 |
| The Web of Life by Fritjof Capra |
The spiritual mind, I suggested in The J.K. Rowling Effect, can be likened to a type of self-organizing system with a complex "phase portrait." Accordingly, it is prone to critical "points of instability" or "bifurcation points." I imagine that one of these spiritual bifurcation points corresponds to being born again, in evangelical Christian terms, or to the Dark Night of the Senses spoken of by Catholic mystics like St. John of the Cross.
The person who has experienced this crisis and crossed into new (for him or her) spiritual territory can easily believe that whatever is not adulterated by man's original sin is expressly ordained by God. The idea that all good things are divinely ordained chimes with the story of creation in the Book of Genesis, chapter 1, in which every living creature appears on the scene at God's immediate behest. No wonder those who live in this particular spiritual frame of mind have trouble with Darwin's theory of evolution.
Another point of spiritual bifurcation can follow later on: the Dark Night of the Soul, in which the seeker eventually ceases to be able to maintain that mistrustful, standoffish, all-things-must-pass attitude toward the events of this world. Now the material world exerts its own pull upon the spiritual mind, leading, in famous cases like that of Thomas Merton, to a Zen awakening.
I cannot claim a Zen awakening, but I have developed a deeper appreciation for the organic, as opposed to the ordained, aspects of this world. In fact, I think that the ordained/organic dichotomy is one of the key differences between two major basins of attraction of the spiritual mind.
A basin of attraction in a self-organizing system, such as I hypothesize the human mind to be, is like a drainage basin in the geography of a continent. In such a drainage basin, a river, lake, or some other prominent body of water toward which rainfall naturally gravitates, corresponds to an "attractor" in a self-organizing system.
For example, any rain that falls in the United States east of the Continental Divide and west of the Appalachians winds up in the Great Lakes or Mississippi River. Rain to the west of our mid-continent drainage basin heads for the Pacific Ocean. Rain that falls on the East is Atlantic-bound.
Likewise, in self-organizing systems there is a "virtual landscape" in which multiple basins of attraction exist, each comprising a discrete set of the totality of available system states. In any particular basin of attraction, some of the possible system states in that basin form an "attractor" toward which all the other system states in that same basin of attraction inexorably flow. If the system happens to be operating within a certain basin of attraction, but not on that basin's attractor, it will move to a state on the attractor itself. Once a state on the attractor is arrived at, all successive system states are also on the attractor.
Small or large perturbations can cause the system to jump unpredictably from one state to another. The new system state may or may not be in the same basin of attraction as the old. If the system is a reasonably stable one, small perturbations will usually leave it in the same basin. Larger perturbations can put even a stable, non-chaotic system in a wholly different basin of attraction.
The attractor in that new basin may be a "strange" (i.e., chaotic) one. Strange attractors are associated with mathematical "chaos." Some or all of the attractors in the abstract topography of a system at any moment in time can be "strange" attractors. In fact, some systems have just one single attractor: a "strange" one.
Systems whose attractor is "strange" ans whose future path in moving from one state to the next is chaotic will cycle back around and repeat an already-visited state only after visiting every other state available to the system. In chaotic systems of great complexity in which the number of available states is great, the time needed to cycle around and repeat a state can be a large multiple of the age of the universe.
Systems in chaos are extremely sensitive to initial conditions. Any imprecision, no matter how tiny, in measuring the initial state of a system will render predictions about future states of the system increasingly unreliable as time goes on. What's more, the degree of predictive unreliability increases exponentially. This is why it is impossible to predict the weather more than a few days in advance.
Although, it is impossible to predict chaotic systems' long-term behavior, this behavior is nonetheless deterministic. That is, the system's initial conditions do in fact determine its entire future path. It's just that there is no computer in the world capable of doing the necessary computations precisely enough (or, for that matter, swiftly enough) to arrive at an accurate prediction.
Exogenous changes in the system's parameters can put an otherwise non-chaotic system in a basin of attraction associated with a strange attractor: chaos can come out of order, seemingly. But Capra makes clear that a chaotic, strange attractor is in fact orderly. Just because we can't predict the system's future doesn't mean that its future is random. It is in fact as deterministic as that of a system in a basin of attraction whose guiding attractor is a "point attractor" (a single destination state) or "periodic attractor" (an endless loop of repeating states). Barring external perturbations or changes to the fundamental parameters of the system, the future path of the system is set in stone.
Moreover, a self-organizing system's virtual landscape can exhibit change over time. Its configuration of basins and attractors can be revised, sometimes greatly, by even small changes in the numerical parameters of the nonlinear mathematical equations that describe the system (see Web of Life, pp. 135-137). This is another reason why systems that start in a stable and orderly basin of attraction can end up in another which may be chaotic, or vice versa.
But there is yet another source of indeterminacy and unpredictability in dissipative structures such as all living systems represent. This one interests me more than that associated with "chaos" and "strange attractors." The indeterminacy that occurs at the system's "bifurcation points" is apparently one that couldn't go away even if our computer models were to become infinitely fast and infinitely precise.
Capra discusses this topic in chapter 8, which deals primarily with the late Nobel laureate Ilya Prigogine's theory of "dissipative structures." A dissipative structure is one through which there is a continual flow of matter and energy. The strength of the matter-energy flow determines whether the system needs nonlinear equations to model it, as opposed to just linear equations. In nonlinear equations, corresponding to a strong or swift flux of matter and energy through the system, all of the equations' variables are raised to the power of two or higher. Hence there are multiple possible solutions to the set of equations by which the dissipative system is modeled.
A system whose modeling equations are nonlinear maintains itself far from thermodynamic equilibrium, the state of maximum entropy. "Entropy" is the degree to which a system has "run down" toward the minimum possible level of order, as dictated by the Second Law of Thermodynamics. For example, if you have a container with two compartments, one containing nitrogen and one oxygen, and you remove the barrier separating the compartments, the molecules will tend to mix into a single uniform distribution of nitrogen and oxygen.
Given sufficient time, that expected result — minimum order, maximum entropy — is almost certain to eventuate. It is the result of the motion of the gas molecules, and it happens faster when the gases are heated than if they are cool.
Although it may not be technically correct to put it this way, I think of the behavior of far-from-equilibrium dissipative systems, including living organisms, as "exporting" entropy: the heat energy they give off adds more to the disorder of the external environment than the amount by which the system itself reverses its own entropy. Accordingly, dissipative systems manage to take themselves in the opposite, anti-entropic, direction, at the expense of increasing the entropy in their surroundings. The further from thermodynamic equilibrium the system is, to more entropy it exports to its environment.
But a dissipative structure is typically able to arrive at any of multiple possible stable states far from thermodynamic equilibrium. The farther from equilibrium it is, the more nonlinear it is, and the greater the number of possible solutions there are to its set of equations (see Web of Life, p. 182). Capra describes it this way: "New situations may emerge at any moment. Mathematically speaking, the system encounters a bifurcation point in such a case, at which it may branch off into an entirely new state."
Here is where things get really fascinating ... and a bit confusing. At each bifurcation point, the system must "choose" — metaphorically speaking, since the system generally lacks intentionality — one of two or more possible paths. Which path it will choose is not knowable by an outside observer. The "choice" cannot be predicted, much less controlled, by an external agent. As Capra says, "There is an irreducible random element at each bifurcation point" (p. 183).
Even so, the branch of the path which the system will "choose" for its future trajectory at any given bifurcation point "depends on the previous history of the system," Capra says (p. 182). Unlike systems that can be modeled by linear equations, dissipative systems operating in the nonlinear range do not "forget their initial conditions."
This is, admittedly, a point which confuses me. My confusion comes to a head on page 191. In one place on the page, Capra says:
A bifurcation point is a threshold of stability at which the dissipative structure may either break down or break through to one of several new states of order. What exactly happens at this critical point depends on the system's previous history. Depending on which path it has taken to reach the point of instability, it will follow one or another of the available branches after the bifurcation.
At another point on the same page he says:
At the bifurcation point, the dissipative structure also shows an extraordinary sensitivity to small fluctuations in its environment. A tiny random fluctuation, often called "noise," can induce the choice of path. Since all living systems exist in continually fluctuating environments, and since we can never know which fluctuation will occur at the bifurcation point just at the "right" moment, we can never predict the future path of the system.
So, which is it? Does the system's history "choose" which branch the system will take, or does a random fluctuation make the crucial choice? Perhaps it is a combination of both, involving some probability function. All I can really say is that Capra is, to my mind, uncharacteristically unclear about the interplay of history and chance as they affect dissipative systems at critical bifurcation points.
An example of a linear dynamical system is that of a planet orbiting the sun. The shape of its elliptical orbit never varies, which means that we can run the imaginary "movie" of its motion backwards and forwards in time, with perfect predictability as to where the planet was on any given date in history and as to where it will be on a given date in the future. Its "initial conditions" — such as where the planet came from in the first place — make no difference.
Not so with nonlinear dissipative systems operating far from equilibrium. At their bifurcation points they take this branch or that as a result of the details of their unique histories and/or small random fluctuations in their environment. The most minute differences in their initial conditions or in their environmental circumstances will bias them in favor of branch A and away from branch B.
To me, their imperviousness to external prediction and control and the absolute autonomy of their unique histories and futures make their behavior trajectories organic rather than ordained.
Yet common sense tells us that we living beings — however autonomous, however unique, however unpredictable — exhibit an awful lot of expectability. Sons and daughters tend to look like their mothers and fathers. Identical twins tend to look like each other. Swans don't come from ducks' eggs.
We must all be something like fingerprints. Every human finger can be expected to possess a fingerprint. Yet each fingerprint is unique. Even identical twins have different fingerprints.
Fingerprints show up on fingertips, obviously, at some stage of human embryonic development. A human being in utero develops from a fertilized egg cell. During the process of development, the zygote — the fertilized egg — divides and makes two cells, then four, then eight, and so on. In the early embryonic stages, there are no detectable differences among the cells. Soon enough, however, the cells start to differentiate and form distinctive tissues and organs.
Presumably, if Prigogine's ideas about dissipative systems and their bifurcation points hold for embryos, the embryo is continuously "choosing" certain branches along its own developmental trajectory and discarding other equally available branches. Somehow, some combination of these "choices" results in the formation of ten unique fingerprints ... while at the same time (if the embryo is normal) guaranteeing that there will be ten fingers and ten prints.
Thus is there a mix of unpredictability (the distinctive loops and whorls the individual fingerprints will wind up having) and expectability (that there will indeed be fingers, and fingerprints).
I imagine that, as with other aspects of emergence in living dissipative systems, the human embryo has its associated "phase portrait," its own abstract topography of attractors and basins of attraction which account for its potentialities as it develops. This topography produces both comforting expectability and unpredictable uniqueness.
I also imagine that the same principles apply to the spiritual mind within each unique human being. Our spiritual paths are indeed individual and unique. Yet, at the same time, there are certain expectable patterns in our spiritual life. I suggest the commonality and expectability in our spiritual paths are due to certain basins of attraction universally present in the human spiritual mind.
Let me suggest three such basins of attraction. The first is the one characterized by not being "spiritual" at all, by having no particular religious beliefs, etc. This, canonically, is the state one starts out in and then leaves behind when (say) one is "born again," after which the former, non-spiritual state is typically thought of as having been a "godless" one.
The second basin of attraction of the spiritual mind is that in which there is a profoundly God-oriented (shall we call it?) "steady state" toward which the experiencer is pulled by an "attractor" which is, quite naturally, the experiencer sees as God or Christ or the Holy Spirit. (I am speaking in Christian terms; other religions have their corresponding equivalents.) The spiritual mind that is in thrall to this attractor wants more than anything else to experience God as ordaining every blessed outcome in this world.
The third basin of spiritual attraction corresponds to Merton's Zen awakening following his Dark Night of the Soul ... and (I hope) to my own spiritual embrace of the organic nature of life. Once one's mind is in that third basin, or so my feeling goes, it becomes important to see the things of this world as emerging out of organic, self-organizing principles that guide the evolution of dynamic, ever-changing, living systems. The question of worldly outcomes ordained directly by God becomes much less important when one is in this third spiritual basin of attraction.
Some questions arise: where do these three spiritual basins of attraction come from? By virtue of what occurrences do we move from one to another? Is the progression from seeing the world as "godless" to seeing it as "divinely ordained" to seeing it as "organically emergent" typical, and if so, why? Finally, is there any way to bridge the dichotomy between the last two, such that God can be seen as influencing or even directing the emergence of organic novelty in this world?
More about these questions in later posts ...
No comments:
Post a Comment