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[ 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

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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)

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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

[ by Charles Cameron — ternary logic is of special import because it upsets binary oppositional thinking ]
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In a recent comment, I said that to connect with my various posts on three-player games, there’s this from an episode of Designated Survivor:

transnational three-way spy trade

For the record, that’s a win-win-win strategy.

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While we’re on the subject of threeness games, there’s Brett Kavanaugh‘s explanation of Devil’s Triangle as a drinking game in his testimony:

Sen Whitehouse: Devil’s Triangle?
Judge Kavanaugh: Drinking game.
Sen Whitehouse: How’s it played?
Judge Kavanaugh: Three glasses, in a triangle..
Sen Whitehouse: And?
Judge Kavanaugh: You ever play Quarters?
Sen Whitehouse: No.
Judge Kavanaugh: It’s a Quarters game.

Here’s a more conventional explanation:

A “Devil’s Triangle” is a widely used term for an act of sexual congress between two men and a woman; but during his hearing, Brett Kavanaugh nonsensically insisted that this was some sort of drinking game.

Okay, these matters are interesting not because they deal with threeness as in friend or foe games in which temporary alliances (twos) can overcome single ones while new alliances can switch losers for winners — nor as in Konrad Lorenz‘s goose pecking order example, where a > b > c > a — but simply because threeness is involved — three players, three cups &c.

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For good measure, from MIT Tech Review, The first “social network” of brains lets three people transmit thoughts to each other’s heads:

In recent years, physicists and neuroscientists have developed an armory of tools that can sense certain kinds of thoughts and transmit information about them into other brains. That has made brain-to-brain communication a reality.

These tools include electroencephalograms (EEGs) that record electrical activity in the brain and transcranial magnetic stimulation (TMS), which can transmit information into the brain.

That — apart from the brains themselves — is the basic tech involved.

In 2015, Andrea Stocco and his colleagues at the University of Washington in Seattle used this gear to connect two people via a brain-to-brain interface. The people then played a 20 questions–type game.

An obvious next step is to allow several people to join such a conversation, and today Stocco and his colleagues announced they have achieved this using a world-first brain-to-brain network. The network, which they call BrainNet, allows a small group to play a collaborative Tetris-like game.

That’s the gaming.

And here’s the pretty diagram that allows those like myself who have only the haziest of ideas where or what the occipital cortex is to nod sagely, acknowledging that we learn something new every day..

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One isn’t, I’ve argued, even a number: one is one and all alone, and ever more shall be so. Two is the first number, standing as it does both for binary systems (duel and duet, competition and collaboration) and for many or all, as in the one and the many, or one and all..

But three — ah, three is the first differentiated number, neither two nor two plus two (aka two multiplied by two, two to its own power, two squared, four).. It stands in its own right: three.

In the number series, it offers us our first hint that there are shades of grey possible between none and one, yes and no, day and night, black and white..

Three is the tie-breaker, the umpire, balance, justice — three is the liminal number par excellence.

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And one last scrap of detail:

The proof-of-principle network connects three people: two senders and one person able to receive and transmit, all in separate rooms and unable to communicate conventionally. The group together has to solve a Tetris-like game in which a falling block has to be rotated so that it fits into a space at the bottom of the screen.

The two senders, wearing EEGs, can both see the full screen. The game is designed so the shape of the descending block fits in the bottom row either if it is rotated by 180 degrees or if it is not rotated. The senders have to decide which and broadcast the information to the third member of the group.

This is all a bit primitive thus far, but then it’s also a beginning — a window on vast possibilities.

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Zenpundit, Numbers by the numbers: three / pt 1,

Zenpundit, Spectacularly non-obvious, I: Elkus on strategy & games

Zenpundit, Spectacularly non-obvious, 2: threeness games

Zenpundit, Spectacular illustration of a game of three

& no doubt, more..

Three — watch out for it, in Hegel, in CS Peirce, in George Boole, in Clausewitz, everywhere!

[ by Charles Cameron — a third can destabilize two, but it can also ignore or deny them ]
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Here:

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I’ve written previously about ternary logic and games of three, which open up questions about alliances and trust, some of which President Trump might want to ponder next time he feels like wading into NATO or sidling up to Putin.

When the gameplay is equitable, there is no “third” — just a succession of “seconds” — or in strategic terms, repidly shifting alliances. When the “third” is a constant, at least for a while, he she or it is at times a peace-maker, at times the one to be bypassed by the other two players — andd as here, at times the one who doesn’t want to know!

Anyway, a worthy addition to my earlier posts:

Zenpundit, Spectacularly non-obvious, I: Elkus on strategy & games

Zenpundit, Spectacularly non-obvious, 2: threeness games

— and there re very likely others..