Saturday, May 6, 2017

albers einstein


Figure 1: Monument to Change as it Changes
Piano teachers know the antidote to insipid interpretation: call for a change of color. Monochromatic treatments of harmonic transitions have a flattening effect, while inflection lifts latent pitches from the page. This applies on canvas as well as in concert, according to Josef Albers’s Interaction of Color, wherein “the relationality of the former [interaction]” depends upon the “relativity of the latter [color].”¹ In addition to characterizing color’s interactive infinitude, Albers demonstrates that tone and color operate along axes of time and space, respectively. Peter Wegner’s Monument to Change as it Changes (Figure 1), however, eludes this essential distinction by fusing both variables into spacetime.

Throughout Interaction of Color, Albers employs myriad musical metaphors. One such example neatly establishes the essentiality of contextual consideration: “In musical composition, so long as we hear merely single tones, we do not hear music. Hearing music depends on the recognition of the in-between of the tones, of their placing and of their spacing.”² Likewise, isolated colors convey little visual information, however richly conceptual their presentation. Words, chemical elements, human beings—all such specimens seek to bond with others in pursuit of meaning. Albers continues the musical metaphor, elaborating upon “placing and spacing”: “The tune of ‘Good morning to you’ consists of 4 tones. It can be sung in a high soprano, a low basso, and in all in-between voices, as well as on many levels and in many keys… In all possible ways of performance, this melody will keep its character and be recognized instantly. Why? The intervals of the four tones, that is, their acoustical constellation (again comparable with a topographic relationship), remains the same. Although it is not common practice, one can also speak of intervals between colors. Colors and hues are defined, as are tones in music, by wavelength.”³ For example, complementary colors span the widest interval. Information lives in the distances between endpoints, rather than in the colors themselves. Such qualities enable the swift transposition of chords, as well as translation and transformation of graphs (thus the comparison with a topographical relationship). Despite such shifts, relationships remain intact, and retain the construction’s original “character.” Such a de-emphasis of the wavelength itself speaks to Albers’s focus on the interaction, rather than the physical properties, of color.



Figure 2: Homage to the Square: Lone Light
Following this distinction, Albers dismantles the ongoing comparison between tone and color, disclosing that “the metaphor misleads because basic conditions of these media result in different behavior.”⁴ First, Albers addresses music’s dependence on time: “Tones appear placed and directed in the time from before to now to later. Their juxtaposition in a musical composition is perceived within a prescribed sequence only. Vertically, so to say, one tone, or several simultaneously, sound for a varying but restricted length of time. Horizontally, the tones follow each other...only in one direction—forward. Tones heard earlier fade, and those farther back disappear, vanish. We do not hear them backward.”⁵ Music, then, depends entirely upon the progression of time; is an essential variable in its formulation. The unidirectionality of time’s arrow ensures music’s ephemerality, despite recording as a mechanical means of reproduction. In contrast, colors “appear connected predominantly in space. Therefore, as constellations they can be seen in any direction and at any speed. And as they remain, we can return to them repeatedly and in many ways.”⁴ The formula for color, then, rests upon variables xy, and z, all of which exist within the confines of three dimensions, and independently of the fourth: t. Constellations of color, then, arise from manipulations of space. Albers thus summarizes such thoughts: “This remaining and not remaining, or vanishing and not vanishing, shows only one essential difference between between the fields of tone and color.”⁴ Arrays of visual and aural possibility propagate endlessly, but orthogonally. Sound and light waves, crossing without constructing (or cancelling), interfere only in the imagination. According to Albers, the “field of color” does not vanish, despite time’s negligible efforts to fade, tarnish, or touch it. (Though to dust all return, art does so rather imperceptibly). Time, in fact, works to color’s advantage: while performers have a mere instant to produce the desired tone, visual artists may pause between brushstrokes, perfecting their product more peacefully. Space affects tone more significantly than time does color, as sound waves propagate through air and bump into objects, turning back the way they came for better (resonance) or for worse (audio feedback). Tones, therefore, are slaves to both time and space. Though endless, such “essential differences” between the interactions of color and of tones may be reduced to functions of x, y, z, and t.

When Peter Wegner constructed his Monument to Change as it Changes (Figure 1) in 2011, fields of tone and color had long collapsed and into a single coordinate system, as exemplified by video art. Having taken Albers’s “Color” course as an undergraduate, Wegner also appreciates visual relativity: “Because color is contextual, you can create a rich palette simply by varying the rhythm of a few different shades. Six sheets of this color followed by ten sheets of that. Different people would tell me a given paper installation had nineteen colors, or eleven or thirty, and in a sense, each was correct.”⁶ Varying numbers of colored sheets induces rhythm (though of a stop motion, illusory variety), considered by Wegner a critical component of color creation. In Monument to Change as it Changes, however, colored sheets are at the mercy of truly rhythmic flip-digit modules, the technology behind European train station arrival/departure boards. This time-dependent technique enables Wegner to “bend color the way Coltrane bends a note,”⁶ fusing both color and motion into perpetually-evolving contexts. 

The formal parallels between Albers’s and Wegner’s works enable further interaction between color and time. In an essay entitled “The Artist as Alchemist,” Nicholas Fox Weber observes that Albers “found multitude and stability in a few forms.” Albers’s nested squares, for instance, corralled color combinations both careening and calm (Figure 2). This particular Homage to the Square, evocative of egg, derives its architectural soundness from the perspective-preserving alignment of corners. According to Tate Modern curator Achim Borchardt-Hume, Albers likely selected squares for their abstract accessibility: “[Homage to the Square]’s primary concern was with the visceral nature of color perception. Yet, it is telling that the series’ title, rather than alluding to color, references the dominant shape; the word Homage suggesting Albers’s reverence for the square’s formal authority free from any representational associations.” Thus, the ubiquitous and therefore unfettered square best facilitates “visceral” detection of color interaction; representational forms would enforce a more limited reading of reality. Wegner favors the similarly-facilitative faculties of grids, which he calls “a distribution of cells. The distribution is universal. It’s how bodies and buildings and terrorists organize themselves. A painting or sculpture that borrows this form is just one more instance of the perpetual grid.”ٰ¹ Just as pixels codify information-dense imagery, squares and grids simplify chaos into constituent components. Grids, with their repeating rectangles, accomplish this in an especially meditative manner: in Albers’s early work Glitterbild (Figure 3), tinted glass nestles neatly into wire cells, while further cell-divisions evoke fractals. Wegner’s Monument to Change as it Changes also showcases the grid’s rationalizing rhythm, sectioning continuous colors just as measures mark music. 


Figure 3: Glitterbild
Grids create considerations of quantity. Albers muses that “although quantity and quality are considered disparate, in art and music they appear closely related. We may even hear, ‘Quantity is a quality,’ because here quantity not only designates amounts, as of weight or number, but also is a means of underlining, of pronouncement, and a means of equilibrium, of balance.”¹¹ For example, considerations of equilibrium may direct Albers’s placement of warm and cool colors throughout Glitterbild, while considerations of pronouncement determine his proportioning of Homage to the Square. The acts of placing and proportioning both require quantitative calculation and qualitative consideration. Wegner’s 3-ton, 2,048-flip module Monument certainly posed technical challenges in addition to its aesthetic puzzles. Albers continues: “The two basic quantity questions, how much and how often, distinguish two kinds of quantity: one of size (extension in area) and one of recurrence (extension in number). Both measurements… establish weight in space—and weight in time.”¹¹ Size obviously corresponds to “weight in space”: weight is a function of gravity, which increases proportionately with mass. By linking “recurrence” to “weight in time,” Albers suggests that repetition of two- or three-dimensional objects throughout space simulates the passage of time, possibly because one’s perception evolves as his or her eyes travel over a pattern. With 2,048 recurrences of the same form, Wegner’s Monument to Change as it Changes convincingly establishes weight in time; even in photographs, the colored cells possess the graduality of storyboards.

Figure 1 (detail)
In Interaction of Color, Albers refrains from characterizing color without context. If color is truly “the most relative medium in art,”¹³ how may one ascertain the attributes of a single shade? Synesthetically, perhaps. Critic Frederick Horowitz whimsically observes that “in Albers’s metaphorical world, free studies became orchestral sounds, cooking ingredients, flavors, geographical locations, actors in performances. Colors noticed other colors, dominated other colors, formed dictatorships and democracies… some [colors] were children who reflected the qualities of the parents,”¹ confirmed by the Homage[s] to the Square unambiguously titled Lone Light, Autumn Scent/Smell, and Advancing Spring. Note, however, that the aforementioned “[sounds, ingredients, flavors, locations, and actors]” remain particles eager to engage with others; the “dictatorships and democracies” depend upon constituents; and “children” inherit the traits of their parents—truly, colors resonate only in combination. Horowitz ascribes these comparisons to Albers’s familiarity with “Goethe’s ascription of character to colors in the Farbenlehre. Goethe, for example, saw ‘vivacity and nobility’ in yellow, ‘a strong feeling of warmth and joy’ in orange, and ‘a feeling of cold’ in blue.”¹ While most agree upon the orangeness of tangerines and other concrete objects, a color’s abstract associations vary. Thus, “Albers rarely talked about the character of color in the abstract. As a color could have one character in one place and a very different character in another, each ‘performance’ would necessarily stimulate different reactions in the observer.”¹ Both blood and certain berries absorb about the same amount of light; depending on context, the same hue elicits a spectrum of reactions. As Monument to Change as it Changes cycles through its eight hours of programmed choreography, changing context too quickly for conceptualization, the work preserves the purity of color in motion. Prismatic lenses, after all, demonstrate that all wavelengths sum to white light.

Throughout Interaction of Color, Albers “[looks] at the world with a scientist’s rigor to find… a language commensurate with his vision.”¹ Should this suggest physics envy, Albers insists that “just as the knowledge of acoustics does not make one musical—neither on the productive nor on the appreciative side—so no color system by itself can develop one’s sensitivity for color. This is parallel to the recognition that no theory of composition by itself leads to the production of music, or of art.”¹ Why, then, did Albers bother to transcribe color’s conversations, then prescribe them to his art students? In “grasping the action and interaction of color as registered in our minds,” he answers, “we practice first and mainly a study of ourselves. Thus, we replace… retrospection [art historical and theoretical studies] with introspection… This proclaims creative action ahead of retrospective reaction."¹ While such a statement seems to supplant art historical inquiry with the psychological (not physical, as originally suspected) variety, this is not the case. Rather, Albers articulates an additional mystery to be solved before (for the previously untrained), alongside, or after historicization: the artistic history of oneself, arising from momently interactions with color. Indeed, Weber wrote that “[Albers] wanted [his] art to be immediate and inclusive, intelligible without any art-historical knowledge or academic education. Above all, [he] wanted it to be of its time.”¹⁹ Albers’s monumental text on color features in the etymology of Wegner’s Monument to Change as it Changes, which—for its relative contemporaneity—commemorates the complexity of our time. Throughout the time I spent studying economics in the building opposite Monument to Change as it Changes, I saw fluctuating market data in its cells, while other observers fathomed its hypnotic harmonies according to their own experience—such is the beauty of abstraction, more real to Albers than nature. The monument composed of color spins through spacetime, changing {you} with every interaction.

Figure 1. Peter Wegner, Monument to Change as it Changes
2,084 flip digit modules, each with 80 colors screen printed onto polycarbonate, steel, software, 108 × 384 × 3 in., 8 hrs of programming, 2011. (Consulting architect: Matt Flynn) Permanently installed at Stanford University.

Figure 2. Josef Albers, Homage to the Square: Lone Light, 1962
oil on masonite; 18 × 18 in. (45.7 × 45.7 cm)
Figure 3. Josef Albers, Gitterbild (Grid Mounted), ca. 1921
glass, metal, and wire; 123⁄4 × 113⁄8 in. (32.4 × 28.9 cm)
¹Nicholas Fox Weber, the artist as alchemist to Josef Albers: A Retrospective, comp. Solomon R. Guggenheim Museum, New York (New York: Harry N. Abrams, Inc., Publishers, 1988), 99.
²Josef Albers, Interaction of Color: New Complete Edition (New Haven, CT: Yale University Press, 1963), 5.
³Albers, Interaction of Color, 32.
⁴Albers, Interaction of Color, 37.
⁵Albers, Interaction of Color, 37.
⁶Peter Wegner, "10 Questions for Peter Wegner," interview by Cynthia Houng, KQED Arts.
⁷Nicholas Fox Weber, the artist as alchemist to Josef Albers: A Retrospective, comp. Solomon R. Guggenheim Museum, New York (New York: Harry N. Abrams, Inc., Publishers, 1988), 40.
ٰ¹⁰Peter Wegner, P,E,T,E,R,W,E,G,N,E,R, (n.p.: Griffin Editions, 2007).
¹¹Albers, Interaction of Color, 40-41.
¹³Albers, Interaction of Color, 1.
¹⁴Frederick A. Horowitz and Brenda Danilowitz, Josef Albers: To Open Eyes (n.p.: Phaidon, 2009), 32.
¹⁵Horowitz and Danilowitz, Josef Albers, 32.
¹⁶Albers, Interaction of Color, 2.
¹⁷Albers, Interaction of Color, 47-49.
¹⁸Weber, the artist as alchemist, 74.
¹⁹Achim Borchardt-Hume, ed., Albers and Moholy-Nagy: From the Bauhaus to the New World (New Haven, CT: Yale University Press, 2006), 78.

Sunday, January 1, 2017

The Pinkness of Pudding and Artistic Progress

Thomasina's jammy rice pudding
The notion of determinism confines historical developments to antecedent causes, conditions, and laws of nature. Though dangerous as a potential excuse for “inevitable” historical horrors, determinism may apply to artistic advent. William Dray writes apropos Ernest Nagel that “the third argument against historical determinism to be considered cites ‘the production in the human scene of new ideas, novel modes of behavior, and unprecedented works of imagination and skill.’ Whatever may be true of the natural world, the constant emergence of creative novelty in the realm of culture is held to be incompatible with a belief that everything falls under laws. What those who advance this argument have in mind, Nagel assumes, is such things as Faraday’s inventing the telephone, or Mozart’s composing The Magic Flute, or Newton’s arriving at his general theory of gravitation. His response is that, although such achievements may raise prima facie difficulties for determinism, these can be resolved” (Dray 133). Here, Dray presents novelty and creativity as forces that undermine historical determinism. In the spirit of Nagel, I aim to gently resolve the “difficulties” they present by citing causally-constructed developments in art, music, and physics.
In tracing innovative processes, “Internet of Things” pioneer Kevin Ashton identifies “tool chains” of creative causation, and embeds a Martin Luther King Jr. sermon on interrelation to illustrate the term: “‘Whatever affects one directly, affects all indirectly… You get up in the morning and go to the bathroom and reach… for a bar of soap, and that’s given to you at the hands of a Frenchman. And then you go into the kitchen to drink your coffee in the morning, and that’s poured into your cup by a South American… Before you finish eating breakfast in the morning, you’ve depended on more than half of the world.’ Half the world and the two thousand generations that came before us. Together, they give us what computer scientists call ‘tool chains’: the processes, principles, parts, and products that let us create” (Ashton 147). Thus, as artists further their traditions, they have “two thousand [generations’]”-worth of wisdom at their disposal. The cumulative nature of creation enables art historians to evaluate a specific artist’s tool chain, snugly fitting them into an overarching, epochal chain of creative cause and effect. For example, western classical music promenades beneath Baroque, Classical, Romantic, and Contemporary umbrellas, with each period building upon the principles of the preceding; visual art demands more comprehensive classification.
Bild mit Weissem Rand
Because artworks deliver instantaneous sensation, such lengthy derivations fade from audience consideration. Yet no epigram rings more truly for artists than this: “Though this be madness, yet there is method in it” (Shakespeare 2.2.195). Indeed, inspiration seeps from the patient curation of input over long stretches of time, rather than in spurts of emotional Eurekas. For example, while Wassily Kandinsky’s abstract canvases belie inspiration’s instant implementation, a bit of investigation into his Painting with White Border affirms that “art is the mastery of making appearance deceive. Kandinsky spend five months planning every stroke of his apparently spontaneous painting and years developing the method and theory that took him to it… The process took five months. The twenty-first picture, Kandinsky’s final work, is very similar to the first” (Ashton 56), but the subsurface variances from sketch to sketch speak to the gradual, deliberate nature of artistic work, a process often mischaracterized as arbitrary or impulsive. Each brushstroke influences the next, fanning into possibility.
Music matures similarly: Nagel cites Mozart’s The Magic Flute as an impromptu instance of creative novelty. Though unprecedented in musical and philosophical depth (as a diatribe against the political takeover of Freemasonry), the opera depends upon “all the major musical styles of opera in Mozart’s day. Effortlessly Mozart combines the coloratura of opera seria in the Queen of the Night, the simple elegance of opera buffa in Pamina and Tamino, simple German song in Papageno, the spiritual and oracular declamations of Sarastro, and even throws in an old German chorale for good measure” (Seifert). Mozart arranged these formulaic operatic components extra-mellifluously; Antonio Salieri (of Amadeus and actual fame) combined equivalent devices to lesser success. The same italicized elements deliver distinct results depending on their arrangement, and therein lies the mystery that somewhat diffuses determinism. In addition to listing obscure-sounding components, program notes also offer historical contextualization that functions similarly to the chronology that opens a classic novel: to connect creative motives to certain environmental causes.
formulaic operatic components
Collingwood contributes to the chorus with a word on contextualization, incorporating his emphasis on historical re-enactment: “No historian of music deserves the name unless he has studied for himself the old music whose growth and development he is trying to describe. He must have listened to Bach and Mozart, Palestrina and Lasso, and possess personal acquaintance with the works. This means that he must have been present at the actual performances of these works either physically or in imagination, and in the latter case the imaginative power is acquainted only by actually hearing similar things performed… We may therefore boldly say that the sine qua non of writing the history of past music is to have this music re-enacted in the present” (Collingwood 441). While outlining the work of a musical historian, Collingwood insists that "imaginative power” increases in direct proportion with “hearing similar things performed.” Indeed, composers such as Mozart consumed Baroque masterworks by the likes of Palestrina and Lasso as part of their training, tuning their inner ears to better carry on the composing tradition in new epochs. Personal acquaintance with preceding monuments of one’s medium permits informed interpolation, or the insertion of new data points within the range of already-known data points. Timeless music thus lays bare its etymology.
fractal-like Hegelian dialectic
Composers closer in temporal proximity exerted more observable influences on each other. Beethoven famously idolized Mozart, and though the two never met in person, the former would quote and re-mix the latter’s ideas: “On a sketch leaf from about October 1790 Beethoven wrote down a brief C-minor passage in 6/8 meter, in two-staff piano score, and then wrote down these words, between the staves, about the little phrase: 'This entire passage has been stolen from the Mozart Symphony in C…’ Then Beethoven writes the passage again just below and a little differently, on the same sketch page, and signs it 'Beethoven himself'” (Lockwood 57). Beethoven both acknowledges Mozart and attributes the thought to himself in a burst of benign plagiarism, invoking imitation as the sincerest form of flattery. According to musicologists, the following earworms by Beethoven contain direct quotations of Mozart: Symphony No. 5, Piano Concerto No. 3, Quintet for Piano and Winds, String Quartet in A Major, Piano Sonata No. 8 (Pathetique), and four sets of variations on themes from The Magic Flute, among others (Marshall 300-301).
Bach's harmonic matrices
In the wake of this dynamic duo, Mendelssohn altered the course of western music with a monumental re-discovery: “Johann Sebastian Bach's stature as a composer of such extraordinary genius and widespread influence is so firmly established in Western culture that it is difficult to imagine that only a little over a century-and-a-half ago, his music and reputation languished in obscurity, virtually unknown to all but a few specialists. It was through Mendelssohn's recognition of Bach's genius and his efforts in making Bach's works accessible to a wider public that these works are today recognized as summits of musical expression” (Library of Congress). The majority of Bach’s manuscripts had become sandwich-wrappers at at monasteries, but Mendelssohn rescued a portion by performing them for his contemporaries to hear, spawning Romantic revival of Baroque forms. Chopin’s “piano poems” merit much ado because they match the harmonic matrices laid out by Bach, whose works Chopin practiced for two hours each day as a warm-up prior to composing. With a prophetic chromaticism that verged on jazziness, Bach also provided the sonic skeleton for other late Romantic and Contemporary compositions. Prokofiev, for example, hearkens back to Bach with his Four Pieces, Op. 32, and to Mozart with Symphony No. 1 in D Major (“Classical”), and to this day piano performance students must learn one Bach Prelude & Fugue from the Well-Tempered Klavier per week as part of a balanced musical diet.
M. C. Escher: Cycle
In renewing the ancient structures of Bach, composers practiced history as John Lewis Gaddis suggested via Henry Adams: “‘We should discover the simple under the complex; then the complex under the simple; then anew the simple under the complex; and so on without ever being able to foresee the last term’” (Gaddis 73). This continuum of ever-resolving theses and antitheses, reminiscent of the fractal-like Hegelian dialectic, supports the notion that art recombines itself infinitely. The aforementioned Painting with White Border exemplifies the dialectic coming to rest:  “Kandinsky’s journey did not begin with Sketch I, and it did not end with Painting with White Border. His first works, painted in 1904, were colorful, realistic landscapes. His last, painted in 1944, were atonal, geometric abstracts. His first and last pictures look wholly unalienable, but everything Kandinsky painted in the intervening years was a small step along the road that unites them… Even in a lifetime of art, creation is a continuum… As Karl Duncker showed, all creation, whether painting, plane, or phone, has the same foundation: gradual steps where a problem leads to a solution that leads to a problem” (Ashton 56). Cyclical movement--from simplicity to complexity, from problem to solution--characterizes the creative process. Completed paintings and symphonies come to fruition when and wherever the dialectic settles momentarily; an artist’s complete oeuvre thus accumulates throughout a lifetime.
The farther artists progress into spacetime, the more chaotic their interpretation of it becomes. Simultaneous developments in physics seek to reconcile multiple measurements of singular occurrences: an event E that appears static in one frame and surges forward in another, with neither state more true than the other. Gaddis bemoaned relativity’s historiographical implications, allowing “William H. McNeill [to describe] the process: ‘The old certainties of the Newtonian world machine… unexpectedly dissolved into an evolving, historical, and occasionally chaotic universe.’ If conceptions of time and space were themselves relative, if the observation of phenomena itself distorted phenomena, then it was difficult to see how historians or anyone else could achieve certainty… Physics offered little basis for thinking you could triangulate the future, because there was no way to be sure that you’d correctly triangulated the past” (Gaddis 77). In just a half-year, Einstein authored a paper that overturned three centuries of Newtonian perspectives, loosening the limits of natural philosophy to leave more room for possibility and also uncertainty. As even time and space “were themselves relative,” nothing could be called absolute, or provide a fulcrum about which the universe could turn. Chaos became the one certainty, and complexity the excuse for vagaries.
multiple measurements of singular occurences
Yet within relativistic chaos and complexity, causal connections exist between events: Gaddis’s traffic illustration and Arcadian Valentine's deriving a snowstorm from its constituent snowflakes represent efforts to triangulate, or make sense of, the unpredictable future and nonexistent present in light of what has already transpired. Gaddis discusses escalation: “Each driver who sees the flashing blue lights of the police or the emergency vehicles will slow down accordingly, but not at the same rate. Soon there’ll be a traffic backup extending for miles. This will result, however, not directly from the precipitating event, but rather from tens of thousands of individual decisions to hit or release the brakes, each of them made in relation to what all the other drivers are doing… Predictable and unpredictable phenomena are occurring within the same system… What’s unpredictable is the aggregate behavior of all these drivers, the macro-effect that comes from their micro-responses” (Gaddis 75). Those tens of thousands of individual decisions unfold “in relation to… other drivers” indicate an interdependency amongst the multiple causes of a larger effect. Gaddis posits that each isolated decision to brake could have been pre-determined, just as individual steps toward a completed artwork can be clarified, but also that compounding them obscures certainty. In contrast, Valentine postulates that both micro- and macro-effects may be traced to their causes, and that only intermediate phenomena evade triangulation: “The unpredictable and the predictable unfold together to make everything the way it is. It’s how nature creates itself, on every scale, the snowflake and the snowstorm… Relativity and quantum… only explained the very big and the very small. The ordinary-sized stuff which is our lives, the things people write poetry about--clouds--daffodils--waterfalls--and what happens in a cup of coffee when the cream goes in--these things are full of mystery… We’re better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it’ll rain on auntie’s garden party three Sundays from now. We can’t even predict the next drip from a dripping tap when it gets irregular. Each drip sets up the conditions for the next, the smallest variation blows the prediction apart… The future is disorder” (Stoppard 52). Such language, blooming with metaphor, needs little explication; but to highlight that “each drip sets up the conditions for the next” affirms the dependency and impact of variables, respectively, upon their immediate predecessors and successors. Demystification occurs only in isolation, which most historical events evade. Artworks, at least, have clearly delineated boundaries and spacetime coordinates which streamline their contextualization.
Retrospection permits the identification of artistic turning-points: works that altered the formula, or re-directed the fractal, for the absorbent imaginations that followed. Gaddis writes a recipe that likens historical and scientific inquiry: “in [physics] it’s done by looking for phase transitions, those points of criticality at which stability becomes unstable: where water begins to boil or freeze, for example, or sand piles begin to slide, or fault lines begin to fracture… What we’re looking for, then, as we trace processes that led to particular structures, is the point at which these processes took a distinctive, abnormal, or unforeseen course” (Gaddis 99) At these prediction-defying "points of criticality,” art undergoes a phase transition. Such works of artistic criticality linger with us today. Explication often strips “extraordinary” of its prefix; thus, works that disguise their deterministic traits entertain and enlighten timelessly. The visionaries responsible for such artworks certainly fought through friction as they progressed, which Ashton details in an impassioned anecdote about guitarist Robert Johnson: “When [he] came to the crossroads at midnight, it was temptation that said, ‘Do not practice, do not play, do not write, do not stretch your hands across the frets until they ache, do not press your fingers into the strings until they bleed, do not play to empty chairs and chattering drunks who boo, do not perfect your music, do not train your voice, do not lie awake with your lyrics until every word sounds right, do not study the skill of every great player you hear, do not invest your every breathing, waking minute pursuing your God-given mission to create. Take it easy, mourn your wife and child, get some rest, have a drink, play some cards, hang with your friends--they do not spend all day and night messing with guitars and music.’ And Robert Johnson looked at temptation and said no. Then he took his guitar to the Mississippi Delta and for six years played music so great it changed the world, music so great we are discussing him now not because our topic is guitars or even music but because his story breathes life into the true meaning of creative commitment” (Ashton 176). Temptation rankles all who attempt to realize visions of better versions of what they hear, see, and use. Thus, persistence and ingenuity in the face of universal opposition distinguish the truly novel and creative from the foreseeable. No human can completely rationalize Beethoven’s immutability with or without hearing, for example. Artworks produced in such circumstances immortalize struggle--they are miraculous.
Tom Stoppard stirs together all related ruminations in a passage from Arcadia wherein his precocious heroine Thomasina appraises “the ordinary-sized stuff which is our lives”:
Thomasina: When you stir your rice pudding, Septimus, the spoonfuls of jam spread itself round making red trails like the picture of a meteor in my astronomical atlas. But if you stir backward, the jam will not come together again. Indeed, the pudding does not notice and continues to turn pink just as before. Do you think this is odd?
Septimus: No.
Thomasina: Well, I do. You cannot stir things apart.
Septimus: No more you can, time must always run backward, and since it will not, we must stir our way onward mixing as we go, disorder out of disorder into disorder until pink is complete, unchanging and unchangeable, and we are done with it for ever.
Time’s arrow is unidirectional, pressing forth irreverently despite human scrambling; the distance between historical event and observer only increases. Collingwood insisted that “the historian’s business is to know the past, not to know the future,” (Collingwood 309), and to prematurely ascribe effects to retrospectively-ascertained causes indicates that “something has gone wrong with [the historian’s] fundamental conception of history. Or, as… Thomasina puts it in [Tom Stoppard’s] play Arcadia: ‘You cannot stir things apart.’” (Gaddis 58). Historians may merely comment upon the divine stirring of antecedent causes and ensuing effects, extracting harmonies from “disorder out of disorder into disorder.” As Thomasina rhapsodizes about history’s entropic unfolding in terms of the pinkness of her pudding, she places her audience in the privileged present, the relativistic frame from which they may review the cumulative whole of artistic progress, positioning themselves within tradition to stir until pink is complete.
"You cannot stir things apart."

Works Cited
Ashton, Kevin. How to Fly a Horse: The Secret History of Creation, Invention, and Discovery. 2015.
Collingwood, Robin George. The Idea of History. 1976.
Dray, William Herbert. Philosophy of History. 2nd ed., 1964.
Gaddis, John Lewis. The Landscape of History. 2002.
Kandinsky, Wassily. Painting with White Border. 1913.
Lockwood, Lewis. Beethoven: The Music and the Life. 1992.
Marshall, Robert Lewis, compiler. Eighteenth-Century Keyboard Music. 2003.
Seifert, Stephen W. “The Origins, Meanings, Rituals, and Values of The Magic Flute.” Conspirazzi, www.conspirazzi.com/the-origins-meanings-rituals-and-values-of-the-magic-flute/.
Shakespeare, William. Hamlet. 1603.
Stoppard, Tom. Arcadia. 1993.