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## Archive for the ‘mathematics’ Category

### 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:

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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 —

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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:

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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?

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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:

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

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I mean:

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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:

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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..

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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
• ### 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? ]
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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.

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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.

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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 ]
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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.

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#### 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.

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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.

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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?

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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.”

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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: thirteen

Friday, December 21st, 2018

[ by Charles Cameron — the Trinity and National Security, Game Boards and Mathematics, Japanese wave patterns, Maestro Harding on the interconnectedness of “all branches of human knowledge and curiosity, not just music” — plus Blues Clues at the tail end ]
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Not only have the last couple of days been riotous in Washington, with more news to track than I have eyes to see, but today, still reeling under the weight of Mattis‘ resignation, McConnell‘s statement in support and other matters, I found myself with a richesse of board-game and graph-related delights.

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Trinitarian NatSec:

Followers of this searies will be familiar with the Trinitarian diagram juxtaposed here with its equivalents from classical Kabballah and Oronce Fine:

That little triptych is from my religion and games avenues of interest, but of course I’m also interested in matters of national security, as befits Zenpundit, the strategy & creativity blog. You can imagine my surprise and delight, then, in coming across a natsec version of the trinity diagram, in a tweet from Jon Askonas.

Here’s my comparison:

My own attention was first drawn to the Trinitarian diagram as a result of reading Margaret Masterman‘s brilliant cross-disciplinary work, “Theism as a Scientific Hypothesis”, which ran in four parts in a somewhat obscure and difficult to find journal, Theoria to Theory, Vol 1, 1-4, 1966-67.

See:

• Margaret Masterman, George Boole and the Holy Trinity
• Margaret Masterman’s “Theism as a Scientific Hypothesis”
• **

Game Boards and Mathematics:

I could hardly fail to be intrigued by Calli Wright‘s piece titled The Big List of Board Games that Inspire Mathematical Thinking, eh? And look, the first game they show is a graph-based board game, Achi:

Dara also looks somewhat relevant.

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Japanese wave designs:

Again, those familiar with my games will know of my juxtaposition of Von Kármán with Van Gogh as a DoubleQuote — but let me quote from an earlier post, Sunday’s second surprise — the Van Gogh DoubleQuote:

Here’s the Von Kármán / Van Gogh DQ, which I value in light of Hermann Hesse‘s Glass Bead Game as a clear bridge between one of the crucial dualities of recent centuries — the needless and fruitless schism between the arts and sciences, which has given rise not only the rantings of Christopher Hitchens and his less elegant disciple Bill Maher, but to such other matters as the Papal condemnation and “forgiveness” 359 years later of Galileo Galilei, Charles Babbage‘s Ninth Bridgewater Treatise, Andrew White‘s A History of the Warfare of Science With Theology in ChristendomW, and CP Snow‘s The Two Cultures:

And finally, here’s an ugraded version of the other DQ of mine that seeks to bridge the arts and sciences — featuring Hokusai‘s celebrated woodblock print, The Great Wave off Kanagawa (upper panel, below) and Jakob aka nikozy92‘s fractal wave, which I’ve flipped horizontally to make its parallel with the Hokusai clearer (lower panel) — Jakob‘s is a much improved version of a fractal wave compared with the one I’d been using until today:

That brings me to the Met’s marvelous offering, to which J Scott Shipman graciously pointed me:

Here’s where you get the collection:

• Rich pickings!

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Maestro Harding and the Glass Bead Game:

Finally, I’ve been delighted today to run across a couple of vdeos of my nephew, Maestro Daniel Harding, conducting the Swedish Radio Symphony Orchestra some years back in programs exploring the interplay of mathematics and other disciplines and music:

and:

Daniel is not working the graph-based angle that my games explore, but his thinking here is pleasantly congruous with my own. His work with the SRSO has, he says in the first video here, “to do with all branches of human knowledge and curiosity, not just music — because everything is connected”.

You can’t get much closer in spirit to Hesse‘s Glass Bead Game than that!

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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
• **

BTW:

NatSec, yes, and a DoubleQUote. Too good to miss. Thanks again to John Askonas..

### Journal — Illuminatus! trilogy, QAnon!! and more..

Monday, August 20th, 2018

[ by Charles Cameron — a dayalong cabinet of curiosities, really — the essence of creativity, paradox, and America, via conspiracies this way and that, contrasts between clearances, and key Rwanda para from the NYorker ]
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Here’s a Diary — a miscellaneous catch-all for today :

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**

Robert Anton Wilson, The Illuminatus saga stumbles along:

Wilson and Shea derived much of the odder material from letters sent to Playboy magazine while they worked as the editors of its Forum.[19] The books mixed true information with imaginative fiction to engage the reader in what Wilson called “guerrilla ontology”, which he apparently referred to as “Operation Mindfuck” in Illuminatus!

Wilson and Shea mashed up the ten thousand conspiracies and facts of their times to create one fact-spattered fiction, the Illuminatus! trilogy — one from many, e pluribus unum ahem! — whereas in our own day the inventors of QAnon invoked a massive outpouring of different conspiracies within conspiracies:

In November 2017, a small-time YouTube video creator and two moderators of the 4chan website, one of the most extreme message boards on the internet, banded together and plucked out of obscurity an anonymous and cryptic post from the many conspiracy theories that populated the website’s message board.

Over the next several months, they would create videos, a Reddit community, a business and an entire mythology based off the 4chan posts of “Q,” the pseudonym of a person claiming to be a high-ranking military officer. The theory they espoused would become Qanon, and it would eventually make its way from those message boards to national media stories and the rallies of President Donald Trump.

From many, one, and from one, many — Pythagorean sacred mathematics, America, expansive and synthetic thinkjing, the origins of paradox, essence of creativity — between one and many, it’s all there..

**

Quick thought:’

We’ve seen Jared Kushner having his clearance restored, and John Brennan having his clearance withdrawn, but just fr the record, they bear considering in tandem, DoubleQuote style.. Right here I’m making the connection.

**

Rwanda:

Key NYorker para on Rwandan warning to Kofi Annan, upon whom be the peace, requiescat in pace, a reminder:

Annan then wrote, “We do not recall any specific reports from Kigali to this effect.” A review of the peacekeeping files, he wrote, had turned up only four cables from Kigali in the months preceding the genocide that mentioned “ethnic tensions as being possibly related—or not related—to specific incidents of violence.”

But, in reality, one of the four cables Annan listed consisted of an alarmingly specific report of preparations for the genocide, sent by his force commander in Kigali, the Canadian General Romeo Dallaire, in January of 1994. Dallaire had heard from a trusted informant on the payroll of Rwanda’s ruling party, who described plans to “provoke a civil war,” and to kill Belgian peacekeepers in order to scuttle the U.N. mission. The informant himself said he was involved in drawing up lists of Tutsis in Kigali, and Dallaire wrote, “He suspects it is for their extermination. Example he gave was that in twenty minutes his personnel could kill up to a thousand Tutsis.” Dallaire asked for permission to act on this information by raiding and seizing illegal arms caches. Annan’s office replied at once, in a cable under his name, and signed by his deputy, telling Dallaire not to act but, rather, to follow diplomatic protocol and share his information with Rwanda’s President—the head of the party that Dallaire wanted to act against. Three months later, in April of 1994, everything that Dallaire described in his warning took place, and in the course of a hundred days around a million Tutsis were massacred.

**

Ordinary:

Lovely prose, extraordinary normalcy in the New Yorker, Hearing Aretha Franklin’s “I Say a Little Prayer” in the Soviet Union

I was gazing ahead, out the half-shaded window, sitting in the diffuse circle of warm light from a tall floor lamp to the left of me, with my elbows propped on the table and my head resting in the palms of my hands, in front of a half-empty bottle of an acrid, half-dry Bulgarian red called The Evening Bells and a white faience teacup with a chipped rim. In the boreal darkness outside, there was nothing for me to perceive but an irregular checkered pattern of blue- and yellow-lit windows in the apartment building across the way.

Beyond those windows, perfectly and naturally unaware of my existence, ordinary Soviet citizens like me silently lived their ordinary human lives: hugging or ignoring one another, standing still in their kitchens in tank tops and nightgowns and saying something silently to someone unseen, flinging angry words at one another, gesticulating broadly and opening and closing their mouths, drinking tea, eating something greasy from an aluminum pan on the stove, or just staring into the night’s emptiness with unseeing eyes, their foreheads pressed against the windowpane, a slow-burning cigarette squeezed between their pressed lips.

It is into such lives, among so many, that Aretha’s voice penetrates. Whenever we consider any of this world’s painful pasts, dire future threats, and potent presents, we should quickly run them up against all those audiences, normal and overwhelmingly influential, who may be affected.

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I’m reminded..

Okay, I saw that New Yorker piece today on the penetration of Aretha‘s voice into a bloc of Soviet flats in Leningrad, Hearing Aretha Franklin’s “I Say a Little Prayer” in the Soviet Union, and reading it, I’m reminded of the Japanese cult Aum Shinrikyo and its interest in nuclear, biological and chemical weapons.

You’ll remember they attained world notoriety after attacking the Tokyo subway system with sarin gas.. Specifically:

Aum dabbled in many different biological agents. They cultured and experimented with botulin toxin, anthrax, cholera, and Q fever. In 1993, Ashahara led a group of 16 cult doctors and nurses to Zaire, on a supposed medical mission. The actual purpose of the trip to Central Africa was to learn as much as possible about and, ideally, to bring back samples of Ebola virus. In early 1994, cult doctors were quoted on Russian radio as discussing the possibility of using Ebola as a biological weapon.

So, here’s my take:

Some journo sending an early report on the Ebola outbreak was read by someone involved in the Aum Shinrikyo chemical weapons team, who thereupon suggested a trip to Africa to Aum’s guru, Shoko Asahara. I’m sure the journo concerned wasn’t thinking that some member of a a relatively obscure Japanese cult would read their report! — but news ripples out to obscure corners of the world, Aretha‘s voice reaches Leningrad, news of an outbreak in Africa reaches Tokyo, more generally the world is porous, and these things have consequences…

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The world is porous, and there are causes and consequences…

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