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In honor of the SuperBowl, which I as a Brit know nothing about

Saturday, February 2nd, 2019

[ by Charles Cameron — the curious language and precise scientific timing of tomorrow’s game ]
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The curious language of the Superbowl:

Memorable Trick Plays of Super Bowls Past

Sometimes trick plays are all about players’ resourcefulness—what they’re willing to do with what they’ve got. Last year, at Super Bowl LII, Nick Foles, the Eagles’ backup quarterback, who has become known for his fighting spirit and mystifyingly magic touch, called and executed perhaps the most famous trick play in recent history, “The Philly Special,” which is actually a combination of three lesser trick plays: a snap to the running back, a pitch to the tight end, and a pass to the quarterback. In 2006, at Super Bowl XL, the Steelers pulled off a similarly discombobulating series of tricks-within-a-trick, a fake double-reverse pass that ended with a forty-three-yard touchdown pass by Antwaan Randle El, the receiver with the golden arm.

Other trick plays come from coaches with no-guts-no-glory attitudes, who approach games as if they are leading the Spartans into battle. In 2010, at Super Bowl XLIV, the Saints’ coach, Sean Payton, successfully called the first ever onside kick to be attempted before the fourth quarter of a Super Bowl game (a play he nicknamed The Ambush).

There’s a video on the New Yorker page those paras are taken from, but I’m not going to steal it — if you’re into [American] football, you should go watch it there, and read the whole piece while you’re at it!

Eh?

Somewhere else, I saw a reference to “throwing the hook and ladder” — would anyone care to translate? That’s the most troublesome of the phrases I’ve seen, but “snap to the running back, a pitch to the tight end, and a pass to the quarterback” (above) comes close — what’s the difference between a “snap”, a “pitch”, and a “pass”? — and a “double-reverse pass” (above, likewise) — what’s that? Do two reverses make a straightforward? If not, why not?

Oh, and then a friend mentioned “flea flickers” and “quarterback sneaks”. Language is a terrific sport!

**

The precise scientific timing of the Superbowl:

For nerds who may wonder, turning aside from the upcoming game to my twitter feed, there’s this:

What Time Is the Super Bowl?

6:30 p.m. is the time the Super Bowl will start in Atlanta. Most of us are not in Atlanta. So for us, the game will start later than that. You need the time for the images to be captured by the cameras, be broadcasted to air or cable, be captured by my TV screen, leave my TV screen, get to my eyes (not to mention the time my brain needs to process and decode the images). You may say this is fast — of course this is fast. But it takes some time nevertheless, and I am a physicist, I need precision. For most of us, the game will actually start some time later than the kickoff in Atlanta.

**

Popcorn?

GBG: another form of associative linkage

Friday, January 11th, 2019

[ by Charles Cameron — a meander to ponder, wonder, wander, a maze to amaze, or as CS Peirce might say, a muse to amuse, an amuse-bouche ]
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Here’s a quick, long run-down of my HipBone games, where they came from, and where they’ll be going if book and online game plans come together.

My various HipBone and related games are intended as playable variants on Hermann Hesse‘s great Glass Bead Game (GBG for short).

You remember this?

As I said before:

I don’t know how Theodor von Kármán came by his Vortex Street, and I’ve spent a decade in Pasadena wandering its streets and even picked up his four volume works — signed — at a CalTech book sale — but if he had the Van Gogh painting in the back of his mind, there’s the beginning, the seed of an awesome leap.

And you might say van Gogh made a mighty leap, pre-intuiting the von Kármán pattern in the night sky..

This DoubleQuote is my favorite move in the game that has obsessed me for the last thirty or so years, the Glass Bead Game as described in Hermann Hesse in his Nobel-winning novel of the same name.

Linking arts and sciences as it does, I see it as a move at the nave roof-apex of what Hesse describes as the “hundred-gated cathedral of mind”.

The essence of a move in Hesse‘s game is associative linkage.

**

I’m using this post as something of a primer on my game thinking, before proposing a recent instance of a type of associative leap / example of a game move.

**

There are many fairly basic types of associative linkage that provide the connextive tissue between the items in an ontology:

  • this is the same as that
  • this causes that
  • this is the opposite of that
  • this symbolices that
  • this is above that
  • this is inside that
  • this is the parent of that
  • this follows that
  • this governs that
  • this proves that
  • **

    Getting more complex and multi-layered, John Robb once 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?
  • **

    From a process orientation, it’s pretty clear that the fundamental way in which most associative leaps occur to human minds takes the form:

  • this reminds me of that
  • — and that holds true even of conspicuous creative leaps not just out of the box but into the unknown — as when Yutaka Taniyama proposed his hypothesis that there exists a correspondence between elliptic curves and modular forms in 1955. Andrew Wiles eventually proved the linkage in what is now known as the Modularity theorem, as the key part of his proof of Fermat’s Last Theorem in 1993 [don’t ask me to explain, I’m not a mathematician]

    **

    Creative leaps are in general the basis of much “opening of fields” both in the arts and sciences, as described by Arthur Koestler in his Act of Creation:

    and elaborated by Douglas Hofstadter in eg his Fluid Concepts and Creative Analogies and Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, and at a depth of penetration equivalent to Robb’s questions above, by Fauconnier and Turner in The Way We Think: Conceptual Blending And The Mind’s Hidden Complexities..

    **

    Level on level, the structure of a gothic cathedral is arch building on arch (forgive my Spanish):

    Erwin Panofky‘s masterwork, Gothic Architecture and Scholasticism, argues for a common mental structure explaining the simultaneous occurrence of Gothic cathedral architecture and the scholastic argumentation characteristic of Peter Abelard and Thomas Aquinas..

    **

    The music of Hesse’s cathedral?

    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.

    And the game’s ultimate destination – besides the creation of an overarching synthesis uniting sciences and arts, great leaps of discovery and profound flights of imagination?

    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.

    In the coincidence of opposites — the buttressed left side of the cathedral’s gothic arch leaning into, against and with the buttressed right side, culminating in the high vaulting that characterizes the nave — transcendence of the physical in the spiritual..

    **

    An aside:

    Okay, very quickly, one associative link that jumped out at one poster recently after the Democratic response to Trump’s resolute desk address was the similarity between Schumer and Pelosi‘s stilted appearance, standing shoulder to shoulder at a single podium [left], and — returning to our theme of gothic as in a fugue — the celebrated painting titled American Gothic [composite, right] —

    That’s a “haha!” (comedic, laughter) rather than an “aha!” (creative, excitement) or “aah!” (tragedic, tears) explosion, to return to Arthur Koestler’s notion of bisociation and its various types and expressions.

    But that’s just fun, and will quickly become dated.. that’s an aside.

    **

    A new category of linkage:

    More seriously, I’d like to suggest that one faascinating type of linkage, close kin to “this is similar to that” is the category of mistake:

  • this is, has been, or can be mistaken for that
  • My example here is the weird sonic effect that seems to have physically hurt American diplomats and other embassy employees in Cuba, and confused national security analysts —

    That headline was taken from an article dated December 12, 2018, less than a month ago at time of writing. Doctors called in to examine embassy workers were flummoxed:

    The patients complained of intense ear pain, hearing loss, headaches, dizziness and difficulty with balance, as well as increased anxiety and irritability, doctors found, but who or what caused the damage is still unknown.

    From The Atlantic:

    Various parties argued that the strange noise was the result of a sonic weapon, a microwave attack, or malfunctioning eavesdropping equipment.

    And back to ABC:

    “The possible sources and the medical findings we have here do not have a quick or easy solution,” said Dr. Carey Balaban, a professor of otolaryngology at the University of Pittsburgh School of Medicine who contributed to the study. “I wish someone could tell us that right now. I wish we’d have that.”

    Damn commie Cubans!

    The thing is, otolaryngologists and high-tech security experts were the wrong people to solve the problem. Whenentomologists listened to a recording of the sound, they recognizedd it —

    as the mating call of Anurogryllus celerinictus, the Indies short-tailed cricket.

  • the cricket’s call has been mistaken for a devious commie attack on American diplomats
  • **

    Very briefly, then, to wrap up, since the idea is to link one concept to another, I use graphs as my game boards, assigning the concepts (images, quotes, clips &c) to numbered positions (nodes) on the boards, with the lines between them (edges) representing their associative links, which can be spelled out in however much detail a given game requires:.

    top left, the standard WaterBird board; top right, a board from the Sembl game as played on iPads in the National Museum of Australia; lower left, the Doublequote board, for direct comparison of two concepts / images; lower right, the Said Symphony board, for us in “aymphonic” games.

    The idea of conceptual graphs precedes Margaret Masterman by centuries:

    Left, the Sephirotic Tree of classical Kabbalah; middle: Oronce Fine’s diagram of the elements and humors; right: a medieval Trinitarian diagram

    And as a grace note — my two now ancient pages on Masterman, Boole and that Trinitarian diagram are still a quiet delight for scholars of conceptual graphs and the like. Masterman really was an unsung genius, and her curious and vastlky erudite paper Theism as a Scientific Hypothesis proves it..

    I wonder when AlphaZero will be playing a game like this:

  • HipBone, What sacred games shall we have to invent
  • On the felicities of graph-based game-board design: fourteen

    Tuesday, December 25th, 2018

    [ by Charles Cameron — this one, on sacrament, symbol and such, winds up being an intro to #15, not yet written ]
    .

    My last post On the felicities of graph-based game-board design drew forth a stunning tweeted response from JustKnecht, friend and fellow explorer or Hesse’s Glass Bead Game and the magic of ideas behind it:

    **

    That’s a fascinating graphical DoubleQuote, at first glance, so I dug into the two images, the left hand one coming from a Sembl post of mine in this series, On the felicities of graph-based game-board design: two dazzlers.

    It’s the one on the right, however, that opened doors for me — one door being the article by Gentner and Jeziorski, the other being Richard Boyd‘s article that follows it in Andrew Ortony (ed), Metaphor and Thought, 2nd ed, CUP (1993):

  • Gentner & Jeziorski, The shift from metaphor to analogy in Western science
  • Richard Boyd, Metaphor and Theory Change: What is ‘Metaphor’ a Metaphor for?
  • Notice, incidentally, the beautiful ouroboros in Boyd‘s title!

    Okay, that’s my Christmas reading.

    **

    It seems I’m way behind, and it’s time maybe for the HipBone Games to enter the slipstream of Philosophy as she is practiced these days.

    But first, and to put the good folks of Elizabeth Anscombe‘s discipline off the scent, there’s the question of Sacrament to consider. Sacrament, along with Entropy, is something Gregory Bateson instructed his medical students to comprehend if they are to be civilized in their discourse as future doctors and psychiatrists. In the first paragraph of the Introduction to his Mind and Nature, Bateson writes:

    Even grown-up persons with children of their own cannot give a reasonable account of concepts such as entropy, sacrament, syntax, number, quantity, pattern, linear relation, name, class, relevance, energy, redundancy, force, probability, parts, whole, information, tautology, homology, mass (either Newtonian or Christian), explanation, description, rule of dimensions, logical type, metaphor, topology, and so on. What are butterflies? What are starfish? What are beauty and ugliness?

    Note that the concept of “sacrament” occupies a place of honor second only to “entropy” in Bateson’s listing.

    **

    Sacrament?

    Sacrament?What does that have to do with the philosophy (and graphical rendering) of metaphor?

    First, here’s a quick look at the notion of Sacrament, from the Introduction: Mapping Theologies of Sacraments (pp. 1-12) of Justin Holcomb and David Johnson’s Christian Theologies of the Sacraments: A Comparative Introduction:

    In the prologue of the Gospel According to John the apostle writes about the incarnation of the Word of God, Jesus Christ, that “from his fullness we have all received, grace upon grace” (1:16). One of the means by which Christians believe we receive the grace of God in Christ is the sacraments. But what are the sacraments? As many Christians know, Augustine of Hippo succinctly defined a sacrament as being “an outward and visible sign of an inward and invisible grace.”

    The central sacrament of Christianity is the Eucharist, instituted by Christ with the words — pointing to the bread about to be broken and shared, in a complex that includes his coming crucifixion, and the institution of the Church as his continuing body or presence on earth — This is my Body.

    The Catholic view:

    The doctrine that Christ’s real presence is thus to be found in the communion wafer consecrated with the remembrance of those words at Mass is that of Transubstantiation — a contested doctrine to be sure. And the contest is viewed theologically as being between metaphor and simile.

    Thus, as I have noted before, Northrop Frye in his Anatomy of Criticism writes:

    The animal and vegetable worlds are identified with each other, and with the divine and human worlds as well, in the Christian doctrine of transubstantiation, in which the essential human forms of the vegetable world, food and drink, the harvest and the vintage, the bread and the wine, are the body and blood of the Lamb who is also Man and God, and in whose body we exist as in a city or temple. Here again the orthodox doctrine insists on metaphor as against simile, and here again the conception of substance illustrates the struggles of logic to digest the metaphor.

    The Reformed view:

    Simply put, the Reformed view, contra Frye, considers the Words of Institution as simile, see Literary Devices in the scripture [Caution: this link auto-downloads a Word doc]:

    A metaphor is an abridged simile

    — ie, Matthew 26.26 is to be understood as meaning not “this is my Body” but “This is like my Body”..

    Thus Daniel Featley DD in his Transubstantiation Exploded (1638) writes:

    If in this sentence “This is my Body,” the meaning be “this Bread is my Body,” the speech cannot be proper, but must of necessity be figurative or tropical.

    But in this sentence, “This is my Body,” the meaning is, “This Bread is my Body.“

    Ergo this speech cannot be proper, but must of necessity be figurative and tropical; and if so, down falls Transubstantiation built upon it, and carnal presence built upon Transubstantiation, and the oblation and adoration of the Host built upon the carnal presence.

    That’s a whole lot of toppling of the Catholic edifice, all predicated on a reading of Christ’s words as simile, not metaphor.

    Here “simile” seems to mean figurative rather than literal — where the Catholic view, as we have seen, aka “metaphor”, posits literal real presence in the form of a (transcendent) inward and spiritual grace..

    **

    A by-gone Queen of the Sciences

    How does this theology of metaphor fare today? Theology, my own discipline at Oxford, sadly seems a by-gone Queen of the Sciences. Thus William Grassie writes:

    Our medieval ancestors understood theology to be the queen of the sciences. Her twin sister Sophia — the Greek word for “wisdom” — was also venerated in the discipline of philosophy. It was hard to tell the two beauties apart, but together they once ruled the many domains of human knowledge.

    Theology departments today, however, are increasingly irrelevant backwaters in the modern university, engaged in seemingly solipsistic debates.

    Ouch.

    Just for the record, while we’re slipping a theological understanding of metaphor into our thinking on the topic, should also consider Coleridge on symbol:

    Now an allegory is but a translation of abstract notions into a picture-language, which is itself nothing but an abstraction from objects of the senses; the principal being more worthless even than its phantom proxy, both alike unsubstantial, and the former shapeless to boot. On the other hand a symbol … is chaacterized by a translucence of the special in the individual, or of the general in the special, or of the universal in the general; above all by the translucence of the eternal through and in the temporal. It always partakes of the reality which it renders intelligible; and while it enunciates the whole, abides itself as a living part in that unity of which it is the representative.

    **

    In the spirit of Hermann Hesse‘s Nobel-winning Glass Bead Game — and if you can’t abide the arts and humanities, then of EO Wilson‘s concept of consilience — these notions of sacrament, metaphor and symbol should be entered into the philosophical and scientific thought-stream on metaphor and its graphical representation, IMO, YMMV, &c.

    In case you missed all that.

    And so to the present readings, Boyd and Gentner & Jeziorski..

    **

    **

    Earlier in this series:

  • On the felicities of graph-based game-board design: preliminaries
  • On the felicities of graph-based game-board design: two dazzlers
  • On the felicities of graph-based game-board design: three
  • On the felicities of graph-based game-board design: four
  • On the felicities of graph-based game-board design: five
  • On the felicities of graph-based game-board design: six
  • On the felicities of graph-based game-board design: seven
  • On the felicities of graph-based game-board design: eight
  • On the felicities of graph-based game-board design: nine
  • On the felicities of graph-based game-board design: ten
  • On the felicities of graph-based game-board design: eleven
  • On the felicities of graph-based game-board design: twelve
  • On the felicities of graph-based game-board design: thirteen
  • Jews converting to Catholicism, a Dual

    Saturday, December 22nd, 2018

    [ by Charles Cameron — “Conversion is sort of like the untouchable ‘third rail’ of religion” ]
    .

    It’s an ancient, uncomfortable story:

    The Genetic Legacy of the Spanish Inquisition
    As Spain simultaneously persecuted its Jews and expanded its colonies in the Americas, conversos secretly came over to the New World. Their legacy lives on in DNA.

    In 1492, best known as the year Columbus sailed the ocean blue, Spain also decided to expel all practicing Jews from its kingdom. Jews who did not leave—and were not murdered—were forced to become Catholics. Along with those who converted during earlier pogroms, they became known as conversos. As Spain expanded its empire in the Americas, conversos made their way to the colonies too.

    The stories have always persisted—of people across Latin America who didn’t eat pork, of candles lit on Friday nights, of mirrors covered for mourning. A new study examining the DNA of thousands of Latin Americans reveals the extent of their likely Sephardic Jewish ancestry, more widespread than previously thought and more pronounced than in people in Spain and Portugal today. “We were very surprised to find it was the case,” says Juan-Camilo Chaco?n-Duque, a geneticist at the Natural History Museum in London who co-authored the paper. [ .. ]

    In the case of conversos, DNA is helping elucidate a story with few historical records. Spain did not allow converts or their recent descendants to go to its colonies, so they traveled secretly under falsified documents. “For obvious reasons, conversos were not eager to identify as conversos,” says David Graizbord, a professor of Judaic studies at the University of Arizona. The designation applied not just to converts but also to their descendants who were always Catholic. It came with more than a whiff of a stigma. “It was to say you come from Jews and you may not be a genuine Christian,” says Graizbord. Conversos who aspired to high offices in the Church or military often tried to fake their ancestry.

    The genetic record now suggests that conversos—or people who shared ancestry with them—came to the Americas in disproportionate numbers.

    Paper:

  • Nature, Latin Americans show wide-spread Converso ancestry and imprint of local Native ancestry on physical appearance
  • **

    A variant on that story then reappears in the life of Gustav Mahler. My nephew Daniel Hardin explains:

    Two comments on Mahler and conversion:

    On 23-02-1897 (Year 1897) Gustav Mahler walked into the St. Michael’s church in Hamburg and was “received” or baptized into the Roman Catholic faith. The rite of conversion, Mahler believed would clear away a major stumbling block as a prerequisite for being named principal director of the Vienna Hofoper, the Court Opera, today’s Vienna State Opera, and a position for which he and his supporters had been discreetly campaigning for many months.

    and:

    Conversion is sort of like the untouchable “third rail” of religion: switching faiths is frequently the cause of family rupture, personal torment and bitter theological debates. Some parents consider converted children to be dead, both spiritually and physically.

    Sources:

  • National Catholic Reporter, Unconventional converts
  • Gustav-Mahler.eu, Religion
  • See also:

  • Simon Dubnow Institute, Christianity and Conviction: Gustav Mahler and the Meanings of Jewish Conversion in Central Europe
  • Academia.edu, The Conversion of Gustav Mahler
  • **

    Here Daniel Harding conducts the Vienna Philharmonic in Mahler‘s 5th Symphony, in a live recording this year:

    Daniel’s recording of the Mahler 5th with the Swedish Radio Symphony Orchestra,very recently released by Harmonia Mundi, won enthusiastic praise from The Gramophone, the reviewer concluding:

    In a market where modern rivals sound pedestrian or perfumed with finesse by comparison, this Fifth raises high hopes for what the graphic cover artwork implies may become a complete cycle.

    Here’s from another review of the same recording:

    Rarely have I heard the few opening measures of this symphony unleashed with such oppressively inexorable force, and its final minutes infused and driven by such ecstatic euphoria, with everything in between shaping the radical transformations that link the two extremes. After all the Symphony No. 5 in C-sharp minor by Gustav Mahler (1860-1911) is an expansive epic journey ‘per aspera ad astra’ (‘through hardship to the stars’) from fears of oppressive intolerance to great feelings of overwhelming joy.

    Highly, obviously, recommended.

    Arts & Sciences, models & illustrations, Buddhas within mandalas

    Friday, June 29th, 2018

    [ by Charles Cameron — on the illustration, visualization and modeling of supposed reality — note: I am no scientist, no artist, in fact an aphantasic ]
    .

    A telling caption to an image in New Scientist gave rather more of the game away than was maybe intended.

    The image:

    The caption:

    We have no pictures of the real thing, so enjoy this one instead. Oliver Burston/Alamy

    **

    It’s a nice image, and could be used to represent Lise Meitner‘s discovery of nuclear fission, or some new feature of Kepler’s Supernova, or even, Lord knows, to sell collectible gold coin or diamonds.. And it brings up in acute form an issue I’ve long had with science — in the context of education and the last century’s growing indifference to the arts and humanities.

    How much of what passes for science in the pop science press is in fact art, and specifically photography? And as a sub-question, how much of the impact a particular piece of scientific work receives is dependent on the various qualities of the illustrations used to accompany and promote it — which all too often fit the description in the caption above:

    We have no pictures of the real thing, so enjoy this one instead.

    Or alternatively, shooting for something a little more frank, but not too terribly impolite:

    We have no pictures of the real thing, so enjoy this bullshit instead.

    **

    We hardly ever have a picture of the real thing — which occurs at nano-scale, or outside the visible spectrum, or —

    Well, some while back, we discussed (ignorantly, rest assured, De Docta Ignorantia, qv) a mathematical object of interest to physicists known as The Amplituhedron:

    The Amplituhedron can alternatively be illustrated thus:

    There’s a donut for anyone who can imagine what can possibly merit both illustrations!

    **

    On our way to an understanding of the Amplituhedron, we pass by diagrams such as this:

    — immediately followed by these words:

    Although it is hard to draw the complete four-dimensional polytope, its four three-dimensional faces each define square-pyramidal regions of G(2, 4)

    — as, for instance, this:

    **

    Oh, c’mon, it’s not that hard, just visualize it!

    Tibetan monks can visualize things like this 3-D palace replete with Vases, Wish-granting Trees, Bodhisattvas, Tathagatas and Shaktis, all surrounding the deity Kalachakra and his Consort, Vishvamata

    And the vajrayanist Tibetan practitioners, yes, manage this just by PhD and postdoc level visualization practice, with diagrammatic assists like this:

    — and a blueprint like this:

    — always bearing in mind that, eh, “Kalachakra is a black skinned, four-faced god with twelve arms and twenty-four hands, in passionate embrace with his consort”:

    Kalachakra and Vishvamata, from the Rubin Museum of Art

    **

    Ah, but that’s arts and humanities > comparative religion > Tibetan meditation, not sciences > physics > mathematical physics, eh?

    In all this, I intend to defend both science, properly so understood, as practiced bt qualified practitioners within its various subdisciplines, and arts and humanities, properly so understood, as practiced bt qualified practitioners within their various subdisciplines — while making clear the overwhelmingly important distinction that illustrations are all too often not science but STEM-propaganda, glossy / shiny objects passing for science while in fact falling under the categories of illustration or photography.

    **

    This isn’t, for instance, in any scientific sense, the Horseshoe Nebula

    It’s, as its title suggests, a reproduction of a compositie color image of the Horseshoe Nebula

    — and to be honest, it may bear as much resemblance to a horse’s head as this reoroductionf of a color image of a seahorse does:

    **

    Just let’s keep the arts’ contribution to science illustration filed under arts (illustration), and math diagrams filed under math (diagrams) — I’ve included some of both above — and maybe the arts and humanities will get to siphon off some of the excitement and funding currently pouring into the coffers of (poor little) science.

    Tibetan Buddhists FTW!

    **

    Ooh-wah!

    Art or science?

    Gravitational lens RX J1131-1231 galaxy with the lens galaxy at the center and four lensed background quasars

    That, at least, is what they tell me..


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