average and applying a function to it, instead of averaging the functions –a violation of Jensen’s inequality [Jensen’s Inequality, definition: a function of an average is not an average of a function, and the difference increases with disorder]. Distortions from mean field techniques will necessarily occur in the presence of nonlinearities.

What I am saying may appear to be complicated here –but it was not so with the story of the average water consumption. So let us produce equivalent simplifications across things that do not average.

From the last chapter [Minority Rule],

The average dietary preferences of the population will not allow us to understand the dietary preferences of the whole.

Some scientist observing the absence of peanuts in U.S. schools would infer that the average student is allergic to peanuts when only a very small percentage are so.

Or, more bothersome

The average behavior of the market participant will not allow us to understand the general behavior of the market.

These points appear clear thanks to our discussion about renormalization. They may cancel some stuff you know. But to show how under complexity the entire field of social science may fall apart, take one step further,

The psychological experiments on individuals showing “biases” do not allow us to understand aggregates or collective behavior, nor do they enlighten us about the behavior of groups.

Human nature is not defined outside of transactions involving other humans. Remember that we do not live alone, but in packs and almost nothing of relevance concerns a person in isolation –which is what is typically done in laboratory-style work.

Some “biases” deemed departures from “rationality” by psycholophasters interested in pathologizing humans are not necessarily so if you look at their effect on the collective.

What I just said explains the failure of the so-called field of behavioral economics to give us any more information than orthodox economics (itself rather poor) on how to play the market or understand the economy, or generate policy.

But, going further, there is this thing called, or as Fat Tony would say, this ting called game theory that hasn’t done much for us other than produce loads of verbiage. Why?

The average interaction as studied in game theory insofar as it reveals individual behavior does not allow us to generalize across preferences and behavior of groups.

Groups are units on their own. There are qualitative differences between a group of ten and a group of, say 395,435. Each is a different animal, in the literal sense, as different as a book is from an office building. When we focus on commonalities, we get confused, but, at a certain scale, things become different. Mathematically different. The higher the dimension, in other words the number of possible interactions, the more difficult to understand the macro from the micro, the general from the units.

Or, in spite of the huge excitement about our ability to see into the brain using the so-called field of neuroscience:

Understanding how the subparts of the brain (say, neurons) work will never allow us to understand how the brain works.

So far we have no f***g idea how the brain of the worm C elegans works, which has around three hundred neurons. C elegans was the first living unit to have its gene sequenced. Now consider that the human brain has about one hundred billion neurons. and that going from 300 to 301 neurons may double the complexity. [I have actually found situations where a single additional dimension may more than double some aspect of the complexity, say going from a 1000 to 1001 may cause complexity to be multiplied by a billion times.] So use of never here is appropriate. And if you also want to understand why, in spite of the trumpeted “advances” in sequencing the DNA, we are largely unable to get information except in small isolated pockets of some diseases.

Understanding the genetic make-up of a unit will never allow us to understand the behavior of the unit itself.

A reminder that what I am writing here isn’t an opinion. It is a straightforward mathematical property.

I cannot resist this:

Much of the local research in experimental biology, in spite of its seemingly “scientific” and evidentiary attributes fail a simple test of mathematical rigor.

This means we need to be careful of what conclusions we can and cannot make about what we see, no matter how locally robust it seems. It is impossible, because of the curse of dimensionality, to produce information about a complex system from the reduction of conventional experimental methods in science. Impossible.

My colleague Bar Yam has applied the failure of mean-field to evolutionary theory of the selfish-gene narrative trumpeted by such aggressive journalists as Richard Dawkins and Steven Pinker and other naive celebrities with more mastery of English than probability theory. He shows that local properties fail, for simple geographical reasons, hence if there is such a thing as a selfish gene, it may not be the one they are talking about. We have addressed the flaws of “selfishness” of a gene as shown mathematically by Nowak and his colleagues.

Hayek, who had a deep understanding of the properties of complex systems, promoted the idea of “scientism” to debunk statements that are nonsense dressed up as science, used by its practitioners to get power, money, friends, decorations, invitations to dinner with the Norwegian minister of culture, use of the VIP transit lounge at Kazan Airport, and similar perks. It is easier to take a faker seriously, since science doesn’t look neat and cosmetically appealing. So with the growth of science, we will see a rise of scientism, and my general heuristics are as follows: 1) look for the presence of simple nonlinearity, hence Jensen’s Inequality. If there is such nonlinearity, then call Yaneer Bar Yam at the New England Complex Systems Institute for a friendly conversation about the solidity of the results ; 2) If the paper writers use anything that remotely looks like a “regression” and “p-values”, ignore the quantitative results.