Trees: Phototropic Simplexities

[ Cross-posted from Zenpundit — this one’s a prose poem: it begins with a statement so tight it needs to be unwound, and unwinds it ]

I wrote this urgently starting when it “woke” me at 4am one morning in the late 1990s or 2000, and as soon as it was out, I found myself writing another piece in the series, a game design. Together, the pair of them represent a stage in my games and education thinking intermediate between Myst-like Universities of 1996 and my vision today of games in education. In this posting, I have added the words “figuratively speaking” for absolute clarity: otherwise, the piece remains as written all those years ago.


A copse. Photo credit: Ian Britton via under CC license. Note how the wind sweeps the trees into a group shape.


Trees: Phototropic Simplexities

Trees are phototropic simplexities, no wonder we like them they cowork so well too: copses, see.



Trees we know: I as writer can refer you, reader, safely to them, “trees”, in trust that the word I use will signal to you too — triggering for you, also — pretty much the assortment of branching organic thingies about which I’m hoping to communicate that they are complex entities whose complexity comes from a simplicity of rule — branching — repeated with variations, said variants doing their branching in thirst of light, each trunk rising, limb outpushing, branch diverging, twig evading other twig much as one who seeks in a crowd a clear view of a distant celebrity shifts and cranes and peers — branching, thus, by the finding of light in avoidance of nearby shadow and moving into it, into light as position, that light, that position, growing, and thus in the overall “unified yet various”, we, seekers of the various and unified love them, to see them in greens themselves various in their simplexity is to say “tree” with a quiet warmth; while they themselves also, by the necessity of their branching seeking, if clumped together seek in an avoidance of each other’s seeking, growing, thus space-sharing in ways which as the wind sweeps and conforms them to its own simplex flows, shapes them to a common curve we call aerodynamic, highlit against the sky huddled together as “copse” — this, in the mind’s eyes and in your wanderings, see…



Trees we can talk about. Simplexity is a useful term for forms — like trees — which are neither simple only nor complex only, but as varied as complexity suggests with a manner of variation as simple as simplicity implies.

Trees? Their simplexity is conveyed in principle by the word “branching”. Its necessity lies in the need of each “reaching end” of the organism to ascertain from its own position and within the bounds of its possible growing movement, some “available” light — this light-seeking having the name “phototropism”.

Simplexities — and thus by way of example, trees — we like, we call them beautiful.

Clustered together, too, and shaped by the winds’ patterns of flow, these individual simplexities combine on an English hilltop (or where you will) to form yet other beauties.



Trees are phototropic simplexities, no wonder we like them they cowork so well too: copses, see.



I love trees. Want to talk about simplexities, beauty.

I wish to talk about beauty because it is beauty that I love, if I love it, that is beauty: love is kalotropic, a beauty-seeking. I am erotropic, love seeking — you can find in this my own simplexity, my own varieties of seeking, of the growths that are my growth, and clumping me with others under the winds, the pressures that form and conform us, you can find also the mutual shapes that we adopt, beautiful.

Simplexity, then, is a key to beauty, variety, self, character, cohabitation… Tropism, seeking, is the key to simplexity. Love is my tropism. Ours, I propose.



Beauty is one simplexity perceived by another: the eye of the beholder, with optic nerve, “brain”, branching neuron paths that other simplexity, “consciousness” the perceiving.


Meaning also:

That all is jostle, striving — a strife for life, in which the outcome overall is for each a “place in the sun” but not without skirmishes, shadows. The overall picture, therefore, beautiful — but this overall beauty hard to perceive when the specific shadow falls in the specific sought place of the moment, the “available” is not available, and the strife of the moment is paramount.

Branching being the order behind simplexity, differentiation…

Differentiation for maximal tropism at all levels — life seeking always the light, honey, beauty, is always and everywhere in conflict also with itself, competitive: and competition the necessary act of the avoidance of shadow, and the shadow creating act.

And beauty — the light, thing sought, implacably necessary food and drink, the honey — thus the drive that would make us kill for life.

I could kill for beauty.

I could kill for honey.

Figuratively speaking.



Paradise and Fall, simultaneous, everywhere.

It is at this juncture, at this branching, that we are “expelled from the garden” — can no longer see the beauty that is and remains overall, that can allow us to say also, “we are never outside the garden” — for the dappling of light on and among the leaves has become to us, too closely jostled, shadow.

And shadow for shadow we jostle, and life is strife.



The dappling of light on leaves, beautiful, is for each shadowed leaf, shadow, death-dealing, is for each lit leaf, light, life-giving: a chiaroscuro, beautiful, see.

Roots, too, have their mirror branchings.

On stereo thinking

I was writing a post for Zenpundit a day or two ago about two topical interests of mine — religiously sanctioned violence and social media — which came together some while ago when a Taliban spokesperson began using Twitter to make press announcements, and a press officer of the NATO-led International Security Assistance Force (ISAF) began tweeting back.

I wandered a bit off topic in the middle of the post to discuss something I might as well call stereo thinking — which is certainly an aspect of Sembl thinking, so I thought it belonged here. Here, then, is an excerpt from that post, with a bit of the original context left in place so that the whole passage hopefully makes sense without requiring further editing.

From Zenpundit:


A while back, on my way to make other points, I posted this:

I wasn’t the first or last to make the connection between A Balkhi and the Taliban, nor to note the Twitter-exchanges between Balkhi and the ISAF press office — but I happened to have this habit of juxtaposing similars and opposites, and had developed the “Specs” format used here, with the little binoculars inset, to suggest the idea of seeing parallel or opposite things in parallel or opposition — a sort of mental equivalent of stereoscopic vision or stereophonic sound — in the hope that something about the comparison and contrast would add a depth dimension to understanding.

As a footnote to a footnote to a footnote, I think the Necker Cube can add an interesting aspect to this business of stereoscopic thinking:

When two things are so much the same and so utterly different that, as with a Necker Cube (or the positive and negative of a photo rapidly alternating) the mind flashes rapidly from one view to its exact and opposite other, a metacognitive insight arises about what I can only term the two in one in twoness experienced.

File that under number theory, koans.


That’s the excerpt from Zenpundit. What follows is a quote from Michael Polanyi which Critt Jarvis supplied me with in a comment on that post — food for thought:

The fusion of the two stereoscopic pictures to a single spatial image is not the outcome of an argument; and if its result is illusory, as it can well be, it will not be shaken by argument. The fusion of the clues to the image on which they bear is not a deduction but an integration.

You can find that and much more in his essay The Structure of Consciousness, also found in Polanyi’s book Knowing and Being, pp. 211-13.

Of orangutans and cathedrals

I don’t think you want to see me attempting to draw an orangutan – but if I was persuaded to try, I’d probably use a technique along the lines of DragonArt’s post on the topic, from which the two illustrations above are drawn.

I came across this site, by the way, while looking for a version of this puzzle diagram:

And I was looking for that not only because it’s the solution to a neat creative-thinking puzzle that my father showed me when I was a kid, but also because it’s a graph — and thus a potential board on which Sembl games could be played.

In fact I used an analogous device once, during a live intercontinental phone-feed HipBone game, to tilt and transform a 10-position WaterBird board which had already filled with moves into a 12-move board to continue the game, the excitement and the brainstorming just a little longer by popular request..


Back to our orangutan board.

What interests me here is the intersection of the notion of graphs with that of Venn diagrams

Semiotic translation between verbal and visual elements is a fascinating creative challenge in its own right.

Indeed, one aspect of what’s up for grabs here is the possibility of an overall semiotics of conceptual mappings — which in turn would facilitate the development of a new style of world mapping, capable of crossing the (leaky) “cartesian divide” between mental and physical realms, while exploring the multiple links and dependencies in our complexly interwoven world.

That’s a topic I’m hoping to post on shortly…


It would, for instance, be interesting to develop maps that can transition smoothly from Markov:

to PERT:

to Forrester-style visualizations:


Back to the Sembl games, back to graphs as boards, back to fun.

One of the most creative aspects of developing the HipBone and Sembl family of games has been the discovery of potential boards in the most intriguing of places.

This board, for instance, is based on the design of the star-vaulted ceiling in a old British cathedral…

Sketching data structure & interface

Thinking about how in Sembl, the lines that connect things are not lines but, actually, circuits – because they are always already mutual, originating from and applying equally to both things – I started to imagine how the network of aggregated game data would look, and how you could interact with it to explore both the whole and its parts.

Pencil drawing of four ways of representing a network diagram, with the words 'A line resolves into a circle.'

In Sembl, node-connecting lines are actually circuits.

Lines between things could be spring-like. On hover, they could draw the two things closer and resolve into a circular facet or disc, perpendicular to the connecting line. You could click to enlarge the posited semblance.

In the next sketch I’m wondering if the data structure could really be this simple. Each semblance is linked to (its rating and) two things, which in turn have title/s and persistent identifiers (PIs).

Pencil drawing showing a resemblance and its rating between two things represented by their title/s and a persistent identifier

A resemblance and its rating are at the centre of two items comprising title/s and a link to their location.

The data is generated in the game and editable via a wiki, so we are also likely to capture metadata about who created it (username or IP address), and possibly also when, where etc – but those few fields form the foundation.

A Rembrandt resemblance?

When I was searching for illustrations for my piece on ancient Sembl boards, I was under the impression that Rembrandt had made an illustration of some old sage having a vision of a slightly unusual form of the Sephirotic Tree of Jewish Kabbalah.

I wasn’t able to find it: what I did find, however, was a different but similar Rembrandt etching, showing a wise old man having a diagrammatic vision – but not of the variant Sephirotic Tree that I recalled seeing…

And although I could also have used Athanasius Kircher‘s highly wrought version of the Tree…

in the end I opted for a simpler diagram, which I juxtaposed to a Christian diagram of the Trinity:

Today, however, while browsing for something completely different – a map of Washington DC if you must know – I ran across the image I’d been thinking of – it’s on the title page of Paulus Ricius‘ Latin translation, Portae Lucis, of the Hebrew Kabbalistic text Shaarei Orah by Abraham Joseph Gikatilla, which concerns the Tetragrammaton or four-lettered Name of God:

Okay, I went back to check on the Rembrandt, and found it on the Rijksmuseum site dated “c. 1652” with the comment:


What the etching exactly represents is unclear. In the early eighteenth century, the print earned the title ‘Dr Faustus’ and in 1791 Goethe used it on the title page for his publication of Faust. However, it is just as possible that this has nothing at all to do with Faust, but is a portrait of a scholar. It may be the ‘practising alchemist’ to which references were made in the seventeenth century. The posture of this ‘Faust’ has much in common with that of a scholar in an earlier print of Rembrandt’s. Rembrandt did not portray alchemists in the traditional way – that is, with fire. The enigmatic text in the radiating light could be a magic spell.


So here’s the business my unconscious seems to have had in mind during this whole process of searching in Rembrandt’s works for an image that resembled one of his etchings from around 1652.

I was conflating the Rembrandt with the image found on the title page of a book printed in Augsburg in 1516 — and that’s how the creative leap happens, in this case from a 1516 image in Augsburg to a 1652 image in Amsterdam.

At the point that I realize this, there’s an aha! in me, a Sembl move I can make linking the Portae Lucis title page to Rembrandt’s Faust etching – and a vista opening in the realm of art history, in which one could (and perhaps someone should) research the availability of the Ricius translation of Shaarei Orah to Rembrandt himself, and in the rabbinic libraries of his time in Amsterdam.

Because – and this is not art history but art historical hypothesis – the Ricius title page may well be a significant source of Rembrandt’s etching, of which the Rijksmuseum itself says:

What the etching exactly represents is unclear.


I have no idea how original an idea this is, and others may well have considered the possibility and researched the matter before me.

I do know that Rembrandt’s Jewish connections have been examined in detail, and would love to have seen the ‘Jewish’ Rembrandt exhibit at the Joods Historisch Museum.

But there you have it.  The “unconscious” mind finds resemblances and in effect makes leaps, which the “conscious” mind then stumbles across – and on occasion those leaps deserve to be followed up, researched, confirmed or refuted.

In this case, I’m hoping my friend Michael Robinson will come to my rescue with some informed commentary – this is in his field, not mine.


In the meantime, the central rosette or mandala in the Rembrandt prominently features the letters INRI for Iesus Nazarenus Rex Iudaeorum (Jesus of Nazareth, King of the Jews), which was the title Pilate ordered nailed to the cross above Christ’s head in Hebrew, Latin and Greek (John 19.20).  So even if Rembrandt had seen the Ricius Kabbalistic Tree diagram in the collection of one of his Jewish neighbors and been influenced by it, his own version is explicitly Christian…

And INRI, if you think about it, it a sort of Christian variant on the Tetragrammaton: a four-lettered title for Christ.

But that would be another possible Sembl move, for another day.

Play as if your life depends on it

[ from the Glass Bead Game via the HipBone Games to Sembl — cross-posted with minor changes from

Play most assiduously is how Edgar Wind translates the motto of Marsilio Ficino — the man who more or less single-handed, built the Florentine Renaissance: studiossime ludere. Play most studiously.

Play as if your life depends on it.


Hermann Hesse crowned his life-work with the great, boring, utterly riveting novel Das Glasperlenspiel, The Glass Bead Game, sometimes better known in the English-speaking world by the (Latin) title, Magister Ludi — which means both school-teacher and Master of the Game.

And game there is: the Glass Bead Game itself, or GBG for short.

The book centers around a game of ideas — a game in which the most profound conceptual systems of all human cultures are brought together in a grand architecture that Hesse calls “the hundred-gated cathedral of Mind”:

A Game, for example, might start from a given astronomical configuration, or from the actual theme of a Bach fugue, or from a sentence out of Leibniz or the Upanishads, and from this theme, depending on the intentions and talents of the player, it could either further explore and elaborate the initial motif or else enrich its expressiveness by allusions to kindred concepts.

Here Hesse mentions astronomical, musical and textual concepts — the game, like the digital world of the internet, allows mathematical, textual, musical and visual elements to be juxtaposed and combined, just as Sven Birkerts described in an interview with Cliff Becker:

There are tremendous opportunities, and we are probably on the brink of the birth of whole new genres of art which will work through electronic systems. These genres will likely be multi-media in ways we can’t imagine. Digitalization, the idea that the same string of digits can bring image, music, or text, is a huge revolution in and of itself. When artists begin to grasp the creative possibilities of works that are neither literary, visual, or musical, but exist using all three forms in a synthetic collage fashion, an enormous artistic boom will occur.

Birkerts was concerned that these “tremendous opportunities” might drown out “the old quiet pastime of reading mere words” — but Hesse’s great game is a contemplative one, in which Hesse proposes:

Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.



We play, we play games, we play music… we play wargames… all the world’s a stage, and we are (merely) players.

Consider: Play is what children do to learn, so brilliantly, language, languages, geography, mathematics, history, chess, go, music, politeness, discipline, excess, consequences, moderation… And play is what masters do to express their mastery — Picasso plays, Casals plays, Einstein plays… And the motto of Ficino, mentor to the Florentine Renaissance, is play most assiduously.


The Glass Bead Game is a game, then, to compare with the greatest of games — Chess, Go, name your poison — indeed, with the greatest of intellectual endeavors — the Encyclopédie, the gesamtkunstwerk, the long-sought Theory of Everything…

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.

How can taking that idea and making it playable not be a worthy challenge, in this world that is daily more absorbed in digital play in its arcades and cinemas, on its consoles, tablets, phones, and computers?


Just reading the book made me want to play the game, but I like to keep things simple. I needed to be able to play it with a pencil and paper napkin over a cup of coffee — or on an email list or in the online forums that were beginning to spring up while I was figuring out some early boards and rules. I took Hesse’s basic concept of juxtaposing ideas and applied it on simple graph-like boards, on which each circle represents an idea, and each line a resemblance. I called my playable variants the HipBone Games.

More recently, my friend and colleague Cath Styles has been working on the development of iPad and web-playable versions of the games. We call them Sembl, because they explore the resemblances between things, ideas — and at a deeper level, the patterning of the world itself.

But the game remains the same: to juxtapose one thing — an idea, an object, a work of art, song, person or event — with another, in a way that generates the aha! of creativity. And to do that repeatedly, weaving an architecture of related ideas, on our way to weaving Hesse’s cathedral of Mind.

Our world has never been in greater need of creativity and connectivity — our future depends on them — and in the Sembl game, every move you make is a further link in the pattern that connects, every move you make is a creative leap.

More on that in an earlier post, The crackling energy of a Sembl move.

The crackling energy of a Sembl move

image credit The Movie Poster Art Gallery /

I’m always looking around for ways to describe the leap between two ideas (concepts, people, events, things) that occurs when you make a move in a Sembl game. On the game board, the ideas are shown as circles and the links as lines between them.

In the case of the museum version, the “ideas” are objects in the Museum’s collection – but the same principle applies whether we’re talking objects, concepts, events or people: entities of whatever type go in the circles, the lines between them signify the exploration of their resemblances and differences.



In more technical terms, Arthur Koestler in his classic book about the conceptual structure of creativity, The Act of Creation, diagrammed the intersection of two conceptual frames as representing the place where the joyous aha! of discovery, the gasped ah! of tragedy or the delightful ha! of laughter is generated, and this more recent version of his diagram gets the essence:


But wait!

There’s a lot going on here, there’s a distinct leap – think: creative leap, even perhaps leap of faith.

It was the leap between two ideas – electricity and magnetism – that gave Faraday his dynamo, Maxwell his equations, and the modern world almost its whole existence. It was the leap between two ideas – modular forms and elliptic equations – that gave Taniyama his conjecture and Wiles his proof of Fermat‘s Last Theorem.

The leap that intuits similarities, particularly between rich similarities between rich concepts in widely separated fields, is the most powerful tool of the thinking mind – and playing Sembl amounts to nothing more or less than a repeated, playful, delightful invitation to make leaps of exactly that kind.

So a Sembl leap of resemblance can be anything from training wheels for creativity to a prize-winning long-jump at the conceptual Olympics.


Maria Popova at Brainpickings quotes Steve Jobs:

Creativity is just connecting things.

And she quotes James Webb Young, back in 1939:

Consequently the habit of mind which leads to a search for relationships between facts becomes of the highest importance in the production of ideas.

This isn’t some hidden secret, but it’s not exactly common knowledge either, it’s not something many schools teach — which is why the great anthropologist Gregory Bateson famously told his fellow Regents at the University of California:

Break the pattern which connects the items of learning and you necessarily destroy all quality.

Which is also why Eliot Eisner, Stanford professor and former President of the American Educational Research Association, said of Sembl’s precursor HipBone Games, “the cognitive processes you are interested in developing are critical to a decent education”.


And just what does this have to do with Van der Graaf Generators, you might wonder?

There’s a cracking sense of energy discharged when you connect two ideas in a Sembl game move – not unlike the discharge of energy between the spheres of two Van der Graaf Generators picture here:

Imagine the spheres as two ideas in place on a Sembl game board, and the electrical discharge as the excitement of seeing how they mesh together to create that ah!, aha! or ha!

Or watch the whole, ultra-short video from which that image was taken, courtesy of the folks at MIT:

Conceptual blending

Gilles Fauconnier and Mark Turner‘s The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities gives us a fascinating look at the way the human mind weaves a world out of seemingly disparate elements — in a very similar manner to that in which the creative mind weaves an aha! out of seemingly disparate ideas. The book deals with the formation of perceptions as well as ideas, but it was a specifically conceptual blend that intrigued me the other day.

First, they note that when we use expressions like “I had reached the boiling point. I was fuming. He exploded.” we are making a metaphorical mapping in which “a heated container maps to an angry individual, heat maps to anger, smoke and steam (signs of heat) map to signs of anger, explosion maps to uncontrolled rage.” Then they add in the “folk theory of physiological effects of anger” including ” increased body heat, blood pressure, agitation, redness of face” – and thus we have a threefold scheme, in which physiology, emotions and the physics of heat are intricately cross-correlated, so that we can say without much thought “He was so mad I could see smoke coming out of his ears”.

Here Fauconnier and Turner describe the mechanics of this remarkable conceptual blending process – which can yield such a seemingly unremarkable phrase:

In addition to the metaphoric mapping between Heat and Emotions and the vital-relation connection between Emotions and Body, there is a third partial mapping between Heat and Body. In this mapping, steam as vapor that comes from a container connects to perspiration as liquid that comes from a container, the heat of a physical object connects to body heat, and the shaking of the container connects to the body’s trembling.

The three partial mappings set the stage for a conventional multiple blend in which the counterparts in the inputs are fused, yielding, for example, a single element that is heat, anger, and body heat and a different single element that is exploding, reaching extreme anger, and beginning to shake. Once we have this blend, we can run it to develop further emergent structure and we can recruit other information to the inputs to facilitate its development.


What interests me here is the phrase:

the inputs are fused, yielding, for example, a single element that is heat, anger, and body heat

and what it reminds me of is CS Lewis writing in The Allegory of Love:

It must always be remembered … that the various senses we take out of an ancient word by analysis existed in it as a unity.

Thus the King James Version of the Bible, John 3.8, reads:

The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth: so is every one that is born of the Spirit.

In the Greek, the word here translated wind is pneuma, and the sentence accordingly means “the pneuma blows where it wills, and you hear its sound but can’t tell where it comes from or is going: and so it is with all those born of pneuma“…

Recalling Lewis’ remark about the “various senses we take out of an ancient word”, this in turn means simultaneously and without separation:

the wind blows where it wills, and you hear its sound but can’t tell where it comes from or is going: and so it is with all those born of wind…

the breath blows where it wills, and you hear its sound but can’t tell where it comes from or is going: and so it is with all those born of breath…


spirit blows where it wills, and you hear its sound but can’t tell where it comes from or is going: and so it is with all those born of spirit…

Take this a step further, realize that spirit can be defined as what inspires us, and we have:

inspiration blows where it wills, and you hear its sound but can’t tell where it comes from or is going: and so it is with all those born of inspiration…

Four meanings, all making good sense, and all present simultaneously and inseparably in the one gospel phrase…


Now consider that Fauconnier and Turner are speaking of how “three partial mappings set the stage for a conventional multiple blend in which the counterparts in the inputs are fused, yielding, for example, a single element that is heat, anger, and body heat” and compare it with Lewis’ “unity” from which we take out “the various senses” by “analysis”, as applied to the “ancient word” pneuma, with its meaning encompassing wind, breath, spirit… inspiration.

Are wind, breath and spirit or inspiration in fact three “primitives” that conceptual mapping in ancient Greek thought has brought together? What do we gain, and what do we lose if we view them this way?

And what do we lose, what do we gain if we view them as a single rich concept, now reduced to three or four separate — and separately less complexly interesting — ideas?

A glimpse of Sembl thinking: Virginia Woolf

What is the thing that lies behind the semblance of the thing?

Virginia Woolf poses that question in her 1931 novel The Waves. Here’s the passage surrounding the question:

‘An axe has split a tree to the core; the core is warm; sound quivers within the bark. “Ah!” cried a woman to her lover, leaning from her window in Venice. “Ah, ah!” she cried, and again she cries “Ah!” She has provided us with a cry. But only a cry. And what is a cry? Then the beetle-shaped men come with their violins; wait; count; nod; down come their bows. And there is ripple and laughter like the dance of olive trees and their myriad- tongued grey leaves when a seafarer, biting a twig between his lips where the many-backed steep hills come down, leaps on shore.

‘ “Like” and “like” and “like” — but what is the thing that lies beneath the semblance of the thing? Now that lightning has gashed the tree and the flowering branch has fallen and Percival, by his death, has made me this gift, let me see the thing. There is a square; there is an oblong. The players take the square and place it upon the oblong. They place it very accurately; they make a perfect dwelling-place. Very little is left outside. The structure is now visible; what is inchoate is here stated; we are not so various or so mean; we have made oblongs and stood them upon squares. This is our triumph; this is our consolation.

The sweetness of this content overflowing runs down the walls of my mind, and liberates understanding.

— a glimpse of Sembl thinking, with thanks to Derek Robinson.