Thinking in Fractals: Balance after Smashing the Dichotomy

An essay in response to Robert Pirsig’s Zen and the Art of Motorcycle Maintenance

Pirsig’s metaphysical motorcycle is whizzing across the universe at just about the same speed as one’s ‘train of thought’ –roughly one second per second. While his story spares no detail in the assembly and maintenance of the subcomponents of his own Quality philosophy, he offers little assistance in finding balance in the larger machine. Pirsig leaves that job to the reader, to sort things out and play out a little part in the delicate balancing game. I asked then, how can one find a culturally grounded, and stable, theory for balance? The obvious place to start my search was in my undergraduate work in Robotics Engineering at Worcester Polytechnic Institute. The paper moves from a concrete example, to an abstraction, to epistemology, and back down to application. I hope to leave the reader with a new and distinct way of looking at the patterns that life plays out, as well as practical tips to keep the machine working. 

Assume now, I have decided to commandeer Pirsig’s motorcycle and automate it. I want to make it work by itself. One of the largest problems to be addressed would be, how do I make the machine balance? After finding or making a mechanism that I believe would work (probably something gyroscopic), I could start it up and see what happens. Unfortunately, without directions, the mechatronic system I just developed would fall over within seconds. In my next step, I would attach sensors to the motorcycle. The machine would now be able to observe its current state and make changes accordingly. But, that requires some means of control. The method that I could employ first is a proportionally-based feedback loop. The cycle would strive to correct its balance in direct proportion to the amount of its error from the setpoint. 

Yet I would find soon enough that there are two problems. First, if the motorcycle was told to balance but was initialized rather far away from its balancing point, the motorcycle could very well over-correct and send itself hurtling up and over the balancing point and onto the ground opposite where it started. Second, if the motorcycle was told to balance but was started at a small offset from its setpoint, the proportional control could in all reality not send a large enough signal to the gyroscopic mechanism, and eventually fall over due to the small error compounding over time. To solve the problem I could spend some time researching to find that there have been many smart men before me that have studied control theory and have come up with various ways to solve the same problem. 

The simplest one, and the one that solves those two flaws above, is an aggregation of proportional, integral, and derivative (PID) control. While the proportional factor sets the balancing motion in the right direction, the derivative control stops it from accelerating too greatly, and overshooting its setpoint. Meanwhile, when nearing the desired balancing point, the integral factor comes into play, correcting that steady state error which caused the cycle to fall to entropy in the second case. Now I can step back and say, “Why does it work so well?” as my motorcycle balances in front of me, seeming to defy the natural forces that want to topple it. Finally I think, “If it works so well for a robot, can it work just as well for people?”

What I would like to show the reader is that the idea, or pattern, of PID control has been working behind the scenes for thousands of years. I use the term ‘working’ here in the lightest sense, as there is a problem, a gap, that has been growing wider, and is one of Pirsig’s main topics. The seemingly great polarization is between two modes of being that Pirsig calls ‘romantic’ and ‘classic’. Romantic he defines as a mode of being influenced mainly by intuition, and is concerned with surface appearance. Pirsig defines Classic as the opposite, as dealing with logic, and concerned with underlying form (84, ZAMM). Imposing the two terms on their PID control equivalents, the pairs of classic-integral and romantic-derivative become apparent. 

The classic-integral pair is born of the idea that they are both summations. The Classic mode of reality is an aggregation of knowledge, observations, and abstractions. Its pair, the integral, sums numbers. 

The romantic-derivative duality is based on the idea that the derivative is tied to action as related to change. Emotive and intuitive forces drive the Romantic mode of being, and cause the most change. 

Thus the gap, the problem, that Pirsig is picking up on is an unbalanced system. One way the pattern, thus balance, breaks down is by means of the constants associated with each of the control functions being improperly tuned. Another method to cause disharmony is through rapidly changing the setpoint of the function. I argue that both methods are being applied by the classic-integral and romantic-derivative sides currently. Accordingly, the ‘culture’ system is showing erratic behavior, which the unnamed narrator is tuned into.

The PID system can be abstracted out and overlaid onto a culturally significant thought. Dr. Jordan B. Peterson introduced in his lectures on the Psychological Significance of the Biblical Stories a diagram which has deep religious and mythological meaning. Originally, the diagram was the Christian Trinity of God the Father, Spirit, and Son. Dr. Peterson abstracted out those concepts into a tripartite Principle, Chaos-Potential, and Order split (Peterson, Lecture 1). Please reference the diagram below. 

The Principle is something approaching Pirsig’s Quality. It is an event, possibly, an ongoing pattern that one can try to reach, but mostly observe and feel. The Principle is the end-all-be-all. Existence comes from it, and trickles down through time into Pirsig’s two modes of being, Classic and Romantic. Its PID equivalent would be the proportional factor, which is located in the here and now, without any other adjustments. The ‘flow’ mentioned above falls (currently, though I hope to change that) down through the two vertices in different directions. One passes first through Chaos-Potential and the other through Order. They are the feeling and observing sides respectively. 

The Chaos-Potential vertex describes the ether, the spirit, entropy, the unknown, and change. A mouthful to say the least, but I hope the idea of what it represents is apparent from that amalgam of terms. Its PID analog is the romantic-derivative pair. It has many literary symbols, but the most common is water or the sea. At the base level of narration one can interpret Pirsig’s narrator riding across the country on his motorcycle, dividing up his memories and categorizing the world. But, when he encounters the classic symbol of infinite potential, the ocean, “The source of it all,” he says, Phaedrus takes over and the narrator finds zen (519, ZAMM). It is a perfect example of coming up against the reality of nature, realizing the system is out of order, and then transitioning to a more fulfilling direction. 

Order is that which gives form. Its religious connotation, the Son, is of the spoken word, and consciousness. Dr. Peterson said of order and spoken word, “[until an object is named] it is part of the blurry background. Once something is named, it exists, and can be understood and manipulated” (Peterson, Lecture 2). Its PID symbol would be the classic-integral pair. Pirsig’s narrator spends his journey in the Classic mode. The narrator is locked inside his head making observations, cataloguing past events, and reasoning out the causes and effects of high philosophy. He spends his time less conscious of his immediate surroundings than of his own thoughts. His devotion to the function of Order is rather impressive, but there are recursive complications that arise quickly out of such single mindedness. 

The chief problem of adhering only to Order is that each time one tries to pin down an idea, it splits into multiple pieces. The best example that comes to mind is the myth of King Midas with a little twist. The change being that whenever he touches something it no longer turns to gold, but becomes recognizable only in the underlying form of the parts that make it up. His daughter in this case would not turn to gold, but to an assembly of arms, legs, torso, head. Head would then turn into a collection of eyes, mouth, nose, ears, and on and on. Every time the king would try to ‘grasp’ something, it would become more distant. Pirsig’s analogy, along those same lines, is that of the ‘analytic knife’. It goes about in the world chopping ideas into smaller pieces. “With a single stroke of analytic thought [Phaedrus] split the world into parts of his own choosing, split the parts, and split the fragments of the parts, finer and finer and finer…” (Pirsig, 93). 

The analytic knife follows a pattern though, and I hope that in the greater context introduced on Peterson Diagrams, its movements will be shown to be impractical. The knife and its work is a form of re-entry, as defined by Louis H. Kauffmann in his paper on Self Reference and Recursive Forms. In the paper he puts forward the notation of a ‘self pointing arrow’ to assist in explanations (Kauffmann, 53-8). The diagram below outlines an example of this notation, in the context of the knife making a simple slice in half. The knife slices the original ‘thought’ in two, and then those two into two new parts, and so on ad infinitum. 

It seems that the only way to stop the endless slicing would be for the slices to become too small for the knife to accurately hit. The blade of analytic thought would be thicker than the slice that one wants to cut. It seems humanity has hit a physical representation of this thought in recent developments in the field of physics, where observation at the picoscopic level changes the nature of the object being observed.

And thus I forward the thought that the dualistic system of knowledge (night/day, classic/romantic, true/false) that we have built up is less practical than a tripartite system. And first, a discussion of that system. Plato’s answer to the question, “What is knowledge?” was originally a tripartite system of justified-true-belief, JTB (Getter, 121). He concluded that one can know only if,

  1. The proposition is true
  2. One believes the proposition
  3. One’s belief is justified

Many experts in the field of Philosophy took this as a well thought out explanation for knowledge until Edmund Gettier foiled the tripartite system by poking at its third axiom, that the belief is justified. He developed a formula which made it seem as though a subject knew something, but in reality was duped into it by making false assumptions (Gettier, 122-3). I argue that this sleight of hand may have foiled the surface-level interpretation, but that is because they did not apply the theory of re-entry to an obviously recursive and self-referential system. Thus, Plato’s original diagram below expands into the second iteration and third, etcetera. 

Each vertex of the triangle is supposed to be ‘true’ for something to be known to be ‘true’. Thus, each vertex has its own supporting triangle that verifies its ‘truth’, and each of those vertices have supporting truths so that we can ‘know’ it to be true. Accordingly, Gettier’s ‘end-all’ is just a second-order third axiom, referenced in the second pane of the diagram above, which in everyday english would translate to something like, ‘one justifies their belief in their justification of their belief’. Which is, of course, entirely different than the first-order justification of belief. I also theorize that one could forge Gettier problems for each of the eight other vertices that at the first level seem to be correct, but second order knowledge catches the trick.

Truth then becomes no longer ‘true/false’, but a kind of ‘tri-th’ (supported, unsupported, expand context) which is governed by order or magnitude of truth. A first-order truth would be less sound, or stable (since I am following the balancing route), than a second or third order truth. Unfortunately, our trained dualistic mind will still truncate the results, and translate from the trichotomy into a dichotomy of true/false. 

The best physical analog I can imagine is that of a computer circuit. The computer reads in data on a digital line and if the signal is above or below a certain threshold (usually there are two thresholds, one for high and one for low), it declares the input to be digital-high, truth, or digital low, false. Yet, it leaves out the nature of the electrical signal, which is something much more than a true or false. A whole spectrum lies in between those two extremes. Our minds are in this case like the computer, which pushes the signal towards one extreme or the other. And it is no surprise that one may have problems when pushing ideas in the middle of the two, as one moment one may want to push a truth, and the next, a false. Adding more minds complicates the mixture even more and creates a veritable battle in the middle that fights over which way to push the status of ideas.

To find balance we need to expand our system of thought to rejoin the three great modes of being. The balancing function that is comprised of the Classic/Romantic split is unsupported by the reality of experience. We need the third, Theos, which had its apparent value eviscerated and reduced to near nothing by progress in the Classic and Romantic modes, to bring some semblance of order back. The pattern’s flow, input, must touch all the modes of being/knowing, function, to produce a stable culture, output.


Gettier, Edmund L. (1963). “Is Justified True Belief Knowledge?”. Analysis. 23: 121–123.

Kauffman, Louis H. (1987). “Self-reference and Recursive Forms”. Social Biology. 10: 53-72

Pirsig, Robert M. (1974). “Zen and the Art of Motorcycle Maintenance”. HarperTorch

Peterson, Jordan B. (2017). “Psychological Significance of the Biblical Stories” . Lecture. 1-2. 

Published by lombardiengineering

Always striving to be an all around great individual

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