Let us take the idea of the last chapter [the intransigent minority’s disproportional influence] one step further, get a bit more technical, and generalize. It will debunk some of the fallacies we hear in psychology, “evolutionary theory”, game theory, behavioral economics, neuroscience, and similar fields not subjected to proper logical (and mathematical) rigor, in spite of the occasional semi-complicated equations. For instance we will see why behavioral economics will necessarily fail us even if its results were true at the individual level and why use of brain science to explain behavior has been no more than great marketing for scientific papers.
Consider the following as a rule. Whenever you have nonlinearity, the average doesn’t matter anymore. Hence:
The more nonlinearity in the response, the less informational the average.
For instance, your benefit from drinking water would be linear if ten glasses of water were ten times as good as one single glass. If that is not the case, then necessarily the average water consumption matters less than something else that we will call “unevenness”, or volatility, or inequality in consumption. Say your average daily consumption needs to be one liter a day and I gave you ten liters one day and none for the remaining nine days, for an average of one liter a day. Odds are you won’t survive. You want your quantity of water to be as evenly distributed as possible. Within the day, you do not need to consume the same amount water every minute, but at the scale of the day, you want maximal evenness.
The effect of the nonlinearity in the response on the average –and the informational value of such an average –is something I’ve explained in some depth in Antifragile, as it was the theme of the book, so I will just assume a summary here is sufficient. From an informational standpoint, someone who tells you “We will supply you with 0ne liter of water liter day on average” is not conveying much information at all; there needs to be a second dimension, the variations around such an average. You are quite certain that you will die of thirst if his average comes from a cluster of a hundred liters every hundred days.
Note that an average and a sum are mathematically the same thing up to a simple division by a constant, so the fallacy of the average translate into the fallacy of summing, or aggregating, or looking at collective that has many components from the properties of a single unit.
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 “irrational” 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.
On his facebook page, Nassim shared the fact that he recently presented “an English translation” of his technical thesis on violence, co-authored by Pasquale Cirillo and written in response to Steven Pinker’s assertion that violence has declined, to the Nobel Symposium, a three-day retreat for the president of the Nobel Peace Prize Committee, the secretary of the Prize, a few committee members, and 20 scholars. He wrote:
I presented the paper on violence. Bear Braumoeller presented another one similarly critical of Pinker. After our session, the audience was split into:
1) Those who thought that Pinker was wrong
2) Those who thought that Pinker was not even wrong (i.e. not worth discussing).
And the agreement was to not talk about his thesis any further. Further, the organizer was told by Pinker that he did not wish to rebut our papers.
Pinker builds his thesis on works by Richardson in a way that is NOT compatible with the way Richardson [which is compatible with our result] and without showing the derivations. This it turned out is a CRITICAL flaw. Words and words and the central point is pulled out of nowhere.
In our paper: “As we also find out in our data analysis, consistent with Richardson (1960), there is no sufficient evidence to reject the null hypothesis of a homogenous Poisson process, which denies the presence of any trend in the belligerence of humanity. Nevertheless, Pinker refers to some yet-unspecified mathematical model that could also support such a decline in violence, what he calls a “nonstationary” process, even if data look the way they look.”
In its early phase, as the church was starting to get established in Europe, there was a group of itinerant people called the gyrovagues. They were gyrating and roaming monks without any affiliation to any institution. Theirs was a free-lance (and ambulatory) variety of monasticism, and their order was sustainable as the members lived off begging and from the good graces of townsmen who took interest in them. It is a weak form of sustainability, as one can hardly call sustainable a group of a people with vows of celibacy: they cannot grow organically and would need continuous enrollment. But their members managed to survive thanks to help from the population, which provided them with food and temporary shelter.
Sometimes around the fifth century, they started disappearing –they are now extinct. The gyrovagues were unpopular with the church, banned by the council of Chalcedon in the Fifth Century, then again by the second council of Nicaea about three hundred years later. In the West, Saint Benedict of Nurcia, their greatest detractor, favored a more institutional brand of monasticism and ended up prevailing with his rules that codified the activity, with a hierarchy and strong supervision by an abbot. For instance, Benedict’s rulesiii, put together in a sort of instruction manual, stipulate that a monk’s possessions should be in the hands of the abbot (Rule 33) and Rule 70 bans angry monks from hitting other monks.
Why were they banned? They were, simply, totally free. They were financially free, and secure, not because of their means but because of their wants. Ironically by being beggars, they had the equivalent of f*** you money, the one can get more easily by being at the lowest rung than by being member of the income dependent class.
On his facebook page, Nassim recently posted links to a new short technical paper on the probability distribution of p-values and a video commentary. He wrote:
I was able to pull out the exact meta-distribution of p-values (i.e. p-values as random variables).
The point is that the same phenomenon will produce p-values all over the map. A true p-value of .12 will produce p-values <.05 more than half the time, so people may never replicate and get the same result.
One Hundred Years of P-Value Bullshit!
Nassim just posted this one-page refutation to Stephen Pinker’s claim that violence has dropped since 1945. On his facebook page he says that “journalist-passing-for-scientist” Pinker cites “political science bloggers innocent of fat tails, who seem clueless about the difference between data and information. How to separate anecdote from evidence, sampling error from truth, journalism from science? Well there is something called a “test statistic.”
This also illustrates how to do rigorous statistics in the absence of a textbook recipe for a fat-tailed process, by means of Monte Carlo analyses. I will be teaching a course called “Extreme Risk Analytics” at NYU-Engineering this fall and will have to produce an 80 page lecture notes booklet, which I will write progressively from interaction with the class. SILENT RISK is too advanced, so I need a more introductory book.”
Nassim’s statement on climate models, along with Joseph Norman, Rupert Read, and Yaneer Bar-Yam. He says, “We have *only one* planet and need to learn to live with imperfection of models.”
Posted on Nassim’s facebook page.