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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 ]
.

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
  • 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.

    On the felicities of graph-based game-board design: fourteen

    Tuesday, December 25th, 2018

    [ by Charles Cameron — this one, on sacrament, symbol and such, winds up being an intro to #15, not yet written ]
    .

    My last post On the felicities of graph-based game-board design drew forth a stunning tweeted response from JustKnecht, friend and fellow explorer or Hesse’s Glass Bead Game and the magic of ideas behind it:

    **

    That’s a fascinating graphical DoubleQuote, at first glance, so I dug into the two images, the left hand one coming from a Sembl post of mine in this series, On the felicities of graph-based game-board design: two dazzlers.

    It’s the one on the right, however, that opened doors for me — one door being the article by Gentner and Jeziorski, the other being Richard Boyd‘s article that follows it in Andrew Ortony (ed), Metaphor and Thought, 2nd ed, CUP (1993):

  • Gentner & Jeziorski, The shift from metaphor to analogy in Western science
  • Richard Boyd, Metaphor and Theory Change: What is ‘Metaphor’ a Metaphor for?
  • Notice, incidentally, the beautiful ouroboros in Boyd‘s title!

    Okay, that’s my Christmas reading.

    **

    It seems I’m way behind, and it’s time maybe for the HipBone Games to enter the slipstream of Philosophy as she is practiced these days.

    But first, and to put the good folks of Elizabeth Anscombe‘s discipline off the scent, there’s the question of Sacrament to consider. Sacrament, along with Entropy, is something Gregory Bateson instructed his medical students to comprehend if they are to be civilized in their discourse as future doctors and psychiatrists. In the first paragraph of the Introduction to his Mind and Nature, Bateson writes:

    Even grown-up persons with children of their own cannot give a reasonable account of concepts such as entropy, sacrament, syntax, number, quantity, pattern, linear relation, name, class, relevance, energy, redundancy, force, probability, parts, whole, information, tautology, homology, mass (either Newtonian or Christian), explanation, description, rule of dimensions, logical type, metaphor, topology, and so on. What are butterflies? What are starfish? What are beauty and ugliness?

    Note that the concept of “sacrament” occupies a place of honor second only to “entropy” in Bateson’s listing.

    **

    Sacrament?

    Sacrament?What does that have to do with the philosophy (and graphical rendering) of metaphor?

    First, here’s a quick look at the notion of Sacrament, from the Introduction: Mapping Theologies of Sacraments (pp. 1-12) of Justin Holcomb and David Johnson’s Christian Theologies of the Sacraments: A Comparative Introduction:

    In the prologue of the Gospel According to John the apostle writes about the incarnation of the Word of God, Jesus Christ, that “from his fullness we have all received, grace upon grace” (1:16). One of the means by which Christians believe we receive the grace of God in Christ is the sacraments. But what are the sacraments? As many Christians know, Augustine of Hippo succinctly defined a sacrament as being “an outward and visible sign of an inward and invisible grace.”

    The central sacrament of Christianity is the Eucharist, instituted by Christ with the words — pointing to the bread about to be broken and shared, in a complex that includes his coming crucifixion, and the institution of the Church as his continuing body or presence on earth — This is my Body.

    The Catholic view:

    The doctrine that Christ’s real presence is thus to be found in the communion wafer consecrated with the remembrance of those words at Mass is that of Transubstantiation — a contested doctrine to be sure. And the contest is viewed theologically as being between metaphor and simile.

    Thus, as I have noted before, Northrop Frye in his Anatomy of Criticism writes:

    The animal and vegetable worlds are identified with each other, and with the divine and human worlds as well, in the Christian doctrine of transubstantiation, in which the essential human forms of the vegetable world, food and drink, the harvest and the vintage, the bread and the wine, are the body and blood of the Lamb who is also Man and God, and in whose body we exist as in a city or temple. Here again the orthodox doctrine insists on metaphor as against simile, and here again the conception of substance illustrates the struggles of logic to digest the metaphor.

    The Reformed view:

    Simply put, the Reformed view, contra Frye, considers the Words of Institution as simile, see Literary Devices in the scripture [Caution: this link auto-downloads a Word doc]:

    A metaphor is an abridged simile

    — ie, Matthew 26.26 is to be understood as meaning not “this is my Body” but “This is like my Body”..

    Thus Daniel Featley DD in his Transubstantiation Exploded (1638) writes:

    If in this sentence “This is my Body,” the meaning be “this Bread is my Body,” the speech cannot be proper, but must of necessity be figurative or tropical.

    But in this sentence, “This is my Body,” the meaning is, “This Bread is my Body.“

    Ergo this speech cannot be proper, but must of necessity be figurative and tropical; and if so, down falls Transubstantiation built upon it, and carnal presence built upon Transubstantiation, and the oblation and adoration of the Host built upon the carnal presence.

    That’s a whole lot of toppling of the Catholic edifice, all predicated on a reading of Christ’s words as simile, not metaphor.

    Here “simile” seems to mean figurative rather than literal — where the Catholic view, as we have seen, aka “metaphor”, posits literal real presence in the form of a (transcendent) inward and spiritual grace..

    **

    A by-gone Queen of the Sciences

    How does this theology of metaphor fare today? Theology, my own discipline at Oxford, sadly seems a by-gone Queen of the Sciences. Thus William Grassie writes:

    Our medieval ancestors understood theology to be the queen of the sciences. Her twin sister Sophia — the Greek word for “wisdom” — was also venerated in the discipline of philosophy. It was hard to tell the two beauties apart, but together they once ruled the many domains of human knowledge.

    Theology departments today, however, are increasingly irrelevant backwaters in the modern university, engaged in seemingly solipsistic debates.

    Ouch.

    Just for the record, while we’re slipping a theological understanding of metaphor into our thinking on the topic, should also consider Coleridge on symbol:

    Now an allegory is but a translation of abstract notions into a picture-language, which is itself nothing but an abstraction from objects of the senses; the principal being more worthless even than its phantom proxy, both alike unsubstantial, and the former shapeless to boot. On the other hand a symbol … is chaacterized by a translucence of the special in the individual, or of the general in the special, or of the universal in the general; above all by the translucence of the eternal through and in the temporal. It always partakes of the reality which it renders intelligible; and while it enunciates the whole, abides itself as a living part in that unity of which it is the representative.

    **

    In the spirit of Hermann Hesse‘s Nobel-winning Glass Bead Game — and if you can’t abide the arts and humanities, then of EO Wilson‘s concept of consilience — these notions of sacrament, metaphor and symbol should be entered into the philosophical and scientific thought-stream on metaphor and its graphical representation, IMO, YMMV, &c.

    In case you missed all that.

    And so to the present readings, Boyd and Gentner & Jeziorski..

    **

    **

    Earlier in this series:

  • On the felicities of graph-based game-board design: preliminaries
  • On the felicities of graph-based game-board design: two dazzlers
  • On the felicities of graph-based game-board design: three
  • On the felicities of graph-based game-board design: four
  • On the felicities of graph-based game-board design: five
  • On the felicities of graph-based game-board design: six
  • On the felicities of graph-based game-board design: seven
  • On the felicities of graph-based game-board design: eight
  • On the felicities of graph-based game-board design: nine
  • On the felicities of graph-based game-board design: ten
  • On the felicities of graph-based game-board design: eleven
  • On the felicities of graph-based game-board design: twelve
  • On the felicities of graph-based game-board design: thirteen

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