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[ by Charles Cameron — on creativity at the intersection of the fleeting and the eternal ]
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Centaur, displayed in the International Wildlife Museum, Tucson, AZ

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You know Lao Tzu’s “uncarved wood” (pu) — and Spencer Brown’s “Mark” or “first distinction? It is hard to speak of “the one and the many” without language itself favoring the many, the one being “one” and the many “another”. The Greek phrase “Before Abraham was, I am” attributed to Christ may be as close as we get.

The “uncarved wood” is not some definite -– named and thus defined -– “one” -– it is also “raw silk” (su), the simple -– the natural way or stream, from which things have not yet been separated out by naming.

There is delight, however, both in one becoming two and thus many, in the making of distinctions and naming of names, and no less in two (or the many) becoming one, in the resolution of paradox, the release of tension, peace after strife. In human terms, there is joy in both solo and collaborative achievement.

What better, then, than the perfect fit between disparate entities?

I have written often enough about Arthur Koestler and the place where two disparate spheres of thought link up — the centaur links horse and man in an indissoluble unity — there’s no question here of dismounting after a ride, giving the horse a rub down and some feed, then retiring to the verandah for a whiskey…

The mythological aha! we get from the centaur displayed in the museum hinges on the fit of horse and human skeletons, the perfection with which disparates are joined.

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Thus far, whenever I’ve discussed Koestler‘s notion of bisociation, I’ve focused on the sense that it liea at the heart of creativity. Koestler himself takes it deeper. Here’s Nicholas Vajifdar, in a review titled Summing Up Arthur Koestler’s Janus: A Summing Up:

Koestler .. asserts that there are two planes of existence, the trivial and the tragic. The trivial plane is the stage for paying bills, shopping, working. Most of life takes place on the trivial plane. But sometimes we’re swept up into the tragic plane, usually due to some catastrophe, and everything becomes glazed with an awful significance. From the point of view of the tragic plane, the trivial plane is empty and frivolous; from the point of view of the trivial plane, the tragic plane is embarrassing and overwrought. Once we’ve moved from one plane to the other, we forget why we could have felt the way we used to.

That’s not just any old distinction between two realms, that’s the one Koestler himself prioritizes. And following his basic principle that a creative spark is lit when two disparate “planes of ideas” intersect, we shouldn’t be too surprised to find Vajifdar continuing:

“The highest form of human creativity,” Koestler writes, “is the endeavor to bridge the gap between the two planes. Both the artist and the scientist are gifted — or cursed — with the faculty of perceiving the trivial events of everyday experience sub specie aeternitatis, in the light of eternity…”

William Blake made a similar observation in The Marriage of Heaven and Hell, writing:

Eternity is in love with the productions of time.

Finally, Vajifdar tells us why he finds Koestler’s definition of art maybe the best he’s ever read:

What I value in this definition of creativity is its emphasis on the subjective being of those who experience the work of art or scientific theory, a surer gauge than cataloguing formal properties or whether it’s “interesting.” Art has always seemed like a kind of sober drunkenness, or drunken sobriety. Most people probably have wondered whether the feelings they felt while drunk were more or less real than their sober feelings. Koestlerian art joins these seemingly irreconcilable feelings together.

Let’s just go one step further. In Promise and Fulfilment – Palestine 1917-1949, Koestler specifically singles out this intersection as an aspect of the experience of warfare:

This intense and perverse peace, superimposed on scenes of flesh-tearing and eardrum-splitting violence, is an archetype of war-experience. Grass never smells sweeter than in a dug-out during a bombardment when one’s face is buried in the earth. What soldier has not seen that caterpillar crawling along a crack in the bark of the tree behind which he took cover, and pursuing its climb undisturbed by the spattering of his tommy-gun? This intersecting of the tragic and the trivial planes of existence has always obsessed me in the Spanish Civil War, during the collapse of France, in the London blitz.

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I am grateful to David Foster for his ChicagoBoyz post The Romance of Terrorism and War which triggered this exploration, and that on the glamour of war which will follow it.

[ by Charles Cameron — via Christopher Alexander, Arthur Koestler, James Clerk Maxwell, Hermann Hesse, and Wells Cathedral ]
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My topic today is a comment that John Robb just posted on his FaceBook page. As so often, I’ll proceed by indirection. Here’s a wild DoubleQuote illustrating a blogger’s perceived similarity between the “scissors arch” at Wells Cathedral and one of the models in Jean Paul Gaultier‘s 2009 Spring collection:

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John Robb posted:

Some philosophical thinking:

Human knowledge, at an elemental level, can be described as a “transformation” of data.
Complex ideas are built using layers of “transformations” with each layer feeding into the next (think pyramid)
We teach these transformations at home and at school to our children.
We communicate by sharing transformations.
Questions We Need to Answer in the Age of Cognitive Machines:
How many transformations would it take to model all human knowledge?
How deep (how many layers of transformation is human knowledge) is human knowledge? Both on average or at its deepest point?
How broad is human knowledge (non-dependent transformations)?
How fast is the number of transformations increasing and how fast is it propagating across the human network?

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My interest is in John’s pyramid, considered as a pyramid of arches.

My starting point (with Hermann Hesse‘s Glass Bead Game ever in background) is Arthur Koestler‘s observation in The Act of Creation that the creative spark occurs at the intersection of two planes of thought —

— or to put that another way, that the creative leap is an associative leap between two concepts, disciplines or aspects of knowledge — thus, an arch:

Likewise:

— which in my own DoubleQuotes notation gives us:

— thus, many arches build to a pyramid:

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Of course, with arches one has to be very circumspect, buecause in rich contexts, they’re not simple creatures:

Among the greatest such arches I know are Taniyama‘s 1955 “surmise” as Barry Mazur puts it, that “every elliptic equation is associated with a modular form” — arching way above my pay grade — an insight that was to bear rich fruit forty years later, in Andrew Wiles‘ proof of Fermat’s Last Theorem; and Erwin Panofsky‘s great book similarly linking the structures of medieval cathedrals and scholastic thought:

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White we’re on the topic of gothic iconography, another form of arch we might consider is the vesica piscis:

— frequently found in medieval art and architecture:

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I’m not suggesting, John, that your inquiry and mine are identical — far from it — but that they have a sufficiently rich overlap that an appreciation of one is likely to spark insight in terms of the other.

And with Hesse’s Game, with which I recall from our earlieest conversations you are familiar..

I mentioned Hesse and Christopher Alexander in my bracketed note at the top of this post. It’s my impression that both were striving for a similar encyclopedic architecture to the pyramid John proposes. Hesse on the Glass Bead Game:

All the insights, noble thoughts, and works of art that the human race has produced in its creative eras, all that subsequent periods of scholarly study have reduced to concepts and converted into intellectual values the Glass Bead Game player plays like the organist on an organ. And this organ has attained an almost unimaginable perfection; its manuals and pedals range over the entire intellectual cosmos; its stops are almost beyond number. Theoretically this instrument is capable of reproducing in the Game the entire intellectual content of the universe.

And Hesse is clear that individual moves within the games take the form of parallelisms, resemblances, analogical leaps — writing, for instance:

Beginners learned how to establish parallels, by means of the Game’s symbols, between a piece of classical music and the formula for some law of nature.

Speaking of the playing of his great Game, Hesse said:

I see wise men and poets and scholars and artists harmoniously building the hundred-gated cathedral of the mind.

And Alexander? His book A Pattern Language is pretty clearly his own variant on a Glass Bead Game, following on from what he terms his Bead Game Conjecture (1968 – p. 75 at link):

That it is possible to invent a unifying concept of structure within which all the various concepts of structure now current in different fields of art and science, can be seen from a single point of view. This conjecture is not new. In one form or another people have been wondering about it, as long as they have been wondering about structure itself; but in our world, confused and fragmented by specialisation, the conjecture takes on special significance. If our grasp of the world is to remain coherent, we need a bead game; and it is therefore vital for us to ask ourselves whether or not a bead game can be invented.

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Gentle readers:

For your consideration, delight, temptation, confusion or disagreement, here are three more of Gaultier’s arches, as perceived by Kayan’s Design World:

[ by Charles Cameron — how two ideas beget a third ]
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I’m a Brit, so the motto Mind the Gap is familiar to me — it warns people not to step between platform and train when entering or exiting the Tube —

— as is the London Underground symbol — and for that matter, the glyph for female, earlier the alchemical symbol of Venus.

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Today’s Telegraph contains a graphic that interests me a whole lot, under the title Equal Pay Day: 14 ways to visualise the gender pay gap:

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Does it interest me because I’m a fan of the London Underground? Not exactly. The Underground’s graphics, then? I’ll admit to an admiration for the Underground’s justifiably celebrated map —

— which I’ve long thought would make a superb extended HipBone Game board, shown above in its 1968 incarnation. But that’s not it either. And although I don’t think gender should influence the pay a person receives for a given quantity or quality of work — Quant and Qualit again, one of the weirdst paradoxes my min d has ever encountered — it’s not the politics of the sign that interests and delights me.

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It’s the way two disparate elements — tube and gender graphics — are combined to create a remarkably powerful third:

It’s a simple, elegant illustration of the intersection of two sets of ideas that Arthur Koestler talked about and that I’m constantly drawing on in my own work:

And yes, I’m aware that technically the equation I’m pointing to happened in two stages, with the substitution of the phrase “mind the gap” for the word “underground” in the blue bar of the tube logo — but the bar was also used, among other things, for the names of individual stations, so I don’t consider that much of a creative leap.

No, it’s the juxtaposition of underground logo with the gender sign by means of a conflation of their respective circles that’s impressive, coupled with the pun on the gender-specific and underground meanings of “mind the gap”.

That’s the very essence of the intersections Koestler was talking about, and illustrates as vividly as I know how, the power released by such an intersection.

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Oh, and yes — fair play clearly requires fair pay.

And it’s Hedy Lamarr‘s birthday, dammit.

[ by Charles Cameron — Aristotle, the Ismailis, CG Jung ]
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Two is the first number:

From the tenth-century Rasa’il Ikhwan al-Safa’ (Epistles or Treatises of the Brethren of Purity) as found in Seyyed Hossein Nasr & Mehdi Aminrazavi, eds., An Anthology of Philosophy in Persia, vol. 2, Ismaili Thought in the Classical Age:

We say that one is the source and generator of the numbers because when one is removed from existence all the numbers are removed with it, but when the numbers are removed from existence, one is not removed. We say that two is the first whole number because numbers are a plurality of ones, and the first plurality is two.

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I am delighted to find myself in the company of the Ismailis, having written in On two, one, seven plus or minus, and ten – towards infinity:

When I worked as senior analyst in a tiny think-shop, my boss would often ask me for an early indicator of some trend. My brain couldn’t handle that — I always needed two data points to see a pattern, and so I coined the mantra for myself, two is the first number.

One isn’t a number until there are two, because it’s limitless across all spectra and unique, and because it is its own, only context.

One isn’t a number unless there’s a mind to think of it — in which case it’s already an abstraction within that mind, and thus there are, minimally, two. At which point we are in the numbers game, and there may be many, many more than two — twenty, or plenty, or plenty-three, or the cube root of aleph null, or (ridiculous, I know) infinity-six…

Go, figure.

Two is the first number, because the two can mingle or separate, duel or duet: either way, there’s a connection, a link between them.

And in Of a non-comparative use of the DoubleQuotes method:

Putting it bluntly, one point is pointless — things could go anywhere from there. Two points suggest a line, a link, a connection — a possible, maybe even plausible, trend.

It’s that sense I have of two being the beginning of thought that makes me so fond of the DoubleQuotes format — and of Arthur Koestler‘s insight about creation occurring at the intersection of two spheres..

If I’m a fundamentalist about anything, it’s the notion that it takes two to tango!

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Furthermore..

From CG Jung, A Psychological Approach to the Dogma of the Trinity, in Psychology and Western Religion:

The number one claims an exceptional position, which we meet again in the natural philosophy of the Middle Ages. According to this, one is not a number at all; the first number is two. Two is the first number because, with it, separation and multiplication begin, which alone make counting possible. With the appearance of the number two, another appears alongside the one, a happening which is so striking that in many languages “the other” and “the second” are expressed by the same word.

And from Leonardo Tarán, Speusippus of Athens: A Critical Study With a Collection of the Related Texts and Commentary:

Now we know that Speusippus did consider one to be the first odd number, whereas Aristotle thinks that two is the first number and explicitly denies that one is a number. [ … ]

Concerning the One, then, the differences between Speusippus and Aristotle amount to this: For the latter the One is not a number, nor a separately existing entity, but the principle of number because, each number being a plurality of abstract monads, the One is its measure.

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As Emerson wrote:

The world is young; the former great men call to us affectionately.

[ by Charles Cameron — further thoughts on the advantages of seeing double ]
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I’ve said before that when I was at The Arlington Institute, my boss used to ask me to watch out for “early indicators”, and joked that in my book, two is the first number — I don’t see an “indicator” until I see a pattern emerging.

Dutch artists celebrate George Orwell's birthday by putting party hats on surveillance cams http://t.co/qOM7i8FL4u pic.twitter.com/0YjATl3sH5

— Aruna Sekhar (@aruna_sekhar) August 18, 2015

Putting it bluntly, one point is pointless — things could go anywhere from there. Two points suggest a line, a link, a connection — a possible, maybe even plausible, trend.

And so it is with the two photos above. Here the point is not to compare and contrast the two images of surveillance cameras wearing party hats, but to see that they represent a class — the presence of two concrete instances strongly implies the higher level abstraction: hah! they’re watching us!

It’s that sense I have of two being the beginning of thought that makes me so fond of the DoubleQuotes format — and of Arthur Koestler‘s insight, which I’m always quoting, about creation occurring at the intersection of two spheres..

If I’m a fundamentalist about anything, it’s the notion that it takes two to tango!