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On the felicities of graph-based game-board design: three

Monday, August 24th, 2015

[ by Charles Cameron — cross-posted from Sembl ]
Following up on two previous posts on graph-based design: Preliminaries and Two dazzlers


Here are two old HipBone boards that have the curious property of looking very different while being, in fact, topologically identical. Moves played on either board will feature the same set of links — although, given the visual impac ts of proximity and distance, they may “feel” very different to the players themselves:

Petersen graph boards

I call them the Pentagram and Mercedes boards, for what I trust are obvious reasons. They are both based on versions of the Petersen graph, and I’m grateful to Walter Logeman and Miles Thompson for introducing me to them.


One of the vivid differences between my childhood memories and present experience has to do woth the time when the table, the place where food or whatever was, was above my head.

Of course, the table was flat — but it was flat above my head, and I had to reach up into that unknown flatland to grab what I could. Unless of course there was a tablecloth trailing over the edge of the flat, down towards eye-level, in which case.. voila!

Hence my ongoing notion that something tasty might be literally above my head, and my associated excitement. Hence, too, my excitement at the prospect that tasty ideas might also be above my head, and that I might reach up into unknown intellectual flatlands — or pull them down to my own level with a tug of the intellectual tablecloth.


That may sound foolish, but it’s entirely in line with Eric Drexler’s advice — and Drexler published the first scientific paper on molecular nanotechnology [.pdf] in 1981.

Here’s what Drexler has to say about reading scientific journals:

Read and skim journals and textbooks that (at the moment) you only half understand. Include Science and Nature.

Don’t avoid a subject because it seems beyond you – instead, read other half-understandable journals and textbooks to absorb more vocabulary, perspective, and context, then circle back.


Okay, I’m in over my head as they say.

Here’s an artist’s rendering of something called, I guess, an amplituhedron, a (relatively) newly discovered mathematical object that has the world of physics all excited:


Here’s another, titled for some reason “droplet”:


Neither of those is anything I could conceivably use to come up with a HipBone or Sembl board, is it?

But get this:


This is another way of looking at the same corner of mathematical physics — one of over a hundred diagrams in the same paper— and here are the two “lesser” diagrams that caught my attention and made me think back to the Petersen graph boards earlier on today:

twistor-diagrams- scientists discover a jewel

Now my itch is to figure out what use the “filled” and “open” nodes in these two graphs might serve in game-playing terms, and how on earth to interpret in game terms the complex weavings of the colored lines in the larger image / board.


And hey, while we’re at it, Here are the Wolfram variants on the Petersen graph — striking, aren’t they?

PetersenGraphEmbeddings wolfram

Food for thought is food for play.



  • N. Arkani-Hameda et al, Scattering Amplitudes and the Positive Grassmannian
  • Nima Arkani-Hameda and Jaroslav Trnkab, The Amplituhedron
  • Check out the stunning physics — deeper than time and space? — if you don’t already know it, and explain it if you do!

  • Natalie Wolchover, A Jewel at the Heart of Quantum Physics
  • And for Wolfram on the Petersen Graph:

  • Eric W. Weisstein, Petersen Graph
  • Leap Worlds: my 3QD attempt

    Wednesday, December 11th, 2013

    [ by Charles Cameron — another runup to the glass bead game ]

    Below you can read my submission to the wonderful 3 Quarks Daily “web aggregator” site as a candidate to join their regular Monday blogging team — it didn’t even make their “close but no cigar” list, but I wrote it and I like it, so I’m posting it here.


    They are both fine American authors, stylists of high repute yet little known, Annie Dillard and Haniel Long, but I hadn’t associated the two of them particularly closely until that day. I’d snarfed up a copy of Long’s Letter to Saint Augustine from the dollar box at Pasadena’s magnificent Archives theological bookstore, and on my way home to nearby Eagle Rock, stumbled on a passage that seemed hazily familiar.

    My friend Jens Jensen, who is an ornithologist, tells me that when he was a boy in Denmark he caught a big carp embedded in which, across the spinal vertebrae, were the talons of an osprey. Apparently years before, the fish hawk had dived for its prey, but had misjudged its size. The carp was too heavy for it to lift up out of the water, and so after a struggle the bird of prey was pulled under and drowned. The fish then lived as best it could with the great bird clamped to it, till time disintegrated the carcass, and freed it, all but the bony structure of the talon.

    By the time I arrived back at my books, I knew it was Annie Dillard I’d been reminded of, and a quick, no, excited but fumbling search turned up this passage from her Teaching a Stone to Talk:

    And once, says Ernest Seton Thompson–once, a man shot an eagle out of the sky. He examined the eagle and found the dry skull of a weasel fixed by the jaws to his throat. The supposition is that the eagle had pounced on the weasel and the weasel swiveled and bit as instinct taught him, tooth to neck, and nearly won. I would like to have seen that eagle from the air a few weeks or months before he was shot: was the whole weasel still attached to his feathered throat, a fur pendant? Or did the eagle eat what he could reach, gutting the living weasel with his talons before his breast, bending his beak, cleaning the beautiful airborne bones?

    They’re emblematic, those two quotes, the way I see them: emblematic in the sense that each could be the basis for a heraldic shield, the eagle stooping to carry off the weasel, air creature triumphant over creature of earth in the one, the fish dragging the bird down in the other — creature of water gathering the air creature into its own fatal realm.

    Emblematic too, I see them, of the possibility of a rhyme between thoughts — and I have quoted them as such in previous essays, alongside rhymes of sound and rhymes of meaning, womb and tomb being the classic examples of choice, but also rhymes of image, the fan rotors and helicopter rotors in the opening sequences of Coppola‘s Apocalypse Now, rhymes of melody in counterpoint, in fugue… and rhymes, yes, in history, as when Sir Frederick Stanley Maude told the people of Baghdad in 1917, “Our armies do not come into your cities and lands as conquerors or enemies, but as liberators…” and Donald Rumsfeld chimed in, telling his own troops in that same weary city, almost a century later, “Unlike many armies in the world, you came not to conquer, not to occupy, but to liberate and the Iraqi people know this.”

    Oh yeah?


    The world is woven, Jung tells us in one of his most original and illuminating insights, of woof and warp, causaland acausal principles , it is at once at every point synchronic and diachronic.

    Moving through time, we have the causal, diachronic principle, one things leads to another: let us sort and analyze the actions of one thing on another until psychology becomes sociology, sociology turns into evolutionary biology, biology into genetics, genetics a form of chemistry that is essentially physics — and physics, at the quark-level at last, a matter of statistics, mathematics unfettered even by the dualism of wave and particle.

    Let me be clear about this. I do not begrudge Higgs his boson or his Nobel, nor Chandrasekhar his Nobel or his limit. But both men followed the warp, the causal, time-bound length-wise threads of discovery to their fraying edges. And the causal threading of events, time’s warp in our lived universe, is the mode best suited to quantity, to the determinable, and knows little of mystery unless magnitude alone — the infinities of astronomy, the infinitessimals of subatomics, alone will qualify.

    Oh, scale is a marvel, true enough — but it is quality, not quantity, where the mystery and the greater meaning resides.


    And so we come to the mind’s other faculty, the other manner in which the world is woven, the manner of rhyme and repetition, synchronicities and semblances, of patterns recognized within and across disciplines. The cross-weave.

    This has been the step-child of cognition for too long — but with the rise of cybernetics, feedback loops, complexity theory, network thinking and multi-causality, we can no longer think only in linear progressions, but must also cultivate associative, lateral, sideways thinking — in short, creative leaps.

    Creative leaps occur when we recognize commonalities across conceptual distances — theme and variations, as musicians would say, rhymes in the nature of things, multiple perspectives and voices in counterpoint. So the nature of our current world, in all its complexity and variegation, calls for what I would call a music of ideas.

    I’m not the first to have this idea, Glenn Gould was pursuing it in his work for radio, blending the many voices and conversations in a train compartment, or at the different tables in a truck-stop café, to form an interwoven whole that comprehended all of its voices, all of its parts in a greater music. But it is Edward Said — another musicians, when he was not occupied with Israeli-Palestinian politics or literature — who observed in an essay in Power, Politics and Culture, p. 447:

    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.

    So that’s the symphonic scope of the thing, seeing the whole with all its fractures and dissonances as a music — a music that calls for harmonization, but remains in complex counterpoint.


    Hermann Hesse was the first great proponent of the music of ideas, at least in modern western times, and his glass bead game — evoked but never defined in his Nobel-winning novel of that name — offers us a glimpse both of the nature of moves and of the possible grandeur of an implicit world-architecture, formed of resonances and semblances, rather than of causes and effects.

    Hesse gives us an insight into how the game is played at the level of moves and themes when he says a given game might have explored “the rhythmic structure of Julius Caesar’s Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns” — but he could hardly have known, back in the 1940s, that in 1978 the University of Wisconsin Press would publish Jane-Marie Luecke OSB’s monograph, Measuring Old English Rhythm: an Application of the Principles of Gregorian Chant Rhythm to the Meter of Beowulf. Intentionally or unintentionally, his game is played by all whose minds play with meanings. And there’s a game move right there, in the conviviality between the fictional move of Hesse himself, and the monograph, years later, of a Benedictine nun.

    Tiny, you say, a tiny move — but a move in what Hesse termed the “hundred-gated Cathedral of Mind.”

    And the scope of that cathedral, in its gradual entirety, is vast — encompassing all the vast quantities of the sciences, with the qualitative depths and heights of the arts and humanities too:

    The Glass Bead Game is thus a mode of playing with the total contents and values of our culture; it plays with them as, say, in the great age of the arts a painter might have played with the colors on his palette. 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.

    We are drawing close, in a humanly possible way and without making any predications of the being or non-being of such a supposed entity, to the very mind of god.


    And with immediate real world application, as when Maxwell sees the commonality between electricity and magnetism, Kekulé the serpent-biting-it’s-tail like form of the benzene ring — or Taniyama‘s 1955 “surmise” as Barry Mazur puts it, that “every elliptic equation is associated with a modular form” — an insight that was to bear rich fruit forty years later, in Andrew Wiles‘ proof of Fermat’s Last Theorem.

    Hesse’s vision of the game was lucid, elegant, intellectual — but lacked real world application. Viewed as a method of scoring the music of ideas, it offers illuminations from the most abstract and theoretical of mathematics to the most complex of opposed political intrangencies — from Tamiyama to Edward Said, and from Christopher Alexander‘s Pattern Language to John Holland‘s “genetic algorithms“. Alexander and Holland each indicate their debt to Hesse’s fictional game in their own respective works.

    How, then, to notate this game, these moves that leap side-wise, pattern-wise, semblance-wise across boundaries and boxes, limitations and disciplines — for it is these leaps, as Arthur Koestler notes in his The Act of Creation, that give us the surprised aha! of discovery, the unexpected ha! of laughter, the gut-wrenching wail aiiyeee! when tragedy strikes.

    My own inclinations favor play — solo or with a friend — at a coffee house, with pencil and paper napkin, with a small graph for a board, ideas played at its nodes, connections and resonances represented by its edges. I’m thinking of network mapping on a human scale, between seven and a dozen nodes, each one rich in meaning, anecdote, quote, statistic, image, snatch of song…

    But the essence is the single move, the single resemblance. And for this I have a form which I would like to offer you, downloadable, for your own experiments:

    Download the image and fill the two spaces with what you will — whatever you can sketch, whistle, count out or scribble —

    I think you’ll find the greatest reward comes when the two ideas, visuals, verbals, aurals you juxtapose are closely related yet drawn from distantly separated regions of thought.

    At their best, such juxtapositions cross galaxies. My own most cherished example to date compares a night sky by Van Gogh with a von Kármán diagram of turbulent flow…


    And where does this lead us? What becomes of CP Snow‘s famed Two Cultures?

    Two great rows of pillars in Hesse’s hundred-gated cathedral, perhaps — best appreciated when one looks up, and sees the great vaulted roof, the magnificence of the arches between them.

    In future Monday columns here on 3QD, I hope to bring you some further moves in the great game of correspondences, weaving together topics that have caught my attention in the preceding month — now in poetry, now on the morning news.

    The leaps.


    I’m happy to report that friend Bill Benzon made the 3 Quarks Daily cut and will be blogging there, and that friend Omar Ali is already one of their regulars.

    Sunday surprise 9: surreal art imitates real life?

    Sunday, October 20th, 2013

    [ by Charles Cameron — my semi-official idiocy to cap the week ]

    Here, surreal art imitates real life — ahead of time, and or much later.



  • Tokyo Times, An abandoned and atmospheric Japanese school in the mountains
  • Salvador Dali, The Persistence of Memory

  • A tip of the hat to Bryan Alexander of Infcult
  • **


    Time itself is a curious business, and the question of its “reality” comes up from time to time. Physicist Sean Carroll talked about it a while back on the pompously named Closer to Truth series, and makes some interesting points. I have to say, though, that I wasn’t overwhelmed — Carroll may be the equivalent of Hawking when it comes to physics, but the equivalent of Wittgenstein when it comes to philosophy he has yet to prove himself.

    But then of course we have never seen Wittgenstein talking off the cuff on YouTube: my sense is that this was a wise decision on his part — although many of the slips of paper on which he typed the aphorisms that go to make up his Zettel might well have been Tweeted, give or take a century.

    Twitter’s immense fan-base does include thousands — and likely hundreds of thousands — of folks who would follow a Witty Wittgenstein twitter-feed among it’s half-billion (2012 estimate) users if wittgenstein were alive and tweeting… Indeed, the entirely posthumous Wittgenstein Tweets feed has more than 4,000 followers, and you might care to join them — although the quotes in the tweets are more than 60 years old at time of tweeting. My own preference for a philosophical feed, btw, runs to Kim Kierkegaardashian.

    But it’s Sunday, we were talking surrealism, and I digress.

    Single Quote: Robert B. Laughlin

    Monday, August 26th, 2013

    [Extracted by Lynn C. Rees]

    From A Different Universe: Reinventing Physics from the Bottom Down (2006) by Robert B. Laughlin:

    The transition to the Age of Emergence brings to an end the myth of the absolute power of mathematics. This myth is still entrenched in our culture, unfortunately, a fact revealed routinely in the press and popular publications promoting the search for ultimate laws as the only scientific activity worth pursuing, notwithstanding massive and overwhelming experimental evidence that exactly the opposite is the case. We can refute the reductionist myth by demonstrating that rules are correct and then challenging very smart people to predict things with them. Their inability to do so is similar to the difficulty the Wizard of Oz has in returning Dorothy to Kansas. He can do it in principle, but there are a few pesky technical details to be worked out. One must be satisfied in the interim with empty testimonials and exhortations to pay no attention to the man behind the curtain. The real problem is that Oz is a different universe from Kansas and that getting from one to the other makes no sense. The myth of collective behavior following from the law is, as a practical matter, exactly backward. Law instead follows from collective behavior, as do things that flow from it. such as logic and mathematics. The reason our minds can anticipate and master what the physical world does is not because we are geniuses but because nature facilitates understanding by organizing itself and generating law.

    An important difference between the present age [i.e. the Age of Emergence] and the age just past [i.e the Age of Reductionism] is the awareness that there are evil laws as well as good ones. Good laws, such as rigidity or quantum hydrodynamics, create mathematical predictive power through protection, the insensitivity of certain measured quantities to sample imperfections or computational errors. Were the world a happy place containing only good laws, it would indeed be true that mathematics was always predictive, and that mastering nature would always boil down to acquiring sufficiently large and powerful computers. Protection would heal all errors. But in the world we actually inhabit, dark laws abound, and they destroy predictive power by exacerbating errors and making measured quantities wildly sensitive to uncontrollable external factors. In the Age of Emergence it is essential to be on the lookout for dark laws and artfully steer clear of them, since failure to do so leads one into delusional traps. One such trap is inadvertently crossing a Barrier of Relevance, thereby generating multiple ostensibly logical paths that begin with nearly identical premises and reach wildly different conclusions. When this effect occurs it politicizes the discussion by generating alternative “explanations” for things that cannot be distinguished by experiment. Another trap is the hunt for the Deceitful Turkey, the mirage law that always manages to be just out of focus and just beyond reach, no matter how much the measurement technology is improved. Ambiguities generated by dark law also facilitate fraud, in that they allow a thing to be labeled quantitative and scientific when it is, in fact, so sensitive to the whim of the measurer that it is effectively an opinion.

    The Greek pantheon came into being through a series of political compromises in which one tribe or group, prevailing over another in warfare, would exercise its authority not by wiping out the gods of the losers, which was too difficult, but by making those gods subordinate to their own. The ancient Greek myths are thus allegories of actual historical events that took place in the early days of consolidation of Greek civilization. While the “experiment” in that case was war, and the “truth” it revealed was some political reality, the psychological elements for inventing mythological laws were the same as those we use today to identify physical ones. You may feel that both are pathological human behaviors, but I prefer the more physical view that politics, and human society generally, grow out of nature and are really sophisticated high-level versions of primitive physical phenomena. In other words, politics is an allegory of physics, not the reverse. Either way, however, the similarity reminds us that once science becomes political it is indistinguishable from state religion. Under a system of truth by consensus one expects false gods to be systematically enshrined in the pantheon as a matter of expedience, and the cosmogony on occasion to become Fictional, just as occurred in ancient Greece, and for the same reasons.

    Greek creation myths satirize many things in modern life, particularly cosmological theories. Exploding things, such as dynamite or the big bang, are unstable. Theories of explosions, including the first picoseconds of the big bang, thus cross Barriers of Relevance and are inherently unfalsiable, notwithstanding widely cited supporting “evidence” such as isotopic abundances at the surfaces of stars and the cosmic microwave background anisotropy. One might as well claim to infer the properties of atoms from the storm damage of a hurricane. Beyond the big bang we have really unfalsifable concepts of budding little baby universes with different properties that must have been created before the infationary epoch, but which are now fundamentally undetectable due to being beyond the light horizon. Beyond even that we have the anthropic principle—the “explanation” that the universe we can see has the properties it does by virtue of our being in it. It is fun to imagine what Voltaire might have done with this material. In the movie Contact the Jodie Foster heroine suggests to her boyfriend that God might have been created by humans to compensate for their feelings of isolation and vulnerability in the vastness of the universe. She would have been more on target had she talked about unfalsifiable theories of the origin of the universe. The political dynamic of such theories and those of the ancient Greeks is one and the same.

    The political nature of cosmological theories explains how they could so easily amalgamate with string theory, a body of mathematics with which they actually have very little in common. String theory is the study of an imaginary kind of matter built out of extended objects, strings, rather than point particles, as all known kinds of matter—including hot nuclear matter—have been shown experimentally to be. String theory is immensely fun to think about because so many of its internal relationships are unexpectedly simple and beautiful. It has no practical utility, however, other than to sustain the myth of the ultimate theory. There is no experimental evidence for the existence of strings in nature, nor does the special mathematics of string theory enable known experimental behavior to be calculated or predicted more easily. Moreover, the complex spectroscopic properties of space accessible with today’s mighty accelerators are accountable in string theory only as “low-energy phenomenology”- a pejorative term for transcendent emergent properties of matter impossible to calculate from first principles. String theory is, in fact, a textbook case of a Deceitful Turkey, a beautiful set of ideas that will always remain just barely out of reach. Far from a wonderful technological hope for a greater tomorrow. it is instead the tragic consequence of an obsolete belief system—in which emergence plays no role and dark law does not exist.


    The painful echoes of ancient Greece in modern science illustrate why we cannot live with uncertainty in the Age of Emergence. at least for very long. One often hears that we must do so, since the master laws do not matter and the little subsidiary ones are too expensive to ferret out, but this argument is exactly backward. In times of increased subtlety one needs more highly quantitative measurements, not fewer. A measurement that cannot be done accurately, or that cannot be reproduced even if it is accurate, can never be divorced from politics and must therefore generate mythologies. The more such shades of meaning there are, the less scientific the discussion becomes. Accurate measurement in this sense is scientific law and a milieu in which accurate measurement is impossible is lawless.

    The great scientific art-grab

    Wednesday, February 20th, 2013

    [ by Charles Cameron — a poet’s rant against the hubris of scientists and the poverty of so much of what passes for art ]

    Gorgeous. And fascinating.


    I’d like to begin by saying beauty is not the same as prettiness any more than joy is the same as fun or truth than popular opinion. In fact I have an aphorism:

    if you shoot for beauty, you’re liable to hit prettiness; if you want to achieve beauty, shoot for truth.

    Okay? The beautiful can be grotesque, utterly normal, joyously peaceful, extremely violent, or simply gorgeous — and be beautiful in each case.

    Having said that, I’d also like to say that the world, the universe in all it immense scope and scale and variety and possibility, isn’t “science” or “art” — we find science in exploring it one way, find art in exploring it another.

    And when scientists want to impress, they often do it by choosing elements of beauty in what science has recorded of a universe that is neither science nor art but seamlessly filled to the brim with both — by appealing to our aesthetic taste, to the “art” side of our being, while claiming the result is science.


    Case in point:

    The graphic above, from the I fucking love science photo timeline on FaceBook, which comes with the caption:

    Caddisfly larvae build protective cases using materials found in their environment. Artist Hubert Duprat supplied them with gold leaf and precious stones. This is what they created.

    Did you get that? It’s from a site that bills itself I fucking love science that specializes in presenting, how can I make this simple, nature’s art. It’s the recognition of beauty that makes this site so wonderful — and in this particular case, the work of Artist Hubert Duprat.


    I’ve been working with jewelry recently, and as you can see from this image of a Hematite “Tricubi” necklace by Bernd Wolf, the influence goes both ways.


    What is beauty? And why does science as an institution so often want to claim what properly belongs in the realm of art? Or is science, perhaps, an art or cluster of arts? I’m tired of these ceaseless wranglings between two supposedly opposing cultures.

    Paul Dirac:

    I think that there is a moral to this story, namely that it is more important to have beauty in one’s equations that to have them fit experiment.

    As art, the jewel-like protective cases those caddisfly larvae make are simply beautiful. The fact that they make them is fascinating.

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