The smooth, moist sand of a wave-swept beach provides a grand and empty slate, a blackboard, a virgin ground on which to make one's mark. Put a child there with a stick and he will draw a line. The first art of a budding creator is comprised of lines woven or scratched into symbols expressive of his earliest visualizations, the living ideas burgeoning within his waxing mind. Apart from sound, the line is the most fundamental of instruments for communicating ideas amongst human beings. It contains the innate potentiality of an unlimited language, enabling man to mark his earthly home with a continual record of himself. The child walking down the beach, dragging a stick behind him, adds to his oozing footprints an unbroken line in declaration of a unique passage. That this is done unconsciously only adds to the significance of this common act. Some may liken it to the territorial instinct of an animal which prompts it to demark the perimeters of its domain. But the spindly line of the child neither encloses an area nor acts as a boundary. It merely marks the course of a brief sojourn in the world, a presence and the path that it etched out of the matrix of possibilities. Such a line is lonely, and one senses the toil and wonderment that accompany it, the purposefulness and the lack of aim. It suggests infinite time forwards and backwards, a sort of endless extension in space. And yet it appears and disappears with the presence of the child.
Lines indicate division, measurement, boundary and extension. They pull the eye with their force of direction. They separate categories or define moral choices where people "draw the line". An undeviating course of conduct is suggested by a straight line, whilst a vertical line implies attention, dignity, aspiration or assertiveness. In mystical symbology the vertical line represents the active aspect of the spiritual world, whilst the horizontal is a measure of time in the temporal world, a boundary between the celestial and terrestrial realms. The horizontal surface of a lake or of the horizon itself suggests calmness, repose and the breadth of receptivity. Other lines appear relative to these fundamental types: curved lines define themselves against the straight in their sweeping flow, and diagonal lines lend drama as they pull the eye into imbalance. Such oblique lines charge the visible world with a sense of electric dynamism, change and growth, even while the curved lines coil and weave together the myriad levels of cosmic design.
More strictly, a fundamental straight line is the shortest distance between two points. Axiomatically, one could formulate this by saying that two distinct points in a plane determine a unique line on which they both lie. Such a plane or surface is produced by the motion of a line as it moves perpendicular to its own direction, whilst angles are formed by the more specific extension of two lines from the same point. Angled lines can then describe and enclose numberless figures and forms, but at the root of its geometric potential the line simply lies between points. Coming from the Greek λίνον (linon), the etymology of the word itself suggests something of this fundamental simplicity. The Greek term described flax thread and anything that was made from it. Such fabric as crinoline takes its name from the linen warp of its weave, and the term 'lingerie' reveals that in France, at least, undergarments were originally fashioned out of flaxen cloth. But the more essential and abstract meaning of the term is carried in etymological derivatives like 'lineal', which means 'direct descent', 'lineage', implying a mathematically precise and irrefutable pedigree, and 'liner', which is a ship or plane belonging to a succession of such vessels plying between certain points on the globe.
It has been asserted that in Nature there are no lines, only light and dark masses, colours meeting and defining themselves against one another. Scratches made by animal claws, wind and water marks, geostriations or spiders' threads are mere interruptions of molecular surfaces whereupon light and shadow only seem to define edges and lineal traces. But in the human mind there are lines, and in visualizing the mysteries of life their force has always asserted itself in the language and art of man. The pictograms of ancient peoples made accessible to the eye an invisible world. They did not try to depict external things, but rather something interior which was experienced in dreams and visions. The earliest forms of cave art reveal humanoid stick figures alongside eloquently rendered naturalistic animal paintings. The power of these compelling illustrations is only partly explained by the dynamics of imitative hunting magic. The real mystery lies in the unwillingness of these anonymous artists to lend to the human form the realism they so lavished on those of the animals. The simple lines comprising the human forms address themselves to a more abstract, interior reality experienced by these men within themselves as an inner power capable of being exerted upon the world of exterior forms. In time this mode lent itself to the stylized signs of pictographic writing and the rudiments of geometry. But to the artist of ancient times as to the child of any time, the line remains the magical mark that delineates an inner presence, an axis between heaven and earth, a threshold across which glide the connecting links of structure and form.
For millennia artists of Oriental climes have been keenly aware of the intrinsic and symbolic power of the line. While the centuries witnessed an increasing preoccupation with exterior subject matter in European cultures, the fine hair-brush of Chinese or Japanese calligraphers explored the dynamics of shape, texture, plane and line for their own sake. The forty thousand word-pictures which were symbolic of situations, actions and things expressed in classical Chinese writing lent themselves to a highly idealized art form, capable of revealing a universe "quickening with lines and rhythms of the greatest richness and variety". Persian art was replete with linear frameworks within frameworks - stems, branches, grass, rocks, human or animal forms - all outlined and surrounded by lines of exquisite script. Artistic traditions of Rajasthan, Mewar, Garhwal and that exemplified so vibrantly in the caves at Ajanta relied strongly upon the power of line to define, delimit and structure their idealized themes. In Tibet the painter of a tanka began with points connected by threadlike lines - the blueprint of an emerging presence. Only when this was perfectly completed according to the strict rules of an occult geometry capable of expressing mystically perceived archetypes did the painter concern himself with the elements of planes, textures, shapes and colour.
In Europe the Renaissance ushered in an eclipse of the line in art and what was to become a many-centuried preoccupation with light and shadow manifesting as three-dimensional forms against a background. Lines existed only through implications, typified in the work of Rubens, Rembrandt or Vermeer. It was felt that lines did not exist in Nature and therefore should not be painted, and it was only with the advent of a stunning exhibition of Japanese prints shown in Paris at the end of the nineteenth century that they reasserted themselves. Painters like Gauguin, Van Gogh and Cézanne were profoundly influenced by this rebirth of linear consciousness and opened the doors of inner spaces delineated by lines that defied the limitations of external experience. In the works of Cézanne powerful lines integrate the near and the far, the inner and outer. They course through space like vectors, carrying the eye far beyond camera vision, coalescing space and form into a dynamic whole.
If lines do not exist in physical Nature, they certainly seem to be implied. The human eye, observing a row of trees, fills in the spaces between a series of dots. From a philosophical standpoint a line is an idealization of what we generally call a line. It is straight and extends infinitely far in both directions, inviting the mind's eye to travel along its movement into the past or future. It is impossible to avoid the notion of movement away from a point while making this journey, for though one may consider a segment of line as a whole, there is still the dynamic interconnection between its two end-points to be accounted for, and one is thus conceptually involved in the realm of time. Euclidean geometry asserts that two parallel straight lines extend into the past and future without ever meeting. Either lines intersect, are divergent or run parallel to one another in this view, leaving the problem of indefinite extension open, along with the question of infinity. With the development of perspective geometry under Gerard Desargues and, later, Johannes Kepler, a set of parallel lines was said to pass through a point at infinity, a phenomenon analogously experienced by the human eye in the physical world. Thus the notion arose of extending the Euclidean plane by adding to it points considered to lie on a line at infinity, rendering the idea of endlessly parallel lines an impossibility. This entire question plunges the mind into ruminations about points of origin, infinity and time and reference points of endless duration from whence all points and lines of emanation arise.
To human beings in the world of relativities, lines occur as continual realities, marking, dividing and ordering existence. They are always with us in our thoughts as we trace relationships, draw conclusions from points, follow lines of history, evolution, poetry and thought, as well as the direction of arguments or various kinds of developments. We "draw the line" when we "lay down the limits" and we warn friends that maybe something is "not quite in their line", even while we continually hope to start fresh by "taking a new line". Children's intelligence is tested by their ability to perceive lines of connection between points, and the sane are similarly examined to separate them from the insane. So ubiquitous are the lines we see between material or metaphorical points that we tend to assume that such a tendency must be a universal quality of human consciousness. It is, therefore, provocative to learn that some people in the world do not seem to share this extreme lineality of thought. Cultural and linguistic studies of people like the Trobrianders of Melanesia reveal a mode of thought and expression which focusses on being, wherein each event is timelessly part of a larger ordained pattern. There is a noticeable absence of axiomatic lineal connections between events and objects. They do not speak of rows of trees, lines of development or relationship. Things are referred to and treated as aggregates within patterns, whose ingredients do not rely upon reference to tense or interconnections for meaning.
The Trobriander may be said to be point oriented (treating patterns as a whole or as points) rather than line oriented, as industrialized man seems to be. Hannah Arendt, in her perceptive critique of western civilization, pointed out that modern man exists in consciousness within a sort of tunnel which moves in a line from past to future. As he gropes his way along, he is continually pressured by events and impressions from the past which fill him with hopes and anxieties about the future. So overwhelming is this pressure from behind and in front that such people do not live in the present at all. To modern man the Trobriander's world seems static, unchanging and repetitious, but to the Trobriander the strangers who visit from the outside world seem unable to grasp the fundamentals of life which continually and cyclically reappear.
Every human consciousness experiences time according to its condition. When largely determined by the shared collective notions of others, it will reflect a linear or cyclic perspective according to its cultural conditioning. When rising above the collective through the process of individuation, it will penetrate more deeply into the question of recurrence and succession. Scientific thought such as that of Newtonian physics, wherein the geometrical line describes measurable time and space, or the second law of thermodynamics, which asserts the universal and irreversible loss of energy in every physical process, conditions minds to maintain a forcefully linear perspective. In his ingenious Flatland: A Romance of Many Dimensions, Edwin Abbott depicted a world of one dimension called Lineland, whose monarch thought that the straight line in which he passed his existence constituted the whole of the cosmos. All that inhabitants of this world experienced was limited to that which they perceived directly behind them or before them on this line. In a two-dimensional world two lines can intersect, but at one point only, a third dimension being required to produce the environment so familiar to human physical senses. In such a three-dimensional realm a line is still determined by two points, and a plane can be uniquely determined if there are three distinct points that do not lie on a line. Lines or planes in such a world may intersect one another or merely sustain a parallel relationship.
With the development of non-Euclidean geometry the rejection of the axiomatic assertion that two parallel lines can never meet becomes possible. Probing space with this mathematics, one finds that such lines as those traced by light-rays may intersect as they bend their way through a four-dimensional cosmos, wherein time itself acts as a dimension and non-coplanar points connected by lines determine unique solids. Here planes become meeting points between solids, and lines become links, angles and structural constructs for doorways leading into other spatial and temporal frames. The simple line between two points thus becomes a participant in greater and greater seeming complexities which, by their essential meta-geometrical nature, lead through increasingly abstract realms back to the base line of infinity.
Pre-manifestation cannot be symbolized nor can boundless space. The eternal Reality which ever is in potentia has neither circumference nor centre. Only in the highest states of meditation is it possible to gather an inkling of what H. P. Blavatsky meant by "the line we draw between the absolutely Ideal Universe and the invisible though manifested Kosmos". By the dawn of manifestation, reference to the appearance of the Second Logos or even the Third might be meant. One may well ponder the diagram of the immaculate circle in the Proem to The Secret Doctrine and question whether the point that appears in it which transforms into a line is, indeed, the threshold of the Absolute. The point is said to be the first differentiation of potential space within abstract space. It is the laya point at which primordial substance first begins subtly to particularize, to be transformed into a horizontal diameter line which represents divine immaculately androgynous Nature within the Absolute. When the vertical line bisects the horizontal, the Mother-Father separates and the fall of spirit into matter begins. Though thought of as feminine and relatively passive, the horizontal line actually divides that which was one into an upper and a lower world. The active and masculine vertical, though in danger of falling into concretization, is, nonetheless, capable of penetrating and cutting through this relatively passive division and bringing the two together again, a theme ever echoed in the poetry of mythical metaphor.
The line is preceded by the point. In pre-manifestation the First Unmanifest Logos is the Point which is everywhere and nowhere. In accordance with a pulse-beat which can only be conceived of as an inaudible, invisible, endless and beginningless, innate aspect of potentiality itself, this attributeless point periodically flashes out the Ray, which momentarily thrills through the Germ of potential being before withdrawing once again within itself and retiring into darkness. One might identify the flashing Ray as the first line, one which only fleetingly appears to link the absolutely Ideal and Unmanifest with the realm of immanent manifestation. But the symbolic illustrations in the Proem indicate the first line to be horizontal, and elsewhere one learns that this line is simultaneous with the appearance of the first Point. This would seem to suggest that the Ray is not capable of being symbolized by a line. It would also appear to question whether, in fact, the line is preceded by the point.
The line which remains when the point of the first Unmanifest Logos retires is the Mother-Father from which proceeds the Second Logoic Point containing the Third, the Manifesting Word. The First Logos, manifesting periodically and only through its Ray, ever stands aloof, preceding and succeeding all that participates in manifestation. This Point, which is everywhere and nowhere, is thus prior to the diameter line of the Mother-Father, which must, therefore, extend between two derivative points. In the Pythagorean tradition this process is put in terms of the true Tetraktys, the Invisible Monad or Ray which descends from Aloka, "through the planes of non-being into the first world of being, and gives birth to Number One; then branching off, to the right, it produces Number Two; turning again to form the base-line it begets Number Three, and thence ascending again to Number One, it finally disappears therefrom into the realms of non-being as Pythagoras shows". The base-line here is the Mother-Father diameter from which proceeds the Second Logos, the abstract collectivity of the Builders still hidden within the bosom of Mulaprakriti. But the other connecting 'branches' are lines as well, the left being that of the Mother, the right being that of the Son.
The Secret Doctrine depicts the first Point as retiring into the circle after "emanating" the first three points and "connecting" them with lines, "thus forming the first noumenal basis of the Second Triangle in the Manifested World". Emanation in this sense implies the issuance of that which bears within it the seed of all that is to follow. Thus the potential for Oneness reflected in the subsequent point (Number One) is accompanied by the potential for duality reflected not only in the second point but also in the line that connects it to the second point. One might assume on the basis of this that the line has nothing to do with unity, but this is easily set aside upon reflection. It is the line which unifies the second and third points and sets the stage for the next triadic generation. It is true, however, that the base-line is not in itself capable of reproduction. Nor are the two lines that diverge out from the apex point. But when the bottom line joins these two duads in union, it becomes a fertile basis out of which the scintillas (gods, monads and atoms) take birth. Thus the living Spiritual Fire is in the possession of the triangles, but it is only the lower line of the triangle that can furnish that in which the Builders or Dhyan Chohans clothe themselves when a form is needed.
Strictly speaking, an ideal triangle has no lines. Imaginary mathematical lines supply the connections between the points. And yet in arcane teachings a line is said to be produced by the first motion from indivisible Nature. The question arises as to which triangle, which point, which Logos, is being referred to in all these highly symbolic metaphysical descriptions. The mind trips over what seem to be conflicting or at least shifting levels of discussion, and it is perhaps only in glimmers and occasionally piercing beams of connective insight that the intuitive faculty grasps a portion of the arcane pattern. If one reconsiders the diameter line in the symbolic circle, it is this which arises simultaneously with the First Logos. In comparing this to the Pythagorean teaching, one may find it difficult at first to reconcile it with the triangle which appears after the Ray descends through the planes of Non-Being into the first world of Being. This may especially be so because the triangle that unfolds from the point Number One does so along a divergent line connecting it to the duad of the Mother before linking up to create its horizontal base. But these symbolic modes of describing what is in essence a non-linear phenomenon merely represent two different approaches focussed upon the same process. One utilizes a one-dimensional and two-dimensional geometry, whilst the Pythagorean mode employs that of planes.
These may be reconciled by thinking of the descent of the highest monadic Ray as it pulsates forth in the immaculate, boundless circle. In its primordial flash the simultaneous blueprint of the triangular archetype impresses itself within and upon itself even as the first thrill in spirit-substance heralds the subsequent differentiation of potential space. The 'transformation' of the point into a diameter has already suggested itself, but it is only with further descent through the realm of Non-Being (to use the Pythagorean metaphor) that the immaculate Mother actually comes to lie - as a subtly specialized aspect - in the embrace of the Absolute. At this stage the Second Logos or Point flashes forth, not as something distinct from the First but as a second throbbing which vibrates through a gathering matrix. Again the triangular archetype simultaneously appears, with its base acting this time as a true diameter of the circle. Now the duality, anticipating in the first emanating flash of the One, expresses itself in a subtle separation between spirit or motion and the mater materia upon which it broods. This subtly dividing line, symbolized by the diameter in the circle, establishes the separation, the juxtaposition, the increment of tension and opposition necessary to produce the third Logoic point (Brahmā), which precipitates the involvement of intelligent spirit (Mahat) in increasingly differentiated matter. With each generational flashing forth of the Absolute Essence, the impress of wholeness, of the One symbolized in the Point, is carried into increasing manifestation. And with each such universal impress, the invisible and eventually visible points of the archetypal triangle of becoming are simultaneously registered. At the highest level they are too ideal, too much at one with the One Reality, to participate in the duality of the line. Their simultaneity is timeless and needs no lines to connect its parts. Only with the whisper of separation in spirit-substance belonging to the Second Logos can one imagine a boundary line drawn "between the absolutely Ideal Universe and the invisible though manifested Kosmos".
How do emanation and connection take place? One might ponder whether this involves an extension out of the One and whether such an extension 'drops' in a vertical line from one Logoic point to the next. Is this the patterned dynamic of the sacred Tetraktys? H. P. Blavatsky forcefully argued that the idea of inertia as understood by modern science was unacceptable to the philosophical mind. The notion that a line of extension continued without change until an external force was exerted upon it was inadequate as an explanation of the processes of change and growth in the world. From an occult standpoint, there can be no such thing as inert matter but, rather, the extension of gods, monads and atoms which bear within themselves the force' of motion and life itself. This does not mean that higher forms of intelligence do not direct lower forms. Gods and higher monads affect and direct atoms in myriad lines of activity. But their extension is, in a very real sense, an illusion, for the moving force impelling lower forms is no different from that which already resides within them and constitutes the eternal Jiva that permeates the whole of manifested existence. Lines of extension can be said to exist relative to the gods, monads and atoms involved, but they are, in reality, a shadowy tracery replete with reflections of varying levels of expressed intelligence.
In the world of matter they are deeply etched: lines dividing, triangles, squares, cubes and so on. In the astral world they open up to curve and bend in unexpected ways. Three-dimensional guidelines crumble and shoot off along four-dimensional or five-dimensional corridors that lead into uncharted vastitudes. Leibniz thought that by eliminating the notion of extension, atoms could be considered as centres of force in themselves and the whole, so-called, material world realized as suffused with an immanent spiritual reality which intersected with the plane of the physical world at myriad points. But even this wonderfully liberating vision still raises the question of extension, albeit in a subtler sense, when two planes meet at more than one point and thus can be said to meet in a line. Is this a sort of boundary line, and does it have extension? Are planes in some sense discrete, necessitating an extension into one another, or are they all in coadunition with one another, only appearing to involve different substances, motion and space? Can one thus erase the incredible multi-layered structure of Being with one stroke of the pen, labelling it maya even while struggling in its net?
The more one bathes one's mind in the richly nutritive waters which pour through and in between the lines of the Teachings of Gupta Vidya, the greater one's ability to transcend the illusions of the world even while perceiving their sacred core. One way of imagining this is to envision the horizontal and vertical lines of the Mother-Father within. One is in the world but need not be of it. It is possible to celebrate the horizontal repose of Vishnu Narayana upon the limitless waters of space while participating in the vertical fire rising up between Shiva's closed eyes. The U-shaped mark on a Vaishnavite's brow suggests the cyclic presence of the divine in the world, the taking on of the mother-substance differentiated at the horizontal dividing line. But the vertical spiritual axis represented in the fiery Mahayogin becomes graduated through the three horizontal marks on a Shaivite's brow in an acknowledgement of the relative planes to be traversed. Combining these two, one becomes more than that represented by the cross in the circle. Embracing simultaneously compassion and enlightenment, one gradually comes to express on all levels of one's being the nature of the circle which has its circumference nowhere and its centre everywhere. Thus the uncontrolled, mechanical-seeming extensions; the lines of thought, action and karmic result which shape one's world can become deliberately directed and made to form constructs reflective of higher truths capable of uplifting other human souls. Whether these are straight lifelines thrown out to those who might grasp them, or whether they are connective of complex points, forming planes and solids through which others may observe and assimilate a many-faceted display of Truth, such extensions would never lose sight of the one eternal and invisible Reality.
Lying at the crossroads between the eyes, where renunciation and emancipation meet and where the Light of the Logos shines as parent of the Mother and Son, the one ever unmanifest Point blends utterly the dual forces of the world, Krishna and Shiva are one, each reflective of the whole, each infinitely extended within that which has no extension at all.
A line upon the sand curves to meet the water's edge.