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  Mach Bands  


by Jo Baer




Two main queries have developed and informed the science of today: questions put and answered to the enigmas of colored light and mass in motion, and a rigorous assay of the enquirer and his measures. This essay will deal principally with the color lights of science and painting, their standards and interrogators. There is an old, rather unscientific yet very perceptive theory which holds color to be a darkening of light. Aristotle, in his Treatise on Colors, places white and black at the beginning and end of the color scale and derives all the other colors from them. However, he warns us that We must not attempt to make our observations on these effects by mixing colors as painters mix them, but by remarking the appearances as produced by the rays of light mingling with each other.(1) Leonardo, in the Trattato della Pittura, agrees with Aristotle's viewing black and white as colors, but he further informs us that blue may be produced by the actual mixture of black and white (pigments) provided they are pure.(2) Goethe's Theory of Colors, modeled on Aristotle's Treatise, also regards all the colors as resulting from the mixture of black and white and he ascribes to the colors their quality of darkness by the differing degrees in which they are distinguished, passing from white to black through the gradations of yellow, orange, red, violet and blue; green appears to be intermediate between yellow and blue.


The various observations upon which these authors based their theory were compounded and confounded catoptrics (the geometry of reflected light) and dioptrics (the physics of transmitted light). However, the theory is still useful if one deals only with the perception of reflected lights from objects, for this older theory's conflict with modern Newtonian theory is mainly one of class discrimination. Newton's discovery that white light is the mixture of all the colors as opposed to all the colors a mixture of white is of course the reverse of the former idea, but Newton's theory is strictly and only derived from the light transmitted through a prism. There is an interesting note on the illumination mode differences between Flemish and Italian Renaissance painting made by the English translator of Goethe's Farbenlehre (1840), Charles Lock Eastlake, where he differentiates the northern and southern painting in terms of the two diverse light modes.(3) Eastlake points out that Italian painting, especially the Venetian, appears to imitate the colors and qualities of gems and glass; this is accomplished by the use of a dark ground and white highlights, which allow the intervening opaque colors to become very intense, brilliant and flashing. The strong color to dark contrasts reiterate reflected lights in both prototype and painting. In the North the Flemish and Dutch appear to imitate stained-glass windows. Here a white ground and thinly glazed, finely pulverized pigments are used, allowing the ground lights to reflect back and up through the semitransparent colors much as light is transmitted through a window. The tones are very muted and the paintings are remarkable for their cool lights, extreme depth and a certain subdued splendor.


Aside from the modes of light themselves, color theory and physiology are afflicted with two diverse yet true sets of data. Goethe, Chevreul and later Hering, evolved an opponent theory of color: color-contrast observations were the basis of this theory where it was noticed that red-green or blue-yellow have marked effects on one another if viewed next to each other, and an empirical map of the normal retina does show a four part color sensitivity. The retina is sensitive to yellow over the largest area, to blue over one almost as large, to red over a still smaller area, and to green over the smallest. Location of these areas shows a fairly restricted zone in the center of the field of vision where all color qualities can be seen; surrounding this zone is an area in which no redness or greenness is visible but where blueness and yellowness can be seen; in the extreme periphery all color experience is restricted to blacks, greys and whites. Electrophysiological data on fish also show retinal ganglion cells beyond the retina which have opposed-spectral responses.(4) One type has a single maximum at about 575 millimicrons, another type has a maximum in the red part of the spectrum and a maximum of opposite polarity in the green part, and a third type has its two maxima of opposite polarity in the yellow and blue regions of the spectrum.


Opposed to the opponent-color theory is the equally demonstrable Young-Helmholtz theory of color. Here only three mechanisms of color perception are postulated: red, green and blue. This trichromatic theory does not account for color contrast effects, but does account for Colorimetry data which have demonstrated that a color stimulus may be accurately matched by a mixture of correct amounts of three color stimuli. It is physiologically assumed here that there are three kinds of retinal cones, each with pigments sensitive to light of different absorption spectra. The means of combining the Young-Helmholtz theory and data with the color-contrast theory and its data is not at hand, so that Turtles appear to hate blue while frogs seem rather fond of it is about the clearest, least complicating kind of statement one can make about color vision at this time. However, data and theory on luminance vision, a prior aspect of all color vision, are highly developed, sophisticated and fairly straightforward in implications. It appears the lights and darks of ancient arts and science are still productive standards for new endeavor.


Most sensation is the edge of things. Visual systems schematize; they look to physical boundaries, edges and contours to select from the immense detail in the retinalimage data which are most significant to the organism. What the receptors of the retina see is not what the organism sees. Changes and transitions from one intensity of light to another or, less importantly, from one color to another are more important for seeing than the absolute light intensities and colors themselves so that boundaries edges and contours — the change points — are physiologically preferred. The price of this change or edge preference is a loss of absolute visual accuracy while the gain is toward salient information.


What is fundamental for organisms is essential for art. The paintings on which this article is based (painted in '62'69) were intuitively fashioned with the above data somewhere in mind. Among other factors these paintings were made to work through boundary and luminance phenomena. Briefly described, the paintings make use of a continuous black band at the outer front edges which, moving in, is adjacent to a continuous narrow color band that is in turn adjacent to an interior large white square or rectangle (see cover). Tucked in between the white and black, the narrow color band gains a vast brightness due to two separate and distinct edge effects working at the color interfaces. At the white-to-color edge, retinal glare or scattering occurs: like all white surfaces the large white area reflects diffusely in all directions and appears to swell and go past its boundaries so that the color band gains in apparent luminosity. At the black-to-color edge a different thing. happens. Brightness contrast effects push the color band still higher into luminosity through a physiological neural phenomenon called Mach bands. Both phenomena are subjective not physical and cannot be measured outside their context. In the paintings the two events noted at the color interfaces combine and allow color-light aspects which can range from fluorence to luminescence, from phosphorescence to twilight. This essay will treat principally with Mach bands, the black-to-color edge phenomenon.


A brief sketch of Mach's place and the pivotal work he did is desiderate. About a hundred years ago Ernst Mach, an Austrian physicist-philosopher-psychologist discovered and postulated in mathematical form a subjective brightness contrast effect known now as Mach bands or rings (1865). In experiments using a rotating disc, Mach measured and analyzed the light and dark striped ring which rotation magically offered to the viewer's perception. As the ring was a new shape with its own qualities which are not physically present on the disc, and as this ring could be modified by changing the luminance and spatial factors on the disc, Mach's discovery and its implications put a crucial question to both science and philosophy: how distinguish between properties of the observer and properties of the thing observed.


Mach's subsequent writings were deeper investigations into this relationship between the subjective sensations of the beholder and the nature and measurements of the thing observed. Mach felt both to be of equal reality and importance. He was the first to systematically question the classic Newtonian mechanics with their yardsticks of absolute fictitious measures, and during this lifetime his work was profoundly germane in the development of relativity theory. Mach's experiments and theories had been well known and much debated when, around 1880, physical science was rocked and subsequently redefined by the failure of the Michelson-Morley experiment, an attempt to measure the speed of light. Contrary to classical expectations, a light beam projected in various directions with respect to earth's motion discovered no differences due to the fabric of space itself, the Newtonian ether which classical mechanics needed as its fixed reference point, its absolute rest to which all other things in motion must refer. Suddenly there was no such thing as absolute motion or absolute space. Mach had called to question both principles in his writings. At this point, G. F. Fitzgerald advanced a possible explanation for the Michelson-Morley failure when in 1893 he suggested that all matter contracted in the direction of its motion; this meant that all possible measuring devices, including the human sense organs, would be foreshortened in the same way. H.A. Lorentz took Fitzgerald's idea one step further: a flying charged particle foreshortened in the direction of its travel would be compressed into a smaller volume and the mass of the particle would have to increase. According to the equations worked out by these two scientists, at the speed of light a measuring rod, its length in the direction of the motion, would be zero; at the speed of light an electron's mass would be infinite. In 1900 W. Kauffman proved that the electron's mass increased as predicted by the Lorentz-Fitzgerald equations. Excepting the speed of light there were no more absolute measures and the subjective element of science could not be eliminated. Mach's epistemology, his concern with the observed and the observer, was intimately connected with these events. His concepts of space, time and mechanics influenced Einstein and in 1916 Einstein wrote: Mach clearly recognized the weak points of classical mechanics and was not very far from requiring a general theory of relativity and all of this almost a half a century ago! It is not improbable that Mach himself would have discovered the theory of relativity, if, during the time that his mind was in its prime, physicists had been concerned with the importance of the problem of the constancy of the speed of light. (5)


Mach and Einstein disagreed on many points however; one difference was in the matter of gravitational theory. Einstein's theory of gravitation still requires some use of the concept of absolute space. But according to what is now known as Mach's principle, inertial forces are due to acceleration relative to distant matter in space, not to empty space. As Mach put it, When we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe.(6)


In the world of philosophy Mach's contributions were equally significant. He exerted a strong influence on the Vienna Circle and the Unity of Science movement (Wittgenstein, Carnap, et al) and their subsequent development of modern logical positivism. He also influenced the Russian critical-empiricists provoking Lenin to write the polemical Materialism and Empirio-Criticism (1909) against Mach's Russian followers. Mach's own philosophy was skeptical and similar to Hume's, though derived from one of Hume's contemporaries (Lichtenberg). Mach read Hume somewhat later. Mach's early positions were taken in rejection of Kant. He often cited Berkeley an influence but made much of his differences with Berkeley's Idealism. In 1914 Mach wrote: Shall I once again state the difference in a word? Berkeley regards the elements as conditioned by an unknown cause external to them (God), — accordingly Kant, in order to appear as a sober realist, invents the thing-in-itself; whereas on the view which I advocate, a dependence of the elements on one another is theoretically and practically all that is required. (7)


A dependence of the elements on one another is a succinct statement of a Mach band's external modus operandi. Wherever there is a change in light to dark between two areas Mach bands will appear: on the light side of the edge or contour a lighter stripe is manifested, on the dark side a darker band. These light and dark bands are not objective for they are not on the physical surface. They occur in the viewer's visual system. However their brightness and darkness are specifically dependent on the elements, the magnitude and spatial distribution of the physical illumination. If the edges are sharp or the contrast in light intensities great, the Mach bands will be quite apparent. These bands are always present at all boundaries, though at middle values and at dull edges they are seldom noticed. Color edge-effects show a more complicated variant of the same phenomenon, but depend mainly on luminance differences rather than color differences. Curiously, Mach bands are not symmetrical, that is, the bright stripe is more pronounced, much lighter relative to its light area than the dark band is dark to its dark area. The bright band also becomes significantly narrower with increasing contrast relations. The occasion for the asymmetry, indeed for the entire Mach band phenomenon, involves the nature, structure and desideratum of the visual system itself. Imperfections in the lens and other dioptric apparatus of the eye (cornea, vitreous and aqueous humors) cause blurring and a degradation of the sharpness of the image formed on the retina; the degradation occurs through diffraction, chromatic and spherical aberrations and so forth and cause considerable blur, especially when contrasts or edges are sharp. The Mach band effect, which occurs beyond the retina in the lateral neural networks of the eye, compensates and rectifies the retinal blur. On the other hand, since Mach bands occur at all boundaries even where blur is minimal, they also accentuate edge and contour information. Their role is therefore dual — to preserve and to enhance.


A dependence of the elements on one another delineates the Mach band's interior process as well, its physiology. Mach postulated an interdependence of neighboring elements in the retina; his mathematical model formulated a non-linear, reciprocal, inhibitory interaction. An integration of opposed excitatory and inhibitory influences still describes most modern quantitative attempts dealing with neural network contrast effects.


Mach's initial assumption rested on a diagnosis of psychophysical data. If one charts an objective average luminance curve for an edge transition, the coordinates are light-intensity against distance and the slope between a change from light to dark will depend on how much the light-intensity changes in how much space. The point of change from a uniform intensity to the change slope might be simple and abrupt or gradual, while the slope itself may range from an almost vertical drop parallel to the light intensity ordinate (a white painted area next to a black painted area, very hard edged), through ascending diagonals expressing half-shadow areas between the light and dark intensities. All the information on this graph can be measured with a light meter on a physical surface: it is an objective light curve and looks somewhat like the three parts of a step.


Calculated mean luminance or light curve (dashed line) and apparent luminance or sensation curve (solid line).



Now the subjective light curve for this same chart turns out to look quite different. An observer's sensations may be charted with respect to the same edge transitions to give an apparent brightness curve. This curve starts out parallel to the uniform objective horizontal. Somewhat before the objective edge transition the apparent light curve goes up in a spike for a short space to a height well above the objective light level. The sensation slope then descends in a similar (not identical) fashion and at its bottom overshoots and goes well below the objective change point of the lower uniform horizontal. This bottom spike is shallower and broader than the one at the high light-intensity level; when this bottom spike comes up, it continues as a line parallel to the bottom objective horizontal. The spikes of course represent the apparent Mach bands:


What is important here is that at a point of change a viewer experiences an exaggerated point of change in the direction opposite to the given physical stimulus (mathematically characterized as the negative of the second derivative: that is, the instantaneous amount of change of the amount of change in an opposed direction. Second derivatives are always large since they start at and return to zero for any amount). Since these subjective change points always move in a relatively large, reversed way, Mach assumed an inhibitory factor at work in the viewer's optical system. Now inhibition often means a simple lessening of a quantity, but here it is complex and really means opposed in a significant amount. The inhibitory factor postulated by Mach was the divisor in an integration of intensity minus a constant times excitation over inhibition, where the inhibitory influence divides a summated gross excitation of light into its subsequent not effect.


Electrophysiological data not available in Mach's time confirm and locate an inhibitory factor in the neural networks beyond the retina and the unit of neural activity is now identified as the nerve impulse. Electrophysiological studies of the horseshoe crab limulus (an arthropod compound eye) have given the clearest data and mathematical terms for inhibitory networks. The compound eye is made up of little eyes (ommatidia) so that both the excitatory and inhibitory influences in the retina may be observed directly. If a mask is placed over the eye so that only one ommatidium sees a pattern, then the responses faithfully reproduce the objective stimulus; when the mask is removed so that interaction can take place among the neighboring elements, the Mach band spikes appear in the response curve. The inhibitory influences are exerted mutually among the ommatidia so that each inhibits, and is inhibited by its near neighbors. The amount of the inhibition on a particular element depends on the response of those neighboring elements rather than upon the stimulus to them. In other words, the inhibition is recurrent, exerted back on the site of generation. A network of tiny fibers laterally connects each ommatidium, albeit all eyes of fish, birds, cats, monkeys, even mudpuppies have lateral interconnections in their post-retina[ neural fibers. And all eyes show the Mach band response to edge transitions in much the same form.


A number of mathematical models have been devised to deal with the excitatory-inhibitory components: nonlinear and linear statistics with negative weighting f unctions, non-linear ratios, and sets of simultaneous equations describe Mach bands, depending on who, how and what is observed and measured. However, the precise mathematical formulations are unclear if similar in all but the limulus eye data. The many and diverse formal models indicate the intricacy and complexity of the retinal-neural interplay which accomplishes the viewer's discernment of boundary change. These perceived changes of illumination are fundamental, for without them, all things would seem to be invisible.


Change of light in space is a form of motion but the vertebrate retina also has a striking sensitivity to temporal changes in illumination: the most natural cause of these temporal changes on the retina come from objects which are moving. Furthermore, although an object viewed might be still and without motion, the eye itself is in continual motion. There are experiments where the effects of eye movements are canceled: a contact lens with a mirror attached plus a complicated projection system of other mirrors which compensate the angular motion of the eye produces a stationery retinal image on the receptor mosaic.(8) All details of illumination viewed this way appear sharp and clear at first, then, in a few seconds they gradually fade out. All contrast and form disappears and the stationery image on the retina appears uniform no matter what the physical pattern of illumination; there is no vision without change. Outside the lateral neural networks in the vertebrate optic nerve itself, the highest proportion of retinal ganglion-cell axons are movement sensitive: they are either quiescent or discharge very slowly under steady-state, uniform conditions. These ganglion cells respond very vigorously, however, when the illumination is changed.


The shape of an edge determines the response of other ganglion cells.(9) In frogs, a large pattern with a straight edge might yield no response at all, yet a small, circular stimulus might yield a vigorous response when moved into the same fields. Curvature of the edge, rather than size appears to be the determining factor. These cells also respond strongly to a sharp corner of a stimulus pattern; there are similar findings in the brain of the cat and monkey. Other ganglion cells in the retina seem to be highly specialized in a selective sensitivity to direction of movement.(10) They respond to movement in one direction, but not to movement in the opposite direction; that is, the preferred direction of movement is generally horizontal or vertical. Similar data occur in the brain of higher forms here also, and none of these ganglion responses is the direct result of receptor activity. They seem to be a product of integrative activity, an interplay of excitatory and inhibitory influences which occur somewhere between the receptors and their second- or third-order neurons in the visual system or in the brain.


An elucidation of these particulars is perhaps best expressed by the neuro-physiologists Huggins and Licklider: ... The nervous system often hedges. Instead of presenting a single transform (a change of information from one kind of signal to another) of the peripheral centers to the higher centers, the ... tract may present a number of transforms... As a rough analogy, one can improve upon the transmission of a message in noise by using a number of channels, one for the message itself, one for its time derivative, another for its second time derivative, perhaps another for its time integral. These several transforms of the message protect different aspects of the message from the effects of the noise. The receiver, trying to reconstruct the original message, can come much closer by operating upon the set of transforms (though they are all contaminated) than it can with only the noisy message itself to work on. (11)


The neural network interactions and the specific ganglion cell responses, each functioning as different kinds of information, together present an integration of information from several different points of view. So edges and boundaries, corners and sharp curves, motion and the direction of motions horizontal and vertical prevail as a physiological bias for both vertebrate and invertebrate. These rudiments are the signal points of view in all well developed visual systems.


Since it is a pretty long leap from physiological bias to modern art, a short review of modern art's nature and development seems in order. A useful analysis of the general dialectics appears in Clement Greenberg's essay, Modernist Painting (1960-65): The essence of Modernism lies, as I see it, in the use of the characteristic methods of a discipline to criticize the discipline itself — not in order to subvert it, but to entrench it more firmly in its area of competence. The essential norms or conventions of painting are also the limiting conditions with which a marked-up surface must comply in order to be experienced as a picture. Modernism has found that these limiting conditions can be pushed back indefinitely before a picture stops being a picture and turns into an arbitrary object, — but it has also found that the further back these limits are pushed the more explicitly they have to be observed. Each art... had to effect this ... demonstration on its own account. What had to be exhibited and made explicit was that which was unique and irreducible not only in art in general but also in each particular art. (12)


To chronicle the particulars and beginning with Manet's Olympia (1863), the subject of modern painting has been a suppression and dispelling of the sculptural from the painted canvas with the defining means the flat surface, the shape of the support, and the properties of pigment. The Impressionists began the differentiation through their use of dabs and pats of paint which asserted the immediacy of the painted surface; they also diminished value contrasts, the blacks and whites of sculptural modeling and substituted color relations instead. Cezanne took the Impressionist paint surface, the points and pats, gave them directions on the plane, and modeled for pictorial depth in the warms and cools of Impressionist theory. These factors, plus his habit of drawing which tilted the picture plane forward from the top, established a flat surface in dialogue and tension with pictorial illusions of deep space.


Evolving from Impressionist tenets and Cezanne, the Fauves and later the Orphists and Synchromists focused on an elaboration of color relations, orchestrating brilliant design rhythms. Cezanne's flat surface developed further in the hands of Analytic Cubists: early Cubism muted the broad color contrasts, modeling value on shapes which had been flattened out through looking behind and presenting back aspects of the pictured object simultaneously with its frontal aspect. The Cubists also developed a taut unification between their faceted forms and the rectangular shape of the picture itself. The later Synthetic Cubism eschewed modeling and favored flat bright colors and interlocking, quasi-geometric silhouettes, which rendered a more obvious flatness of surface. The final reduction in Cubism was soundly effected by Mondrian (and Malevitch and Kandinsky before); they dispensed with all representational content and reduced form to the nonobjective.


Somewhat later and in America, Abstract Expressionism invested the properties of pigment with their most material sense — every mark made on a canvas was explicit in its manner of generation. More recently, attention to the shape of the support evolved into shaped canvases, and the properties of pigment turned into Color-field painting. At the present state of the art, these latter two concerns have been successfully unified and joined by contemporary artists (Newman, Noland, Stella, etc.). None of this short art history has to do with physiological bias. It is rather a synopsis of a reduction to what are still immensely complicated locutions: color, shape, plane, form, material, space.


Advanced art is radical, and radical in its most literal meaning describes a root, base, foundation. Advanced art is thus an art which works for and effects change, within the general Modernist dialectic, towards a more basic and particular substance of art. At present, a radical redefinition of current painting is pertinent and possible.


All the pictorial terms given above (color, shape, plane, form, material, space) can be summed up and reduced to a single term: reflected light with its boundaries and gradients. Now in everyday language light signifies three quite different phenomena. There is a light from a source, that is a lamp or the sun; there is a light transmitted through a transparent or translucent medium — Newton's rays through a prism or smoke in a room; and there is a light reflected back from the surface of an object allowing us to see this object. There are also combinations and transition states between the three light modes. This section is addressed to the third mode, the reflected surface light, because paintings are essentially objects of their outermost boundary, a skin of matter reflecting lights.


Reflected light brings us to color, plane and material. All reflected light prerequires a surface (a plane) in order to become reflected light — the terms are correlatives. At this surface an energy exchange between a source light and the materials on or of the surface determines the color of the reflected lights which are then seen. While all surfaces are material, pigment materials are intrinsically energy filters which manifest colors through their specific and selective properties. A particular pigment absorbs particular fractions of the source-light. What we see reflected back, i.e., the color, has been transformed into that fraction of the original source light which the pigment has not absorbed. So reflected color light is the remainder of an energy exchange of heat and light in a material. Our ancient progenitors understood this retroflexion, for among the European languages six of the seven unique colors derive their names from the energy transformations of fire and flame. Black, F. blanc (bleached white), L. flavus (yellow), and Rom. bhlavus (blue) all come from the same Indo-European base flag- (to blaze, burn). A Greek grey (spodios) is ashes, and even the Greek green (khloros) derives from the Indo-European base glodi- (hot coal, fire). (The green of a hot coal is most likely its corona, where the encircling envelope of light takes its color from a contrast effect with the red coal.) All Indo-European reds come from the same root: red has always been red. Its etymology is lost or never was. Besides the colors, even the word material participates in the fire schema; material, from Latin, means hard part of a tree rendering the Greek mater (mother, i.e., the trunk of a tree producing shoots). These ancient and very perceptive observations of energy barters, the wood, fire, lights and heats, show that in that long ago color was also appreciated as the remaindered result of something else. Form, shape, space are principally boundary and gradient phenomena. In paintings it is convenient to let form mean the markings which articulate a surface, the lines, areas, bands, figures, etc. Forms on a surface become visible through the differential light and color intensities and absorptions: the lines, areas, bands and figures are the materialized edges and gradients. Shape, the outside physical perimeter of a painting, is a little more complicated since a shape is three-dimensional. However, shape edges and surfaces are also made visible by reflected-light, though the comprehension of an object needs other objects or a wall to appear as shape. Objects occur in deep space, but the space on a painting surface can be made as flat as the surface itself and need not set up illusions of depth. Marks on such a surface then merely mark edge intervals and gradients between reflected light intensities and color lights.


The definitive means of painting (color, material, plane, form, shape, space) are now encompassed by the more fundamental limits of reflected-light boundaries as means. This reduction includes the former terms but makes possible new questions, ways, explications and interpretations What remains to be formulated out of this revised dialectic is a differentiation of the sculptural from the pictorial.


Certain properties are obviously shared, indeed intrinsically mutual.


There are three necessary mutualities. First, both paintings and sculptures are shape objects, for even when a painting is a mural done directly on a wall, the wall becomes its object shape; so-called two dimensional art is a fiction. The second property shared by painting and sculpture is their surface; all objects have surfaces. The last shared property between the two arts is materials — mainly pigments for painting and much of the rest of the material world for sculpture. Put another way, if all the lights in a room are turned out, there isn't much to know about a painting excepting its texture and its shape against the wall. In that same dark room, there is a great deal that can be known about a sculpture: bumped into, one can feel all the masses, their possibly moving articulations and the particular materials used. So bounded, colored surface light is painting's ontological bottom. A painterly guess in the direction of sculpture's fundamental terms would be mass (including tangibility — touch Mach bands exist for the skin's sensorium), the variousness of materials, and perhaps the movement of parts.


Art is a very complexed affair. So is physiology. However, if we wish to deal with that which is unique and irreducible, we must attend closely to the explicit properties of the observed and of the observer and to the intimate nature of their juncture. A known physiological preference for edges, boundaries, and contours, for corners and sharp curves, and for particular directions of change is most certainly pertinent to aesthetic preferences and the continuing development of art. It is illuminating to go to Clement Greenberg again, for exception must be taken with him at this point. The quotation is from an essay titled "American Type" Painting (1955, 1958): ...the new emphasis on black and white has to do with something that is perhaps more crucial to Western painting than to any other kind. Value contrast, the opposition of the lightness and darkness of colors, has been Western pictorial art's chief means, far more important than perspective, to that convincing illusion of three-dimensionality which distinguishes it most from other traditions of pictorial art. The eye takes its first bearings from quantitative differences of illumination, and in their absence feels most at loss. Black and white offers the extreme statement of these differences. What is at stake in the new American emphasis on black and white is the preservation of something — a main pictorial resource — that is suspected of being near exhaustion; and the effort at preservation is undertaken, in this as in other cases, by isolating and exaggerating that which one wants to preserve. (13)


It is doubtful if value contrasts, the opposition of the lightness and darkness of colors, can be a main pictorial resource...near exhaustion if such value contrasts are intrinsically essential, preferred, even enhanced by the nature of all visual systems. Visual systems do not need the illusion of three-dimensionality on flat surfaces; in fact, neither does the great bulk of the world's art excepting the Western European tradition. Over the last hundred years Western painting has successfully suppressed and dispelled the sculptural third-dimension from its surface and at the same time, Western painting has also successfully engaged the sub-rosa aspects of full-out color (hedonism) against the blacks and whites of good and evil (puritanical pleasure-pain). Since biological preference for illumination qualities, boundaries and sharp changes precede and underlie the more complicated color and sociological factors; and since they are a known, universal visual necessity, it would be well for the proceeding arts to investigate and keep these constants in mind. Perhaps it is now propitious for radical painting's surfaces to mediate new color and value relations between a more closely examined observer and an expanded, more worldly observed.


As the eye looks to boundaries for its most significant information, so does a Xerox duplicator in its earlier and most intrinsic forms. In fact, early Xerox only reproduced edges. Visual systems and Xerox copiers both distort the edges of what is seen in a similar fashion, and these distortions are similar because in each case the product of the viewing is a result of the interdependence of neighboring points in the viewing systems. (Mach, in 1882, remarked on the similarity of equipotential curves and the curves representing visual contrast effects.) The systems are otherwise dissimilar however in that organic edge distortions are subjective, the result of living, changing responses to relative light boundaries; Xerox distortions are entirely physical, printed on a page and unchanging once the instrument has placed them there. The Mach band edge enhancement of a biological visual system is due to the integrative activity of neural networks within the organism. The edge enhancement from a Xerox copier is due to the particular charge densities of an electrostatic field.


An electrostatic force field is any interval between two oppositely charged objects. An electrostatic system, as distinguished from current electricity, is one in which the voltage, the electric pressure or force is great, stored up even, to charge a field rather than to discharge current (amperes) along a conducting wire. The field intensity or volts per micron are much higher near one or another of the charged objects (electrodes or particles) than out in the middle where the field is weakest. In general, the strength of an electrostatic field at any point is given by adding vectorially (quantities of direction versus magnitude) the fields produced at that point by each positive charge. All high voltage systems will either spark over discharges or leak corona currents if the systems are inadequately shielded or badly built. Corona is of interest here, since the Xerox process is initiated by a spray of corona discharge. The word corona comes from Greek where it meant anything curved or bent, and this early meaning quite nicely describes a corona's electrical conduct. Wherever there are sharp edges, sharp curves or flexions in a voltage system, charge densities build up strongly there and then tend to leak out at these highly charged places. (Over-volted current systems will also discharge corona, but all over, along the line as well as at the sharp edges, flexions or curves. And natural coronas occur when an atmospheric high-intensity electric field finds the tip of the mast of a ship: sailors call it St. Elmo's fire.) This corona leakage of charged particles changes nearby molecules of air into a flood of ions which can grow into an ionic current or an electric wind.


In a Xerox machine a zig-zag charged wire (lots of bends) sprays a uniform layer of positive ions, in the dark, onto the neutral smooth surface of a selenium-coated drum. When an image is to be duplicated, it is projected by light through a lens onto the ionized selenium surface so that the surface becomes selectively charged. Selenium is a photoconductor, which means that wherever light strikes its surface it discharges and becomes neutral again; the electrical potential decays and dissipates leaving a distribution of positive electrostatic charge corresponding only to the dark areas where light has not fallen. Next, a black powder is spilled over the revolving drum; the powder particles have been tumbled together with little beads somewhere else in the system to build up a negative static charge. This negatively charged powder now clings to the positively charged areas which have remained on the drum and a visible image becomes manifest. We are still on the drum, but paper is forthcoming: a positive charge has been applied by stroking ordinary paper with plastic fur and the paper attracts the negatively charged powder to its surface. Off the drum and onto the paper, vaporized solvents or heat are used to soften and fuse the powdered image. The image is now part of and as permanent as the paper itself.


The accompanying Xeroxed edge-effect illustrations are useful as a physical model of subjective optical phenomena. If there is doubt in the reader's mind as to whether he is seeing subjective Mach bands or instrumental edge distortions in this material, cover one side of the Xeroxed edge with hand or paper and notice that the phenomena remain the same: it is printed there. Next, cover the contrast-edge of the photographed original and notice that the subjective Mach bands disappear. (Mach bands appear in photographs because the photographic process distributes light with the same brightness relations to the eye as occur on the original.) The Xeroxed illustrations presented here are in two forms: there is a standard line duplication of a painted original and there are several halftone duplications where white Zip-a-tone dots or a finer white screen developed by Xerox has been laid on top of the original painted canvas prior to its Xerox reproduction. On the standard, unscreened line pictures a value asymmetry is apparent, since a bit more black powder is attracted to that side of the edge where less light has fallen to discharge the field. The middle areas between the boundaries do not reproduce because, while the charge particles are dense near an edge due to the fringing-effect of the electrostatic field, the centers of the field are very weak.


The nature of an electrostatic field is such that the amount of black powder attracted to any point on the charged selenium is determined not by the charge at that point alone, but by the integrated effects of all charges whose fields act at that point. The same edge phenomena become more apparent with the screened Xeroxed illustrations although the middle areas are now printed. The white dot screens give a continuous tone to areas by breaking up the components so that there are changes from light to dark everywhere. This breaking up of extended dark areas into many narrow lines or dots yields many narrow fields of full strength throughout the center of the area where the field would otherwise be zero.


The band widths painted on the subject prototypes are on canvas and proportional to those used on existing paintings. The color of the narrow band between the black and white is phtalo-green mixed with titanium white; a 2400 Xerox duplicator was selected because its spectral sensitivity is particularly good for this color. It would be well to remember that these presentations illustrate a multiplicity of processes, all differing in their outsets yet similar in their outcomes. The sequence goes from art (intuited artifacts), to painted abstracts (selected physiological data) and then branches into instruments: photo reproductions (Talbot-Plateau law of absolute light intensity) and Xeroxed copies (electrostatic forces). The printer's lithography will also affect the illustrations to some extent. And the observer's eye still stands behind all these models as the touchstoned backbone of their visual effects


Subject A demonstrates contextual contrast effects most clearly, although the Mach bands themselves are not too apparent here. The 1116" color line (pthalo-green as on the cover painting) is identical in all three contexts — in the right-angled formation, as a straight line between white and black, and all alone in white space. The isolated color line looks almost as dark as the black in the other formations since there is no black adjacent to it to effect a contrast.


Subject B is about line width: the wider the color line the darker it appears. Note the difference in value between the 1/4 " line and the 1/16" line, even though their black bands are proportional and their contexts thus the same. Mach band (or charge density) effects cause the discrepancy although the Zip-a-tone screened illustration is the only one which noticeably prints out the edge effects themselves.


Subject C exhibits the charge density and Mach band edge enhancements plus Subject A contextual isolation effect. The upper V of white-color, black-band prints out a pretty good Mach band on the Zip-a-tone illustration: the black area shows a blacker line of dots at its color interface and the color band shows a wider, white area next to the black. Within the body of the figure where the color band continues through the black, the edge effects are working both sides of the color band so that its entirety appears lighter altogether. Where the ends of the color band trail off into the white only,


the color band becomes quite dark. The narrowness of the interior color band is not caused by electrostatic forces or visual effects (the black was painted over the color band a bit too far because the artist's hand was hurried, harried and unsteadied). The line only, unscreened illustration of this subject also demonstrates a nice differentiation between the outer black-to-white and inner black-to-color edges. The outer bounds of the black areas are considerably darker than their interior color-edge relations since the light contrast is greater between black and white than between black and any color.


Asimov, Isaac, The Intelligent Man's Guide to the Physical Sciences, Basic Books Inc., Now York, 1960.

Dessauer, J.H. and Clark, H.E., Xerography & Related Processes, Focal Press, New York, 1965.

Greenberg, Clement, Art& Culture, Beacon Press, Boston, 1961.

Judd, Deane B., A Five-A ttribute System of Describing Visual Appearance, American Society for Testing Materials, Philadelphia, 1961.

Mach, Ernst, The Principles of Physical Optics, Dover Publications, New York, 1926 (1913).

Moore, A.D., Electrostatics, Doubleday & Co., Garden City, New York, 1968.

Onions, C.T., The Oxford Dictionary of English Etymology, Oxford University Press, London, 1966.

Ratliffe, Floyd, Mach Bands, Holden-Day Inc., San Francisco, 1965.

v. Goethe, J.W., Theory of Colours, Frank Cass & Co. Ltd., London, 1967 (1810).


Personal thanks and much gratitude for their assistance is extended to R.W. Gundlach and A. Dinsdale, Xerox Corp.; J. Krauskopf, Bell Laboratories; S. Hanlon, Mathematics Department, Riverdale Country School for Boys; W. Agee, Museum of Modern Art; and R. Lobe and D. Graham, Departments of Humoring, Editing and Morale.


1 Theory of Colours, G oethe, pp. 385-386.

2 Id.

3 Ibid., pp. 365-366, 377.

4 Mach Bands, Ratliff, pp. 190-191.

5 Ibid., p. 31

6 Id.

7 Ibid., p. 24

8 Ibid., pp 169-170

9 Ibid., p. 178

10 Ibid., p. 179

11 Ibid., pp. 79-80

12 The New Art, Gregory Battcock, E.P. Dutton & Co., New York, 1966, pp. 101, 102, 106.

13 Art & Culture, Clement Greenberg, pp. 220-221.



Original format: 16-page booklet, 7-5/8 by 9-7/8 inches.



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