The Emergence of Emergence and the Limitations of Reductionism: An Exploration of Hierarchies

This is really a postscript to the last post, "This Is Your Brain On Fractals."

One of the interesting slides in the Gazzaniga Gifford series lectures was one that concerned a "Hierarchy of Structure" of the natural world in the following categories:

1.  Particle Physics
2.  Atomic Physics
3.  Chemistry
4.  Biochemistry
5.  Cell Biology
6.  Physiology
7.  Mental States

The idea behind this list is that each category operates with a set of rules that gives rise to the next category as set of emergent properties of the former.  But the rules and observations that apply in one category do not necessarily apply in the others, or do not apply in the same way.

I went to look for antecedents of this idea and discovered a wonderful old paper written by P.W. Anderson, who later was awarded a Nobel Prize in Physics.  The paper, entitled "More is Different" was published in Science magazine in 1972, three years before Benoit Mandelbrot coined the word "fractal" to describe a different but ultimately related idea.

In his article, Professor Anderson describes the then-problem with over-applied scientific reductionism between the sciences, which over a decade later led to the founding of the Sante Fe Institute and the development of complexity theory.  He writes:

"The reductionist hypothesis may still be a topic of controversy among philosophers, but among the great majority of active scientists I think it is accepted without question.  The workings of our minds and bodies, and of all the animate or inanimate matter of which we have any detailed knowledge, are assumed to be controlled by the same set of fundamental laws, which except under extreme conditions we feel we know pretty well.

It seems inevitable to go on uncritically to what appears at first sight to be an obvious corollary of reductionism:  that if everything obeys the same fundamental laws, then the only scientists who are studying anything really fundamental are those who are working on those laws. . . .

The main fallacy with this kind of thinking is that the reductionist hypothesis does not by any means imply a "constructionist" one:  The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe.  In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society. 

The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity.  The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles.  Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.  That is, it seems to me that one may array the sciences roughly linearly in a hierarchy, according to the idea:  The elementary entities of Science X obey the laws of Science Y."

Whereupon, Professor Anderson provided a list similar to the one Gazzaniga used in 2011, where each succeeding field was the X for the preceding field Y.  His list was:

1. Elementary particle physics
2. Solid-state or many-body physics
3. Chemistry
4. Molecular Biology
5. Cell Biology
6. [Skipping several levels]
7. Physiology
8. Psychology
9. Social Sciences

"But this hierarchy does not imply that science X is "just applied Y."  At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one.  Psychology is not applied biology.  Nor is biology applied chemistry."

He then goes on to discuss this in terms of superconductivity, which could not be predicted or deduced from quantum physics.  He observes that while everything is symmetrical, or undifferentiated, at the fundamental level, such symmetry breaks down and things become differentiated as one moves up the scales.  He concludes:

"The arrogance of the particle physicist and his intensive research may be behind us . . ., but we have yet to recover from that of some molecular biologists, who seem determined to try to reduce everything about the human organism to "only" chemistry, from the common cold and all mental disease to the religious instinct.  Surely there are more levels or organization between human ethology and DNA that they are between DNA and quantum electrodynamics, and each level can require a whole new conceptual structure."

In 2003, Professor Anderson gave a lecture (video here), where he reflected upon these thoughts after 30 years of further development that included much of what we see through the Fractal Lens.  He made the following points, among others:

• "Reductionism does not imply constructionism" or "strict-sense reductionism."
• Thus subject matter of a more fundamental or microscopic hierarchy forms the substrate upon which the next level is built.  But one cannot assume that the properties or laws at the higher level are merely a trivial consequence of the laws of the more basic level.  
  
• There is Intellectual autonomy between the sciences. Economics or human behavior is not applied biology;  biology is not applied chemistry;  chemistry is not applied physics; and so on.  Each has its own set of properties that, while consistent, cannot be drawn up or intuited by examining the more basic level more closely.
• The intellectual autonomy of the higher, macro order is not dictated by the tyranny of the equations that govern the microscopic order.
• In the case of moving from the microscopic quantum world to the macroscopic world:  Each particle like an electron is identical to every other one -- there is symmetry.  But the macroscopic world is one of broken symmetry where things become identifiable as separate objects.
• Differentiation or identity only becomes possible at macroscopic levels.  The microscopic or quantum laws are laws pertaining to undifferentiated substances.
• Scale changes can lead to qualitative differences, not just more of the same but bigger.  Indeed, "Science has become qualitatively different as it has grown."
• Another example:  Money and markets do not exist in hunter-gatherer societies, but appear almost spontaneously in a human society that becomes sufficiently large and organized.
• La Place's perfect computer (a/k/a "La Place's Demon") is not a physically realizable machine and determinism in the laws of physics is a nonsense.
• Thus, any so-called "Theory of Everything" is in fact a theory of almost nothing.  Instead, there are layers upon layers of emergence.
• Causality and rigidity exist in large scale systems, but are not present in the lower level microscopic or quantum systems.
• ​The brain could not exist or function without the concept of irreversibility, which is part of causality and rigidity.
• Power-law distributions of things as varied as citations to academic publications, populations of cities and wealth distribution seem to indicate that there is a fundamental law there to be understood.​
  

Considering what this all means in terms of our Lenses of Wisdom, what Professor Anderson is talking about is essentially part of the theory and history behind the construction of Fractal Lens, which wedded Mandelbrot's fractal geometry and observations with Anderson's insights into the inherent limitations on scientific reductionism.

The "fundamental law" that Anderson alluded to in his lecture is not so much a law per se, but an observation of Mandelbrot that much of both the natural and human world is organized in fractal dimensions, including not only the items Anderson mentioned, but also coastlines, trees and the weather.  As discussed on the main Lenses page, Nassim Taleb has labeled these types of distributions as "Extremistan", while populations that can be modeled by bell curves as "Mediocristan". 

The reason this law (essentially what we mean by the Fractal Lens) seems to be ubiquitous, applying from everything from the appearance of rocks to the behavior of financial markets,  may have something to do with what Anderson observed about the difference between the quantum and observable worlds, which is the concept of irreversibility, a core idea from thermodynamics relating to entropy that has broad application, especially to complex biological systems and other systems characterized by growth and collapse.  Thus, the sand-pile model described on the Fractal Lens page has broad applications indeed.

Looking through the Prospecting Lens, we see what amounts to category 7, Mental States, on Gazzaniga's list of scientific hierarchies or number 8, Psychology, on Anderson's list.

We also can appreciate the prescience of Anderson's assertion that it was important for scientists not fixate on what they believed were the "fundamentals", but to explore each level of the hierarchy as its own dimension with its own governing laws and rules, and to appreciate each other's work on that basis.  And the painstaking work of Kahneman, Tversky and others has led a much more complete understanding of human decision-making over the past 50 years. 

As we explored in the last post, Professor Gazzaniga confirms that Professor Anderson's idea was correct as to the relationship between neuroscience and psychology.  While the former forms the "substrate" of the latter, psychology and human decision-making cannot be "constructed" through the study of neuroscience, but must be investigated on its own, and in the context of not just one brain, but many brains operating in the same environment and influencing one another.

Finally, the Prospecting Lens hints at the problems one may encounter in seizing upon one set of rules of laws applicable at one level and trying to apply them directly at another.  We see this in the modern phenomenon that has been labeled "Quantum Woo", whereupon ideas from fundamental particle physics have been applied inappropriately at to higher levels of organization, including human behavior.  Gazzaniga observes the same problem in his discussion of determinism and free will -- explaining that the former is an idea captivated by neuroscience, while the latter is one that belongs with psychology and human decision-making in groups.  Neither really makes much sense when divorced from its proper context.

Now looking through the Mimetic Lens, we see that we are essentially looking at something that -- while incorporating basic psychological mechanisms that are almost universally accepted, namely that human beings have a tendency to imitate each other and have some propensity for violence -- is really at another hierarchical level, namely that of the foundations of stable cultures.  This is where we discover the rules that govern the behavior of crowds and the mechanism of scapegoating, as discussed in the posts about our WEIRD society and crowds.  This is also the same level where the work of Ian Morris lies.

But at the risk of venturing into our own version of Quantum Woo, we also do see an interesting parallel between Professor Anderson's discussion of symmetry and Mimetic theory regarding differentiation.  Anderson observed that everything in the quantum world is characterized by symmetry and is undifferentiated -- e.g., every electron is just like every other election.  It is only when we move up the hierarchical scale to many-bodied physics and beyond are we able to start to differentiate one object from another.  As Anderson puts it, the symmetry is "broken".  According to Mimetic Theory, stable traditional societies are born from differentiation.  Everyone is expected to be differentiated so that each can put in their proper place.  Thus, identical twins were often thought to be curses -- and still are in some places.  To a traditional society, an undifferentiated group represents chaos that needs to be resolved, usually through sacrifice:

"Girard also considers that prior to the scapegoating mechanism, communities go through a process he calls a ‘crisis of differences’. Mimetic desire eventually makes every member resemble each other, and this lack of differentiation generates chaos. Traditionally, this indifferentiation is represented through various symbols typically associated with chaos and disorder (plagues, monstrous animals, and so forth). The death of the scapegoat mechanism restores order and, by extension, differentiation. Thus, everything returns to its place. In such a manner, social differentiation and order in general is also derived from the scapegoat mechanism."

And so it was in many traditional societies, that one of a set of identical twins was sacrificed for precisely that reason.

More recent Western-based thinking following the Christian ethic often turns this on its head and makes the "undifferentiated" the victim-hero.  You see this everywhere from the classic "The Tale of Two Cities" to the modern usage of the Guy Fawkes mask to symbolize the oppressed.  This also raises ire whenever social differentiation conventions are challenged in everything from racial and gender segregation to rules about marriage and bathrooms.  Those who argue for tradition often couch their positions in maintaining social order and avoiding chaos by maintaining differentiation.  The trend that started 2000 years ago is definitely toward more symmetry and less differentiation, both socially and economically.

So maybe we are returning to the quantum states of our undifferentiated roots.  (Not that I'm holding my breath.)  Now cue Twilight Zone music . . .