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Three is a general purpose interest of embodied minds

Friday, April 5th, 2019

[ by Charles Cameron — threes in knotting, braiding, math and bell ringing — in service to governance, and the recognition of pattern within complexity ]
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One is one and all alone and ever more shall be so..
Two is both duel and duet..
and three:

**

Well, those are knots, of the Celtic variety. I cam across those images because Tony Judge pointed me to the animations in a piece he’d written, Exploring Representation of the Tao in 3D: Virtual reality clues to reconciling radical differences, global and otherwise?

which gets me thinking about thinking in threes —

— which has been an interest of mine for some time, see below —

**

And as is always the case with Judge‘s offerings, a plethora of his links called to me, and I wound up taking a look at his paper, Governance as “juggling” — Juggling as “governance”: Dynamics of braiding incommensurable insights for sustainable governance

— incommensurable insights is another topic of considerable interest to me —

— and that in turn brought me to this illustration of two instances of triple thinking about incommensurables from Australia — a triple helix and braiding:

**

Which brings us in turn to Borromean Rings and Knots:

Now the question to consider with each and all of these illustrations of threeness is whether they trigger any thoughts about the juggling and hopefully braiding and balancing of incommensurable forces in governance.. okay?

**

You’ll have noted that the braiding illustration from the Australian double illustration above is a representation of a juggling pattern. Wikimedia has dozens of such patterns with various numbers of balls, heights to which they are lobbed, &c, — and they’re fascinatingly eye-catching — mesmerizing, in fact.

Take a look at just three of them:

Juggling trick 3b box3BallBurkesBarrage3-ball Mills mess

Selection of animations of 3-ball juggling patterns by one juggler
(derived from juggling patterns in Wikipedia)

**

I mean:

**

Wow, and okay:

Now if a pattern of juggling can be represented as a pattern of braiding, we have a comparable situation to Ada Countess of Lovelace‘s brilliant cross-disciplinary leap of insight that the logical patterns Charles Babbage used to program for his proto-computing Analytical Engine could be represented in the punched cards used by Jacquard looms in the production of patterned fabrics:

  • James Essinger, Jacquard’s Web
  • **

    Am I — is Tony Judge — are we — out on a limb?

    Judge offers documentation of the mathematical side of things here:

    As indicated by Burkard Polster (The Mathematics of Juggling [excerpt], Monash University, 2003), the diagram above-right shows what the trajectories of juggling the basic 3-ball pattern look like (viewed from above). The three trajectories form the most basic braid. Braids are recognized as important mathematical objects. It has been shown that every braid can be juggled in that sense (Polster, 2003; Matthew Macauley, Braids and Juggling Patterns, 2003; Satyan Devadoss and John Mugno, Juggling braids and links, The Mathematical Intelligencer, 29, 2007). The implications have been further discussed separately (Potential cognitive implications of toroidal helical movement, 2016; Category juggling reframed through visualization dynamics, 2016).

    And again, let’s remember Tony Judge‘s reason for his interest in juggling and braiding in the first place:

    “juggling” is widely used as a metaphor to describe the challenge of responding to conflicting priorities in governance

    Judge has eighteen bibliographic supports for that assertion, including:

  • Trump Forced to Juggle Syria Response, Rage Over Mueller Probe (WSJ, 13 April 2018)
  • Trump juggling 75 pending lawsuits with a presidential campaign (CNBC, 27 October 2016)
  • The art of juggling political values and Trump (WaPo, 13 April 2018)
  • **

    Noting the correspondence between juggling — a circus-performer’s art — and braiding — not quite knitting, not quite knotting, and don’t those two words fit well together — an art associated with the decoration of hair and ribbons — I wondered whether there might not be a musical analog in counterpoint, and posted my inquiry on Twitter using this diagram of braiding:

    **

    I was fortunate: Change-ringing, surely very speedily responded to my inquiry:

    Change-ringing, surely

    The art of change-ringing in British churches and among hand-bell ringers is indeed the classic example of highly constrained and patterned musical counterpoint, so I happily Googled away in search of a change-ringing pattern comparable to my braiding patternc[left side, below], and came across the pattern [right side] in a page on the Cambridge Surprise Minor changes:

    Just Knecht, too, had some interesting observations & questions..

    **

    Metaphor, analogy, parallelism — these are avenues into the creative process in general, and threeness analogies and metaphors interrupt our usual binary cognitive processing in a way that enhances our capacity to comprehend complexity.

    I’m therefore offering this post to Ali Minai and Mike Sellers, in the hope that it will serve as a provocation to their already advanced thinking about systems dynamics. Tony Judge, obviously enough, it’s also a tribute to you…

    Previous posts of mine with threeness as a topic include

  • Of games III: Rock, Paper, Tank
  • Numbers by the numbers: three / pt 1
  • Spectacularly non-obvious, I: Elkus on strategy & games
  • Spectacularly non-obvious, 2: threeness games
  • Numbers by the numbers: three .. in Congress
  • Spectacular illustration of a game of three
  • Threeness games — some back-up materials
  • It’s snowing metaphoric chyrons, ignore unless interested 15

    Sunday, March 3rd, 2019

    [ by Charles Cameron — a bit of a hodge-podge, also known as an olla podrida — i hope you’ll find it tasty! ]
    .

    Headlines, no chyrons:

    You know, I think this is the first bazooka metaphor I’ve seen since I started looking:

    **

    Game, war-game and game theoretical references, as you know, are always of interest to me, but the addition of a nuclear component makes such references irresistible:

    Sample paragraph:

    As Trump sought to persuade Kim to give up his nuclear weapons, enticing his young “friend” with visions of a disarmed North Korea as an “Economic Powerhouse,” India and Pakistan were trading blows in a case study of what conflict looks like when countries successfully obtain nuclear weapons despite international opposition.

    Latest on that:

  • BBC, Abhinandan: Crowds gather for Indian pilot’s release
  • Pakistan’s Prime Minister Imran Khan said the pilot would be released as a “peace gesture” on Friday. India’s military welcomed the move.

    Ali Minai comments on FB:

    Not only the right and mature thing to do, but also a great tactical move. The Pakistan government- the PM, the opposition, and the military – have handled the situation with great skill – a benefit of “unified command and control”. Even the media in Pakistan has not gone completely nuts – though the same can’t be said for some of the Indian media. Both sides seem to have de-escalated, but it is too early to breathe a sigh of relief given Pakistan’s fragile economic state and the temptation of the electoral benefits of belligerence on the Indian side.

    **

    And then there’s this:

  • Small Wars Journal, US offers $1 million reward for information on Hamza bin Laden
  • There’s an obvious DQ there with his father’s wanted listing with a bounty on his head.

    **

    I thought this was an eye-catching description of doctrine, used as an epigraph to the UK Doctrine of War:

    I cam by it via a War on the Rocks piece, Mal Craghill‘s Thinking about thinking in the Royal Air Force, which pointed me to the UK Doctrine document. I syuspect that document may be worth a post exploring the conceptual and moral components of war (the physical component is not in my bailiwick), and in particular how the moral component and morale are related. TBD.

    **

    Back to politics, US:

  • WaPo, House Democrats exploded in recriminations

  • Fighting words, if that ain’t a contradiction in terms:

    House Democrats exploded in recriminations Thursday over moderates bucking the party, with liberal Rep. Alexandria Ocasio-Cortez threatening to put those voting with Republicans “on a list” for a primary challenge.

    In a closed-door session, a frustrated Speaker Nancy Pelosi (D-Calif.) lashed out at about two dozen moderates and pressured them to get on board. “We are either a team or we’re not, and we have to make that decision,” Pelosi said, according to two people present but not authorized to discuss the remarks publicly.

    But Ocasio-Cortez (D-N.Y.), the unquestioned media superstar of the freshman class, upped the ante, admonishing the moderates and indicating she would help liberal activists unseat them in the 2020 election.

    **

    That’s enough for now. I’ve a blizzard coming..

    Physicists playing Calvinball

    Saturday, February 23rd, 2019

    [ by Charles Cameron — wishing I was fluent in music, and might as well ad mathematics, Hebrew, Arabic, classical Persian, you know the drill, Sanskrit, Tibetan, Japanese.. and their courtly modes and rituals, and could play badminton, chess, dharma combat, go, eh? ]
    .

    Here’s a wonderful description of a game in which the rules — in this case, mathematical languages — change from move to move:

    It happens again and again that, when there are many possible descriptions of a physical situation—all making equivalent predictions, yet all wildly different in premise—one will turn out to be preferable, because it extends to an underlying reality, seeming to account for more of the universe at once. And yet this new description might, in turn, have multiple formulations—and one of those alternatives may apply even more broadly. It’s as though physicists are playing a modified telephone game in which, with each whisper, the message is translated into a different language. The languages describe different scales or domains of the same reality but aren’t always related etymologically. In this modified game, the objective isn’t—or isn’t only—to seek a bedrock equation governing reality’s smallest bits. The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.

    That’s from A Different Kind of Theory of Everything in The New Yorker, an intriguing rerad, though as a non-physicist, seeing an equivalence with Calvinball — a game in which the game in play constantly changes — is about as far as I can go.

    When I was talking with Ali Minai, I said that both music and math were languages I didn’t speak, and that cut me off from much by way of discourse with mathematicians (Ali himself) and musicians (my nephew the conductor Daniel Harding), and Ali commented that music is at least an embodied abstraction, whereas math is a pure abstraction with no embodied component. I hope I’ve understood and expressed that well enough. Anyway, it was a striking comment, and not one that had ever crossed my mind, on a topic of considerable interest and real regret.

    **

    Calvinball:

    Richard Feynman would have enjoyed a Calvinball reference, methinks — but for any sober-sided physicists who don’t play bongos, here’s the philsopher Alasdair MacIntyre to much the same effect:

    Not one game is being played, but several, and, if the game metaphor may be stretched further, the problem about real life is that moving one’s knight to QB3 may always be replied to by a lob over the net.

    **

    I’d hoped to have more intriguing math or game quotes to offer here, but no luck so far, so I’m gonna post anyway.

    Remembering mathematician and Glass Bead Gamer Bob de Marrais

    Monday, February 11th, 2019

    [ by Charles Cameron — this is strictly for the record — you don’t need to read it unless — like Bob — you’re a poly-mathematician, para-biologist, meta-psychiatrist or native-born glass bead gamer ]
    .

    1984. Illustrating for Bob de Marrais‘ article on Computer Graphics,
    published in Digital Deli: The Comprehensive, User-Lovable Menu
    of Computer Lore, Culture, Lifestyles and Fancy
    , ed. Steve Ditlea.

    **

    My late friend Bob de Marrais wrote a five-part short-book-length essay, Catastrophes, Kaleidoscopes, String Quartets: Deploying the Glass Bead Game, which is so wide-ranging in its scholarship that no single journal had peers sufficient to review it, so witty, subtle, enchanting, and generally impossible that its continued existence on the web and in the time-worn hard drives of a scattering of computers has made of it a sort of samizdat — a secret publication passsed from hand to hand, or in this case memory to memory, and in this post I wish to memorialize both the essay and Bob himself.

    Here are five sips, to give you a sense of the work.

    **

    Catastrophes, Kaleidoscopes, String Quartets:

    Part I: Ministrations Concerning Silliness, or: Is “Interdisciplinary Thought” an Oxymoron?

    We seek deep concepts by silly means. Think of this, for openers at least, as a cerebral equivalent of a well-known Monty Python skit: welcome to the Ministry of Silly Thoughts. [ … ]

    Essential to easy generation of the “silliness effect” – as in the frivolous juxtaposing of Kings Arthur and Elvis in the last paragraph – is production of collisions between disparate things, which context makes us associate unexpectedly. No one not on drugs or writing late-night standup material would be likely to seek a link between the latest news from robotic interplanetary exploratory vehicles and political upheaval in the Hispanic community in the general vicinity of Miami. But when Elian Gonzales’ mom fled Castro’s regime on a flimsy makeshift boat and died at sea while getting her son to (what she thought would be his) freedom, Jay Leno noted how scientists had just discovered water on the Red Planet, “and in an unrelated story, a boat of Cuban refugees washed up on Mars this morning.”

    Aside from late-night comedic unwinding from the day’s events, there is only one other area where such juxtapositions are hunted down and put to use. (No, not dreams: that’s involuntary; and besides, many people today no longer have any.) This area is largely deemed, regardless of lip services paid, “absurd; trifling; frivolous” in academia – when not, that is, subjected to sober attempts at its production which typically display all these three aspects in spite of themselves. This is the domain of what often passes for an oxymoron in our supremely specialized research establishment: interdisciplinary thought. And this, of course, is what we’re here to talk about.

    Compare “the silliness effect .. is production of collisions between disparate things, which context makes us associate unexpectedly” with, from this morning’s diggings:

    Brecht:

    He [Darko Suvin] cites Brecht as follows: “A representation which estranges is one which allows us to recognize its subject, but at the same time make it seem unfamiliar.” This permits a new cognition of the now and creates a moment which is potentially liberating. Placing familiar objects (or subjects) in unfamiliar settings allows us to see differently. Our old and tired perceptions can thus be revitalized and transformed. — Lucy Sargisson, Fool’s Gold?: Utopianism in the Twenty-First Century

    Boulez:

    For Boulez, the challenge was to present the borrowed ideas in a new light that could lead to results far removed from the original, which had provided only a single solution. — The Gramophone

    Both quotes via JustKnecht, another Glass Bead Game-player of note, discussing his Rattlesnake Games.

    **

    Part II: Canonical Collage-oscopes, or: Claude in Jacques’ Trap? Not What It Sounds Like!

    For this section of Bob’s work, I’ll just post a snippet referencing the Catastrophe Theory of René Thom:

    Of the many, many ways to frame the two-control Cusp, the most interesting for us is the predator-prey chain, due to Thom himself. Let us frame it mythically: in the Vedic lore of pre-Hindu India, the great god Indra – the Zeus of the Aryan invaders – had (or was trapped in) a magical net. Depending on the story told, and teller’s point of view, Indra is the hunter and the hunted too. According to the mathematics of Catastrophe Theory, this is fundamental, not unusual. The theory’s creator typically focuses on the single Cusp as the basis of all richer models .. Its stable “splits and mergers” mode of yoyo-ing between the Two and the One, he tells us, is “the most fundamental regulatory process” in non­linear dynamics: not only in the abstract, but, under the guise of the “predation loop,” in the ultimate concreteness of animal feeding. At least since the emerging of the amoeba, this is, sim­ply, merging: “fundamentally, engulfing a prey into the organism” … and herein resides an enigma.

    It’s a rich broth, you see — connecting perhaps to Ali Minai‘s comment tweeted today:

    Polyphony, in an abstract sense, applies not just to human complex systems but to all complex systems. .. One of the most unappreciated facts about natural complexity is that it emerges from interaction of simpler processes, and not from some prior complexity.

    **

    Part III: Grooving on the Sly with Klein Groups

    No one knows that this tale is a part of an immense poem: myths communicate with each other by means of men and without men knowing it. … The situation which Le Cru et le cuit describes is analogous to that of musicians per­form­ing a symphony while kept incommunicado and separated from each other in time and space: each one would play his fragment as if it were the complete work. No one among them would be able to hear the concert because in order to hear it one must be outside the circle, far from the orchestra. In the case of American mythology, that concert began millennia ago, and today some few scattered and moribund communities are running through the last chords.

    That’s Octavio Paz writing on Claude Lévi-Strauss, and Bob uses it as the epigraph to section III. Just today I was writing of the various friends of mind who are making profound contributions as islands in an archipelago — and how I long for the richness that will emerge when the connections between them are strong, the transmission of ideas between them fluid..

    Further, from section III:

    Somebody calls you, you answer: “In theory, a twirl of kaleidoscopes” – why?

    If you were called to provide a summary of the first two installments preceding this, to someone who’s only just joined us, the perpetual revolution of Sir David Brewster’s famous tube should certainly be the very first image to pop from that jack-in-the-box you keep in your head. For Jacques Derrida, as we saw, lopped off this capstone of Lévi-Strauss’s extended metaphor of how the mythic mind operates: the workings of “bricolage” were like those of a kaleidoscope, as the anthropologist summed it up; but Derri­da’s demolition job didn’t so much as footnote, much less explicitly point to, this motif. [ … ]

    … Beat­les’ paean to “the girl with kaleidoscope eyes.” …

    Leary and Ralph Metzner meanwhile wrote about, and advocated, the use of low-tech kaleidoscopes, imported from the East, for inner exploration as well: I refer, of course, to mandalas. Mixing scientific and New Age styles, they managed to synthesize, in brief compass and without the “depth psychology,” the gist of what Jung’s approach toward such sacred objects (about which, more in the next installment) is taken to be by those who’d worn bell-bottoms and “love beads” while reading such things:

    [As] the mandala is a depiction of the structure of the eye, the center of the man­dala corresponds to the foveal “blind spot.” Since the “blind spot” is the exit from the eye to the visual system of the brain, by going “out” through the center, you are going in to the brain. The Yogin finds the mandala in his own body. The mandala is an instrument for transcending the world of visually perceived phenomena by first centering them and turning them inward.

    Note that Leary’s reading of the foveal blind spot is markedly at odds with Derrida’s

    **

    Part IV: Claude’s Kaleidoscope . . . and Carl’s

    As before, note that the epigraps to this section contain doors intonwhat is within:

    All the creative power that modern man pours into science and technics the man of antiquity devoted to his myths. This creative urge explains the bewildering confusion, the kaleidoscopic changes and syncretistic regroupings, the continual rejuvenation, of myths in Greek culture.

    That’s Carl Jung, in Symbols of Transformation

    Here he goes:

    For those who’ve tuned in late to this mini-series, the first episode performed a sort of sitcom set­up of the main conundrum: Derrida’s deconstruction launched itself using Lévi-Strauss’ structuralism – as epitomized in his Mr. Fixit figure of the “bricoleur” – as thrust-block . . . the irony being that the latter “failed” analytics of myth proved a harbinger of advanced mathematical toolkits whose utility in linguistic and cultural studies has been burgeoning, while the former “success story” has shown itself to be ever more hollow – intellectually, morally, and spiritually.

    In Part Deux, we blowfished the argument, treating the core event – the 1966 Johns Hopkins con­ference where Derrida struck his “deal with the Devil” – as itself a sort of myth requiring structural analy­sis, inspecting it through the lens of Derrida’s 1987 reminiscences about the postmodernist “quotation market” and his own role in fomenting it . . . and then beefed up our discussion of Lévi-Strauss’ own “canonical law of myths” with Catastrophe Theory mathematics and the tasteful injection of celebrity quotes, movie reviews, and porno­graphic movie ads to, um, “flesh out” the argument.

    Strike three, though, was where the ubiquitous form-language of the so-called “A,D,E Problem” and its lowly instancing as a new sort of Timaeus-style creation myth – based on kaleido­scopes instead of an odd lot of triangles and things whose names rhyme with Tipi Hedron[1] but don’t look half as fetching – was taken much too seriously, with the limitations in Husserl’s phenomeno­logy shame­lessly con­trasted (unfa­v­or­ably) with the concentric run-out groove at the end of the Beatles’ Sgt. Pepper album. The point being, natural­ly, that the Madhyamika Buddhism of Nagarjuna’s “full void” was allowed to under­write the super­po­si­­tion principal of quantum mechanics in spite of its looking like something Derrida liked to mutter about, while all the while all of this was subsumed in some mare’s nest of compari­sons between the struc­tures of mythical argument, their “reincarnation” in the forms of classical music, and the Glass Beads that Hermann Hesse’s Magister Ludi was known to like to play with when he thought no one was watching.

    Of course, if we’re going to keep a load like that down without providing our readers free Pepto-Bismol, it would behoove us to make the people reading this think the linchpins of the argument were some­­how intrinsic. Put another way (which is our specialty here), we could say that it’s all very nice that this “A,D,E Problem” gives us kaleidoscopes as the Meaning of Life and like that there, but wouldn’t it be so much better if we got the same basic mishmash without all the abstraction – if the kaleidoscope could legi­timately be seen as some kind of “archetype” in its own right, which “just happened” to bring in Catas­trophe-type “shock waves” into the argument without all the hand-waving … and all without losing all the rest of our baggage, once the argument has landed?

    **

    Part V: Spelling the Tree, from Aleph to Tav (While Not Forgetting to Shin)

    I didn’t even know there was a fifth part — quint-esseence? — until a couple of days ago, and am very grateful to Steven H. Cullinane for conserving all five for us.

    One of the epigraphs for this fifth section comes from Gregory Bateson, Steps to an Ecology of Mind:

    “The heart has its reasons which the reason does not at all perceive.” Among Anglo-Saxons, it is rather usual to think of the “reasons” of the heart or of the unconscious as the inchoate forces or pushes or heavings – what Freud called Trieben. To Pascal, a Frenchman, the matter was rather different, and he no doubt thought of the reasons of the heart as a body of logic or computation as precise and complex as the reasons of consciousness. (I have noticed that Anglo-Saxon anthro­po­logists sometimes misunderstand the writings of Claude Lévi-Strauss for precisely this reason. They say he emphasizes too much the intellect and ignores the “feelings.” The truth is that he assumes that the heart has precise algorithms.)

    WHat can I tell you? We haven’t delved in any detail into Bob’s mathematical work, but this section contains a footnote — a quotation that delights us with the concept of a perfectly square ship with vertical sides, and offers enough catastrophe-cusp based math to illustrate that central aspect of the whole work:

    Tim Poston and Ian Stewart, Catastrophe Theory and its Applications (Boston, London, Melbourne: Pit­man, 1978): “The commonest kind of water-going vessel which is actually built with vertical sides all the way round is a floating oil-platform. These are normally fixed to the ocean floor when on site, but they float during transport. Often they are built square. This symmetry goes through to the buoyancy locus… and the buoyancy locus is a circularly symmetric paraboloid of revolution. The metacentric locus may therefore, apparently, be found by spinning the two-dimensional case, so that the geometry of the perfectly square, vertical-sided ship is remarkably simple. From a catastrophe theory viewpoint this simplicity is thoroughly deceptive, the energy function takes the form (x2 + y2)2. This is not finitely determined … and so has infinite codimension…. Physically, this means that the apparently simple geometry of the ‘ideal’ vessel .. is violently unstable.”

    **

    Bobert de Marrais was born Nov. 30, 1948, and died April 4, 2011 in Boston, MA. His obit notes he “had a lifelong interest in history, his French heritage, music, history of science, and multidimensional algebras.” He was a remarkable polymath, profoundly loved and deeply admired by the fortunate few who knew him.

    The human voice, counterpoint, & the analysis of complex systems

    Saturday, February 9th, 2019

    [ by Charles Cameron — with Mike Sellers and Ali Minai particularly in mind, and more to come.. ]
    .

    Roomful of Teeth:

    That’s composer Caroline Shaw‘s Partita for 8 Voices, a piece she wrote for Roomful of Teeth.

    A piece she composed and wrote for them — in the remainder of this post, we’ll explore the overlap of text (writing) and music (composition) in increasing subtlety and detail..

    **

    I’m brought to make this post by a paragraph I read in a fascinating New Yorker article, Roomful of Teeth Is Revolutionizing Choral Music. Roomful of Teeth is the group whose music I first praised in Pulitzer : Lamar :: Nobel : Dylan?, and showcase again in the video clip above.

    Here’s that New Yorker para:

    The human voice is the world’s most astonishing instrument, it’s often said. It’s capable of everything from a trill to a bark to an ear-splitting scream, from growling harmonics to liquid acrobatics, lofted on the breath like a lark on an updraft. Instrument is the wrong word, really. The voice is more like a chamber ensemble: winds and strings and blaring horns, strung together end to end. It’s a pump organ, a viola, an oboe, and the bell of a trumpet, each instrument passing the sound along to the next, adding volume and overtones at every step. Throw in the percussion of the lips and tongue, and the echoing amphitheatre of the skull, and you have a full orchestra playing inside you.

    My aim in this post is to add that “full orchestra playing inside you” to that other internal polyphony of contrasting desires, identities, and emergent thoughts, and the external polyphony of all those voices with a stake in our common concerns, risk assessments and deliberations — which are constituent of our complex analytic topics.

    Done.

    **

    The rest is context…

    I’ve often talked about the notion that the analysis of complex human systems involves dealing with multiple stakeholder voices, also on occasion with the many internal voices within each individual, and suggested that music offers the clearest equivalent or analogy that humans successfully and repeatedly navigate. Specifically, the twin notions of polyphony — the sounding together of many voices — and more specifically counterpoint — the juxtaposition of conflicting voices and the possible resolution of their conflicts from dissonance to harmony in an iterative process — are clearly relevant to analytic practice, albeit drawing on a tradition that will seem wildly cross-disciplinary to many analysts.

    Relevant here is Edward Said‘s definition of counterpoint:

    In counterpoint a melody is always in the process of being repeated by one or another voice: the result is horizontal, rather than vertical, music. Any series of notes is thus capable of an infinite set of transformations, as the series (or melody or subject) is taken up first by one voice then by another, the voices always continuing to sound against, as well as with, all the others. Instead of the melody at the top being supported by a thicker harmonic mass beneath (as in largely vertical nineteenth century music), Bach’s contrapuntal music is regularly composed of several equal lines, sinuously interwoven, working themselves out according to stringent rules

    In my view , which I have repeatedly expressed, Johann Sebastian Bach, the master of contrapuntal writing, is a significant exemplar for us at this time. And if it should be argued that musical methods cannot be transposed — another musical term — to matters of verbal thought, let me say that the great Bach pianist Glenn Gould towards the end of his life made specifically contrapuntal human voice radio plays for the Canadian Broadcasting Company..

    **

    Gould’s contrapuntal mind:

    Among Gould‘s eccentricities — David Howes in Glenn Gould’s Contrapuntal Constitution calls them bi-centricities, a phrase that reminds us of Arthur Koestler‘s notion of the creative leap as the bisociation of two planes or matrices, are:

    the way he liked to have one AM and one FM station playing all the time in his apartment, one for news, the other for music; the way he could learn a score while talking on the phone; and the way he enjoyed eavesdropping on three or four conversations at the same time going on at neighbouring tables in the restaurants he haunted (Kostelanetz 1983: 127).

    We can see here that Gould‘s basic thinking is in terms of multiple voices, often contrasting, in simultaneous awareness — Gould, Howes continues, spoke of counterpoint as “an explosion of simultaneous ideas”. As Gould puts it, Howes reports, when speaking of his radio programs for human voices:

    The basis of it was that we tried to have situations arise cogently from within the framework of the program in which the two or three voices … [recorded previously in conversation with Gould, but with the latter’s voice edited out for the final version] … could be overlapped, in which they would be heard talking – simultaneously, but from different points of view – about the same subject. We also tried to treat these voices as though they belonged to characters in a play, though all the material was gained from interviews. It was documentary material, treated in a sense as drama (cited in Payzant 1982: 131).

    This, then, is Gould‘s contrapuntal radio, and we can see Gould vividly transposing conytrapuntal imagination from the musical sphere to that of the varieties of human verbalization.

    **

    As not an aside but the re-introduction of a theme previously only hinted at, here is Arthur Koestler on the conceptual or creative leap:

    **

    Okay, our concept of music must shift, change, expand, if we are to consider Gould‘s Idea of North as a musical composition — in ways that are consistent with my own development of contrapuntal analysis. As Anthony Cushing explains in Glenn Gould and ‘Opus 2’: An outline for a musical understanding of contrapuntal radio with respect to The Idea of North:

    A musical understanding of North requires re-thinking some traditional elements of music theory: harmony must take into consideration semantic content and shifting topic areas; form follows somewhat traditional musical structures (ternary, binary, etc.); and texture encompasses layering of literal voices and dispenses with traditional notions of melody. One must also consider the spatial component of tape composition, in which voices inhabit locations in a sound field. The later documentaries in the trilogy and the Leopold Stokowski and Pablo Casals tribute radio documentaries contribute to a more complete musical concept of contrapuntal radio — complex polyphonic textures, stereo sound, pitch-based harmonic content — the germ of contrapuntal radio was developed and actualized in North.

    I’d like to take that lead, given us by the masterful pianist Glenn Gould, across into the field of analytic understanding — as a stream of analysis complementary and in counterpoint (for instance) to “big data” analytic tools — contrapuntal analysis characteristically working with a few, humanly-selected verbal utterances rather than data-points algorithmically-selected in the millions.

    **

    Moving to a larger geopolitical canvas, Edward Said once told an interviewer:

    When you think about it, when you think about Jew and Palestinian not separately, but as part of a symphony, there is something magnificently imposing about it. A very rich, also very tragic, also in many ways desperate history of extremes – opposites in the Hegelian sense – that is yet to receive its due. So what you are faced with is a kind of sublime grandeur of a series of tragedies, of losses, of sacrifices, of pain that would take the brain of a Bach to figure out. It would require the imagination of someone like Edmund Burke to fathom.

    We see here the invocation of Bach in a context of geopolitical analysis — one paragraph in the life-work of Said, who was a music critic as well as a well-known Palestinian-American public intellectual.

    That single paragraph — and Gould‘s clear understanding that contrapuntal thinking can be applied to the polyphony of human voices, not just in the musical sphere — prompts me to go further, and assert that complexity studies with application to the human condition and intelligence and geopolitical analysis will all, sooner or later, arrive at the practice of contrapuntal thinking as basic to their deeper purposes.

    **

    Refocusing at the national level, on Glenn Gould‘s native Canada:

    I’ve mentioned the simultaneity of voices in social contexts such as listening, hearing and understanding the views and voices of multiple stakeholder. In similar vein, Howes suggests Gould‘s own taste for counterpoint stems from and reflects the Canadian Constitution:

    Gould understood music to provide a model of society, and the performing artist, hence, to be performing society, as well as music. Along these lines, counterpoint, Gould’s preferred musical style, provides a specially apt model for comprehending the constitutional structure of the Canadian state. Gould’s interest in keeping the different voices of a fugue distinct, equal, and bound together parallels the concern of the Canadian state to keep the different parties to Confederation distinct, equal and bound together. In this difficult task, however, there is always a risk of overemphasizing or losing one of the voices. If Quebec is proclaimed “a distinct society” will that disturb the equality of the provinces (for surely all are distinct); if it is not, will that lead to the separation of Quebec and the break-up of Confederation? This bi-cultural counterpoint confronts Canadians daily, from the bilingual product information on their cereal boxes to the reports of English/French political jousting on the evening news.

    Counterpoint, or in more general terms, polyphony, is non-dialectical, for it involves the interweaving of voices, of ideas, rather than the Hegelian process of thesis-antithesis-synthesis. Polyphony as social theory does not, therefore, entail the negation of any countervailing views the way, say, a dialectical social philosophy would. With polyphony, accommodation or peaceful co-presence takes the place of negation.

    **

    Readings:

  • New Yorker, Roomful of Teeth Is Revolutionizing Choral Music
  • NY Times, The Glenn Gould Contrapuntal Radio Show
  • Open Culture, Listen to Glenn Gould’s Shockingly Experimental Radio Documentary
  • Hermitary, Glenn Gould’s The Solitude Trilogy
  • Canadian Icon, Glenn Gould’s Contrapuntal Constitution
  • Politics & Culture, An interview with Edward Said

  • Charles Cameron, Pulitzer : Lamar :: Nobel : Dylan?
  • Charles Cameron, Getting deeper into Koestler

  • Mike Sellers, Advanced Game Design: A systems Approach
  • Ali Minai, A core concern of our research is the desire to catch ‘creativity in the act.’
  • **

    More Teeth — your reward for reading this far:

    And BachGlenn Gould plays Contrapunctus IX from The Art of Fugue — on organ:


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