A Daily History of Holes, Dots, Lines, Science, History, Math, the Unintentional Absurd & Nothing |1.6 million words, 7500 images, 4 million hits| Press & appearances in The Times, Le Figaro, MENSA, The Economist, The Guardian, Discovery News, Slate, Le Monde, Sci American Blogs, Le Point, and many other places... 4,200+ total posts
Confession: this may represent the coziest I'll ever be with the written lessons of Kandinsky's Concerning the Spiritual in Art (1910). It seems to me that anyone who is an artist understands this book; to me, though, as a not-an-artist, it is inscrutable--the book winds up looking not much more to me than this Word Cloud. Its a shame for me, really, as this is one of my favorite periods in the history of art, and I enjoy color theory, and I like mixing up sensations and analogies to describe cross-field experiences (like the broad use Kandinsky makes here in describing artistic qualities in terms of music) all of which are strong elements of the book. Its a lovely book, with heavy paper, wide margins, and beautifully designed, but the text is mostly just words, and sometimes a jumbled pile at that. I've tried to read it many times over the years, but I keep on failing this book.
In a world constructed of nothing but right angles in horizontals and verticals, how would a diagonal fare?
Would it be like extraordinary confusion and then recognition of a sphere in a flat two dimensional world (as in Edwin Abbott’s Flatland), or would it be an astonishing moment of discovery like Robert Hooke’s Micrographia images, or a creeping, sweeping acknowledgment of first-seen perspective in Paolo Uccello? In the case of the cubist Piet Mondrian, it would be revulsion and disgust. Mondrian helped establish1 De Stijl (1917or thereabouts), with a philosophy of using lines to transform artistic thought onto canvas, and the lines were all horizontal or vertical, with square and rectangular shapes. These would represent the pure harmonies of expression, along with the primary colors as well as black and white.
Mondrian wrote “:... this new plastic idea will ignore the particulars of appearance, that is to say, natural form and colour. On the contrary, it should find its expression in the abstraction of form and colour, that is to say, in the straight line and the clearly defined primary colour."
Stijl co-founder, popularist, artist and editor of the movement’s journal, Theo van Doesburgh and his work (1924) introduced diagonals into the horizontal/vertical field in his painting “Arithmetische Compositie” and Mondrian quits the group.Van Doesburgh felt that the diagonal was more vital and important than the vertical and horizontal. Mondrian felt that this was wrong, and clearly raked the original ideals of De Stijl, and so quit the movement, which he felt to be compromised by one of its co-founders. I can certainly appreciate Mondrian’s need to go; though, honestly, what the debate and reticence reminds me of is an episode from the original Star Trek series, “Let That Be Your Last Battlefield" (1969). The story is about an intractable difference between two seemingly identical factions of the planet Cheron2–it turns out that the differences between the two sides is a physical one that was inconsequential to the crew of the Enterprise, but of all-consuming importance to the Cheronites. They were both white and back, their skin color cleanly halving their bodies on the vertical. But the "inconsequential" difference was that one person was black on the right side and white on the left; the other was the opposite. It was this difference that led to their planet-wide schism and abandonment of each other.
Its no wonder that the writers of that episode chose the name "Cheron", which is another accepted spelling of "Charon", the Greek ferryman who transports the dead to Hades.
That's where this particular schism falls to me, though to those involved I've no doubt that the differences were as significant as 2D vs. 3D and flat perspective vs. real perspective, the blatant if not micrographic differences looming mighty small to everyone but those involved. ______ Notes
1. In 1917 it was Mondrian who coined the term Nieuwe Beelding (“the New Plastic”) , or Neo-Plasticism, from which De Stijl took its meaning. He set out the philosophy of the group in that same year in a series of twelve articles in the group’s journal, De Stijl
(On seeing the morning’s rising sun): “Looks like light to
me.” SpongeBob SquarePants
“All the fifty years of conscious brooding have brought me
no closer to answer the question, 'What are light quanta?' Of course today
every rascal thinks he knows the answer, but he is deluding himself.”A. Einstein
“Are not gross bodies and light convertible into one
another, and may not bodies receive much of their activity from the particles
of light which enter into their composition?” I. Newton, Opticks,
1704, Query 30.
Depicting the capacity of sight and nature of light has been
both an easy and a knotty problem in the history of science. Over the
successive theories on the basis of light the artistic presentation of the
phenomenon has been generalized (generally) in a very simple way:by straight lines.There’s certainly nothing wrong with that,
the lines are just parenthetic place-holders suggesting direction, not actual
descriptors of what light “looks” like.
There are literally hundreds if not thousands of images printed 1550-1850 to call upon to make this point, and I've selected but a few. The first belongs to Jesuit astronomer Christoph Scheiner and which appeared in his Oculusm hoc est: fundamentum opticum...,printed in Innsbruck in 1619. His work is an out-and-out landmark in the history of optics, physiological optics and ophthahlmometry, and provided a springboard for two generations following him, not the least of whom was Rene Descartes. The illustration above is the book's frontispiece, and features four camera obscuras demonstrating four principles of the eye, the middle ground of which is a beam of light
Rene Descartes depicted the interpretation (in his Principles of Philosophy of 1644) of light and its physiological reaction in the brain as follows:
the lines of sight depicting binocular vision, observed (and compressed) by the eye's "particles" and processed by the pineal gland which in turn manipulate the "fluids" in the control of nerves and muscles.
Another example of even greater fame than the iconic image by Descartes is that of the diagram showing the connection between color and its reflective index by Isaac Newton, appearing in his Opticae of 1706.
Another fine example comes from Zacharias Traber's (1611-1679) beautifully illustrated classic of optics (and physiological optics) , Nervus Opticus sive Tractatus Theoricus..., published in Vienna in 1690. Traber is a great collector and synthesizer of the work done during and before his time, using the work of Descartes, Kepler, Schott, Kircher, Scheiner and Aguilon (for example), and then further implementing their ideas especially in the areas of color theory and light refraction. The image certainly reflects Jesuit Traber's religious training, depicting the holy source of light (originating with the almighty force) which directs it to the sun; the light then is left to the inquisitive and playful hands of cherubs who reflect and magnify it, as well as use it to start a fire (from the condensing lens) and observe it through a telescope. The main cherub empties a sack containing a number of different optical tools, no doubt for the playful brethern beneath.
And then of course there is the great, unstoppable, polymathic and sometimes incorrect Jesuit Athanasius Kircher. This image appears in his masterwork Ars Magna lucis et umbrae, printed in Amsterdam in 1671, which deals with light and shadow, optical illusions, color, refraction, projection and distortion, sundials, mirrors, as well as astronomical subjects. Most of these subjects are clearly seen in the engraved frontispiece to the work (below), the source of all of the "rays" of light coming from the godhead, relayed through a telescope, reflected from a mirror, and gathered in a camera obscura.
Other interesting images from the Kircher include this spotlight.
if our eyes worked in the “opposite” way?What if we somehow broadcast the lines of reality from our eyes1 rather
than receive photonic emissions from the physical world, that we didn’t specify
the wavelength and frequency of light, and that somehow electromagnetic rumblings
in the “visual range” didn’t apply to our sense of sight?
would certainly make for an interesting existence
if somehow the elements around us weren’t necessarily so.Perhaps this is sort of replacement reality
is just what has been going on in the entire history of humans, altering the
landscape to make it more suitable for our existence, a long history of
painting the physical landscape with something more “suitable”, an
all came up wondering about this fantastic sky, produced 475 years before
non-representational art and 455 years before Gauguin started applying big blankets of red2 :it seems to me
in a distant impression that it is a representation of vision that is more a projector
than a camera..The end result of this
emission and wayward thought is the fabulous red sky in the painting Nativity by Master Francke3 (ca.
1424-1436) is a fantastic red sky with lustrous stars.
painting is otherwise filled with the common reliables of Renaissance iconography
concerning the nativity:the place of “birth”
(a stable or barn-like building, also sometimes appearing as a classical ruin
or cave), a flock of sheep, a stand of trees, and the watch sensate gazes of the near by
beasts.Mary is ecstatic in the same ways
that Joseph is usually not—to me, he usually seems pretty detached from the
whole deal, lost in another space.The
baby Christ is again just a little man (and not a baby) laying there on the barren
ground.[I’ve wondered about Joseph’s
detachment:perhaps the whole scene is
nothing but mysterious, a complexity far removed from his reach and
understanding, a notion of an act that is so phenomenal that there is no
retrievable reaction for it, and so he looks away.Later on in the history of Mary and Joseph,
and deep into the 19th century when the Immaculate Conception—that is,
the sexless conception of Mary the mother of Christ which she would later accomplish
for her own baby—the issue of Joseph’s own virginity comes up, mounting the
confusion no doubt in Joseph’s already-full head.]
back to the sky:certainly skies and
backgrounds of pure gold and blue painted by the masters in Sienna
abound during this time, but red is quite unusual.The sky is accented by the terrific red of
the wings of the angels and more softly so in the hair of the (long-fingered) Madonna.
is also the issue of the hole in the sky, revealing the large-handed Creator with glimpses
of the alternate, higher, existence visible in the background, a taste of the
alpha (or omega?) part of the long arch of Earth-borne humanity.
1.The discussion of optics and vision is one of the most spectacular conversations ever held in the history of science and philosophy (along with "time", "motion" and "the void". I think that Leonardo would've come closest in relatively-modern times to understanding vision if he had the real capacity of dissecting the eye (which in spite of many approaches to experiment) would always go flat, leaving him with an unsatisfying mess.
In Aristotle's Physics (Book II, Part II) we find the following fascinating thought:
"Similar evidence is supplied by the more physical of the branches of mathematics, such
as optics, harmonics, and astronomy. These are in a way the reverse of geometry. While
geometry investigates physical lines but not qua physical, optics investigates
mathematical lines, but qua physical not qua mathematical"
A classical position of the emission theory of optics is stated by Hero in his Definitions:
"Optics does not deal with physical questions and does not study whether given rays
flowing out from the eyes go forth to the boundaries of objects or whether images that are
detached go forth from corporeal objects [and] enter the eye along a rectilinear path or
whether the intervening air is stretched or contracted by the ray-like pneuma from the
eye. It is only concerned whether, at each reception (of an image) the right direction of
movement or tension is maintained as well as the requirement that the convergence to a
point occurs at an angle when objects are seen that are larger or smaller than the eye."
(My thanks to Dr. Kim Veltman for these quotes from her Continuity and Discovery in Optics and Astronomy, Studies on Leonardo da Vinci http://www.sumscorp.com/books/contin/title.html)
2. I had Gauguin's 1888 "After the Sermon/Jacob Wrestling the Angel" in mind for an example of this.
3. Master Francke active (c. 1424 –
36 ), Nativity, in the Kunsthalle, Hamburg; oil on oak,
39x35 inches. Hamburg, Kunsthalle. “German painter who worked in Hamburg, where in 1424 he painted a huge altarpiece for the company of merchants who traded with England, the so-called ‘Englandfahrer Altar’, originally placed in their chapel in the Johanniskirche (remnants in Hamburg, Kunsthalle). When closed, the double-winged altarpiece displayed four scenes from the life of S. Thomas Becket, the patron saint of the company, above four scenes from the life of the Virgin (e.g. Nativity;).
Opened, the altarpiece showed scenes from the Passion of Christ. Francke was a leader of the northern German version of International
Gothic. He had close links with French book illumination (he may
have worked in Paris for some time) and the
paintings of the Rhineland, especially those
of Conrad van Soest
, though it is not known where he received his training.”
greatness had not floated on the ebb of that river into the mystery of an
unknown earth! Heart of Darkness
on the heels of yesterday’s post about (impossible) retinal memory and the
comfort of unusual color comes this bit of oddness from the House of La
Rosa.101 Ways to Prepare Macaroni seems
about as benign and forgettable a title that one could write; that said, once
opened, this little pamphlet poured its heart out to the Naïve Surreal in us
all with the unforgettable (and accurate) color images of the promised linguine
delicacies.Honestly, the cover is why I
have the thing—it is kind of perfect, a spare design that gets the message
across, and leaves plenty of white.It
also uses a macaroni typeface.But once
inside the imagination is left to wander quite a bit between the colors of
these foods that you were supposed to cook. And eat.
long been a fan of taking a good close look at the foods on thetabletops and dining tables of country homes,
diners, and simple restaurants from the 1930’s—actually the Library of Congress
is a wonderful source for this kind of image, having many thousands of them
digitized from their monumental FSA collection.The vast majority of these though are in black and white.There seems to be not much more comforting
than a checkered tablecloth on which a huge spread is laid for a farm family
and their hired hands: giant bowls of mashed potatoes, big plates of corn, a
huge pitcher of milk, and so on. I could
dive right in.(The image below--by FSA great Russell Lee, shows a Kilgore, Texas, roughneck stopping for lunch. This is not exactly what I had in mind, but the man has a real plate, a beautiful bottle of milk, cutlery, and all wrapped up in heavy paper--this is what brought-from-home lunches should look like. And it makes me hungry.)
for some reason I started assembling a few hundred images of red photo ads of
foods from LIFE magazine from the 1940’s—these are truly spectacular things,
the reddest ads in the history of advertising.(I’ll get to these in a week.)
then came this funny little pamphlet and its bizarre display of food coloring
that is so contentious that it might be able to put folks off their food.Have a look. I’m uncertain of what happened
to color selection for food advertising at this time; I do know that it is
confusing to our sensibilities. (Color reproduction is accurate.)
A circus passed the house—still I feel the red in my
mind.Emily Dickinson, 1866
Color expresses something by itself.V. van Gogh
Pure color!You must
sacrifice everything to it…P. Gauguin
Standing in my friends Lucy & Andy Archie’s store, standing near a
window and catching some sun on a cold stinking day, a large red jar cast a
long red shadow along the wall, causing me to think about the color. (It was a
pretty nice shadow.)
Red has turned up as an important color in terms of
patriotic/vitriolic symbolism (as in the revolutions of 1848, Garibaldi,
communism), Aztec cochinealial luxury, important burial dress of the
Cro-magnums,signs of divine favor and
condemnation, Roman red divine, Egyptian danger, royal cinnabar of China ,
Indian bridal dresses, Japanese heroic figures, and on and on (into the lower
realms of red tape, blood red, fire, blind anger, love/passion, evil, crushing
impropriety, and etc.)
Red’s most important contributions, perhaps, at least in
modern times of the past few hundred years or so, comes in the field of art and
science—and its appearance really is pretty monumental, and weirdly
coincidental in their placement in the chronology of Big Important Stuff.The birth of impressionism (with Monet and
the Salon des Refuses), the greatest change in the history of art since the
rediscovery of perspective, and the solidification of spectrum analysis (Bunsen
and Kirchhoff), both occurred around the period of 1859-1863—the great use of
red for both of these developments would come somewhat later, though the red
roots began here.
The achievement of Bunsen and Kirchhoff, started in the
epochal year of 1859 (the same year seeing the publication of the Origin), was
nearly as spectacular as any other scientific achievement of that century.The two men showed—and this would have been
incredible to the mind of the 19th century—that individual atoms had
their own spectral signature.When the
Englishman William Huggins absorbed their work, he realized immediately (as did
Bunsen and Kirchhoff) that the spectroscope could be turned on the sun and all
the rest of it—the results of the experiments of these three revealed the
elements of what stars were made of, something that must’ve seemed like science
fiction come true.The second part of
the second step* in this fabulous discovery and application came 65 years
later, when American astronomer Edwin Hubble** theorized and proved that the red shift that occur in the spectra
of all galaxies actually (a phenomenon which had been observed for years but
not understood) meant that they were all racing away (at a speed proportional
to their distance, Hubble’s Law) from the Earth—the basis of the Big Bang.Cosmological significances aside, this was
also a big deal for the advancement of color, as it really hadn’t played a very
major part at all in the history of science to this point (excepting the
brilliant occasional bits like Newton’s
Opticks). Color just wasn’t a part of
the great systems and ideas of Plato, Pythagoras, Aristotle, Euclid,
and so on—it just didn’t come into play.
Now, as to the importance of Red in art.It comes for me with Gauguin.Gauguin and his red grass.Red grass doesn’t mean anything today, but in
the early 1880’s, well, red grass was, simply, everything.It was a revolutionary idea to make the idea
of what grass”is” subject to the color that the artist thought was demanded by
it subject, and that all of this was an artistic variable in the control of
each individual interpretation.It
happened right there in the middle of the Impressionist movement, and was the
beginning of the end for representational art, the final blow to which would
not occur until 1911 with Mr. Kandinsky.
This was a lot to blow through in under a thousand words,
and undoubtedly I’ve slandered several good ideas—but I think overall that this
is a reasonable idea, this importance of the color RED.There’s much more to be said about the
Impressionists and a whole bunch more on the absence of color in the history of
science, but that’ll have to come later.
Of no importance but of some smiling interest is the notion
that the paintings that were rejected for exhibition in juried salons (in
France in the 1860’s) and which were used in a new movement and in new “juried”
shows called Salon des Refuses, were all stamped with an “R” on the back of
*the first great advancement coming in the solving of the
so-called “ultraviolet catastrophe”, arriving through the Maxwell equations of
1873 and riding into the quanta of Planck in 1899/1900 (and then to quantum
(Almost) in the beginning were monsters.The epic battle that Moses wages early on is not with Pharaohs, but with the dragon(s?) that the creator itself had fought on the opening whisper of creation (Book of Job 26:12, Psalms 89:10) and who would again meet at the very last bits of the closing days.Behemoth, Leviathan, Rehab may all well have been monsters to these ancient folks, but they very well might look like rhinoceros or crocs or hippos to us.Monster demons like Rehab (Psalm 87:4), a slaughtering beast who would be reintroduced to a different part of the world as Tiamar who would or could also be known as the Red Sea, lifted straight from Mesopotamian mythology and placed directly into that of the Old Testament among the rest of the borrowed stories and beliefs, a problem by any other name.
Following names and their cyclonic twists, and absences and sudden re-emergence through the history of storytelling is dizzying—just consult your Robert Graves on myths if you want to have your memory plumbed (the great poet and writer doing not such a poetical or writerly job in this effort in my opinion though most people love it). Keeping an eye on the mix and mash of gods and goddess and associated super beings from thousands of years ago, the god of the Old Testament makes it very clear and precise about just who he is in his self-introduction to Moses:“I am the God thy Father, the God ofAbraham, the God of Isaac, and the God of Jacob” (Exodus 3:6)
Equally almost in the beginning, again so far as the Bible is concerned, are colors—before that maybe everything was black and white, or just white, or maybe just black, depending on your epistemological concept of everythingness or nothingness. (It looks like green may be the first color mentioned in the bible, (Gen 1:30 And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so) though the mixing up of meat and veggie is a little confusing to me.))
Over the years color names themselves have creepethed among themselves like a vocabularic ocean, a fluid dynamic of naming. Names have flowed across their individual spectra, some names sticking, some not; the originator of the concept of the naming of "red", the original namer of the color, lost to the earliest and deepest part f the collective human memory.
I don't know where many of the names of colors come from, or why. Index to Color Names and Color Numbers of the Standard and Season Color Cards of America (published and created by the Textile Color Card Association), and published in 1923, is filled with color names whose meaning and origin are a mystery and whose necessity seem to hinge on sunspots. Which is fine, though it might be interesting to have had color names more dependent on that which went before. Like the names of the streets on most of Connecticut Avenue in D.C. are alphabetical, and once the first 26 letters or so are monosyllabicly employed, the second set starts with two syllables, and then three. It is a system that usefully indicates where long the long avenue you might be. It might be useful to employ such a method in color names; or not.
And I suspect it would be "or not", unless the poetry and art and music inherent in these formulations would be imaginatively employed
But on to the color names: Ambulance, Basketball, Bosom, Cowboy, Squirrel, Chit, Old, Nymph, Old mephisto, Pelt, Racket are examples of some of the mystery colors.
Some names which were part of institutionalized racism I'm sure are now gone: Arab, Negro, African; Bagdahd (?), Bombay Brown, Coolie Yellow, Coolie, Congo Brown, Egyptian Husk, Hankow (yellow), Kyoto Yellow, Korea Yellow, Mandarin Yellow, Punjab Brown, Kafir, Tar Baby.
But I've got to say, even though the names may not have much to do with the colors, most of the names in the pamphlet sound quite lovely, and many are yummy: London Smoke, Log Cabin, Leadville, Madonna, Naked, Pitchpine, Pompeii, Prelate, Smoked Pearl, Swamp, Lucky Stone, to name a few. Overall I doubt that this is what Newton, Goethe, Chevreul, Rood, Maxwell and the rest had in mind when they were figuring out what color *is*, but I do think that all of them had large enough poetic natures (Newton the weakest and Goethe by far the strongest) to appreciate the occasional beauty of naming. The unbelievable Shakespeare seems not to have spent that much time on color (so far as I know, and I don;'t much about the Bard), but (in a dear-sweet-god understatement) other people did: people like Richard Feynman synesthesically thought in mathematical color terms, others created musical instruments which would produce color from music while most of the rest of the world produced music which conveyed color, and on and on. And then of course there's the whole world of art.
But I won't go there now--I just wanted to follow this loose thread in what seemed to be a pretty inert pamphlet--in the end it opened itself to a lot of possibilities with just a little thinking.
Here's a bit of a reach, a very-long-distanced connection, between to unrelated items sharing a similar design and operating at the zenith and nadir of color theory. The first work is the great and nearly unusable work by Oliver Byrne on the first six books of Euclid (The First Six Books of Euclid in which coloured diagrams and symbols are used instead of letters for the greater ease of readers..., printed at the Chiswick Press by C. Whittingham for WIlliam Pickering in 1847). The book is, well, unusual and probably not at all useful. Bryne replaced all of the algebraic notation, identifying letters and almost all of the descriptive text with color and color codes, leaving Euclid mysterious, hidden, awkward, impervious, and, yes, beautiful. as a matter of fact this work presages the cubists (and especially Piet Mondrian) by 60 years, and all by accident.
Augustus De Morgan, mathematician and logician, wrote a very highly critical book A Budget of Paradoxes in which he describes hubbub, fakirs, frauds, perpetual motion machines, squaring the circle efforts, millstones and other useless books in the maths, and in here he sniffily dismisses Byrne's work. At best, to De Morgan, the Byrne book is "curious". But useless and curious, as I have seen many thousands of times, does not mean that it can't be attractive and beautiful, and the Byrne book is probably the leading candidate in the Bad & Beautiful category..In Victorian Book Design McLean calls the Byrne book "...one of the oddest and most beautiful books of the whole century...a decided complication of Euclid, but a triumph for Charles Whittingham [the printer]". (I should point out that the Chiswick press returned to Euclid again in 1893, publishing Gilbert Redgrave's address on Erhard Ratdolt, who was the first scientific printer in history and also the first publisher of Euclid in 1482. See HERE for the digital record of Redgrave.)
Curiously the Pythagorian theorem illustrated on the title page of Byrne's book seems at a fast glance to appear on the front cover of Phillip S. Newton's Color Blindness, Suggested Aids for Correcting 1946. It really isn't all that close except by fleeting recognition, but close enough to stop me in my tracks, to make me think of where my copy of Byrne was and put them side by side. Curious doubly because in Byrne's case color is used exclusively in place of numbers and words and is totally and completely dependent upon it. In Newton (who also has the same name as Sir Isaac, author not only of the Principia but also the second-best book of the 18th century, Opticks) we find the confusion of color and plans to correct the color vision, and in a twisty way, on the opposite end of the interests of Byrne.
(Notes for a Future Post) I found these two beautiful lithographs a while ago—they are really quite gorgeous, and I don’t have a clue to their source. They probably were printed in the 1860s or so, perhaps 1870s, which I thought—given their subject matter—would make their identification easier. The subject matter is old, appearing hundreds of years before these images were published. For example, in 1690 the philosopher and constitutional muckrack John Locke reported on a blind synesthesiastic man “who...bragged one day that he now understood what scarlet signified ... It was like the sound of a trumpet.”
Equating the frequency of sound waves with the corresponding wavelengths of light was a quest by Sir Isaac in 1704 (In the Opticks), while in 1742 the French mathematician Louis Bertrand Castel strengthened Newton’s proposal of a solid relationship between the seven colors and the seven units of the scale. Slightly later he undertook the construction of a clavecin oculaire--a light-organ--as a new musical instrument,. which would simultaneously produce both sound and the "correct" associated color for each note. A century and a half later Bainbridge Bishop had constructed at least three color organs, while in 1893 Rimington had patented the name “color organ,” and had already toured with his own device, performing color tone presentations of the works of Chopin, Bach, Wagner and Dvorak. Experimentation of a new order took place in the early 20th century in the hands of Scriabin (who thought colors were associated with tonality, not with singular notes), Kandinsky, Schoenberg and Marc.
Now, getting back to the “scale of colour” illustration, we find our anonymous author equating the following scales thus, beginning with the first column, reading top to bottom, and looking first at the underlying color: C: red, blue, orange, blue, yellow, violet and green. D: orange, blue, yellow, violet, green, red indigo
E: yellow, violet, green, red, indigo, orange, blue. F: green, red, indigo, orange, blue, yellow, violet.
And so on through the scales of G, A and B.
When you assign numerical values to each one of these colors (green=1, red 2, indigo=3, violet=4, red=5, green=6, yellow=7), the sum is 28. 28 is an interesting number in itself, being the
second perfect number (following the first perfect number which is 6)—a perfect number being the sum of its divisors, including unity but excluding itself (so 28= 1+2+4+7+14).
The color systems proposed by Castel and Bainbrisge are as follows:
B (dark) violet Bb agate A violet Ab crimson G red F# orange F golden yellow E yellow Eb olive green D green C# pale green C blue
Bainbridge B violet-red Bb violet A violet-blue G# blue G green-blue F# green F yellow-green E green-gold / yellow D# yellow-orange D orange C# orange-red C red
The following chart is from the wonderful color/music siteVISUAL MUSIC.
Today’s post comes via my wife Patti’s phoney baloney sandwich for our four-year-old Tessie. It was a tight fit of geometric pieces made to cover slim pieces of bread that would fit into her bento boxes. The form was lovely! And—on the heels of yesterday’s post—it reminded me of the remarkable qualities of geometry, and the role it has played in the creation of the known and visible parameters of our world(s). Geometry has also played a very visible role in removing those parameters, for as much as the art has forced regularity in our thought, it has played just as large a role in challenging that structure. What Euclid has given, Lobachevsky has both taken away (and added to). (Nikolai Lobachevsky [1792-1867] and Janos Boylai [1802-1860] each independently developed non-Euclidean geometries: that is, they replaced Euclid's parallel postulate with the postulate that there is more than one parallel line through any given point, saying that the foundational fifth postulate of Euclid was not true.) Take for example an image and idea from yesterday’s post regarding the engineer and art-geometer Oliver Byrne (who replaced much of the text of Euclid’s first six books by using an odd index of color) and Piet Mondrian. The approach (as noted by Augustus de Morgan among others) is gorgeous but hokum—the effect though is pretty and it does define the areas of the geometric solids that I’d like to use here. The approach that Byrne tried to develop and simplify Euclid for more general readers was to employ a peculiar art form of geometry to help classify the structure of the world—ordering the universe, and vice versa. Piet Mondrian, who was one of the earliest artists to practice the new, revolutionary form of non-representational art—that is, producing art with no recognizable subject matter, no humans, or landscape or animals or bugs or whatever—uses very similar geometrical solids to reclassify all of existence into sensations and color forms. Mondrian is more correctly classified as a constructivist, or cubist, and he uses the same tools to re-identify nature as Euclid developed to help classify the structure of the world. This is his “Composition with red, Yellow and Blue” which was painted in 1930, a full eighteen years after Kandinsky created the first painting in this field. But there were other early pioneers in the non-representation field who exhibited a more mathematical aesthetic in liberating the object than we see in the first works than the great Kandinsky. Umberto Boccioni (1912), Frank Kupka (1913), Olga Rozanova (1913), Liubov Popova (1914), Felix del Marle (1914) come quickly to mind, though none leap to consciousness as quickly as Kasimir Malevich. Malevich begins this work before 1910, and by 1913 he has produced such works as “samovar” in which the (samovar) object is dissected and moved to different places in the visual field on the back of geometrical objects. But it is in 1915 that we are introduced to his extraordinary “Black and red Square”, where we find that he has removed all representation of objects—not only that, he has removed almost all of the forms, period.
On the other hand there is certainly a very long history of artistic adventures which have no recognizable subject, though the artists in these cases I am relatively certain about were not trying to replace the known stuff of our world with the not-yet-known. Geometrical artistic expression at its base has been seen in mazes, labyrinths and mosaics for thousands of years. I guess you could even make a case for architecture fulfilling this role as well it the buildings were taken as art forms. But I’m interested here mostly with the artist intentionally choosing to obscure the known subject.
This leads to the troublesome forms of the French architect Le Corbusier (Charles-Édouard Jeanneret-Gris, 1887 –1965). Leafing through his The Radiant City (Elements of a Doctrine of Urbanism to be Used as the Basis of Our Machine-Age Civilization, 1933) is a confusing affair. As much as the man wants to rectify and save the world (his words, salve me fons pietatis) with his geometrical cities, replacing the mess of disorderly human civilization, his results, while giving a crispy clean order, are formidably lifeless (to me, at least), the organic and messy bits of human life de-fractured and placed in 90-degree containers. Le Corbu complains about the American successes, there in 1930 or so, saying that the U.S. is a monument of achievement but for achieving the wrong things. A little later in 1932 and 1933 however he does take time to make positive comments about the interesting experiments going in Fascist/Mussolini Italy and Stalin’s Soviet Union…it was common I know for thinking people to have such harmonious thoughts about these regimes, but there were plenty of others who kew and wrote about what was really happening in those places, and Le Corbu was not one of them.) The so-called positive elements of American advancements that Corbu took away with him back to France-- Taylorist and Fordist (Henry was a vehement anti Semite and Nazi sympathizer) strategies adopted from American models to reorganize society—I think come vividly alive in his geometrical replacement of human habitation—call me old fashioned, but I just don’t like it. I also don’t like it because it smacks so much of his disgust of capitalism (which he talks about as consumerism) and of his own right-wing political beliefs. Le Corbusier followed these thoughts into the camps of philosophies like the right-wing syndicalism of the French politician Hubert Lagardelle. These also eased him into a position with the traitorous Vichy government during the Nazi occupation of France during WWII—he did cut ties with it in 1942, though only after the architectural plans he had developed for various projects were rejected.
[Another leading 20th century architect, Philip Johnson, had his own problems with admiration of fascist ideas, though the amoral and whorish Johnson would’ve have seen these ideas as “problematic” only insofar as they would keep them from working. He was a decade-long Nazi sympathizer, and among many other things actually followed the Nazis as they stormed their way through Poland—something Johnson described as a (positively) “stirring” experience. He was in a separate class from the kinda-stupid Charles Lindbergh and the empty-suited-but-still-dangerous Prince Harry as Fascist trumpeters. He was more on the level of detestable fascist intellectuals like Martin Heidegger and Ezra Pound. He was awful.]
It just so happens that two of the most towering names in 20th century architecture were embroidered into the fabric of Fascism, and I think that these ideas burn their way directly through the geometrical imagination of Le Corbusier. His brand of geometries lead us towards the human cog-and-wheel, tight-box, suffocating proclivities of his right-wing extremism, and is perhaps the worst sort of illustration for the use of that beautiful branch of mathematics
Just for the sake of clarity I've included this photo of Henry Ford becoming the third recipient of the Nazi Grand Cross of the German Eagle, presented by Karl Kapp, German consul-general of Cleveland (left), and Fritz Hailer, German consul of Detroit (right). The other two recipients were Benito Mussolini and Count Ciano.
JF Ptak Science Books Post #73 The idea of how we put parameters to something like the visual field is a gargantuan topic—it is something that architects and geometers and physicists and mathematicians (in general) have dealt with forever. Mapmakers have perhaps the most visualized aspect of this on paper, performing the semi-miracle of translating three dimensions into two; physicists have a more difficult time, taking the opposite approach, sort of , and translating two or three dimensional space into x-number of dimensions. Anatomists had a difficult time of their subject until relatively recently in human history, what with the sublime religious curfews on messy knowledge and all coming into play, poking around into the heart and such as though it was an affront to the sanctity of the creator (M Servetus’ ideas on the circulation of the blood via the heart, making the heart a tool and not the brain or some odd conjunction of creative divine power, cost him his life, burning slowly alive at the stake…how mysterious the whole world of RNA Genotype-Phenotype Mapping and such would seem to him if he could have a peek into the future/present from wherever he is.) Color theory is old and pretty—as a matter of fact there is a very attractive gathering of color theory models (in black and white, though) displaying some two dozen or more color models from the last 400 years. People like Della Porta (1593), our old friend and resident oddball polymath crank Kircher (1646), the smarter-than-you-could-believe Newton (1660), Waller (1686), Lambert (1772), the wide ranging and again polymathic Goethe (1792), Herschel (1817, who also ushered in our understanding of the other light-sensitive shape spacing medium of photography in 1840), the semi-forgotten Chevreul (1835), the beautiful Maxwell (1857), Wundt (1874, the early experimental psychologist who also looked for spirits/spiritmus and ghosts), von Bezold (1878), Rood (1879), Munsell (1918) Kandinsky (1914 and not decipherable by me) and Klee (1924), and so on towards the present, all tried to analyze the prospects of color.
Not in this list is the very highly problematic Emily Vanderpoel, who in 1901 and 1903 produced (in two editions) a lovely but mysterious book called Color Problems for the Layman, in which she sought not so much to analyze the components of color itself, but rather to quantify the overall interpretative effect of color on the imagination. I know this sounds begging and vague, but I really haven’t been able to make much headway in the work.
I’m attracted to this effort because of its attempt at quantifying such abstract thoughts.
By virtue of this effort, though, Vanderpoel had produced a strikingly illustrated book, with 118 color plates, all very intense, and beautiful, and in its way exceptional—unique perhaps. Had the book been written thirty years or so hence we’d call it some sort of constructivist/constructionist artform. But since the artwork in the book comes a decade before the first non-representational artwork in human history (or so), I don’t know exactly what to call it. I really don’t know what it is, but I know that it is not entirely accidental, this pre-non-representational artform, because controlled geometrical color art is not accidental.
In trying to quantify the color images of the objects in her study, Vanderpoel establishes a 10x10 square grid, dividing all of the color in that object into individual units numbering to 100. Then, somehow, she identifies the major colors and places them according to a system that I cannot understand within the grid.
The net effect is glorious. I just don’t know how she got there—which isn’t normally a consideration in art, except that this work is an instructional on how to understand color in art and nature, and the explanation of the procedure is ethereal. Vanderpoel was and remains a respected author on porcelains and other applied and plastic arts. In this work she looked at her fair share of porcelain, limogues, clay pots, burial urns, glass shards, and the like; she also analyzed clouds, mummy cloths (and casings), dew on morning grass, brocade, the eye of a blue jay, feathers, and another hundred or so poetic arragenments of the stuff of teh world. I still do not know what this book is trying to tell me, but I do know that it is remarkable.