Just in case you thought the musings in this place were a bit run-of-the-mill ;) – here are some posts that take the thinking further afield. Here we honour resonance over and above relevance…

At the round earths imagin’d corners

[ cross-posted from Zenpundit — mapping, holding two worldviews in mind at one time, a conductor’s score, complexity thinking ]


About a year ago, the Atlantic reported that the Library of Congress had been given a map of the flat earth, designed according to Biblical principles — yet showing knowledge of the border between the United States and Canada…

Thanks to a post from Jason Wells, I saw it today.

The view that the earth is flat is one worldview, of course, and no longer the prevailing one. As Nicholas Jackson noted at the Atlantic:

The interesting thing about the map is that it was created about 120 years ago by Orlando Ferguson, then a practicing physician in Hot Springs [South Dakota]. This is more than 500 years after most educated people gave up on the idea of the Earth as flat and accepted the spherical viewpoint first expressed by the Ancient Greeks.


It is, however, possible to hold two worldviews in mind at the same time. John Donne manages it in the first line of his extraordinary poem, written at a time when the two views were clashing:

At the round earths imagin’d corners, blow

AT the round earths imagin’d corners, blow
Your trumpets, Angells, and arise, arise
From death, you numberlesse infinities
Of soules, and to your scattred bodies goe,
All whom the flood did, and fire shall o’erthrow,
All whom warre, dearth, age, agues, tyrannies,
Despaire, law, chance, hath slaine, and you whose eyes,
Shall behold God, and never tast deaths woe.
But let them sleepe, Lord, and mee mourne a space,
For, if above all these, my sinnes abound,
‘Tis late to aske abundance of thy grace,
When wee are there; here on this lowly ground,
Teach mee how to repent; for that’s as good
As if thou’hadst seal’d my pardon, with thy blood.

Donne accomplishes the task of holding two worldviews in mind at one time with four simple words: “round earths imagin’d corners”.


I don’t know how many melodic “lines of thought” the mind can hold in counterpoint at once. I do know it’s an important cognitive skill for us to cultivate. A classical conductor must surely be able to hold as many lines as there are in this page of Olivier Messaien‘s Oiseaux:

As I pointed out in a recent comment here, “somewhere above three and before eleven there’s a point — Miller’s ‘magical number seven, plus or minus two‘ where the human mind can’t hold any more detail, so that’s a cut-off of sorts.”

Well, Messaien clearly imagines the conductor’s mind can follow more than eleven paths…


And then there’s Bob Milne.

I’ll let the Philosophy Compass take it from here:

Bob is predominantly known for his piano concerts of Ragtime and Bogie-Woogie music – and was given the moniker of ‘National Treasure’ by the United States Library of Congress. It was at one of these concerts that drew the attention of Penn State neuroscientist Kerstin Bettermann. At his concerts, Bob often carries on conversations, telling stories and jokes, while simultaneously modulating key signatures over the polyrhythmic Ragtime music. In their broadcast, Radiolab discusses with Dr. Bettermann why this is so surprising.

Language use and musical competency often use the same neural resources: the prototypical language areas in the left hemisphere of the brain, and the working memory circuit that keeps information available and rapidly accessible for a short-period of time. Our ability to use language and engage with music should, on most models of the brain, be competing for these neural resources and interfere with one another. Not so with Bob – he appears to be able to tackle both tasks with ease. Further, while most people can approach this kind of competency in multi-tasking, it usually involves many learning trials, a process of sedimenting the learning into what psychologists call procedural memory, which may have its roots in a different brain region, the cerebellum. But Bob can hear a tune just once, and play it back with commentary.

But that’s not all Bob can do.

In their interview, Dr. Bettermann heard Bob claim something extraordinary. He claims not only to be able to hear a symphony in his head, but that he normally does this with two symphonies simultaneously. Where most individuals would only hear a cacophonous mess – Bob claimed he could dial the relative volume of either symphony up or down, and could zoom in or out of individual instrumentations. To return to the considerations above, Bob further states on the Radiolab website that he does this while driving – another procedural memory task and presumable source of interference. But when Dr. Bettermann challenged him, Bob reluctantly claimed that he could probably do the same (not while driving, mind you) with four simultaneous symphonies.

The claim is something like this: Bob states that he can hold and listen to four symphonies with different keys, instrumentation, tempo and style in his working memory at the same time. And what is stunning is that when they put Bob into an fMRI machine, they verified his claim. Bob could be stopped at any time during his imaginative trip through the four simultaneous symphonies, and hum out the exact phrase that the original recording would be on. Remarkable.


This in turn takes us back to that point Edward Said made, which gave me the basic concept for my Said Sympohony (must get back to that soon):

When you think about it, when you think about Jew and Palestinian not separately, but as part of a symphony, there is something magnificently imposing about it. A very rich, also very tragic, also in many ways desperate history of extremes — opposites in the Hegelian sense — that is yet to receive its due. So what you are faced with is a kind of sublime grandeur of a series of tragedies, of losses, of sacrifices, of pain that would take the brain of a Bach to figure out. It would require the imagination of someone like Edmund Burke to fathom.

Edward W. Said, Power, Politics, and Culture, p. 447 — from the section titled “My Right of Return,” consisting of an interview with Ari Shavit from Ha’aretz Magazine, August 18, 2000.

I asked in a post yesterday how good we now are at modeling or simulating ideas in the “war of ideas” — just for a moment, suppose we could think through all complex geopolitical issues in this polyphonic, contrapuntal way…


Okay, you deserve a reward for faithful reading if you’ve come this far with me. Here’s the incomparable Richard Burton reading Donne’s poem — the text is up above, if you want to follow along:

Of Daffy and Higgs

Daffy Duck teaches Sembl to the kids. screenshot h/t Wm Benzon

I’ve been playing what we’d now call Sembl games for years now, sometimes online and sometimes on napkins in cafes, and because the basic board for this kind of play just consists of some circles with lines joining them — what mathematicians would call a graph — I’ve designed a few boards myself, and found a few ready-made in interesting places.

In fact, part of the fun for me in developing the TenStones > HipBone > Sembl game concept has been precisely in running across graphs that “look like” boards… like the board Daffy Duck is playing on in the screen-cap above.


Quite often the boards I’ve run across have been humorous, as in this example, where the cartoonist [double Pulitzer-winner Steve Breen] portrayed George W Bush as linking Al-Qaida to Iraq because they both had a Q in their name:

In the original, Breen had merely circled the Qs in the two words –I added the red circles and linking line to make the point that Breen himself was playing a bit of a Sembl move.


Sometimes the boards are entirely serious, like this one drawn from a diagram in an article in a science journal, which I call the Hamiltonian board:

What’s interesting about this particular board is that it assigns directions to the linkages — which sets me thinking about the ways in which one thing being like another can be a one-way or two-way street.

When Shakespeare says, “Shall I compare thee to a summer’s day?” the poet is definitely telling the beloved about his enduring love (“thy eternal summer shall not fade”), not using his beloved to explain global warming (“Sometime too hot the eye of heaven shines”). His metaphor moves from summer to beloved, not the other way around.

But that’s not always the case by any means. I’m not much of a mathematician, but as I understand it when Taniyama conjectured that every rational elliptic curve corresponds to a modular form, uniting two previously distinct branches of mathematics, the relationship went both ways



This week, two teams of researchers at the CERN Large Hadron Collider claimed they had very likely found the Higgs Boson — a hitherto elusive particle which in theory accounts for the mass of other particles, and thus the overall coherence of our world.

Here’s a diagram of the elementary particles, as they are understood in terms of the “Standard Model” in particle physics [for comments on the diagram, see Wikipedia Talk]

Of these, only the Higgs Boson remained to be discovered — until this last week!

Physicists broke out the champagne, science journalists had breathless ledes, sailors asked whether anyone had seen the Boson’s Mate, Catholics made jokes about the Higgs boson being Catholic because without it there’d be no Mass… and I found a new and intriguing board for fans of Sembl thinking:

Pretty obviously, I’ll have to call it the Particle Board. But what most interests me about it is the fact that it contains loops — in Sembl terms, implying moves that connect only with themselves — at W, G and H.

I’ve given that idea quite a bit of thought, as it happens. some statements are self-referential — Doug Hofstadter makes a big deal of them in his book, Godel, Escher, Bach. They embody paradox, they astonish, confound or amuse us…

And in a game played on this particular board (pun definitely intended), the three “looped” moves would need to have this strange and charming if quirky quality of self-reference.


The self-referencing thought is in fact the simplest form of Sembl move, since it would be played on a board that consists of one circle connected by a line to itself.

I’ll use one of my own poems as an example:

Is that a self-eating watermelon?

Not exactly. It’s the ourobouros, the serpent of mythology which eats its own tail…

But I do see the family Semblance!

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 FreePhoto.com 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.