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[ by Charles Cameron — graphs and networks, life and death, quality and quantity of life, personal mortality, the (implictly immortal) trinity ].
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I was struck by these items, verbal and visual, in Numberphile‘s YouTube video, The Four Color Map Theorem. The speaker introduces a simple, four color map:

Then indicates:

I’ve turned that map into a network:

The question, can this map be colored using four colors, or better? is the same question as saying, can this network be colored using four colors, or better?

There are things we can learn now about maps, by studying networks instead. .. By studying networks, we can study all the different kind of maps. Now, all maps make networks, but not all networks make valid maps.

Given that my HipBone game boards are graphs — my games as played are conceptual graphs — I’m always on the lookout for easily digested gobbits of graph theory to see if they’re applicable to my games, or to put that another way, whether they can startle me into any new insights.

At least some HipBone games could be played on maps..

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One could thus view maps of the various sectarian interests in play in the Levant / Shams — theologies onto geographic areas, Alevi, Twelver, Salafi, Salafi-jihadist, Yezidi, Druze, Christian etc — as conceptual maps analogous to conceptual graphs.

And these conceptual maps are important in terms of strategy.

from WaPo, The one map that shows why Syria is so complicated

Different graphs could be obtained by articulating the linkages between different sects and ethnicities, eg Turkomen with Turks, Alevi and Ismaili with Twelver Shiism, and Shia with Sunni vs (eg) Christian.. and switching back and forth between map and grapoh might then prove suggestive, instructive..

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Once started on Numberphile’s math-curious videos it can be hard to stop.. Here’s a surprise from the third such video I chased thids afternoon, the one on The Feigenbaum Constant:

Life and Death can be mathematized!

I think that diagram — if it can be believed — answers the vexed issue of quality and quantity, and possibly also the hard problem in consciousness.

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I naturally attempted to place myself on the implicit timeline between Life and Death on that diagram. I’m reasonably far along (minor stroke, check, triple bypass, check, on dialysis, check, etc), and, shall we say, somewhat aware of my mortality.

Someone get me a slide-rule, I’d like to calculate the precise.. unh, on second thoughts, maybe not.

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The only happily viable move from here — I believe — is to infinity, so let’s go.

My games, I’d suggest, make a contribution to graph theory. Specifically, to that branch of graph theory in which Margaret Masterman was a pioneer, is the area of conceptual graphs, which I meantioned above. Indeed, the (theo)logical icon Masterman explored with her Benedictine Abbess friend as described in Theism as a Scientific Hypothesis (part 1), Theoria to Theory Vol 1, 3rd Quarter, April 1967, pp 240-46:

visiting it in Boolean terms:

is none other than the graph used as an exemplar of the map-graph correlation in the Numberphile video, second illustration at the top of this post.

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In the Trinitarian version of this graph, however, two kinds of “edge” or linkage are required: for the links between individual Persons (“non est”) and the links between Persons and Godhead (“est”).

And the same is true, interestingly enough, with even more types of linkage, in Oronce Fine‘s (entirely secular?) map of the elements:

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And that’s enough thinking for one day, perhaps. We shall see..

[ by Charles Cameron — all i do is play / to play is to create / I am creature / I am pawn / < bows lifelong gassho >]
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Here’s a key quote on play from Carl Jung, from Psychological Types, CW vol 6. #197:

My thanks to Mitch Ditkoff for pointing me to this fine quote.

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The question arises, what is this process in which “The creative mind plays with the objects it loves”? There’s an object, right, and the mind, that much is coear — but does the mind observe the object? absorb it? analyzie it? play around with it?

If play is what we’re trying to understand, around would be the word sitting right next to it, so around may be what we should think about.

Around is context. Playing around is seeing in context, seeing from unexpected angels, seeing unexpected close connections. Here’s Arthur Koestler‘s diagram of play, which he thinks of as a diagram of creativity — which he idemntifies with bisociation, or the conjunction of two otherwise separate planes of thought:

You’ve likely seen it before: that’s my personal Diagram in Chief.

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Okay, more basics. Play is how infants so richly learn and masters so richly express their mastery. It is rich, it masters and is mastered — “Thou mastering me God” says Hopkins in Wreck of the Deutschland, “giver of breath and bread; World’s strand, sway of the sea..”

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As a game designer and a Brit with Jungian sympathies, I am also delighted with this other quote:

One of the most striking testimonies to the quality of the English spirit is the English love of sport and games in a classical sense and their genius for inventing games. One of the most difficult tasks men can perform, however much others may despise it, is the invention of good games and it cannot be done by men out of touch with their instinctive values. The English did it and, by heaven, they even taught us Swiss how to climb our own mountains and make a sport of it that made us love them all the more. And their Wimbledon, did they but know it, is in sort a modern version of an ancient ritual.

That’s from Laurens van der Post‘s Jung and the Story of Our Time, and game designer Mike Sellers shares my delight in it.

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Yup:

[ by Charles Cameron — Borges’ finest fiction, read with an eye to serpents within serpents ]
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The pre-conscious mind, it seems to me, runs innumerable options before providing a single, first conscious selection, an initial thought, which we can then ourselves choose or dismiss, swaying away from whatever tendency we might dislike in that first choice, with alternatives then provided until we settle on a thought we can live with — whether because it suits our lust, our liking, our laughter, our love, or — simplest — love itself. The whole enterprise resembles, literarily speaking, Jorge Luis Borges‘ Garden of Forking Paths [link is to a deliciously annotated version, see more below].

But here’s the thing: my mind, at least, offers me quite a mixed bag of lascivious, laughing, light-hearted and level-headed options, all unbidden, and while the courteous Chinese gentleman in Borges’ fine short story would surely only have a selection of insights suitable for the Yellow Empereor among the branchings of his garden’s paths, and his maze of thoughts itself sums up to a transcendant mind, on the wider, non-literary world stage and usual human level there are some pretty dank pools of stagnant ideation to be found, and some skulls among the living that choose to harbor and indeed nourish those pools, hoping their poisonous atmosphere may prove contagious.

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I am driven to these thoughts by a report from yesterday’s Sydney Morning Herald, Revealing the secrets of one of Australia’s worst online trolls.

Ordinarily I might have scanned this account of an online neo-Nazi and moved on, but it contains a built-in ourboros or snake biting its own tail, when the former pulp magazine editor who lost his job after being persecuted for his affinity with Nazi dolls, and who lived alone in a rooming house, self-published a novel featuring, and I quote, “a former pulp magazine editor who lost his job after being persecuted for his affinity with Nazi dolls, and who lived alone in a rooming house..”

Self-publishing is arguably a mildly neurotic ouroboric loop, but William Blake looped it, as did Martin Luther, Jane Austen, Emily Dickinson, Marcel Proust, and Edward Tufte, to name a few..

Self-publishing an autobiographical fiction, however, is more deeply loopy — for the ugly details, see the SMH piece.

Gloriously, Borges reaches as high as the neo-Nazi stoops low: some hope remains for humanity.

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Annotation “o” in the annotated version of The Garden of Forking Paths mentioned above offers us a further — and specifically rhetorical — form of ouroboros to contemplate:

Linguists might classify the phrase “labyrinth of labyrinths” as an example of the genitive of gradation, as in the biblical “King of Kings,” from Daniel 2:37 (originally in Hebrew, “Melech ha-M’lachim”), I Timothy 4:14, and Revelations 17:14 and 19:16 (Curme, [6, p. 88]). Here the repetition of words conveys a sense of preeminence or superiority. A similar rhetorical device occurs earlier in line 30. But “centuries of centuries” might be more readily interpreted as a time span of hundreds of hundreds of years, constituting what is known as the partitive genitive, as in the “land of milk and honey.” Both usages are marvelously recursive, like “wheels within wheels,” and like the Thousand of One Nights, alluded to on line 230, which is a tale of a tale of a tale..

Wheels within wheels — indeed, tiny wheels in a footnote to a larger one — at which point we are back at Ezekiel and his vision of the dry bones, from which I derive my own username, hipbone.

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Fscinatingly, certain equivalent pieces on opposing sides of xiangqi, the Chinese chess game of the sort Borges’ Ts’ui Pên would have played, have different names, though “pieces on the same row in the table below share the same move and ability”:

Their order of battle at the commencement of the game are as follows:

I’m grateful to Robert R. Snapp, Associate Professor of Computer Science at the University of Vermont, for his outstanding contribution to this (mostly) delightful romp through the forking gardens of ideas..

[ by Charles Cameron — graphical thinking really has pretty much permeated the tech end of our culture at this point ]
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Two more examples of graphics — in the double sense of the word, or graphics squared if you like, where graphs, in the node and edge mathematical & network sense are used within graphics, in the visual or illustrative sense:

The first comes from a page on Carnegie Europe’s Strategic Europe blogpost titled Cyberspace and the World Order:

The second is from the Eventbrite invite to The Future of Cybersecurity: A Conversation with Admiral Mike Rogers at Georgia State University on Moday 24th at 10am, courtesy of John Horgan.

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From a graphic (visual) perspective, the symbolic content is in each case interesting, and I’d be glad to read any comments on why, for instance, there’s a honeycomb hex grid in the upper image, and why the information flow is so much more curvaceous after the lock than before it (assuming a left-to-right reading in temporal sequence) — and in the lower image, why some of the nodes and edges are slowly getting stained red (and here I’m guessing an epidemiological image for the spread of a virus).

From a graphic (graph as potential HipBone game board) perspective, the upper graph doesn’t offer a game board as I envisage them, but the lower one certainly does, albeit this would be a complex game, with the sizes of nodes and lengths of edges to be taken somehow into account.

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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

[ by Charles Cameron — sadly, now dunkin’ diabetes ]
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Some might claim that Dunkin is the link between Coffee and Donuts — it’s certainly a link I’ve appreciated myself on more than one occasion. Here’s another, and arguably more subtle linkage — topology.

In verbal format, it’s a mathematician’s inside joke:

The joke goes about topologists is that they can’t tell the difference between a coffee mug and a doughnut. For those who are not familiar with topology, topology is the study of geometrical objects where you don’t care about lengths and you don’t care about angles, what matters is how the spatial relations relate to each other.

Even better, here’s the same joke, illustrated — or refuted, if you prefer — in video by a master maker:

The only problem here — it’ll all prove a little pointless if you dunk your donut into the coffee cup without first supplying some coffee..

But morphing! What an ingenious way to provide and prove a DoubleQuote!