KANDINSKY

POINT AND LINE TO PLANE BY WASSILY KANDINSKY The geometric point is an invisible thing. Therefore, it must be defined as an incorporeal thing. Considered in terms of substance, it equals zero. Hidden in this zero, however, are various attributes which are 11human11 in nature. We think of this zero-the geometric point-in relation to the greatest possible brevity, i.e., to the highest degree of restraint which, nevertheless, speaks. Thus we look upon the geometric point as the ultimate and most singular union of silence and speech. The geometric point has, therefore, been given its material form, in the first instance, in writing. It belongs to language and signifies silence. In the flow of speech, the point symbolizes interruption, non-existence (negative element), and at the same time it forms a bridge from one existence to another (positive element). In writing, this constitutes its inner significance. Externally, it is merely a sign serving a useful end and carries with it the element of the 11practical-useful 1 11 with which we have been acquainted since childhood. The external sign becomes a thing of habit and veils the inner sound of the symbol. The inner becomes walled-up through the outer. The point belongs to the more confined circle of habitual everyday phe nomena with its traditional sound, which is mute. The sound of that silence customarily connected with the point is so emphatic that it overshadows the other characteristics. All appearances that are traditionally familiar because of their singular expression, become mute to us. We no longer react to their appeal and are surrounded by silence; so we succumb to the deadly grip of "practical efficiency.11 The Geometric Point The Written Word Silence 25 Inner Concept Tension Plane Definition 32 At the beginning of this chapter, in the course of the discussion of the practical-useful value of the point in written language, the point was defined as a concept linked with the idea of silence of shorter or longer duration. The point, as such, makes a certain statement which is organically bound up with the utmost restraint. The point is the innermost concise form. It is turned inwards. It never completely loses this characteristic-even when it assumes, externally, an angular shape. Its tension is, even in its last analysis, concentric----also, in cases where it exhibits eccentric tendencies, whereby arises a double resonance of the concentric and the eccentric. The point is a small world cut off more or less equally from all sides and almost torn out of its surroundings. Its fusion with the surroundings is minimal, and seems to be non-existent in cases of perfected roundness. On the other hand, it maintains itself firmly in place and reveals not the slightest tendency to movement in any direction whatsoever, either hori zontal or vertical. Furthermore, it neither advances nor recedes. Only its concentric tension discloses its inner kinship with the circle--while its further characteristics rather point to the square. 1 The point digs itself into the plane and asserts itself for all time. Thus it presents the briefest, constant, innermost assertion: short, fixed and quickly created. Therefore, the point, in its outer and inner sense, is the proto-element of painting and especially of the "graphic." 2 1 For the relationship between colour and form elements consult my article "Die Grundelemente der Form" in "Staatl. Bauhaus 1919-1923," Bauhaus-Verlag, Weimar Munich, p. 26 and colour plate V. 2 There is a geometric designation of the point by means of an "O" meaning "origo," that is, "beginning" or "origin." The geometric and the pictorial views coincide. The point, when looked upon as a symbol, is also termed the "proto-element." ("Das Zeichenbuch" by Rudolph Koch, II Edition, Verlag W. Gerstung, Offenbach a. M., 1926.) The concept, element, can be understood in two different ways: as an external, and, as an inner concept. Externally, each individual graphic or pictorial form is an element. Inward ly, it is not this form itself but, rather, the tension within it, which consti tutes the element. In fact, no materializing of external forms expresses the content of a work of painting but, rath~r, the forces=tensions which are alive within it.1 If by some magic command these tensions were to disappear or to expire, the work, which is alive at that very instant, would die. On the other hand, every accidental grouping of several forms could be called a work of art. The content of a work of art finds its expression in the composition: that is, in the sum of the tensions inwardly organized for the work. This seemingly simple statement has a highly important, fundamental significance: it divides into these two opposing groups not only the present day artists, but the present day men altogether, depending on their acceptance or reiection of it: I. those persons who recognize not only material things but also the existence of the immaterial or spiritual, and 2. those who choose to accept nothing beyond material evidence. For the second category, art cannot exist and, consequently, these people today repudiate the very word "art" while seeking a substitute for it. To my way of thinking, one might distinguish element from "element": that is, the term "element" would signify the form separated from the inner tension, and by element, the tension alive within this form. The elements are, therefore, in reality abstract, while the form is in itself "abstract." If it were actually possible to work with abstract elements, the external form of contemporary painting would become radically Quantita tive Increase Nature 38 A counterpart of this point on the basic plane will produce a still more complex result. Repetition is a potent means of heightening the inner vibration and is, at the same time, a source of elementary rhythm which, in turn, is a means to the attainment of elementary harmony in every form of art. Aside from this, we have to deal here with two double sounds: every part of the basic plane has a sound peculiar to itself and an indi vidual inner colouration. As a result, facts of apparently little importance produce consequences of unexpected complexity. The inventory of the given example is: Elements: two points + plane. Result: I. inner sound of a point, 2. repetition of the sound, 3. double sound of the first point, 4. double sound of the second point, 5. sound of the sum of all these sounds. Since, moreover, the point is a complex unit (its size plus its shape), it is easy to imagine what a storm of sounds can develop from a continuing accumulation of points on the basic plane-even when these points are identical: and how this turmoil develops and spreads out, while its further course points to the ever-growing disparity in the size and form of the points which are projected upon the plane. Also, in nature's unmixed realm, this accumulation of points occurs fre quently; it is invariably purposeful and organically necessary. These nature forms are in reality small space particles and carry the same relationship to the abstract (geometric) point as to the pictorial. However, the whole "world" can, on the other hand, be looked upon as a self-contained cosmic composition which, in turn, is composed of an endless number of inde pendent compositions, always self-contained even when getting smaller and smaller. In the final analysis, all of these-large or small, have been The Dance 42 Already in the classical ballet form existed "points" - a designated terminology which unquestionably is derived from "point." The rapid running on the toes leaves behind on the floor a trace of points. The ballet dancer leaps to a point above, clearly aiming at it with his head and, in landing, again contacts a point on the floor. High leaps in the modern dance can, in some cases, be compared with the "classic" ballet's high leap; that, whereas the leap formerly pointed to a straight, vertical direction, the "modern" leap frequently forms a five-pointed plane with its five extremities-head, two feet and two hands, whereby the ten fingers form ten smaller points (e.g., the dancer Palucca 1 Fig. 9). Further more, the brief states of rigid immobility can be looked upon as points. Thus we have active and passive point formations which bear a relation ship to the musical form of the point. In addition to the beating of the kettle-drum and striking of the triangle, of which we have already spoken, points can be produced in music with all sorts of instruments-especially the percussion instruments. The piano, however, enables the creation of finished compositions exclusively by means of the combination and the sequence of tonal points.1 Strings and piano Beethoven's 5th Symphony {the first measures) . ••• • •• Fig.11 The above music translated into points. 1 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the so-called subconscious "hallucination" of Bruckner, whose meaning had been detected and described: "How could this (his interest in the effect of points after signatures or on doorplates) have been a derange ment of his spirit, when it seems that it was no wandering mind which investigated these points--especially if that one understands Bruckner's nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music 7 It becomes apparent psychological significonce resides in the fact that he was attracted to the reclining proto-unit of all spatial expansion's origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating point." "Bruckner" by Dr. Ernst Kurth, vol. I, p. I 10, footnote. Max Hesses Verlag, Berlin. extension Music: In addition to the beating of the kettle-drum and striking of the triangle, of which we have already spoken, points can be produced in music with all sorts of instruments-especially the percussion instruments. The piano, however, enables the creation of finished compositions exclusively by means of the combination and the sequence of tonal points.1 Strings and piano Beethoven's 5th Symphony {the first measures) . ••• • •• Fig.11 The above music translated into points. 1 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the so-called subconscious "hallucination" of Bruckner, whose meaning had been detected and described: "How could this (his interest in the effect of points after signatures or on doorplates) have been a derange ment of his spirit, when it seems that it was no wandering mind which investigated these points--especially if that one understands Bruckner's nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music 7 It becomes apparent psychological significonce resides in the fact that he was attracted to the reclining proto-unit of all spatial expansion's origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating point." "Bruckner" by Dr. Ernst Kurth, vol. I, p. I 10, footnote. Max Hesses Verlag, Berlin. extension Music: In addition to the beating of the kettle-drum and striking of the triangle, of which we have already spoken, points can be produced in music with all sorts of instruments-especially the percussion instruments. The piano, however, enables the creation of finished compositions exclusively by means of the combination and the sequence of tonal points.1 Strings and piano Beethoven's 5th Symphony {the first measures) . ••• • •• Fig.11 The above music translated into points. 1 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the so-called subconscious "hallucination" of Bruckner, whose meaning had been detected and described: "How could this (his interest in the effect of points after signatures or on doorplates) have been a derange ment of his spirit, when it seems that it was no wandering mind which investigated these points--especially if that one understands Bruckner's nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music 7 It becomes apparent psychological significonce resides in the fact that he was attracted to the reclining proto-unit of all spatial expansion's origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating point." "Bruckner" by Dr. Ernst Kurth, vol. I, p. I 10, footnote. Max Hesses Verlag, Berlin. extension Music: In addition to the beating of the kettle-drum and striking of the triangle, of which we have already spoken, points can be produced in music with all sorts of instruments-especially the percussion instruments. The piano, however, enables the creation of finished compositions exclusively by means of the combination and the sequence of tonal points.1 Strings and piano Beethoven's 5th Symphony {the first measures) . ••• • •• Fig.11 The above music translated into points. 1 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the so-called subconscious "hallucination" of Bruckner, whose meaning had been detected and described: "How could this (his interest in the effect of points after signatures or on doorplates) have been a derange ment of his spirit, when it seems that it was no wandering mind which investigated these points--especially if that one understands Bruckner's nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music 7 It becomes apparent psychological significonce resides in the fact that he was attracted to the reclining proto-unit of all spatial expansion's origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating point." "Bruckner" by Dr. Ernst Kurth, vol. I, p. I 10, footnote. Max Hesses Verlag, Berlin. extension 1 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the so-called subconscious "hallucination" of Bruckner, whose meaning had been detected and described: "How could this (his interest in the effect of points after signatures or on doorplates) have been a derange ment of his spirit, when it seems that it was no wandering mind which investigated these points--especially if that one understands Bruckner's nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music 7 It becomes apparent psychological significonce resides in the fact that he was attracted to the reclining proto-unit of all spatial expansion's origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating point." "Bruckner" by Dr. Ernst Kurth, vol. I, p. I 10, footnote. Max Hesses Verlag, Berlin. extension Music: Music: The geometric line is an invisible thing. It is the track made by the moving point; that is, its product. It is created by movement-specifically through the destruction of the intense self-contained repose of the point. Here, the leap out of the static into the dynamic occurs. The line is, therefore, the greatest element-the antithesis to the pictorial proto point. Viewed in the strictest sense, it can be designated as a secondary element. The forces coming from without which transform the point into a line, con be very diverse. The variation in lines depends upon the number of these forces and upon their combinations. In the final analysis, all line forms can be reduced to two cases: I. application of one force and 2. application of two forces: a) single or repeated, alternate action of both forces, b) simultaneous action of both forces. I A. When a force coming from without moves the point in any direc tion, the first type of line results; the initial direction remains unchanged and the line has the tendency to run in a straight course to infinity. This is the straight line whose __ tension represents form of the potentiality for endless movement. the most concise For the concept "movement," which is used almost everywhere, I have substituted the term "tension." The customary term is inexact and thereby leads us down the wrong roads and is the cause of further terminological misconceptions. "Tension" is the force living within the element and represents only one part of the creative "movement." The second part is the "direction.'' which is also determined by the "movement." The ele ments of painting are material results of movement in the form: I. of the tension, and 2. of the direction. This division creates, furthermore, a basis for the differentiation of various kinds of elements as, for example, point and line. Of these, the point carries only one tension within it and it can have no directionj the line definitely shares in both the tension and the direction. If, for instance, the straight line were to be investigated from the standpoint of its tension alone, it would be impossible to distinguish a horizontal line from a verti cal. The above holds equally true in connection with colour analysis, since some colours are to be distinguished from others only in the directions of their tensions.1 We note that there are three typical kinds of straight lines of which other straight lines are only variations. I. The simplest form of the straight line is the horizontal. In the human imagination, this corresponds to the line or the plane upon which the human being stands or moves. The horizontal line is also a cold sup porting base which can be extended on the level in various directions. Coldness and flatness are the basic sounds of this line, and it can be designated as the most concise form of the potentiality for end less cold movement. 1 See, for example, the characterization 58 of yellow and blue in my book "Uber dos Geistige in der Kunst," R. Piper & Co., Verlag, Munich, 3rd Edition, 1912, pp. 73, 76, 77 and Plates I and 11. (This book hos recently been translated into English and reissued under the title "On the Spiritual in Art" by the Solomon R. Guggenheim Foundation, New York City, and this particular reference will be found on pages 60 to 64, incl.] A cautious use of these concepts is especially important in the analysis of ''form in drawing," since it is right here that direction ploys a definite role. It is to be observed with regret that pointing is least well provided with on exact terminology which renders scientific work exceedingly difficult and sometimes quite impossible. One must start here from the beginning and a dictionary of terminology is a necessary preliminary. An attempt ot this was mode in Moscow about 1919 but hos achieved no results. Perhaps the time was not then ripe. ' 2. In complete contrast to this line, in both an external and inner sense, is the vertical which stands at right angles to it, and in which flatness is supplanted by height, and coldness by warmth. Therefore, the ver tical line is the most concise form of the potentiality for end less warm movement. 3. The third type of straight line is the diagonal which, in schematic form, diverges from both of the above at the same angle and, therefore, has the same inclination to both of them; a circumstance which determines its inner sound-equal union of coldness and warmth. Therefore, the diagonal line is the most concise form of the potentiality for endless cold-warm movement {Figs. 14 and 15).These three types are the purest forms of straight lines and they are differ entiated from each other by temperature: Endless movement. I. cold form, 2. warm form, 3. cold-warm form. Most concise forms of the potentiality for endless movement. To a greater or smaller extent, all other straight lines are only deviations from the diagonal. The differences in a greater or lesser tendency to cold ness or to warmth determine their inner sounds (Fig. 18).I B I. The simplest forms of angular lines consist of two parts, and are the result of two forces which have discontinued their action a~er a single thrust. This simple process leads, moreover, to an important difference between straight and angular lines: the angular line is in much closer touch with the plane, and it already carries something plane-like within it. The plane is in the process of creation, and the angular line becomes a bridge. The differences between the countless angular lines depend entirely upon the sizes of the angles, in accordance with which they can be divided into three typical groups: a) with acute angles b) with right angles c) with obtuse angles 45° 90° 135° The remainder are atypical acute or obtuse angles, and deviate from the typical in the number of their degrees. Thus, with the first three angular lines, a fourth-an atypical angular line-can be included. d) with a free angle, because of which this angular line must be designated as a free angular line. These three sounds can create a triple sound. They can also, on the other hand, be used singly or in pairs-a matter which depends upon the con struction as a whole. All three sounds cannot be entirely eliminated, but one or the other can out-sound the rest to such an extent that they can scarcely be heard. The most objective of the three typical angles is the right angle, which also is the coldest. It divides the square plane into exactly 4 parts. The acute angle is the tensest as well as the warmest. It cuts the plane into exactly 8 parts. Increasing the right angle leads to the weakening of the forward tension and the desire for the conquest of the plane grows in proportion. Thisgreed is, nevertheless, restrained in so far as the obtuse angle is not capa ble of dividing the plane exactly: it goes into it twice and leaves a portion of 90° unconquered. Three Sounds Angular Lines and Colour 72 The three different sounds of these three forms thereby correspond: I. the cold and controlled, 2. the sharp and highly active, and 3. the clumsy, weak and passive. These three sounds and, therefore, these three angles, give a fine graphic translation of the artistic process: I. the sharp and highly active in the inner thought (vision), 2. the cool and controlled in masterly execution (realization), and 3. the unsatisfied feeling and the sensation of one's own weakness follow ing the completed work (in the case of artists, called "hangover"). We spoke above of 4 right angles which form a square. The relationships with the pictorial elements can only be briefly discussed here, but still the parallels of angular lines with colours must be indicated. The cold-warm of the square and its definite plane-like nature, immediately become sign posts pointing to red, which represents a midway point between yellow and blue and carries within it cold-warm characteristics. 1 Not without reason has the red square appeared so often of late. It is not, therefore, completely without iustificafion that the right angle is placed on a parallel with red. Under class d) of angular lines, it is necessary to emphasize a special angle which lies between the right and acute angles-an angle of 60° (right angle - 30° and acute + 15°). When the openings of two such angles are brought together, they produce an equilateral triangle-three 1 See "On the Spiritual in Art," p. 67, Figure II. Also, Table V in "Basie Elements" in the Bauhaus Book, Bauhaus Verlag, 1923.sharp, active angles-and become the sign-post to yellow.1 Thus, the ac:ute angle has a yellow colour within. The obtuse angle increasingly loses its aggression, its piercing quality, its warmth, and is, thereby, distantly related to a line without angles which, as will be shown below, constitutes the third primary, typical form of the plane-the circle. The passiveness in the obtuse angle, the almost missing forward tension, gives this angle a light blue tone. In addition, further relationships can be indicated: the acuter the angle, the closer it approaches sharp warmth and vice versa, the warmth de creases toward the red right angle and inclines more and more to cold ness, until the obtuse ( 150°) angle develops; this is a typical blue angle and is a presentiment of the curved line which, in its further course, has the circle as its final goal. This process can be given the following graphic expression: Fig. 28 System of typical angles +=± colours. 1 Ibidem. ~,, • -Thus it follows: AV B BV ... yellow, AIV B BIV . . . orange. Alli B BIii . . . red. All B Bil . . . violet, Al B Bl Acute angle. Right angle. Obtuse angle. . blue. The next jump of 30° is the transition from angular lines to straight lines: A B C .... black. Horizontal. Since, however, the typical angles in their continued development can form planes, the further relationships between line-plane-colour arise auto matically. We may therefore make the following diagrammatic indica tion of the line-plane-colour relationships: Plane and Colour 74 Angular Lines: Fig. 30 Acute angle Fig. 31 Right angle Fig. 32 Obtuse angle Primary Forms: Primary Colours: If, particularly in the case of the formation of the obtuse angle, a force is regularly augmented and the angle increases in size, this form tends toward the plane and, especially, toward the circle. The relationship of the obtuse-angle line, the curved line and the circle is, thereby, not only of an external, but of an inner nature, as well. The passivity of the obtuse angle and its unaggressive attitude toward its surroundings, causes it to cave in more and more until it ends in the profoundest self-absorption of the circle. II. When two forces act upon the point in such a way that one force continually, but always to the same degree, exceeds the other in pressure, a curved line is created whose basic form is I. the simple curved line. It is really a straight line which has been brought out of its course by constant sideward pressure-the greater was this pressure, the farther went the diversion from the straight line and, in the course of this, the greater became the outward tension and, finally, the tendency to close itself. The inner difference from the straight line consists in the number and kind of tensions: the straight line has two distinct primitive tensions which play an unimportant role in the case of the curved line, whose chief tension resides in the arc (third tension, which opposes and out-sounds the others) (Fig. 34). While the piercing quality of the angle disappears, there is still greater force confined here which, even though it is less aggressive, has greater endurance concealed within it. Something thoughtlessly youthful exists in the angle while in the arc is a mature energy, rightfully self-con scious. This maturity and the elastic full sound of the curved line lead us to seek the contrast to the straight line-not in the angular-but definitely in the curved line: the origin of the curved line and the character proceeding Tensions of straight and curved lines. Contrasts in Lines 80 out of this origin, i.e., the complete absence of the straight line, compel us to state that: the straight line and the curved line represent the primary contrast ing pair of lines (Fig. 35). The angular line must, therefore, be looked upon as an intermediate ele ment: birth-youth-maturity. Whereas the straight line is a complete negation of the plane, the curved line carries within it a seed of the plane. If the two forces, with the con ditions unchanged, roll the point ever farther, the developing curve will sooner or later arrive again at its starting point. Beginning and end flow into each other and in the same instant disappear without a trace. The most unstable and, at the same time, the most stable of planes is created -the circle (Fig. 36).1 1 A form diverging in a regular manner from the circle is the spiral ( Fig. 37); the force acting from within exceeds the outer in a uniform measure. The spiral is, therefore, a going off its track in a uniform manner. Besides this difference, another can be observed which, for painting, is much more significant: the spiral is a line, while the circle is a plane. Geometry does not make this distinction which is exceed ingly important for painting; aside from the circle, it designates the ellipse, the figure eight and similar piano forms as lines (curves). The term used here, the "curved line," is not the equivalent of the more exact geometric terminology ( parabola, hyperbola, etc.) for geometry, from its standpoint on the basis of formulae, must inevitably make classifications which in this connection are out of the question for painting.Contrast in Relation to the Plane Three Pairs of Elements 82 Even the straight line, in the final analysis, carries within it with its other characteristics the desire (even though deeply hidden) to give birth to a plane: to transform itself into a more compact, more self-contained thing. The straight line is capable of doing this, although, in contrast to thei curved line which can create a plane with two forces, it has need of three impulses in plane creation. In the case of this new plane, beginning and end cannot completely disappear, but are observable at three points. Complete absence of the straight and the angular on the one hand and, on the other hand, three straight lines with three angles-these are the signs af the two primary planes which stand in the greatest contrast to each other. Therefore, these two planes confront each other as Three Pairs of Elements 82 Even the straight line, in the final analysis, carries within it with its other characteristics the desire (even though deeply hidden) to give birth to a plane: to transform itself into a more compact, more self-contained thing. The straight line is capable of doing this, although, in contrast to thei curved line which can create a plane with two forces, it has need of three impulses in plane creation. In the case of this new plane, beginning and end cannot completely disappear, but are observable at three points. Complete absence of the straight and the angular on the one hand and, on the other hand, three straight lines with three angles-these are the signs af the two primary planes which stand in the greatest contrast to each other. Therefore, these two planes confront each other as Fig.38 the primary contrasting pair of planes. We have now reached the point where it is logical to establish certain relationships between those three parts of the pictorial elements which actually merge with each other, but which are theoretically separable: line-plane----colour. Straight line, Curved line. 1. Pair triangle, circle. 2. Pair yellow, blue. 3. Pair Three primary contrasting pairs of elements. Curve-free wave-like: Displacement of the above lines with the same horizontal extension: I. the geometric character disappears, 2. positive and negative pressure with irregular alternation, whereby the former gets much the upper hand of the latter (Fig. 42 Time Other Arts Music 98 The element of time, in general, is discernable in the line to a much greater extent than it was in the case of the point: length is a concept of time. On the other hand, the time required to follow a straight line is different from that required for a curved one, even though the lengths are the same; the more animated the curved line becomes, the longer is the span of time it represents. Thus, the possibilities of using line as a time element are manifold. The application of time has a different inner colouration in horizontal and vertical lines, even if of equal lengths, and perhaps it is in reality a matter of different lengths which, at any rate, would be psycho logically explainable. The time element in a purely linear composition must not, therefore, be overlooked and in the theory of composition it must be subjected to an exact examination. As with the point, the line can be used in forms of art expression other than painting. Its nature finds a more or less precise translation in the means of other arts. What a musical line is, is well known (see Fig. 11 ).1 Most musical instru ments are of a linear character. The pitch of the various instruments corre sponds to the width of the line: a very fine line represents the sound pro duced by the violin, flute, piccolo; a somewhat thicker line represents the tone of the viola, clarinet; and the lines become more broad via the deep toned instruments, finally culminating in the broadest line representing the deepest tones produced by the bass-viol or the tuba. Aside from its width, the line is produced in its colour variations by the diversified chromatic character of different instruments. The organ is quite as typical o "linear" instrument as the piano is a "point" instrument. 1 The line grows organic:ally out of points. It can be asserted that in music the line supplies the greatest means of expression. It manifests itself here in time end space just as it does in painting. 1 How time and space are related to each other in the two forms of art is a question by itself which, with its distinctions, has led to an exag gerated scrupulousness and, thereby, the concepts of time-space or space time have been differentiated far too much. The degrees of intensity from pianissimo to fortissimo can be expressed in an increasing or decreasing sharpness of the line, that is, in its degree of brilliance. The pressure of the hand on the bow corresponds exactly to the pressure of the hand on the pencil. It is particularly interesting and significant that the graphic musical repre sentation in common use today-musical notation-is nothing other than various combinations of point and line. The time is recognizable therein only by means of the colour of the point (white and black only, which con sequently leads to the restriction of the means) and the number of pen nant stripes (lines). The pitch is likewise measured in lines, and five hori zontals form the basis of this. The unqualified brevity and the sim plicity of the means of translation, which in clear language convey the most complex sound phenomena to the experienced eye (indirectly to the ear) are instructive. Both of these characteristics are very alluring for the other forms of art and it is understandable that painting or the dance should be in search of its own "notes." There is, however, only one way to arrive finally at their own graphic expression-analytic separation into fundamental elements. 2 1 In measuring tonal pitch in physics, special apparatus is used which projects the vibrating tone mechanically on a surface and which thereby gives the musical tone a precise graphic form. Similar things are also done with colour. In many important cases, the science of art already makes use of exact graphic transla tions as material for the synthetic method. 2 The relationships of the pictorial means to the means of other art expressions and, finally, to the phenomena of other "worlds," can be indicated only very superficially here. "Translations," especially, and their possibilities-in general, the transcription of various phenomena into their respective linear ("graphic") forms-require and colour ("pictorial") a thorough study of linear and colour expression. There is no question that, in principle, every phenomenon of every world admits of such expression-the expression of its inner nature--regardless of whether it be Raphael, J. S. Bach, a storm, element with a "completely" objective BP should only be looked upon as a relative matter. Absolute objectivity cannot be attained. Nature of the BP Sounds Above and Below 118 A fact which is of immeasurable importance and which must be viewed as something independent of the powers of the artist is the dependence of all this not only upon the nature of the individual elements, but upon the nature of the BP itself. means to an end. On the other hand, this fact is a source of great possibilities in composi tion-a The following simple given facts lie at the bottom of this. Every typical BP produced by 2 horizontal and 2 vertical lines has, corre spondingly, 4 sides. Each of these 4 sides develops a sound peculiar to it alone, which passes beyond the boundaries of warm and cold rest. A second sound is, therefore, associated each time with the sound of warm or cold rest, which sound is unalterably and organically bound up with the position of the line= boundary. The position of the two horizontal lines is above and below. The position of the two vertical lines is right and left. That every living thing stands in a fixed relationship to "above" and "be low" and must without question remain that way, is a fact true also of the BP which, as such, is also a living thing. This can be partly explained as association or as transference of one's own observations to the BP. We must assume without question, however, that this fact has deeper roots and that the BP is a living being. For a person who is not an artist, this assertion may appear strange. We must, nevertheless, definitely assume that every artist feels-even though unconsciously-the still untouched BP and that he feels-more "breathing" of the or less consciously-a responsi bility toward this being and is aware of the fact that frivolous abuse of it is akin to murder. The artist_ "fertilizes" this being and knows how obediently and "ioyfully" the BP receives the right elements in the right order. This somewhat primitive and yet living organism is transformed by the right treatment into a new living organism, which is no longer primitive but which reveals, on the contrary, all of the characteristics of a fully developed organism. The "above" gives the impression of a great looseness, a feeling of light ness, of emancipation and, finally, of freedom. Each one of these related characteristics gives off an accompanying sound, which has in each case a slightly different colour. This "looseness" is a negation of density. The nearer to the upper border of the BP the smallest individual areas seem to be, the more disintegrated they appear. The "lightness" leads to further enhancement of this inner quality-the smallest individual areas are not only farther removed from each other, but they themselves lose weight and, thereby, lose still more the capacity to support. Every weightier form thereby grows heavier in this upper posi tion of the BP. The note of heaviness takes on a stronger sound. "Freedom" produces the impression of a rather light "movement.'' 1 and the tension here can more easily play itself out. "Climbing" or "falling" gains in intensity. Restraint is reduced to a minimum. The effect of "below" is completely contrary: condensation, heaviness, constraint. The closer one approaches the lower border of the BP, the denser the atmosphere becomesj the smallest individual areas lie nearer and nearer together and thereby sustain the larger and heavier forms with ever in creasing ease. These forms lose weight and the note of heaviness decreases in sound. "Climbing" becomes more difficult-the forms seem to tear themselves loose by main force and something like the grating noise of friction is audible. (A straining upwards and arrested "falling" downwards.) Freedom of movement becomes more and more limited. The restraint attains its maximum. 1 Ideas like "movement," "climbing," "falling," etc. are derived from the material world. On the pictorial BP they are to be understood as the tensions living within the elements, which are modified by the tensions of the BP. Structure Further Tensions 128 decisive in compositional and, more especially, in abstract art. All the tensions of the individual forms on the BP are given other directions each time, and each time, of course, take on different colours. Drawn upwards, the form complexes also become either compressed or extended. Thus through an unskillful choice of the plane format, a well-conceived order can result in repulsive disorder. Naturally, I mean by "order" not only the mathematical "harmonious structure" in which all of the elements lie in clearly measured directions, but also structure in accordance with the principle of contrast. Elements tending upwards, for example, can be made "dramatic" in the vertical format by bringing them into a milieu of restraint. Let this be mentioned only as a guidepost for the theory of composition. The point of intersection of the two diagonals determines the center of the BP. A horizontal and, subsequently, a vertical line drawn through this center divide the BP into four primary parts, each of which has its specific appearance. The corners of all of these touch at the "indifferent" center, out of which tensions flow diagonally (Fig. 81 ). It must nevertheless be strongly emphasized that the "floating sensations" depend not alone upon the above-mentioned conditions, but also upon the inner attitude of the observer whose eye can be capable of seeing in one or the other, or in both ways: if the inadequately developed eye (which is organically connected with the spirit) cannot experience deeply, it will not be able to emancipate itself from the material plane in order to perceive the indefinable space. The properly trained eye must have the ability partly to see the plane, as such, necessary to the work of art and partly to disregard it when it takes on spatial form. A simple complex of lines can finally be treated in two ways-either it has become one with the BP or it lies free in space. The point clawing its way into the plane is also able to free itself from the plane and to "float" in space. 1 Just as the inner tensions of the BP described above continue to exist in the complex BP forms, these tensions are also transferred from the demateria lized plane to the indefinable space. The law does not lose its effect. If the point of departure is correct and the direction taken is well chosen, the goal cannot be missed. And the goal of a theoretic investigation is I. to find the living, 2. to make its pulsation perceptible, and 3. to determine wherein the living conforms to law. 1 It is clear that the transformation of the material plane and the general character of the elements combined with it are certain to have very important consequences in many respects. One of the most important of these is the change in the feeling for time: space is identical with depth; also, with the elements receding into depth. It is not without reason that I have called the space resulting from dematerialization "inde finable"-its depth is, after all, illusory and, therefore, not exactly measurable. Thus, time cannot in these cases be expressed in figures, and so it cooperates only relatively. On the other hand, the illusory depth is on actual one from the pictorial point of view and consequently a certain, even though immeasurable, time is required to follow the form elements receding into depth. Therefore: the transformation of the material BP into indefinable space offers the opportunity of increasing the span of time. The Observer Goal of Theory 1 Living facts-as isolated phenomena and in their interrelationships-can be gathered in such a manner. It is the task of philosophy to draw conclusions from this material, and it is a work of synthesis of the highest order. This work leads to such inner revelations as can be given to each epoch.