The Edge of Chaos by Mark Maxwell
An essay considering exceptional Dynamic coherence
(or “the sweet spot”)
in Robert Pirsig’s Metaphysics of Quality.
The Master Butcher.
A cook was butchering an
ox for Duke Wen Hui.
This essay wishes to explore exceptional Dynamic coherence (or the “sweet spot”) between static quality patterns as an aid to understand Dynamic Quality as alluded to by Robert Pirsig in his Metaphysics of Quality (MOQ). Additional questions explored in this essay will be:
Is enlightenment a sweet spot?
Is the MOQ an intellectual sweet spot?
Do sweet spots provide evidence for non-anthropic Quality?
The Metaphysics of Quality.
In the MOQ, immediate experience is primary,2 and is termed “Quality” 3 by Pirsig. Quality is analogous to the Tao, Buddhist “nothingness” (sunyata) and F.S.C. Northrop’s “undifferentiated aesthetic continuum.” 4 Pirsig perceives Quality as essentially a Dynamic process from which static patterns of quality emerge. In the MOQ, therefore, discussion of experience is of values and their Dynamic. Moreover, the MOQ suggests that four related levels of static quality patterns have evolved, beginning with inorganic patterns. From these inorganic patterns of quality have emerged biological patterns, social patterns and, most recently, intellectual patterns.
What are sweet spots?
The motivation for writing this essay arose after discovering an idiom used by John McEnroe while commenting for the BBC during Wimbledon 2000. McEnroe stated that players must use the sweet spot of their racquet or otherwise balls could end up anywhere in the stadium. Further research made me suspect that the relationship an excellent tennis player maintains with the racquet is similar to the one noted by Robert Pirsig between Eugen Herrigel’s Zen Master archer and his bow.5 The sweet spot appears to indicate that moment when subject and object are in a particularly high Dynamic Quality relationship.
Over the next three years I found further examples of sweet spots using Internet search engines and discovered they all described high quality relationships at key moments within a process. I considered these examples and thought about them in the context of the MOQ. Consequently, I increasingly felt comfortable in dividing reality between static quality and Dynamic Quality and, in doing so, abandoned my culturally inherited division of experience into subjects and objects (i.e. what Pirsig terms “subject object metaphysics” or “SOM”).6 This process has been underway since reading Pirsig’s second text, LILA.
It soon began to occur to me that sweet spot relationships were particular Dynamic states between static quality (SQ) patterns. Moreover, I began to see from the details of the examples themselves that a high state of coherence or harmony between SQ patterns was precisely what the term sweet spot was attempting to convey.
These considerations lead me to a realisation that the harmonic relationship between SQ patterns is essential to an understanding of the MOQ. The more I thought about it the better it looked. The more I applied it the more it explained. Intuitively, I felt the MOQ would describe the sweet spot as a Dynamic event displaying high coherence within the static value levels between the extremes of chaotic disruption and static stagnation.7 Somewhere between these extremes may be found a sweet spot - a Dynamic relationship that is exceptional. At this point, I intuitively felt patterns became less differentiated though simultaneously retaining structure; hence avoiding the extremes of chaos and stagnation. This understanding had been there all along but had not sufficiently impressed itself upon me. If I found thinking about sweet spots helpful, perhaps others would find them helpful also?
Thus, sweet spots are an appropriate way to explore the MOQ through concrete examples found in everyday life. The following diagram may help to indicate the sweet spot as an intellectual expression of a highly Dynamic relationship between SQ patterns. Please note the diagrams in this paper are purely representational and should be abandoned if found unhelpful.
Each vertical line in Fig. 1. represents a static pattern of quality in a relationship with the Quality event stream.
If a pattern is in too static a relationship, it moves to the right and is evolutionary dead. If the pattern is in too unstable a relationship, it moves to the left.
The sweet spot is postulated as a coherent state somewhere between these two extremes. At the sweet spot of Dynamic Quality (DQ), a pattern is neither too static or unstable. It is here that a process is most efficient, art more beautiful and life more serene.
According to Pirsig, evolution also tends towards DQ. Therefore, sweet spots may be viewed as the immediate cutting pressure in the evolutionary process. Perhaps one may introduce here the simile of the cook’s knife, or the purposeless tension found in Zen in the Art of Archery.8 This essay wishes to promote thinking regarding this Dynamic tension between SQ patterns so, in the following, I shall use examples in the fields of sport, engineering, physics, literature, music, communication and mathematics to illustrate this.
Inorganic sweet spots.
To survive in a variable environment, [a system] must be stable, to be sure, but not so stable that it remains forever static. Nor can it be so unstable that the slightest internal chemical fluctuation causes the whole teetering structure to collapse.
--Stuart Kauffman, At Home in the Universe, Ch. 6
The Edge of Chaos
"Phase transition" is a term used in physics to describe the threshold between the gaseous and the fluid, the fluid and the solid, and so on. It is a point of transition, where ice begins to melt, water begins to evaporate, and vapor begins to condense. In phase transition, a system becomes dynamic and unstable, anticipating the beginning of something new.
For complex system theorist Chris Langton, the idea of phase transition also describes the sweet spot of evolution, where an emerging balance between the solid and the gaseous obtains new behaviors. Systems out of this dynamic and fluid balance, on the other hand, "tend to stall in two ways. They either repeat patterns in a crystalline fashion, or else space out into white noise."  But within the sweet spot, one finds perpetual novelty in constant transition--a transition Langton calls the "edge of chaos.” 9
A synopsis of complexity reads as follows:
Sweet spots may indicate that Quality is not merely a human invention. Sweet spots are to be found everywhere and provide supporting evidence for the cosmological evolution postulated in the MOQ. Examples of sweet spots in nature may be readily seen in the phenomena of phase transitions. These appear to be sweet spots where the freedom of possibility merges with the security of the actual:
The deep natural impulse towards order’ that complexity indicates may be better restated as a balance between SQ patterns. The impulse is DQ and the order is SQ.
At the sweet spot of the tennis racquet during the moment of impact, inorganic patterns comprising the structure of the artefact are in a high state of coherence with the organic patterns of the player. The Quality stimulus of all these patterns (taken as a unitary system) has coalesced into a coherent aesthetic state.
If this coherent state is achievable in all levels (inorganic, organic, social and intellectual) then it becomes possible to imagine a cycle of harmonic coherence throughout the evolution of all levels. Such a cycle of coherence/incoherence would describe the dominant patterns exerting influence in particular relationships. Such relationships may vary over the cycle of a human day, year, lifetime, individual, organisation or institution.
The red standing wave in Fig. 2. may be thought of as the sum total of a system of static inorganic values. The wave emerges in an event stream and oscillates away from, and then towards a sweet spot as shown in Fig. 1. Our tennis example would include the tennis court, player, racket and ball.
The green standing wave in the diagram may be thought of as the sum total of a system of organic values. Our tennis example would include the players and audience.
However, we may wish to see this state over periods of archaeological time? Thus, the coherent state of a biosphere may have at its sweet spot a dominant species or group balanced in an evolutionary stable pattern.
Continuing to look at the diagram, the purple standing wave may be thought of as the institution of Wimbledon, or sporting events in general, and the blue standing wave as the intellect of the player or players.
Note the levels evolve simultaneously in the event stream. Inorganic and intellectual levels are evolving in the same instant, but intellectual patterns are more Dynamic than inorganic patterns - this is represented by a higher frequency standing wave in the diagram.
Pattern levels are also discrete.10 It may be possible for each level to be harmonised in a mutually supportive coherent state —thus, coherence is not simply a matter of one level resonating with Dynamic Quality — all levels in differing degrees may move in a sympathetic aesthetic. For example, audio-visual media may be fruitfully thought of in terms of a relationship between social patterns, (movie, theatre, TV, video, radio, photography) and intellectual patterns, (technological design, language, logic, symbolism). Thus, these value levels form quality relationships with organic (mechanic, teacher, student) and inorganic patterns (engineered artefacts) of which the above video may provide an example. The use of narrative, symbolism, editing, and the innovation of pause, rewind and cue repetition facilities inherent in video and DVD artefacts may produce a sweet spot between all levels, resulting in an event displaying coherence or coalescing of patterns within and across value levels.
The above figure aims to convey a slice of coherence in time. This figure is built from the combination of four Fig. 1. illustrations, and tries to convey further the coherent nature of the sweet spot when all levels are in harmony.
Sixteen great motorcycle engineers and tuners in the motorcycle roadrace industry join forces on what may be the first motorcycle educational how-to information resource available. The synergy among these award-winning authorities is masterful. The sweet spot Video Library is step-by-step video instruction, a must-have for every motorcycle enthusiast!
Virtually every aspect of performance motorcycle set-up has been addressed in this series, in detail and close-up. Major topics include: motorcycle suspension - pre-load, damping, rebound, etc., motorcycle exhaust systems, motorcycle carburetion and jetting, motorcycle tires, motorcycle engine oils and fork oils, motorcycle chain and sprockets, motorcycle brake lines, and much much more. Each of the six videos offers thorough coverage of a topic and together they form an exhaustive source of practical information.11
The above quote demonstrates the importance of experience in tuning. Here, the relationship between mechanic and machine has been distilled into a video of experience for others to share. The peak of tuning in maintenance is referred to as the sweet spot, and for this reason, the video for sale is titled as such.
Every machine has its own sweet spot (best tuning). As also noted by Pirsig (1974), a machine when tuned at its sweet spot will require less maintenance, and operate more efficiently. In other words, a quality machine is one maintained at a sweet spot.
The sweet spot analogy is also used in a variety of ways to indicate high quality in technology as in the examples of peak tuning, efficient dissipation of energy, and minimum friction in engineering. When a physical system is dissipating energy efficiently the system is described as operating at its optimum state — that is to say at its best. An engineered system maintained in this state will last longer than one operating under stress, experience less wear and damage, and aid the evolution of a high quality relationship with the individual using or relying upon it. An engineered system may be viewed simply as a more complex tennis racquet where the sweet spot of the system is the artistic goal of the engineer.
Thus, it becomes clear that the patterns of an engineered system12 and the patterns of the engineer and his/her culture move towards the sweet spot in a process of discovery. Traditionally, this process of discovery of an event displaying coherence or coalescing of patterns within and across value levels is called design, and its maintenance mechanics. It would appear that such discoveries are movements towards coherence, and are therefore really human artistic creations. Good design includes patterns of the designer, and a good designer includes the patterns of technology in coherence and unity.
The manipulation of physical systems is accomplished by balancing opposing inorganic values. For a system to operate at its most efficient there must be an overall harmony between gravity and electrodynamics as basic to their operation. The point of harmony exhibits an aesthetic of ease and grace as mass and acceleration, current and induction dance at the sweet spot in an event displaying coherence or coalescing between differing value patterns. At the apex of these relationships is a point of balance or sweet spot where large forces may be directed without effort.
The sweet spot may convey contradictory natures - fleeting, ephemeral, unpredictable, yet balanced and harmonised — aimed for, yet lost and selfless. Literary and engineering examples indicate beauty, harmony, measure, ratio, ease, perfection and grace. Analogies express it best, but it seems real of the analogy.
To explain it simply, the entire bail-hook firing mechanism is located in the releases head. This entire head floats until the Headlock is pressed. This causes a pin to lock one part of the head while the bail and hook rotate and cause the release to fire with a specific amount of travel. A free-floating head means that the release compensates for terrain and bad form, making the sweet spot the ultra-forgiving, ultimate release.13
Here, technology is trying to cheat the sweet spot. But the sweet spot is simply in a different relationship now — and the individual may still choose to explore SQ relationships for their true worth. However, in western culture, the use of technology appears to be aimed at hitting holes in pieces of paper rather than discovering real Quality.
Organic sweet spots.
The environment has sweet spots of the day and season — biology is the source of the analogy as in good taste, freshness, ripeness, and maturity. Sexual choice has provided organisms with a high quality stimulus for promoting Dynamic coherence of individual organisms. From a biological point of view, sex is high quality activity.14
All organisms reach a state of maturity; indeed, the term sweet indicates the biological maturity of ripe fruit. Biological maturity is evident in the coherent nature of patterns as they reach a tension between static degeneration and Dynamic growth.
Moreover, organisms harmonise with their environment. When an organism flourishes in a stable environment, the relationship is a coherent SQ relationship.
However, sexual choice for human beings appears to have evolved to include social and intellectual levels in a state of coherence. A sexual partner may be valued primarily for Dynamic factors other than biological quality. A recent discussion of the value of social and intellectual patterns over biological patterns in sexual selection is found in The Meme Machine by Dr. Susan Blackmore. Blackmore convincingly argues for memeticly driven sexual selection, which in the language of a value centred metaphysics tells us that intellectual patterns of value in some cases dominate biological patterns in a coherent relationship.
A baseball bat has three "sweet spots"; one of them is called its "centre of percussion" (COP). That's physicists talk for the point where the ball impact causes the smallest shock to your hands. If you hit a baseball closer to the bat's handle than to the centre of percussion, you'll feel a slight force pushing the handle back into the palm of your top hand. If you hit the ball farther out than the COP, you'll feel a slight push on your fingers in the opposite direction, trying to open up your grip. But if you hit the ball right on the COP, you won't feel any force on the handle.
To find one of the "sweet spots" on a baseball bat, hold the bat, hanging down, loosely between your thumb and index finger, just below the knob on the bat's handle. Have a friend tap the bat gently with a hammer, starting at the fat end and moving toward the handle. (You can also do it yourself, although it's easier and more fun with a friend.) You should feel a vibration in your fingers whenever the bat is struck, except when the "node" is hit; then you'll feel nothing. You may also notice a slightly different sound when the node is struck.
When you hit a ball just right, you've hit it on one of the three "sweet spots" of the bat. One of these sweet spots relates to vibration. Whenever an object is struck, it vibrates in response. These vibrations travel in waves up and down the length of the object. At one point, called "the node," the waves always cancel each other out. If you hit the ball on the bat's node, the vibrations from the impact will cancel out, and you won't feel any stinging or shaking in your hand. Since little of the bat's energy is lost to vibrations when this spot is hit, more can go to the ball. The node sweet spot differs from the "centre of percussion" sweet spot. When a ball hits the node, you don't feel any vibration in your hand. When it hits the centre of percussion, your hand doesn't feel any force pushing against it.
Where is the sweet spot? Where can it be found on each bat, racquet, or club, and how do you find it? There is a method for locating it, a quantifiable, eternal, material-world truth, described by scientists in terms like nodes, modes, and amplitude. But then, scientists have described many things they do not know how to use. What good is the information if you do not know how to use it? For example, you may know the principle of "lift" exists, but that does not mean you can fly.
Unless you have had a parent, older sibling, or coach to teach the skills involved in the knowledge, you are in the dark, and if you have played any kind of ball in this condition, you are probably what is known in athletics as a "slap hitter" a "Punch and Judy" contact hitter, a singles hitter, a maker of slices, hooks, and backspins; in short, a pesky lightweight. You may hit for a high average, return service well, and hit the ball straight down the centre of the fairway, but you have no oomph! No homers, no aces, no hitting the long greens in two.15
Investigation revealed the sweet spot of a baseball bat has a scientific explanation exhibiting equilibrium, harmony, ratio, and proportion. The aesthetic beauty of these descriptions indicates a correlation between the intellectual pattern of mathematical and geometric symbolism used in abstract modelling (intellectual patterns) and the immediate quality experience of the artefact at the sweet spot itself (an event displaying coherence or coalescing of patterns within and across value levels.)
Science can model the sweet spot of a baseball bat, but not everyone can maintain a relationship with the sweet spot. However, a hero of the field can.
The shape of the standard baseball bat may have grown out of a relationship between player and bat in response to a sweet spot - the shape of the bat has evolved in a move towards higher quality.
Moreover, tennis rackets have a well-known sweet spot, as do golf clubs and cricket bats, snooker or pool cues, and even football shoes. Experience and utility of the sweet spot in sport distinguishes excellent players from competent players. Sport champions centre and perform at the sweet spot without effort. In other words, a professional sportsperson relies upon his/her maintaining a good relationship at the sweet spot. The relationship involved is a Dynamic one and can include all the inorganic, organic, social and intellectual levels.
This next example remains close to Quality. It is a long quote, but well worth including in its narrative entirety.
Kid finds that sweet spot, and everything melts away. 16
by John Powers 1/20/2001 © Copyright 2001 Globe Newspaper Company.
From the moment her name was called, from the moment the music began, she was in a place where nothing on earth could reach her. A place where the rink has no end, where her blades barely touch the ice, where there is no rule book to limit her, no record book to weigh upon her. A place without judges, without critics. A place where nobody asks Michelle Kwan why she still does this.
''To feel the wind in my face - that's what I love about skating,'' Kwan was saying last night, after she had left her teenaged pursuers on the far side of the FleetCenter dasher with seven perfect 6.0s in the short program, and drawn within 4 minutes of her fifth US title. ''When I get that feeling I say, this is why I'm here.''
Ever since Nagano, ever since Kwan declined to put her silver medal in a drawer and put Olympus in her past, she has been trying to explain why she still laces up. She doesn't need the money. She's won three world titles. She's 20. Shouldn't she get off the stage like Tara?
How could Kwan explain about the wind in her face, ''the freedom that I cherish''? Only a child would understand. Adults think too much. They think about gold medals and money, about pressure and what-if-I-don't? Adults do not live in the moment. Children always do.
Kwan wanted to be a child again, to be the 12-year-old who delighted herself with every new jump. When she talked at the beginning of the season about going back and finding the motivation again, that was what she meant. Back to a place where there was only a girl with a ponytail and an open sheet of ice.
It seemed unlikely that Kwan would discover that place again last night. She was hurting when she arrived here, her back still stiff from practising the triple salchow-triple loop combination that everyone said she needed to keep up with Sarah Hughes. Then she plotzed on a simple triple loop in Thursday's practice and ended up in a most unregal position.
Maybe Kwan was beatable here. Irina Slutskaya had beaten her twice this season. Josee Chouinard (yes, that Josee Chouinard) had beaten her. Coaches of rival skaters had been saying (OK, whispering) that Kwan hadn't upped the technical ante, that her artistry had become predictable. If she had a bad night, as she did in Nashville four years ago when Lipinski lifted her crown...
Kwan knew what everybody was saying about her. She knew what the online gossips were posting on the message boards. It was hard, she said, to hear the criticism. But as soon as she stepped onto the ice last night, Kwan left the babble behind.
''I forgot about Nationals,'' she said. ''I forgot about the competition. I forgot about the Olympic year. I forgot about everything.''
Suddenly, there were no judges, no spectators, no ticking clock, no required elements, no pressure. There was just a place where Kwan felt completely comfortable.
As soon as the music began and Kwan heard the first stirrings of ''East of Eden,'' she was transported. ''It's haunting music,'' Frank Carroll, her coach, was saying. ''It gives me the chills. It's very Michelle.''
When she landed her opening jump, the simple yet treacherous double axel, Kwan could sense the wind in her face. When she did the triple lutz-double toe combination, the program's high hurdle, Kwan knew it. She was in the zone, just as she was in Philadelphia three years ago, when she simply took wing and left Lipinski earthbound.
''Just being out there, being in the moment,'' mused Kwan. ''That's what athletes’ dream about. I felt that sweet spot.''
Dan Jansen felt the sweet spot in Lillehammer, when he finally won his Olympic gold medal. Picabo Street felt it hurtling down the slopes in Nagano. The Boys of winter lived in the sweet spot for a fortnight in Lake Placid.
For 2 minutes 40 seconds, Kwan wasn't East of Eden. She was in the middle of downtown, at the intersection of State and Main, with nothing but green lights as far as she could see.
When the music stopped, she saw the crowds come up out of the seats heard their roar, saw the flowers and teddy bears end-over-ending toward her. The artistic marks - 6.0, 6.0, 6.0, 6.0, 6.0, 5.9, 5.9, 6.0, 6.0 - were thrilling, but irrelevant. Kwan had seen them before in Philadelphia, seen them on both nights.
The sweet spot is a moment in time. It comes and it goes and those who have been in its Zen-like centre can't tell you why. Perhaps Kwan will still be there tonight when the medals are given out and will join the half-dozen women who have won this crown five times. And perhaps the sweet spot will turn sour in the flash of a blade, as it also has for Kwan.
Last night was but a moment in a special place where Kwan has been before, a free and easy place where children live, a place she yearned to locate again. Last night, Michelle Kwan was 12 - and nobody could touch her. (This story ran on page G01 of the Boston Globe, January 20th 2001.)
This example provides an indication of the value of the sweet spot as personally experienced. It would appear there is little difference between the sweet spot as experienced by the skater and that experienced by the mathematician — the starting point is a different level of evolution, but the sweet spot provides a lens through which Dynamic influence illuminates.
Social sweet spots.
Such relationships between value levels have been evolving for a very long time. However, the MOQ clearly affirms that it is crucial for the overall harmony of society that intellectual patterns also support social patterns when biological patterns threaten to undermine social cohesion.
It may be fruitful to reflect upon the poetic use of sweet in the works of Shakespeare? Shakespeare’s sonnets are dense with images of ripeness, in fruit, flowers and people — metaphors for biological, social and intellectual sweet spots - events displaying coherence or coalescing of patterns within and across value levels. The dangers of intellectual support of biological patterns over social patterns are central to many tragic social events in his works.
Society and art express sweet spots in justice, temper, character, and grace. One example presented by Robert Pirsig in LILA is the Marshal plan.17 Here, static social institutions of American government are harmonised with the Dynamic celebrity status of the particular social patterns of the president Roosevelt himself — the result appears to have resulted in an overall higher state of static quality and Dynamic response.
Another example may be the National Health Service (NHS) of the United Kingdom.18 The NHS is a social institution providing inclusive biological, social and intellectual health care for all members of society. Thus, the health of individuals is supported for the benefit of social patterns, and intellectual medical research supports social patterns of quality.
Surgeons very often have rigid routines which are observed meticulously on operating days. This use of ritual kills distracting influences in the surgeons working life so that he/she remains coherent and stable. Returning to Fig. 2 we may envision the life of our surgeon as being organised deliberately in order to coerce a coherent state of patterns to develop during theatre work.
It is said that the sharpest knife is a safe knife. Duke Wen Hui’s cook, whose knife never became blunt because he cut at the animal’s joints, illustrates the way also adopted by surgeons. Here we may see a correspondence between the knife, the arrow and the tennis racquet? Inorganic patterns of a knife will have a sweet spot where control is finely balanced and incision naturally flows in a relationship with the patterns of the surgeon him/her self and the institution of, in the example of the UK, the NHS.
In all these cases the importance of ritual as an aid to coherence is apparent. In the wider social context, social sweet spots may also include a large degree of ritual? Therefore, a social sweet spot may be viewed as a coherent state between institution, celebrity and ritual.
The relationship between static institution and Dynamic celebrity status may provide a fine edge of resonance analogous to the ritual and relationship between artefact and artist. In the tennis example, sporting institutions change in response to the celebrity influence of individual competitors. John McEnroe has influenced the professional status of line judges because of his rituals on court!
The British Broadcasting Corporation may provide another example of a social sweet spot. 19 The BBC is somewhat detached from many other social patterns — government and business for example. It has been a reflection of social values in the UK during its evolution. In its early days the BBC was chartered to promote intellectual values and widen the experience of art among UK citizens, although this has been under pressure since the growth of commercial counterparts with their inherent biological and social domination. The BBC has therefore been a motivating force for the support of intellectual patterns in a coherent state with social patterns.
Performers share a social relationship with an audience, which may provide a starting point for examining a social sweet spot.
Given all the variables from the soles of the feet up to the sweet spot, it is a miracle that anyone can put the right spot to the right object at the right time, but there are those who have done it with ridiculous ease. We refer to them as "naturals", and they have names like, "Slammin’ Sammy", "The Babe", "Rocket Rod" or "The Great One". Masters of the sweet spot become legends in their own time.
Is it any wonder that the term is a metaphor for the equivalent of a home run, ace, or hole-in-one even in non-athletic endeavours? If you cleverly close the big sale, you "hit the sweet spot". If you make the passionate summation that sways the jury, you have "hit the sweet spot" also. It is a matter of vision, timing, physics, luck, and magic. The luck and magic part means anyone has at least a chance to hit the long one.20
The example above indicates that western culture values the celebrity status of a talented player. The social institution of sporting competition (social patterns of quality) have as their driving component a Dynamic social counterpart - the celebrity of the skilled sportsperson. Thus, the harmony between player and artefact also includes, at least in western culture, social patterns of the culture itself. If this view is appropriate, then the sweet spot, as an event displaying coherence or coalescing of patterns within and across value levels, appears to provide an example of how value levels in the MOQ can work together and raise quality at all levels in coherence while remaining discrete.
Intellectual sweet spots.
Intellectual patterns of quality share a relationship with DQ. The intellect of humans may therefore be viewed as being primarily an aesthetic sense of SQ coherence and somewhat included in the coherence itself.
(See typical level diagram.)
The intellectual level of the MOQ may be divided into concepts by intuition and concepts by postulation, following F.S.C. Northrop.21 Concepts by postulation are built up from concepts by prior intuition. For there to be an aesthetic sense of experience, the relationship between all concepts must be in a coherent relationship with DQ.
Symbolism here is not restricted to the sound-light continuum, although many of our shared cultural symbols have emerged in this continuum.22 Smells, tastes and sensations have symbolic representations of which sweet is but one example.
The Dynamic component may be felt as the sweet spot of SQ coherence.
Thus, SQ coherence between the total repertoire and DQ may be the source of human intellectual creativity and insight. Intellectual creativity and insight is felt to emerge at the sweet spot of coherence.
Possibly, Dynamic Quality may never be experienced purely because experience is somewhat patterned and structured - even concepts by intuition have a structure. But to come as close as possible to that which dissolves and yet remain in a coherent state is to be as close to DQ as any patterns can be while still remaining viable.
It has became evident that both scientific and artistic uses of the idiom sweet spot indicate a tension between chaos and static quality. Indeed, as an accumulation of intellectual patterns within human culture, it would appear that science, with geometric and mathematical modelling taken as its tools, is human art also.
All structured intellectual methods and systems of thought may be viewed as SQ coherence - aesthetic creations in response to DQ. So, from the early manipulation of language to the creation of geometry, mathematics and truth, human intellectual evolution has been a growing aesthetic sense of quality in a DQ-SQ relationship.23
As Pirsig quotes in ZMM:
Poincaré then hypothesized
that this selection is made by what he called the "subliminal self,"
an entity that corresponds exactly with what Phædrus called preintellectual
awareness. The subliminal self, Poincaré said, looks at a large
number of solutions to a problem, but only the interesting ones break
into the domain of consciousness.
The description of beauty in terms of SQ tension has been suggested to be:
An intense coherence between static quality within and across levels. The nature of beauty depends on the levels involved and their relationship to each other.
For Poincaré and fellow mathematicians, the true aesthetic feeling, which they all know, may be described as intense coherence between their static repertoire of intuitions and postulations. Along the way, stable sweet spots may appear as eddys and swirls in the differentiated aesthetic continuum. One such mundane coherence may be our very sense of self when our thoughts maintain a stable relationship with Quality.
Such relationships appear to have evolved with the first symbolic social representations many tens of thousands of years ago.25 Symbolic representations of the other have evolved into empathic anticipations to the extent that non-verbal communication is crucial for understanding.26 Thus, in order to teach, or to learn, it is important one become coherent with the other, less social and intellectual cohesion are undermined.
Symbolic communication may also be viewed as SQ tension - that a coherent method for communicating ideas is evident from the enquiry into sweet spots. Skill in communication may also be viewed as art, whether the information is narrative or purely symbolic. As mathematicians know well, there is always more than one way to prove a theorem27 — but there may also be a best way, which is a strange thought in the field of pure abstraction — a thought that becomes coherent when one views mathematics as an aesthetic appreciation within SQ tension.
Thus, the best way exhibits coherence between SQ patterns. Such tension may exhibit, paradoxically, the dissolution of self, as patterns become more coherent. Instead of the self, the MOQ places Dynamic Quality at its centre. Therefore, as intellectual art, the MOQ values intense coherence. Even intellectual manipulation may be transcended at the sweet spot, as stated in Zen in the Art of Archery.28 SQ tension at this point may be explained by the exceptional nature of the coherence of this relationship.
I am delighted to report that I found the "sweet spot" at centerstage of the Recital Hall last Friday night (November 7, 1997). As we were checking microphone placement for Susannah Murray's senior recital, I noticed a spot where the onstage sound was unusually clear and focused. A bit of quick experimentation showed that the sound was well focused from the listener's perspective in the house as well. The spot, 40.5 inches upstage from the lip of the main stage section, was marked by the backstage crew with gaffer's tape and we asked Susannah to sing from that mark for her pre-show warm-ups. The overall sound was clear and true, with the piano clean and focused. This proved to be true listening from the recording studio, too, and we obtained a fine recording that evening when she sang her recital from that mark. Both the accompanying lute and piano were clear and distinct, and several people, including at least two music faculties, commented backstage on what an unusually good sound there was in the house for the performance.
After the show, I did some further experimenting in the Recital Hall and found that raising or lowering the canopy does not affect the location of the "sweet spot," and there is a secondary sweet spot about 10 feet upstage from the first spot (roughly 12.5 feet from the stage back wall). We found that singing, speech, and whispering were all clearest from everywhere in the house when the sound originated from the sweet spot, but tended to lose focus and become more diffuse as the speaker moved away from the spot. This held true regardless of the canopy setting.
(The canopy begins to dominate the onstage sound when it is lowered to the first marker, but the "sweet spot" is still best for the house).
Maybe we should put a small brass star in that spot on the stage?29
The discovery made in the above example is announced with some pleasure.
The relationship between performer and audience in a recital hall is best at the sweet spot. Note that the sweet spot provides a good relationship for much of the house and not just a lucky few that may happen to attend a particularly good position in the audience. The relationship is good for the performer and for the audience as a whole. (A similar sweet spot is found in hi-fi and home cinema speaker placement.)
A feel for the sweet spot of this recital hall enables a Brass star indicator to maintain successively high quality performances. It may be worth noting that the relationship between audience and performer involves a building resonance or coherence in which a good performer/audience can evolve in response to an initial social sweet spot. The confidence of a performer may be enhanced at the stage sweet spot thus influencing audience appreciation of the quality performance, which in turn boosts confidence and raises the quality of the performer into further coherence. All patterns are involved in the coherence.30
Comedy and tragedy may also form a sweet spot. Both can be unpredictable and surprising. Both appear in the best comedy as two aspects of one social continuum. In fact, much tragedy can be viewed as dark humour as in Alan Bleasdale’s Boys from the Blackstuff.
Another example of the interplay between tragedy and comedy is the work of Stan Laurel. Laurel was adept at producing work of impeccable timing, which consistently produced dense sequences of laughter during audience observations. Seen as art, displaying a DQ sweet spot, Laurel was able to create subtle social interplay. The sweet spot is maintained with such consummate ease that audience resonates in a tension between sympathetic response (tragedy) and laughter (comedy).
The tension in Laurel’s work is also provided by the relationship between two individuals — himself and Oliver Hardy. There are myriad subtle contrasts between them, balancing expectation and incongruity: Hardy is a scruffy deep Southern aristocrat — simple unsophisticated Laurel outwits him. Beyond this, the audience of the theatre resonates in a coherent relationship — time and self disappear in laughter and a high quality social sweet spot is discovered and maintained in the ritual of play and theatre.
Powerful social forces are at work in comedy and tragedy and the work of masters such as Laurel and Hardy may provide insights into how they shape the mirrors that reflect celebrity status.31 In China, for example, they were felt to be reflections of China’s social structure.32 The relationship between the individual and the social order is a tension found in comedy.33
The elusive timing that great comedians use may have a simple explanation in the social and intellectual levels of the MOQ — good comedic timing is an art of the Dynamic. In one observed audience response to a Laurel and Hardy sequence in which a gouty foot is hit seven times within a short scene, the following comment was made:
“Now this overdone or come tardy off…” said Hamlet, “cannot but make the judicious grieve.” These are the exact pitfalls avoided by Stan Laurel in this action. The hitting of the gouty foot is never overdone; it is made on each occasion to seem a natural accident. They are spaced by means of good editing so that one is not expecting them and when they come, they are the result of purely natural movement. Nor are the “come tardy off.” They come when they should come, and this is determined in the cutting room.34
Determining when to act and when to hold back has been suggested as one of the early motivations for the evolution of intelligence.35 Such timing appears to be a biological/social sweet spot.
Music displays ratio, proportion, harmony, and many instances of sweet spots. Modern scientific modelling of physical systems borrows the aesthetic of music when analysing sweet spots in sport and engineering. The rational methodology is primarily aesthetic — an appreciation of relationship between symbols and Dynamic Quality.
Modern jazz provides an example of this. An ability to improvise is essential in jazz soloing, but this leads to the question of whether a soloist ever does actually improvise, or whether a repertoire of musical phrases is drawn upon as springboards into new combinations?
J.S. Bach utilised the value of improvisation in his teaching,36 and improvisation was a method of composition in his day. Was this a matter of rearranging already familiar and used phrases?
MOQ coherence suggests a Dynamic movement towards variety with a corresponding potential for increased intensity of coherence. The jazz soloist is trying to escape the sum total of his/her repertoire, and does so by discovering a more intense aesthetic coherence.37
The relationship between musician and instrument is also a product of Quality.
Instruments may be analysed and manufactured but the musician can feel the quality relationship and express it in terms of sweet spots:
Almost every chanter I have used has had a flat B, with no way to get up to the sweet spot without conducting some carving (for which I have lacked either the necessary permission or the intestinal fortitude). So I guess my B is usually floating around somewhere slightly into the lower rough zone. This appears to be the case also for several of the "Great Eight" from the Piping Centre 1996 Recital CDs.38
A chanter is the pipe on a set of bagpipes that plays the melody. In the above example, a barrier to achieving a sweet spot has been identified in the construction of a chanter. Although crafting skills can model the chanter to a certain point, the chanter and player form a relationship which is beyond the tools of modelling. This means that, in practice, experience is of primary importance and suggests that the evolution of this instrument is the result of a relationship between it and the player.
Moreover, some musicians virtually invent their own instruments. For example, Roland Kirk used a type of saxophone that no one else appears to have been familiar with. However, these patterns of his unique instrument formed a relationship with his intellectual, social and organic patterns that made him a master performer — Kirk developed a style of playing two saxophones simultaneously in harmonic unity.39
In the above examples, the sweet spot involves a degree of dissolution of self. However, the sweet spot is can be maintained with ease but also lost with over-analysis. In the work of great authors, language itself can become a thing of outstanding beauty and coherence. The art of rhetoric has a high intellectual component, and may be said to require an aesthetic sense of SQ tension. The work is orchestrated and flows with its own structure. However, creativity may be reduced by too much reliance on static methods. As with the jazz soloist who abandons static limitations, the author must also be free to express feeling and thought on the basis of Quality rather than method.
The jazz pianist and business innovator, John Kao also notes that business organisations are learning to use improvisation or ‘jamming’ to stimulate creativity and innovation.40
Jazz is never the absence
of structure, it's just relative balance between structure and freedom
-- unlike playing classical music, which is just playing the notes as
they're written. There's a rich vein to be mined in terms of what "jamming"
offers as a skill that organizations can practice to create innovation.
That having been said, if I looked at the kind of critical mass of resources
that are required for organizations to take a meaningful cut at innovation,
I immediately turn to the factory metaphor, because the factories are
where processes and know-how and people and resources and knowledge about
the environment are all integrated. And so you have a kind of critical
mass of ingredients that leads to an ability to innovate.41
That industry can be artistic should be recognised. But any art that threatens the welfare of the environment should be questioned on the basis of higher levels of harmony than is perhaps often neglected. If industrial processes crush environmental freedom, then there may be a corresponding limitation in the freedom for individuals to live creative lives.
Social and intellectual patterns continue to evolve to include older patterns thus suggesting an obvious non-anthropic view of Quality - Quality is the source of patterns generated before humans evolved, and continues to be the source of patterns which continue to incorporate humans.
Thus, there should be evidence for sweet spots irrespective of human relationships. Such coherence appears evident in inorganic patterns and non-human biological patterns. Non-human social patterns are also evident in other species.
The sweet spot is an idiom of common language. In the language of the MOQ, a sweet spot may be described as a tension between SQ patterns that produce DQ. The Zen Master uses archery as a means to achieve DQ. The MOQ indicates why this would be a natural use for archery, as the archer must balance his loosing of the shot at a very fine point.
However, there appears to be differences in the intensity of coherence. Perhaps the sportsperson is a pale shadow of the Zen Master’s journey as the primary goal of the sportsperson is very often distorted by social and biological imperatives.42
Of course, it may be the case that the Zen Master spoken of in Zen in the Art of Archery was in fact misunderstood when he expounded his views to Eugen Herrigel.43 Rather than any ‘it shoots’ doctrine it may simply that the Master was voicing approval of a shot well made. On the whole, however, it does appear that the Japanese tradition of inventing and adapting new art forms was the basis for using archery as explained in Herrigel’s book. Moreover, in Japan, one does not simply find the sweet spot just in the practice of art. As noted in the narrative of Duke Wen Hui’s cook at the beginning of this essay, even a butcher can become an artist:
To see the butcher slap the steak, before he laid it on the block, and give his knife a sharpening, was to forget breakfast instantly. It was agreeable, too — it really was — to see him cut it off, so smooth and juicy. There was nothing savage in the act, although the knife was large and keen; it was a piece of art, high art; there was delicacy of touch, clearness of tone, skilful handling of the subject, fine shading. It was the triumph of mind over matter; quite.44
The nature of the sweet spot is such that patterns may be said to resonate in a unique way with DQ in which our patterns are included in the coherence. We may experience high intensity wonder and joy. Intense coherence may be termed beautiful while very high coherence may approach mystic experience. Such may be enlightenment — an exceptional sweet spot between SQ patterns.
Finally, note this quote from LILA:
Good is a noun. That was it. That was what Phaedrus had been looking for. That was the homer, over the fence that ended the ball game. Good as a noun rather than an adjective is all the Metaphysics of Quality is about. Of course, the ultimate Quality isn’t a noun or an adjective or anything else definable, but if you had to reduce the whole Metaphysics of Quality to a single sentence, that would be it.45
Pirsig’s use of the baseball analogy in the above quote indicates that at the end of LILA he has discovered how to maintain a life sweet spot: he is free from karmic friction. When all is said and done, the good life of the MOQ is about freedom, floating between chaos and stagnation, at the sweet spot.46
Clifford Bartlett (1989). Inner sleeve booklet notes to Peter Hurford’s compact disc Playing Organs of Bach’s Time Vol. One.
Susan Blackmore (2000). The Meme Machine. Oxford University Press.
Charles Dickens (1843-44). Martin Chuzzlewit. 1987 Illustrated Oxford Dickens Edition.
Ronaldo Di Santo & Thomas Steele (1990). Guidebook to Zen & the Art of Motorcycle Maintenance. William Morrow & Co.
Ted Gioia (1997). The History of Jazz. Oxford University Press Inc.
Jan Gullberg (1997). Mathematics: from the Birth of Numbers. W.W. Norton.
Eugene Herrigel (1938). Zen in the Art of Archery. 1985 Arkana reprint.
John McCabe (1966). Mr. Laurel and Mr. Hardy: An Affectionate Biography. 1968 New American Library Signet reprint.
F.S.C. Northrop (1946). The Meeting of East and West. 1979 Ox Bow Press reprint.
F.S.C. Northrop (1947). The Logic of the Sciences & the Humanities. Macmillan.
Robert M. Pirsig (1974). Zen and the Art of Motorcycle Maintenance: An Inquiry into Values. 1991 Vintage paperback.
Robert M. Pirsig (1991). LILA: An Inquiry into Morals. Bantam Press..
Robert M. Pirsig (1995). Subjects, Objects, Data and Values. Paper given at the ‘Einstein meets Magritte’ conference at Brussels, June 1995.
James N. Powell (1982). The Tao of Symbols. Quill.
John Skoyles & Dorian Sagan (2002). Up from Dragons: The Evolution of Human Intelligence. McGraw-Hill Education.
Peter Hurford (1989). Playing Organs of Bach’s Time Vol. One. 1993 EMI Eminence edition 7243 5 65028 2 6.
At mid-price, and with excellent recorded sound (DDD) and ambiance, this recording is a real bargain. Peter Hurford plays with his customary clarity and vitality. The high-lights for me are the Toccata & Fugue in d, BWV 565 (despite the fact that it is probably the most-recorded organ composition, Peter Hurford's rendition sounds fresh and attractive), and the Passacaglia & Fugue in c, BWV 582 (the organ's wonderful sounds together with Peter Hurford's monumental, but never overbearing, playing make this an "awesome"listening experience).
Willem Van Galen, March 15th 1996, (http://www.jsbach.org/peter.html).
Roland Kirk with Jack McDuff (1961). Kirk’s Work. 1991 Fantasy/Original Jazz Classics edition OJCD20 459-2 1961.
Roland Kirk, the amazing one-man saxophone section and sublime soloist, had yet to add Rahsaan"to his name when he recorded his first album for Prestige in 1961. It wasn't yet quite clear to many, even people at the center of the jazz community, that Kirk's gifts went considerably beyond the ability to play three horns at once. Gradually, it began to dawn on one and all that the man's almost superhuman energy and dedication were matched by musicianship based as firmly in tradition as in innovation. Eventually, it became possible to accept as parts of Kirk's kaleidoscopic expression those odd instruments the manzello and the strich, not to mention the nose flute and kirkbam that he added later. And what a tenor saxophonist. Kirk's Work is a milestone in the brief, brilliant career of a major artist. It was recorded with Joe Benjamin and Arthur Taylor.”
I should like to thank Anthony McWatt for help in the writing and organization of this paper including access to his Ph.D. work in progress. I also wish to thank Stephen Clark for using standing waves to illustrate the Plotinian continuum between matter and the One and his use of The Master Butcher and Both Ox and Self Forgotten47 in relation to Plato and language. Also, many thanks to the friends I met in the MOQ.org — especially Platt Holden for emphasising ethics and art (many thanks Platt), Khoo Hock Aun for introducing me to The Tao of Symbols, and to Paul J Turner for providing relevant supporting quotes and arguments. I wish to thank Dawn White for being a patient listener, a probing questioner, and for making me realise what is important. I apologise to Horse for being an ignored uncarved block every year is the year of the Horse! Above all, Robert Pirsig must be thanked for the journey.
2 “Phaedrus saw that not only a man recovering from a heart attack but also a baby gazes at his hand with mystic wonder and delight.” (Pirsig, 1991, p. 122)
3 Pirsig (1995).
4 Northrop (1946, p. 450).
5 Herrigel (1938, p. 73). See also note 46.
6 “That is why we think of subjects and objects as primary. We can’t remember that period of our lives when they were anything else.” (Pirsig, 1991, p. 123)
7 “Finally, there’s a fourth Dynamic morality which isn’t a code. He supposed you could call it a ‘code of Art’ or something like that, but art is usually thought of as such a frill that that title undercuts its importance.” (Ibid. p. 167)
8 Herrigel (1938, p. 47).
10 “They all operate at the same time and in ways that are almost independent of each other.” (Pirsig, 1991, p. 153)
12 “In the middle is a sort of grey area, where the materials needed to construct an arch (for instance) would be about equal to the expense of the cabling needed for a suspension design. This is the "sweet spot" for the cable-stayed bridge, which reduces the cabling and the materials.” (http://www.wikipedia.org/wiki/Sweet_spot)
14 “If he excites her sense of Quality she joins him to perpetuate him into another generation, and he lives on.” (Pirsig, 1991, p. 205)
17 “The New Deal was many things, but at the centre of it all was the belief that intellectual planning by the Government was necessary for society to regain its health.” (Pirsig, 1991, p. 278)
19 “Reith's vision was of an independent British broadcaster able to educate, inform and entertain the whole nation, free from political interference and commercial pressure.” (http://www.bbc.co.uk/thenandnow/history/1920s-1.shtml)
21 Northrop (1947).
22 Powell (1982, p. 167).
23 “Genuine mathematics, then, its methods and its concepts, by contrast with soulless calculations, constitutes one of the finest expressions of the Human spirit…”
“Progress is very often made with no reference to the real world, but in response to what might be called the mathematician’s apprehension of the natural dynamic of mathematics itself…”
“One can apply mathematics to solve problems in physics — but it is difficult (though not perhaps absolutely impossible) to conceive of applying physics to solve problems in mathematics.” (Gullberg, 1997, p. xxi)
24 Pirsig (1974, Ch. 28).
25 “Symbols liberated the brain.” (Skoyles & Sagan, 2002, p.206)
26 “Mirror neurons — are activated when we see actions done by others.” (Ibid. p. 252)
27 “There is often more than one way to find an answer or a proof — your approach may be as good as the one in the text.” (Gullberg, 1997, p. xxiii)
28 “If everything depends on the archer’s becoming purposeless and effacing himself in the event, then its outward realisation must occur automatically, in no further need of the controlling or reflecting intelligence.” (Herrigel, 1938, p. 57)
30 Personal note: Upon telling an actor friend of mine about this theatre sweet spot, the actor laughed loudly and said he knew about it. He added that if all stage sweet spots could be indicated with a Brass star then every actor on stage would move towards it!
31 “What exactly is the mechanism by which the culture controls the shapes of the mirrors that produce all these different images of celebrity? Would analysis of that mirror changing force enable the resolution of ethnic conflicts?” (Pirsig, 1991, p. 262)
32 “An English businessman told Stan Laurel some years ago that in an obscure village in China’s heartland , placed prominently in the prayer room of a large house in the midst of the household deities on the alter, rests a picture of Laurel and Hardy. They are worshiped by the villagers as a symbol of China: the fat, all-knowing, well-fed mandarin side by side with the humble, ever-patient, underfed peasant who bears the burden of life with simple and happy placidity.” (McCabe, 1966, p.65)
33 “They are so opposite. You see, that’s why Chaplin always used big men opposite him, like in The Gold Rush. Chaplin is the real law — the little man, the average man — against the big man, the brute force of authority, the unreal law. David and Goliath — and this is a law of the theatre — the law of contrast. Laurel and Hardy knew and they lived it and acted it beautifully on the screen. And they had comedy of character as well as comedy of contrast. They are very endearing men. They are very noble men because there is no evil or thought of evil in them. I can see this in them personally, too. Stan Laurel is personally a good man, and most charming, and simple in the best in the best sense of that word. And I am told that babe Hardy was the same kind of man. Now, all these things I have told you are things that great comedians need but they also need something else and that is control. That is why they are great in mime, because they know how to get a very simple effect by a very simple movement of the body.” Marcel Marceau quoted in McCabe (1966, p. 138).
34 Stan Laurel supervised his own editing because he knew what he wanted. (Ibid. p. 108)
35 Machiavellian neurons. (Skoyles & Sagan, 2002, Ch. 7)
36 “No one has ever tried out organs so severely and yet so honestly as he. He understood the whole art of organ building in the highest degree… Nor had anyone understood organ registration so well. Organists were often terrified when he played their instruments and drew the stops in his own style, for they could not imagine that what he intended would work. But when they actually heard it, the effect astonished them. This knowledge died with him.”
“Bach’s reputation was secure as the leading organist of his time in the land where organ music had achieved a richness and power unknown elsewhere. Composers such as Buxtehude had produced a fine repertoire of substantial, non-liturgical works (generally called Praeludia) contrasting quasi-improvisational brilliance with through-composed sections and fugues.” (Bartlett, 1989)
37 “But this was much more than an expansion of the techniques of jazz improvisation. In establishing a new aesthetics for jazz, (Lester) Young also broadened the music’s emotional vocabulary, broaching an intimacy and subtle gradations of feeling hitherto unknown to the jazz idiom.” (Gioia, 1997, p. 167)
39 “A stellar soloist, he could play with authenticity and forcefulness in any jazz style, from trad to free, and on a host of instruments — not just conventional saxes and clarinets but pawnshop oddities such as manzello, stritch, siren whistle, and nose flute. Kirk’s arsenal of effects was seemingly endless, ranging from circular breathing to playing three horns at once. (Gioia, 1997, p. 329). For an example of Roland Kirk playing, listen to Kirk’s Work.
40 Associated for many years with the business schools of Harvard and Stanford, John Kao is an author, management professor, creativity expert, jazz pianist, Yale doctorate, psychiatrist, former keyboardist for Frank Zappa, entrepreneur, venture capitalist, film and theatrical producer, founder and head of the Idea Factory. (http://www.acm.org/ubiquity/interviews/j_kao_1.html)
41 From an article titled “Searching for the Sweet Spot” from the on-line IT magazine “Ubiquity” (http://www.acm.org/ubiquity/interviews/j_kao_1.html)
42 “The teacher foresees this danger. Carefully and with the adroitness of a psychopomp he seeks to head the pupil off in time and to detach him from himself.” (Herrigel, 1938, p. 64)
44 Not from the Master Butcher poem but Charles Dickens (1843-44, p. 601).
45 Pirsig (1991, p. 418).
46 “American Indians are exceptionally skilled at holding to the ever-changing centre of things.” (Ibid. p. 123)
47 Di Santo & Steele (1990, p. 38).