Tuesday, November 27, 2012

Consciousness Got Geometry

Speculative Flights of Fancy about the Nature of Reality, Part I 

The nature of consciousness is one of the biggest mysteries facing science. No matter how they try, or how much they insist they have done so, scientists have never been able to explain or get rid of something called the homunculus – the little self inside our brain that actually perceives sensations. Perception is related to, but is not identical with, the electrical signal coursing through the neurons that comprise the organ. 

We can try to explain the color red by looking at wavelengths of certain light rays that we identify with red, or with the effect of these rays of light on the rods and cones of the eye which are translated into electrical signals, which in turn light up certain neuronal pathways in the brain’s occipital cortex.  

None of this, however, explains what red looks like when we perceive it. In fact, we have no way of knowing if all of us are even perceiving the color red with the same appearance. We might all agree that an object is “red,” but we have no way to prove that we are all seeing the object in exactly the same way.

An even stranger mystery is that we often all act in unison, such as when we are in the audience of a football game when our home team scores and we all stand as one and gleefully cheer. At those times, it is as if our consciousness becomes fused with everyone else’s who feel as we do.  Some philosophers and even therapists believe that in fact we are all one  - a sort of cosmic unity that is described in, for example, the Buddhist religion - and that our belief in our own individuality is a delusion.

In this post, I am going to go on a flight of fancy. Nothing in the post is an assertion that what I am talking about is true, or that it should be construed as proof of anything. It is all speculation and conjecture. But it sure is fun stuff to think about.

Clearly, the relationship between the individual and the collective is a very complicated one (a constant theme of this blog and my work). Its elucidation is, in the opinion of many, central to devising unified formulations of human psychology that are useful and pragmatic for inducing patients to change their maladaptive behavior problems . 

Psychoanalytic pioneer Carl Jung seemed to be drawing on mysticism when he spoke of something that he called the collective unconscious. He believed it existed along with a personal consciousness and a personal unconscious.  He thought that the individual, while complete unto itself, was simultaneously indefinite and at one with a more universal consciousness.   

While these ideas may seem theological and internally contradictory, the idea that something could simultaneously exist in two different states is hardly unheard of in science. To steal an oft-used analogy from physics, light has been conceptualized as both a wave and a particle, depending on one's reference point, and acts like one or the other depending on how a scientist observes it.

Family systems therapy pioneer Salvador Minuchen spoke of a concept similar to that of the collective unconscious. He viewed the family in particular as more than an ag­gregate of differentiated individuals, but as an organism in itself. Family members could feel the pulse of the entire group, and experience its demands for accom­modation. He used the Greek term holon to designate those “Janus-faced entities on the intermediate levels of any hierarchy.” (Minuchin, 1981, p. 13).

Many authors have discussed the relationship between interacting holons at various levels, or between systems and subsystems.  This has been termed the “entire matrix of human functioning” by Jeff Magnavita, or “foci within the transactional field.”  Various names have been applied to these foci or levels, but generally they consist of units within a system that interact to make up larger units that become something more than the sum of their parts. These larger units then interact to form still larger units and so on.

In systems of biological entities such as human beings, these levels start with the gene and move up through the cell, the organ, the organ system (in particular the central nervous system), the individual, the family, the subculture, the predominant culture, and finally the entire ecosystem. Magnavita notes that “none of these domains can be ignored without a loss of clarity and clinical potency.”

Consistent with a philosophical position known as Hegelian dialectics, the idea of some sort of unifying underlying principle of existence from which spring forth a mul­titude of individual forms which are smaller and smaller versions of the larger forms, almost but not exactly identical, is inherent in the "scientific" fields of astrophysics and evolutionary biology and is even seen in the arena of political science.

Most Physicists and astronomers believe that there is strong evidence that the contents of the universe are hurtling away from one another at enormous speeds and have postulated that all of the energy of the universe - indeed, the universe itself - was originally a single, infinitesimal, infinitely dense, and timeless point. 

The contents of the universe exploded in the "big bang" and then coalesced into stars, plane-­nebulae, galaxies, and a host of other structures, which are gradually dispersing into finer and finer conglomerates spaced at ever-increasing distances.

In biology, the evolutionary proliferation of increasingly differentiated life forms is thought to have sprung from the single DNA molecule. In the political arena, in­creasingly individualistic ideologies have evolved from - and continue to compete with -more collectivist ideologies.

In the same vein and even more startling is how ubiquitous fractal geometry is in nature. A fractal is a rough or fragmented geometric shape that can be split into parts, each of which is, approximately, a reduced-size copy of the whole shape.  This property is called self-similarity. Fractals appear similar - though not quite identical - at all levels of magnification. 

Object exhibiting fractal geometry

Natural objects that appear as fractals include clouds, mountain ranges, lightning bolts, coastlines, snowflakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. In biology,the branching patterns of trees and ferns are fractal in nature. Each time the plant branches into smaller branches, the new branches are all at approximately the same angle with the larger branch from which they spring, and at each node point, the same number of branches emerges.  

Fractal cloud formation

If there is such a thing as a collective unconscious, maybe it has a sort of fractal geometry that can explain the relationship of holons of various sizes and complexities to the whole.

The ubiquity of fractals was a recent discovery made initially by computer animators, of all people. Until they discovered the principle of self-similarity, they found that they had difficulty producing animated movies in which such things as clouds and mountains appeared realistically. After the discovery, their animation looked far more realistic.

Something similar to fractals appears in the seemingly unrelated field of the history of human culture. In his landmark book Escape from Freedom, Erich Fromm noted the and evolution of human culture in which the individual emerges as a free, separate, and potent being from early times during which individuals were pretty much interchangeable. 

In Europe and in some of its colonies, for example, culture has evolved from primitive tribes whose functions were limited to hunting, gathering, socialization, and reproduction, to the early city-states of Greece and Rome, to feudalism, to the Renais­sance and the Reformation, to the democratic and capitalistic ideals of the American and French Revolutions, to the Indus­trial Revolution and the refinement of the concept of division of labor, and finally to the present technological society.

As culture evolves, human beings have become less dependent on the envi­ronment and more able to express their uniqueness.

A good way" to understand the relationship of cultural evolution to the individuation of members of a culture is to think in terms of the phenomenon of interconnectedness. A culture that evolves to a new level allows a loosening of the bonds of the individual to all larger holons (the family system, the ecosystem, and so on) at each stage of individual development. Young adults in feudal society, for instance, were more similar in their level of differentiation from their society to modern 10 year olds than to modern young adults.

Of course, the process of cultural evolution is not a smooth one, nor does it proceed at the same rate everywhere in the world. Different societies can be at very different stages at the same point in history. As civilizations rise and fall, the level of inter-connectedness between individuals and the collective can ebb and flow.

Fromm discussed the level of individua­tion and freedom in the evolving feudal system of the Later Middle Ages and how this changed with the Renaissance. During medieval times, artisans were organized into guilds with rigid rules, which to a major degree blocked competition among the members of the profession. A class system with a pecking order developed, with bound­aries that were, for the most part, impermeable. People not only were fixed at one level socially but seldom wandered geograph­ically.

A person was iden­tical to his role in society; he was a peasant, an artisan, a knight, and not an individual who happened to have this or that occu­pation. The social order was perceived as a natural order, and being a definite part of it gave a feeling of security and of be­longing." He goes on to state that "awareness of one's individ­ual self, of others, and of the world as separate entities, had not yet fully developed.”

So, to sum up, over history individual consciousness seems to have evolved out of a more collective sense of consciousness, with individuals becoming more and more dissimilar from one another as cultural evolution progressed.  

So maybe consciousness has fractal geometry. As time progresses, a more unified collective consciousness splits into smaller and smaller units, very similar to but not identical with the larger units from which they sprung.  Consciousness got geometry!!

In part two of this post, I will offer some more bizarre and hopefully fascinating speculation about the relationship between consciousness and what it is that people are conscious of – what they perceive as external reality. Is reality something that is wholly constructed by each of us and not really independent of our perception of it, or is there an external reality independent of consciousness?


  1. I like this post. I am very fond about seeing the universe, and the various forms of consciousness emerging from it, as a complex hierarchical structure, with holons, and with a lot of fractal properties (although I think fractal interpretations can be abused out-of-context).

    That said, there is some misunderstanding outside of the physics community (and even sometimes inside the physics community) about the nature of light, quantum physics, and whether any modern physics justifies some kind of solipsism. Solipsism is as old as humanity, and while that movement might have known a renewal based on misguided quantum physics interpretations, nothing in modern physics argues against an external reality independent of consciousness (or any observer).

    Schrodinger proposed his famous cat thought experiment as a "reductio ad absurdum" argument. He tried to argue that a "solipsist-like" Copenhagen interpretation of quantum physics was flawed or limited. Unexpectedly, many chose to believe a cat can be both alive and dead rather than renounce a naive (or fanatic) understanding of the Copenhagen interpretation.

    I guess Schrodinger involuntarily illustrated better than anybody else how common is the "justification-based" mode of human thinking where one seems to try to maintain previously acquired beliefs at all cost: if someone started with a strong belief about a naive copenhagen interpretation, then they will rather believe that cats can be simultaneously completely dead and alive as long as they are not looked at, rather than question their understanding or interpretation of subatomic physics. They will rather embrace superstition, and solipsism than simply consider for one minute whether those approximate models, used in a specific atomic or subatomic context, are still meaningful at the macroscopic level.

    I cannot say that external reality exists for sure, but I can say with confidence that in my internal reality representation, anybody confusing external reality and their internal representation of it has never accomplished anything meaningful.

    1. Mr. Holmes - Part II of this post will offer some bizarre speculations on the very points you raise.

  2. Hi My name is Landon Larkey and I am a professor in sociology. I discovered that counciousness is fractal and exponential in nature. any questions you can contact me at