ضمیمه‌ی بخش 3: چند نمونه‌ی خلاف تصور دیگر در مورد جمع

Appendix to book 3 A Few More Counterintuitive Things About the Collective

Antifragile has been about the failure of the average to represent anything in the presence of nonlinearities and asymmetries similar to the minority rule. So let us go beyond: The average behavior of the market participant will not allow us to understand the general behavior of the market.

You can examine markets as markets and individuals as individuals, but markets are not sums of average individuals (a sum is an average multiplied by a constant so they are both equally affected). These points now appear clear thanks to our discussion about renormalization. But to show how claims by 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 automatically 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 works.

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.

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 higher the number of possible interactions, and the more disproportionally difficult it is to understand the macro from the micro, the general from the simple units. This disproportionate increase of computational demands is called the curse of dimensionality. (I have actually found situations where, in the presence of small random errors, a single additional dimension may more than double some aspect of the complexity. Going from 1,000 to 1,001 may cause complexity to be multiplied by a billion times.) 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.

A group of neurons or genes, like a group of people, differs from the individual components—because the interactions are not necessarily linear. So far we have no f***ing 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 genes sequenced. Now consider that the human brain has about one hundred billion neurons, and that going from 300 to 301 neurons, because of the curse of dimensionality, may double the complexity. So the 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 for some diseases, same story. Monogenic diseases, those for which a single gene plays a role, are quite tractable, but anything entailing higher dimensionality falls apart.

Understanding the genetic makeup 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.

The mean-field approach is when one uses the average interaction between, say, two people, and generalizes to the group—it is only possible if there are no asymmetries. For instance, Yaneer Bar-Yam has applied the failure of mean-field to evolutionary theory of the selfish-gene narrative trumpeted by such aggressive journalistic minds as Richard Dawkins and Steven Pinker, with more mastery of English than probability theory. He shows that local properties fail and the so-called mathematics used to prove the selfish gene are woefully naive and misplaced. There has been a storm around work by Martin Nowack and his colleagues (which include the biologist E. O. Wilson) about the terminal flaws in the selfish gene theory.

It is worth mentioning names here as these people acted as attack dogs against those who discounted the selfish-gene theory, without addressing the mathematics provided (they can’t), yet kept barking.

The question is: could it be that much of what we have read about the advances in behavioral sciences is nonsense? Odds are it is. Many people have been accused of racism, segregationism, and somethingism without merit. Using cellular automata, a technique similar to renormalization, the late Thomas Schelling showed a few decades ago how a neighborhood can be segregated without a single segregationist among its inhabitants.

ZERO-INTELLIGENCE MARKETS

The underlying structure of reality matters much more than the participants, something policymakers fail to understand.

Under the right market structure, a collection of idiots produces a well-functioning market.

The researchers Dhananjay Gode and Shyam Sunder came to a surprising result in 1993. You populate markets with zero intelligence agents, that is buying and selling randomly, under some structure such that a proper auction process matches bids and offers in a regular way. And guess what? We get the same allocative efficiency as if market participants were intelligent. Friedrich Hayek has been, once again, vindicated. Yet one of the most cited ideas in history, that of the invisible hand, appears to be the least integrated into modern psyche.

Furthermore:

It may be that be that some idiosyncratic behavior on the part of the individual (deemed at first glance “irrational”) may be necessary for efficient functioning at the collective level.

More critically for the “rationalist” crowd,

Individuals don’t need to know where they are going; markets do.

Leave people alone under a good structure and they will take care of things.

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