Chapter 10 No.10

The Media of New Perceptive Faculties

The Spiritualization of Matter the End of Evolution-Sequence and Design in the Evolution of Human Faculties-The Upspringing Intuition-Evidences of Supernormal Powers of Perception and the Possibility of Attainment-The Influence and Place of the Pituitary Body and the Pineal Gland in the Evolution of Additional Faculties-The Skeptical Attitude of Empirical Science and the Need for a More Liberal Posture-The General Results of Pituitarial Awakening Upon Man and the Theory of Knowledge.

Evolution is a continuous process and the primal impetus back of the great on-flowing ocean of life acts infinitively. It is not terminated when life has succeeded in perfecting a form for the perfection of forms in themselves is not the end of vital activity. The end of evolution is the complete spiritualization of matter. So that it does not matter how perfect a form may be either subjectively or in its adaptation to environments; it does not matter how faultless a medium for the ensouling life it may be, there is ever the eternal necessity that life must drive it back over the path of its genesis until it shall be transmuted into pure spirit. Adaptation succeeds adaptation and with each there is a change in the form and this process continues until there is a more or less perfect congruence between form and juxtaposed environmental conditions. But no sooner than agreement has been attained under one set of conditions new conditions arise and require a new setting, new adaptative movements. Thus there is a continuous proceeding from stage to stage, going from the grossest to the subtlest and most refined, always the form is being pushed onward and upward by life. But adaptation is not undergone for the benefit of the form, but more truly for the informing principle. It is the progression of the life-element which constitutes the adaptation of form to form and to their peculiar environs. The form is a tool or instrument of life which it discards the moment it fails to respond to its requirements. Thus forms are constantly being assumed and as constantly being relinquished. But no effort of life is lost regardless as to whether the action is performed in one or another form. The totality of matter is perpetually being acted upon by the totality of life. Every appulse of life against matter means an added push in the direction of spiritualization. The totality of such appulses of life against matter may seem infinitely small in the visible results which they produce in the process of spiritualization; but with each there is an eternal gain in that movement that shall end in the complete transmutation of materiality into spirituality. This action of life in metamorphosing matter, the nether pole of the great pair of opposites, into spirituality, its copolar factor, in its outward, visible effects, is what we vaguely call evolution. And such it is; for life is merely unfolding that which it has enfolded. Matter, having been involved as a phase of kosmic involution, is now being evolved.

In the genesis of the kosmos there appear to be three great undulations in the universal current of life. The first of these prepares the field by depositing that elemental essence which is to become the world-plasm; the second precipitates the universum of materiality, spatiality and intellectuality, not as we now know them, of course, but as potencies; the third great undulation in the current of life effects the endowment of the world-plasm with those tendencies that are to build around themselves forms appropriate to their fulfillment. This ensoulment of the world-plasm with tendencies and the consequent segmentation of it into separate forms by these tendencies constitute the primary stages of that procedure of life which results ultimately in the up-raisement of matter and its final exaltation into pure spirit. Hence, the entire mass of materiality is besieged on all sides by the sum-total of life and the former is being raised slowly and irresistibly to heights that are immeasurably more sublime than its present degree of grossness.

It appears paradoxical, therefore, that life, although in all respects vastly superior to matter, should become the apparent vassal of materiality and give itself up to all the strict rules of imprisonment which are imposed upon it by the properties and qualities which we observe in matter. It seems so subject to every whim and fancy of matter that one is inclined to think that matter and not life is the chief designer of universal destiny. This is not a condition to be wondered at so much, for the reason that this apparent vassalage, this seeming enslavement of life by matter, is due to that superior and most marvelous adaptability of life which it enjoys in contradistinction to the relative unpliability of matter, and due also to the fact that life is kinetic and matter, being a mere deposit of life, is static. Life is mobility while matter is immobility and thus in possessing a greater range of freedom is, of course, correspondingly superior; but in this adaptation of itself to the labyrinthine cavities and multiformed interstices in matter it exhibits but a seeming serfdom which is really not a serfdom but a mastery. It is as if a man had taken lumber, hardware and stone and built a house wherein he might dwell-life has merely used matter, molded and fashioned it so as to make for itself a medium, a dwelling-place wherein it operates, not as a slave but as a master possessing unlimited freedom of motility. In the production of a form life stamps upon it, once for all time, the path of its engendering action. It leaves its finger-prints upon the mold which it makes for itself. So that if we would know where life has been or where it is we should look for its finger-prints (organization); we should observe the sinuosities which mark its pathway, remembering always that it is life that has formed the intricacies and complexities of the form into which it pours itself so accommodatingly in order that it may raise that form, develop and transmute it into something higher and better.

When we speak of form it must not be understood thereby that reference is made only to the gross physical form, but to the entire range of vital assumptions or vehicles which life ensouls for purposes of manifestation. This range we believe to cover the whole path of kosmogenesis seriating from the densest to the most subtle. Our chief concern, however, is the immediate effect which the totality of life's operations will have upon humanity or the form which it ensouls as the human organism. For it is impossible that humanity shall escape either the general or the specific results of the exalting power which life exerts over materiality and its appurtenances. It is, of course, impossible here to go into the various implications of this general forward movement of the universum of materiality or even to outline briefly the divergent lines of operation into which a satisfactory exposition of this view would naturally lead. And then to do so would be inappropriate in a volume of this kind. So we shall have to be content at this juncture to limit our study to a consideration of what we believe to be some of the immediate indications of this vast and most far-reaching phenomenon.

In the chapter on the "Genesis and Nature of Space" it is shown that the material universe is engendered at the same time and by the same movement or process as the universum of spatiality and intellectuality and that as the passage from chaos to kosmos proceeds the function of this movement is changed gradually from engenderment to exaltation wherein materiality is transmuted into spirituality. It is, of course, obvious that as materiality is exalted so are spatiality and intellectuality; and that as the one becomes more and more refined, capable of answering to higher and yet higher requirements so do all the others. For, at work in all and through all of these, is the current of life which pervades them, engendering, sustaining and elevating as it proceeds. So that as matter has evolved added characteristics and properties, each answering to a given need and arising out of the necessities inhering in the stage at which it appeared, so has the intellect evolved faculties to correspond therewith. In other words, the evolution of faculties for the expression of the human intellect has proceeded synchronously with the evolution of material qualities. And whenever a new faculty or an additional scope of motility is achieved by humanity there is always found a set of kosmic conditions which answers thereto. The cardinal principles of the doctrine of evolution are not, therefore, adverse to the conclusion that the organs of sense-perception-hearing, touch, sight, taste and smell-have not been endowed upon the human race or attained by it at one time; but rather that each answering to a newly acquired need and opening a wider scope of motility for the intellect has been evolved separately and in due order. It would also seem that the quality of consciousness, as it has been manifested in the various stages of life through which it has passed, and especially the mineral, vegetal and lower animal, has not always been of the same degree of efficiency. Nor has it enjoyed the same kind of freedom which it now enjoys in the highly evolved genus homo. It is equally apparent that matter itself has not always been in possession of the same qualities and characteristics which it now exhibits; but that it, too, has gone through various stages of evolution bringing forward into each new stage the transmuted results of each preceding one as a basis for further evolution and expansion. The innumerable arch?ological evidences which support this view make it unnecessary to do more than state the facts, as they appear to be substantiated by indubitable testimonies. Furthermore, it is believed that the outstanding implications of these phenomena will not be successfully controverted by those who are disinclined to see such implications in the evolutionary process. In a previous chapter we have briefly sketched the characteristics which mark the upspringing of a new faculty showing how, at first, it appears as an abnormality which exhibits itself in a very few individuals only, and that in a more or less indefinite manner; and how later the number of individuals in which it appears gradually increases, the definiteness of the faculty, at the same time, appearing more marked; then, like a tidal wave, it recurs in a still larger number of persons until, at last after a long period of time usually several thousands of years, it becomes universal exhibiting itself in every individual and appearing as a hereditary characteristic of the entire human race. It is, therefore, not without assurance as to the ultimate soundness of this view that we make the assertions which follow this brief introduction.

It has already been stated that for a very obvious reason, namely, the satisfaction of the needs of our present humanity, the intuition is for the time dominated by the intellect and held in subjugation by it so that all of man's external operations are governed and dictated almost entirely by the intellectuality, allowing the intuition only rare moments when it can come to the fore at all. This is the rule in the evolution of faculties and characteristics. The higher faculty, although potentially present in every way, is ever held in abeyance while the lower is brought, under the rigors of its own evolution, to a point where its joint operation with the higher may be executed with the least possible friction and retardation as also with the greatest possible co?rdination and co?peration. Accordingly, notwithstanding the fact that materiality must possess in potentiality all the qualities which it will at any time reveal, it is nevertheless necessary that these qualities shall come forth gradually and in due order. Similarly, humanity has come into possession of its various faculties of mind, and powers of physiological functions, by insensible degrees, the higher always being held in abeyance until the lower is fully developed. Those faculties which are to bestow added powers, additional freedom and a greater scope of motility are the ones which appear later than those which are truly primitive in character. These facts have been amply demonstrated by the science of embryology wherein it is shown that ontogeny is a recapitulation of phylogeny. That is, the history of the development of the individual is a recapitulation of the development of the species. Thus the various stages of development through which the human embryo passes while in utero are but a repetition of similar stages through which the entire human species has passed in its phylogenetic development. Wherefore, it is certain that humanity has not attained, at one and the same time, all the powers of mind and body which it now possesses; that the childhood of the human race represented a time when it had but few faculties or organs of sense-perception-indeed a time when the higher sense-organs of smell, taste and sight were entirely lacking although residing in potentiality therein.

It is undoubtedly true that the earth has passed through a similar evolution with respect to its own material characteristics, that its childhood was, in all points, analogous to the childhood of humanity; that the air, earth and water were wholly absent, except in potentiality, during the nebulous youth of its genesis. It is even probable that there are at work to-day processes which in the future shall culminate in the evolution of newer, higher and more complicately organized species of plants, animals and minerals. Every year brings fresh evidences that crystallize the conviction that the earth has been the scene for the appearance of many strange orders of animal life. Fossiliferous strata are continually yielding incontestable testimonies of changing flora and fauna. We count the animal and vegetal life of to-day as being more highly developed than that of any other previous age, and it is well that this is so, for simplicity of organization and primality of manifestation are always succeeded by complexity and a greater scope of adaptability.

We have said that the whole of that movement of the intellect which has brought forth the metageometrical creations of hyperspaces, the curvature of space and its manifoldness together with the entire assemblage of mathetic contrivances are merely the early evidences of the appearance in the human race of a new faculty, a new medium of perception whereby the Thinker shall acquire a still greater range of motility than that now offered by the intellect. Attention has been called also to the fact that this phenomenon has been manifested not alone in the field of mathematics, but in art, religion, politics and also in science in which we have only to witness the marvelous strides already made in the discovery of radio-active substances, the Roentgen, Becquerel, Leonard and other kinds of rays. It Is quite confidently believed that these forward movements in every branch of intellectual pursuit, these combined efforts of the intellect, in peering into the occult side of material things, are in response to the evolutionary needs of the Thinker, and in addition, are the evidences, and shall in time be the cause, of the development of an additional set of faculties. Function, or the performance of acts, determines faculty or the power of action and ultimately the organ itself. Thus the mere wish to perform aroused by desire and vitalized by the will actually terminates, in the course of time, in the genesis of a faculty, or the power to perform. The constant upreaching yearnings of the Thinker through his intellect for greater freedom and a larger scope of action, the desire to peer into the mysteries of life and mind, the infantile out-feelings of the mentality after some safer and surer basis for its theory of knowledge cannot fail in producing not only the faculty or power to satisfy these cravings but the very organ or medium by virtue of which the satisfaction may be attained.

It is not strange that in mathematics the intellect should have found first the clue to the existence of a higher sphere of intellectual research wherein it might become the creator of the various entities which peopled the new found domain; it is not strange that the mathematician should, in this instance, have assumed the role of the prophet proclaiming by various mathetic contrivances (although unconsciously) that the human race is nearing that time when it shall actually be able to function consciously in some higher sphere; neither is it to be wondered at that the voice of the prophet is heard and respected throughout the earth; for, indeed the mathematician is a spokesman who, as a rule, is unmoved by sudden outbursts of passion and ecstatic frenzies of emotions but calmly and dispassionately verifies his conclusions, tests them for consistency and having found them to satisfy the most rigorous mathetic requirements hesitates not to propound them. For this cause humanity respects the mathematician, and when he speaks listens to his voice. It is well, too, that this is so; for the history of mathematics is clearly the history of the development of the intellect. So exact a determinator of the quality of intellectual efficiency is it that its reign may be said to be an absolute monarchism whose lines of dominance extend to the minutest desire or appetency. It has always been the guide of the intellect, going before, as it were, blazing the trail, pushing back the frontiers of the intellect's domain and clearing away the debris so that the intellect with its retinue of servitors might have an easy path of progress.

Mathematics, however, has not the aptitude to serve the intuition as it serves the intellect. So the path into which the intuition would lead humanity the mathematician, because of his training and peculiar functions, is unprepared to enter. It is for this reason that when mathematics leads the intellect up to that point where it encounters life it fails, it becomes confused and its dictatorship becomes a mockery, its decrees remain unexecuted and futile. In taking this view we have certainly no desire to offend the mathematician or to detract from the glory of his monarchistic rulership over the intellectual progress of the race; for, in truth, mathematics is the diadem of gold wherewith man has crowned his intellect. Yet it is well, yea imperative in the light of recent developments in the realm of hyperspace, that a careful discrimination should be made as between the sphere of the intellect and that to which the intuition shall attain.

The intuition, long held in abeyance until the intellect should be fully crowned and reach the zenith of its powers, is now coming to the front. It will be many centuries perhaps before it shall have grown to such proportions as those already attained by the intellect; perhaps a few thousand years may pass before the intuition shall have evolved to that point where it may labor as coadjutor to the intellect; but undoubtedly the time will come when it, too, shall reward the Thinker's labors with that which shall be more precious than the crown of gold which the intellect has won. Then, the intellect, grown old and decrepit with years of reigning shall become dim and crystal-shaped and finally pass into automatism or reflexive movements where without the urge of volitional impulses it will perform with exactness, precision and utter loyalty the tasks which it has learned so well to execute in the days of its forgotten glory. Mankind will then be free. A new freedom, wherein the erstwhile lightning flashes of intuition will become fused into one glorious sheen of all-revealing light, shall come to men and thus the race resplendent will walk the earth enshrined in the majesty of divine powers attained as a result of millions of years of aspiration.

That there are supersensuous realms so far above the range of our senses as to be entirely beyond their ken needs now no proof or argument; for the scientist has demonstrated, by the invention of instruments of extreme delicacy and precision, that such a world does really exist. Already we know of stars so distant that, though light traverses in the brief space of an hour six hundred million miles, they might have ceased to shine before the pyramids were built and yet be visible to us in the skies. If the human eye were as sensitive as the spectroscope many thousand tints and shades might be added to the world of color; if they possessed the magnifying powers of the microscope we should live in constant terror and awe of the monstrous entities that teem in the water which we drink and in the air which we breathe; and if our ears could detect the microphonic vibrations which register in the delicate apparatus of some microphones the dead, vacuum-stillness of nature's great silences would appear as a babel of voices by the seaside. The sense of touch, responding to the same range of vibrations as the micrometer, would reveal actually the interstices between particles of the densest elements; and gold, silver, platinum and mercury would seem but honeycombs of matter. But, to the forward-looking there is no element of absurdity in the expectation that all these senses shall, one day, be able to dispense with the artificial aid of physical apparatus and perform, with even greater precision and faithfulness, the task which they now perform so crudely and ineffectively. There are without doubt vibrations of taste and smell which are so far above the range of these senses that they have no effect upon them whatsoever. Notwithstanding the fact, however, that the galvanometer, microscope, the microphone, the spectroscope and the telescope have extended thus the sphere of sense-knowledge there are yet subtler vibrations to which these delicate instruments do not and ought not be expected to respond. But to say, as do many empiricists, that since these phenomena cannot be detected by scientific instruments they do not, therefore, exist seems to be expecting too much of material means as well as exposing oneself unnecessarily to criticism on the grounds of extreme materialistic appetences.

There is indeed need of a more liberal attitude among men of science towards the world of the unseen. Intolerance of the data which it offers will for a time perhaps preserve the aloofness of scientific dogmatism inviolate but there will most surely come a reaction against the dogmatism of science and men will seek freedom and attain it despite their fetters. Sir Oliver Lodge, in his book, the Survival of Man,[29] says: "Man's outlook upon the universe is entering upon a new phase. Simultaneously with the beginning of a revolutionary increase in his powers of physical locomotion-which will soon be extended to a third dimension and no longer limited to a solid or liquid surface-his power of reciprocal mental intercourse is also in process of being enlarged; for there are signs that it will some day be no longer limited to contemporary denizens of earth, but will permit a utilization of knowledge and powers superior to his own, even to the extent of ultimately attaining trustworthy information concerning other conditions of existence."

It is the author's good fortune that he has for a period extending over several years been able to verify the conclusions which Sir Oliver Lodge expresses in the above, and thus to satisfy his own mind that the process by which man's mental powers are "being enlarged" is indeed demonstrable by actual observation and experimental methods.

Lodge continues:

"The boundary between the two states-the known and the unknown, is still substantial, but it is wearing thin in places, and like excavators engaged in boring a tunnel from opposite ends amid the roar of water and other noises, we are beginning to hear now and again the strokes of the pick-axes of our comrades on the other side."

Camille Flammarion[30] cites 436 cases of psychic manifestations examined by himself and which establish beyond any reasonable doubt that there are certain perceptive faculties, namely, clairvoyance and clairaudience, that crop out in certain individuals, sometimes in abnormal conditions and sometimes normally, the very unusual character of which proves their rudimentary nature and the potency of their maturescence in the humanity of the future. Among the cases cited by Flammarion are 186 instances of manifestations from the dying received by persons who were awake; 70 cases were manifestations received by persons asleep; 57 were observations of direct transmission of thought without the aid of sight, hearing or touch or other physical means; 49 were cases of sight at a distance or clairvoyance by persons awake, in dreams or in somnambulism and 74 cases of premonitory dreams or predictions of the future. Indeed, there are few persons now living who have not had similar experiences, if not exactly like these, of the same nature. These examples, of course, may be greatly multiplied in every country in the world, and it is unnecessary to enumerate them further; for, when once the existence of such faculties has been demonstrated in persons, either in a normal or an abnormal condition, their presence can no longer be questioned by the fair-minded. It is, then, only a question of evolution before they will appear in the normal way and their universalization, as transmissible characters, be an accomplished fact. When we are brought face to face with this sort of phenomenon which seems to be increasing rapidly the conclusion is inevitably forced upon us that since evolution must be a continuous process and matter destined to yield higher and more refined powers and humanity to come into a far more extensive scope of motility because of the opening avenues of knowledge, it is not impossible that these acuter senses, these new faculties are now existing in the human race in a rudimentary stage and are designed to become the universal possession of all. That this is to be the almost immediate outcome of the perpetual exalting power which life exercises not alone over materiality but over human organs and faculties as well, seems to be the one big, outstanding implication of the evolutionary process. The presence of such functions as the ability to sense the invisible and the inaudible, to answer to vibrations far subtler than anything in the scope of our external sense-organs, certainly indicates the existence of rudimentary faculties which make these functions possible. Back of these vague, indefinite functions, back of every supernormal or abnormal manifestation of man's mentality and back of all that class of phenomena which take their rise out of supersensuous areas must lie, in ever increasing potency, faculties and organs, however rudimentary, which are the source of these manifestations. Life, that ineluctable agent of creation, which is incessantly pushing outward the confines of the intellect's scope of motility, never wearying, never tiring nor sleeping, has long ago, in the dim and distant past of man's evolution, laid the foundations; and in fact, with one stroke of its creative hand, has molded the organs which are to become the active media of these new faculties. And now, these incipient demonstrations, these infantile struggles which we see now and again outputting from them, are but the specializing processes through which, in their later development, these organs are proceeding. These are the outward signs which should tell us that life is breaking up these organs into special parts, assigning to each a certain division of labor and making of each a perfect co?rdinate of all the others. It is, by these very dispread exhibitions, cutting up, specializing and by slow degrees determining the function, character and general tendence of the organs of expression wherewith these manifestations shall be centralized and put into effective operation. In doing this, it is but following its accustomed procedure, the procedure which it adopted when it produced the eye, the ear, the heart and the spleen. We shall, therefore, gauge our understanding of the purport and end of evolution; in fact, we shall determine our exact intellectual comprehension of life itself, by the attitude which we adopt towards it and the mode of its appearance. Much depends, accordingly, upon the posture which we assume towards life-whether we shall say the totality of life's creative powers has been dissipated in the bringing of the human body to its present degree of perfection; whether we shall say that it is neither necessary nor possible for life to produce other organs and faculties which shall respond to the unseen world about us revealing its glories in a way far more perfect than do our external sense-organs reveal the wonders of the world of sensation; or, whether we shall conclude from these most palpable evidences that life has yet other powers and faculties which it designs to bestow upon the human mind and other organs and capabilities with which it shall endow the human body so that man, in his evolution, shall be enabled to rise to still higher spheres while yet incarnate. There may be, and undoubtedly are, those who, for various reasons prefer to take the former positions and there are certainly those who like Lodge, Flammarion, Hudson, Crookes and a host of others, preferring the latter view, would rather believe in the strength of the great mass of corroborative testimonies that we are even to-day in the midst of the matutinal hours of a newer, a better and a far more efficient era of human evolution than any through which we have hitherto come.

Already, recent scientific investigations and the results obtained therefrom have begun to turn the attention of medical authorities to the activities of two very small organs situated in the mid-brain and known as the pineal gland and the pituitary body. These organs, and especially the pineal gland hitherto supposed to be a vestige of the past, are now beginning to be recognized as rudimentary organs belonging to the future evolution of humanity. Dr. Charles de M. Sajous, who is an authority on the pituitary body, believes that it has no active internal secretions but is an "epithelio-nervous organ" which controls, through nerves leading to the adrenals and thyroid bone, the processes of general oxygenation, metabolism and nutrition. Little is known of the functions of the pineal gland except that it is an ovoid, reddish organ attached to the posterior cerebral commissure projecting downward and backward between the anterior pair of the corpora quadrigemina. It is otherwise known as the "conarium" the "pinus" or "epiphysis." Situated at the base of the brain, it is held in position by a fold of the pia mater while its base is connected with the cerebrum by two pedicles. It contains amylaceous and gritty, calcareous particles constituting the brain sand. There are, however, marked structural resemblances between the pineal gland and the pituitary body and their formation is perhaps the most interesting feature of the development of the thalamencephalon or mid-brain. The hypophysis cerebri or pituitary body is a small, ovoid, pale, reddish mass varying in weight from five to ten grains and situated at the basal extremity of the brain in a depression of the cranium known as the sella turcica, a configuration very much like a Turkish saddle in shape. It is a composite, ductless gland and consists of two divisions, an anterior and a posterior, connected by an intermedial portion-all of which are attached to the base of the cerebrum by the infundibulum. The anterior lobe is larger than the posterior and very vascular, springing in its development from the buccal cavity of the embryo; the posterior lobe is situated in a depression of the anterior and is a brain-process. The pituitary body itself is lodged in a cavity of the sphenoid bone called the pituitary fossa. This is a most remarkable position, for the reason that the sphenoid, or wedge-shaped, bone which lies at the base of the skull articulates from behind with the occipital and in front with the frontal and ethmoid bones and by lateral processes with the frontal, parietal and temporal bones. From this position it binds together all the bones of the cranium, and moreover, articulates with many bones of the face. It is upon the upper surface of the sphenoid bone which occupies such a prominent and commanding position in the cranium, in a deep depression, that the pituitary gland is located.

Each nasal chamber is lined by a mucous membrane called the pituitary or Schneiderian. This membrane is prolonged into the meatuses and air sinuses which open into the nasal chambers. The pituitary membrane is thick and soft and diminishes the size of the meatuses and air sinuses. It is covered by a ciliated columnar epithelium and contains numerous racemose glands for the secretion of mucous or pituita. It is also vascular and the veins which ramify it have a plexiform or net-work like arrangement. It divides into two membranes-a respiratory, which is concerned in breathing, and an olfactory region. The respiratory region corresponds to the floor of the nose, to the inferior turbinated bone and to the lower third of the nasal septum. The olfactory region is the seat and distribution of the olfactory nerve and corresponds to the base of the nose, to the superior and middle turbinals and the upper two-thirds of the nasal septum.

Recent developments prove that this gland has a profound influence over the animal economy. It is believed by some that the pituitary body actually destroys certain substances which have a toxic influence on the nervous system; others believe that it secretes material media for the proper action of the trophic or nutritive apparatus; still others believe that it influences blood-pressure. It is known, however, from experimentation, that its removal in dogs, cats, mice and guinea pigs causes a fall of temperature, lassitude, muscular twitchings, dyspn?a or difficult breathing, and even speedy death. Hypertrophy of the gland is directly associated with certain diseases, such as giantism and acromegaly. The latter is a disease which causes a general enlargement of the bones of the head, feet and hands, usually occurring between the ages of twenty and forty years, and most frequently in females. The fact that these diseases are so closely associated with a hypertrophic condition of the pituitary gland has led to the conclusion that perhaps the giants or Cyclops of ancient times were cases of giantism or acromegaly. This view, while interesting from the standpoint of the functions of the pituitary gland, is not necessarily a correct one; for the age of giants, when men attained to a much larger stature than at present, can be accounted for on other grounds, namely; that the early mesozoic man, on account of his having to live among animals, trees and other vegetation of such huge size, had naturally to be fitted with a frame proportional to other animals in order that he might successfully cope with his environing conditions. Nature thus wisely fitted him for the conditions which she had prepared for the scenes of his life.

The facts adduced in the foregoing description are purely empirical and may be verified by any who seek to establish their correctness or incorrectness. But we are about to introduce a species of testimony which while it may also be verified will not be found so easy of verification as the above-mentioned physiological facts, and not by the same means; yet they are nevertheless deserving of a place here. It is the liberal attitude that we must adopt towards all phenomena, excluding none that give promise of the widening and deepening of our knowledge and an explanation of much that has seemed heretofore unaccountable.

We have noted how subtle is the physical connection between these two bodies, the pineal gland and the pituitary body; we have seen how profound is the effect which the latter has been demonstrated, in a measure, to have over the entire bodily economy; but there is even other testimony to the effect that those gifted with the inner vision can observe the "pulsating aura" in each body, a movement which is not unlike the pulsations of the heart and which never ceases throughout life. In the development of clairvoyance it is known that this motion becomes intensified, the auric vibrations becoming stronger and more pronounced. The pituitary body is the energizer of the pineal gland and, as its pulsating arc rises more and more until it contacts the pineal gland, it awakens and arouses it into a renewed activity in much the same manner as current electricity excites nervous tissue. When the pineal gland is thus aroused clairvoyant perception is said to become possible. These are facts which cannot be proved by the materialistic man of science nor can they be demonstrated to the layman who has to depend alone upon sense-deliveries for his knowledge. This is true for the reason that, in the first place, it is necessary that he shall either feel in his own mid-brain the energizing activity of these two organs and have his entire nerve-body shaken from crown to toe by the down rushing currents of that subtle energy with which the pituitary body floods it or be himself the perceiver of its activities. Nevertheless attention is here called to these phenomena and the conclusions drawn therefrom are offered as a means of denoting the probable line of investigations which will establish the directions which we should pursue and the source whence we shall find outcropping the new faculties and their organs of expression.

We confess to a knowledge of the fact that men of empirical science have long maintained a rather skeptical, if not contemptuous, attitude towards all these phenomena but it is also felt that there is far more of discredit in their attitude than of credit; for, in so doing, they have voluntarily adopted measures by means of which the knowledge that they so eagerly seek is shut out from their attainment. In vain, then, is appeal made to the intellect to remove the barriers which it unconsciously interposes between itself and the goal of its pursuit; in vain do we appeal to the materialist to give ear to testimony the data of which cannot be made amenable to his knife and scalpel neither to the microscope nor microphone; in sheer vanity is he adjured to look within-into the interior of life, of mind and the things which he handles with his instruments-for the answers to his queries, for the path which leads into the wake of life and consciousness. Because his utter loyalty and devotion to the modus vivendi of the intellect will not permit this; but, after all, it is not wholly wise to allure him away unbetimes from his search after truth through superficialities nor to inveigle him into giving up his tenacious prosecution of the physically determinable. We would not have it so; for, perchance, he, too, one fine day, in the quiet of his laboratory shall come upon the data which may substantiate in his own mind the long settled conclusions of the occultist who, frequently and not without cause, grows impatient at the scientist's obstinate delay. These two workers, the empiricist and the occultist, must ultimately come together as collaborators-the one working upon the form, the vehicle, physical matter and the other seeking to understand the life, the interior forces which produce, the creative element. They cannot remain always aloof from one another; for they, too, are as men digging a tunnel from opposite ends. Finally, the partition will break and thus will dawn a new day for the knowledge of humanity and men will see the rationale, the truth and good sense of co?peration in this respect.

It can be said with confidence that whatever in the future may be learned as to the physiologic functions of the pituitary body and the pineal gland, it suffices to know that it is life which they express and that, too, in a far superior manner than any of the other sense organs. The modus of these two glands differs in a very marked way from that of the organs of sight, hearing, taste, smell and feeling. For these latter are designed for contact with the external, objective world of sensations, their growth and evolution being dependent upon stimuli received from without while with the former the case is far different, in fact, just the opposite. The mode of life of the pituitary body and the pineal gland, instead of receiving sustenance and impetus from external stimuli, is rather dependent upon impacts received from the Thinker's own consciousness and made to impinge upon them by an exclusively interior process. Situated in the mid-brain, safely secluded from all external interference, they are naturally limited to stimuli which come from within, or it may be said, they are responsive to excitations that are more spiritual than those which come through the external sense-organs. If, as has been said they control the internal processes of metabolism (anabolism and katabolism), oxygenation, nutrition, and other important internal movements, none of which can be said to be under the control of the intellect, is it not, therefore, justly assumed that their response is directed towards stimuli which arise interiorly or upon a plane higher than the intellectual? It is a matter of scientific knowledge that those persons gifted with clairvoyance, and commonly known as "sensitives" are far more responsive to nervous excitation than those who are not so gifted. This would seem to imply that, on account of the superactivity of these two organs, the entire nerve-body has, in consequence, become more delicately and subtly organized. They seem to act as a switchboard for the regulation of the flow of the current of life through the body. Not only do they come more nearly to an adequate expression of the physiologic function of life, but, as their energization means an enlargement of the scope of perception by giving the Thinker's active consciousness access to hitherto unapproachable realities and by penetrating the outer mask which life ensouls and also laying bare a domain of unlimited knowledge the manifestation of which is far more real than anything the senses can disclose, it is evident that they constitute, in their collaborative functions, a more highly adaptable medium for the expression of the Thinker's consciousness. And if so, for the kosmic consciousness which is the source of all forms of consciousness, they furnish a specializing and adaptizing agency.

Now, in all those cases of inspirations, revelations, telepathic communications, clairaudience, clairvoyance, dreams, visions, etc., wherein the Thinker is enabled to perceive facts and verities which are then presented to his consciousness in a manner clearly without the province of the common sense-organs, it must be apparent that these manifestations are apprehended by a perceptual mechanism which is entirely independent of external sense presentations but which is an interior and subtler form of psychic activity. Sounds which are heard by so-called "sensitives" and objects which are perceived by eyes that are keener than those organs said to have been evolved from the "medusa" cannot be heard by other persons nor perceived by them in any way. Thus it would seem that there are inner organs of perception which respond to these finer vibrations and which enable the person so gifted to apprehend them.

There are those who, presumably basing their assertions upon actual observation and knowledge, unqualifiedly assert that in order "to gain contact with the inner worlds all that remains to be done is the awakening of the pituitary body and the pineal gland. When this is accomplished man will again possess the faculty of perception in the higher worlds, but on a grander scale than formerly (when humanity was in its infancy and exercised a lower form of psychic power only); because it will be in connection with the voluntary nervous system, and therefore, under the control of the will. Through this inner perceptive faculty all avenues of knowledge will be opened to him and he will have at his service a means of acquiring information compared with which all other methods of investigation are but child's play."[31] It is the lack of this ability to see, with our physical eyes, as it were, by the "Roentgen rays," to penetrate the inwardness of things that has baffled and confounded men for so long a time and which has eventually led certain mathematicians and others to conjecture such strange, and in many cases, illogical possibilities for the denizens of four-space. This inability together with the desire to fathom the innermost complexities of solids and to handle, albeit with unholy hands, the supersensuous, the mysterious and the unapproachable identity of "things-in-themselves" have induced the more zealous among them to contrive some kind of hypothesis which would, at least, offer an explanation of these phenomena. It has driven them to wrestle with metaphysical possibilities in a vain endeavor to grasp that which, ignis-fatuus like, ever evades their slightest intellectual approach. But why this prolonged struggle, why this intellectual maneuvering and sophistry? "We can calculate, compute, excogitate," says Paul Carus,[32] "and describe all the characteristics of four-dimensional space, so long as we remain in the realm of abstract thought and do not venture to make use of our motility and execute our plans in an actualized construction of motion; but as soon as we make an a priori construction of the scope of our motility, we find out the incompatibility of the whole scheme." Thus mathematicians are forced to relinquish all hopes of transforming the world of life into a sort of four-space dwelling place where everything is done according to the laws of mathematics. But whether they shall accept it or not there is a wider, truer and more rational view which recognizes all metageometrical investigations, as well as all kindred phenomena, as universal evidences indeed, as the very causes which, in the future humanity, will actually awaken and cause to be accelerated in their development these little inner sense-organs, the pineal gland and the pituitary body, whose perfect development promises to provide for the Thinker's consciousness an avenue of expression such as humanity has possessed never before. And too, it is not without full knowledge of the fact that it has been customary, among certain scientists or perhaps all of them, to regard these bodies, at least the pineal gland, as vestigal organs belonging to the past of human evolution, that we make these assertions. Yet, as man proceeds in the perfection of mechanical science, in the development of instruments of precision that aid his external senses, responds more and more to the subtle vibrations teeming everywhere in the atmosphere about him, and comes, in the course of time, naturally to possess a more sensitively keyed nervous mechanism, a finer body and higher spiritual aspirations, there will be a corresponding widening of his scope of vision and the attainment of larger powers of perception which must inevitably, in the very nature of things, tend towards a deeper and truer knowledge. In view of the foregoing, it is believed that the general results of this pituitarial awakening which may be expected as humanity continues to evolve should be seen in the marked effects which will be wrought in the entire metabolistic area of the human body whereby a gradual intensification and sensitization of the whole neural mechanism will raise the peculiar efficiency of all the senses whether purely physiologic or psychic. For there are undoubtedly notes so delicate in their intensity that they transcend the grasp of the audital nerves; scents and fragrances so subtle in their excelling purity that it is beyond the powers of our present olfactorial contrivances to detect them; colors and other external stimuli so sublimely supersensuous that a nervous mechanism perhaps ten-fold more delicate and responsive than ours is required to apprehend them. All these, and more than at present is conceivable, will come, with the aid of pituitarial stimulation, within the purview of a more highly developed humanity of the future. And because mathematics have led a movement into the very camp of the intellectuals-logic-bound and tethered by the severest rigors of mathesis-whereby the intolerant intellect has been compelled, by rules of its own making, to recognize the existence of the supersensuous, and by looking into the glaring light of the sun of the intuitable to gain strength of vision and boldness to press forward, a great and far-reaching service has been wrought for humanity. And in the tower of hyperspace mathematics have erected a monument to the intellect which, as long as the human race remains, will mark the great turning point in man's path to the highest life.

What if it were possible that the scientist, when he had carried instruments to their utmost precision and penetration, should suddenly, or otherwise, be endowed with a clear-perceptivity of sight, hearing and smell, so that he could with his own powers of vision, feeling and hearing take up the task where the microscope, the microphone and the micrometer left off and delve into depths far too unfathomable for his appliances, perceiving the innermost realities of things and processes? What if it were possible for him, with these added powers, to see and examine without the aid of the magnifying lens the electron, the atom and the molecule? What if the cell, the bacterium, and other invisible forms of life would then deliver up their secrets to his knowing mind? What if he could sense with his own inner vision, the ultra-violet and the infra-red rays; what indeed, if spirit itself, the innermost sheath of life, should be visible and palpable to him and he could note the internal processes, the action and movements of the infinitesimals of life? Think you not that such direct contact, such immediate and incontrovertible knowledge would be far superior to any advantage which his manufactured devices now bestow? It is even so.

Thus will react upon man's perceptive apparatus the flood of light which the awakened intuition will shed upon them and thus will man rise higher, driven on by the current of life with the mass of materiality, to a point of complete spiritualization and take additional steps in that direction which leads to Raja Yoga or the Royal Union with the divine life of the universe.

Before this step is taken, however, and before the passage from mechanics to biogenetics is made, as made it must be, man must win a complete mastery over matter. But this he will do; for more and more he is learning to put all those forms of labor which are so exacting as to leave him no time for the development of his higher powers into the hands of machinery. He will not be free until he has done this well-nigh completely. This is the task of the intellect and with it man must win his way to these higher faculties which are destined to succeed the intellect whereupon he will be ushered out of a life bound and restricted by mechanics to a life of unimaginable freedom, the intuitive life.

The outcome of these new faculties of perception and the development of the intuition will be the springing up of a new species of art that, turning away from appearances and sinking beneath or rising above, superficialities, will seek to portray in newly found colors, the plastic essence of things so that we shall have an art which pertains to the real, superseding that which pertains to the phenomenal. Language and the need of it will pass away; for man will have outgrown the use of signs and symbols in his communion with his fellows and will use the language of the intuition-direct and instantaneous cognition. Philosophy will be regenerated, re-created. Speculation will give way to truth and there shall be but one philosophy and that shall be the knowledge of the real. Mathematics, the royal insignia of the intellectual life, because it can deal only with immobilities, with segments and parts and has no aptitude for the continuous flow, will yield its kingdom to a higher form of kinetics which will serve the intuitive faculty as mathematics now serve the intellect. Science will then be no longer empirical in its method; but a system of direct and incontrovertible truths. Religion will rise to meet these changes which will come in the path of human evolution; and faith will surrender its place to knowledge. Ethics, recast in a new mold, will deal with the new aspect of man's relation to his fellowmen. Man, for whose highest good these ultimate changes will come, will be a new creature, a higher and better man; and humanity shall evolve a new race. There shall, indeed, be "a new heaven and a new earth."

THE END.

* * *

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* * *

INDEX

A

Abeyance, higher faculties held in, until lower are fully developed, 334

- intuition kept in, 338, ff

Ability, to sense the inaudible and the invisible, 342

Absolute, no room for the, 101

Abstract thought, invigorating power of, 33, 40

Abstractions, realizing, 144, 294

Absurdity, analysis inevitably ends in an, 319-20

Acrobatics, mathetic, 146

Acromegaly, 347

Action, automatic, of the intellect, 253-4

- engendering, of life on the form, 330

Activities, space, as physical and chemical phenomena, 229-30

Actualities of the physical world pushed over into the conceptual, 119

Actuality imperceptible to the intellect, 126

Adaptability of life, 330

- - mathematical laws, 37-39

Adaptation, purpose of, 327-8

Adaptations made by an organism, 162

Additional freedom bestowed by higher faculties, 334

Affinity, zones of, 22, 124

Agency, interpretative, intellect as an, 166-7

Agent, ego as an, of the Thinker, 243, ff

- engendering, life as an, 331

- of creation, life as an, 343

Ahmes, an Egyptian priest, 44

Alchemy of psychogenesis, 225

Alcohols, eight different, from one formula, 155

Algebraic quantities and space, 125-7

Allowability of the rules of logic, 163

Aloofness, the, of scientific dogmatism, 340

Alphabet of space-genesis, 237

- the geometric, 193

Amenability of mind to the laws of evolution, 28-31

Analogies, use of, to popularize the four-space, 128-9

Analogy, difference between two processes illustrated by, 74

Analysis incapable of dealing with life, 319

- the manifold, the fiat of, 77

Analyst and the manufacture of the space-manifold, 77

- disregards the conformity of the nature of things, 84

Analytics and the mechanical origin of the universe, 40-1

- perisophical nature of, 320, ff

- the four-space, a curiosity of, 40

Anchorage, fourth dimension denied, 265

Angularity of consciousness, 120

Answer of the senses to new needs, 332

- the, of consciousness to realism, 97

Anti-Euclidean geometry, 69

Apotheosis of the definition, 78

Apparatus, man's perceptive, 357

Apparent vassalage of life, 329-30

Appearance, dynamic, space as, 104-7

Appetences, materialistic, of empiricists, 340

Appulses of life against matter, 328

Appurtenances of materiality, 331

A priori, 185, ff

- - knowledge, 110-5

Aprioriness, 112, 116

Apriority, the principle of, 113, 223

Arbitrariness of the common mensurative quantities, 41

Archeological evidences, 332

Archimedes, 70

Aristotle, 322

Arrangement of the contents of the kosmos, 317-8

Art and the criterion of truth, 323

- - - higher consciousness, 181

- evidences of new faculties in the field of, 335

Assemblage of mathetic contrivances, 335

Assumptions, category of, 189

- procedure based upon, disadvantages of, 163

At-one-ment, 224, 252, 270

- defined as the end of evolutionary activity, 1

Attachment of the consciousness to the order of becoming, 305

Attainment, the difficulty of, by the intellectual method, 206

- of space-consciousness, 225

Attitude, the need of a more liberal, 340

- towards things spatial, 306

Audital nerves, notes that transcend the grasp of, 355

Aura, pulsating, 348

Automatism of the intellect, 253, ff; 338

Avenues of knowledge opened to inner perceptive faculties, 353

Awakening of the faculty of awareness in a new domain, 90

- - - pituitary body and the pineal gland, 353

- pituitarial, general results of, 355-8

Awareness, a determinant of conception, 120

- as a gauge of the existence of things, 161-202

- degrees of, 165

- hyperspace, a symbol of a more extensive, 180

- progress in, 171

- Thinker's sphere of, 274, 283

B

Baltzer, 66

Barrier, the, to the Thinker's certitude, 186-8

Barriers, freedom determined by absence of, 280

Becoming, endless labyrinth of, 220

- the kosmos, in a state of, 265

- the order of, 305

Becomings, infinity of, 234

Becquerel rays, 336

Being, identification of consciousness with, 205

- kathekotic, 210

Being, the interiority of, 290

- the numericity of, 309

- the range of, co-extensive with reality, 168

Beings, discarnate, 154

Beltrami, Eugenio, 1-2, 63-5, 66-7

- - and the manifold, 317

- - and the pseudosphere, 64-5

Besiegement of matter by life, 329-30

Bessel, on geometry as incomplete, 58

Bewilderment, new realities cause, 169-70

- of the mind, 182

Biogenetics, passage from mechanics to, 357

- turning to, from mechanics, 322

Birth, as a fourth dimensional process, 159

Blind men and the elephant, 257

Bolyai, Janos, 2-3, 46, 60, 66, 83, 87

Boundaries of a hypercube, 136-8

Brain, the physics of, 292

Brain-consciousness, 184, 186

- standards of, 190

Brotherhood, and the tendencies of the Thinker's consciousness, 301

- the keynote of the intuition, 252

Bulwarks, the formal, of geometry, 77-9

C

Carpet, the sensible world as a, 196

Carus, Paul, on four-dimensional space, 254

- - on metageometricians, 102

- - on space, 110

- - on the representation of the tesseract, 136-7

Cayley, 3-4, 54-5, 66-7

Cell-activity as a performance a priori, 114

Cell-colony, 250, 301

Cell-consciousness as an aposterioristic phenomenon, 185

Centers, pyknotic, 232

Certainty, geometric, the basis of, 77-8

- of mathetic conclusions, provisional, 37

Chaogenic period of involution, 208, ff

Chaogeny, 231, 233

- the evolution of chaos into order, 4

- the laboratory of, 193

Chaomorphogeny, defined, 4, 231-2

Chaos, as egg-plasm, 265

- duration of, 268

- movement of life in, 307

- shores of, 307

Chaos-geometricity, 307

- -intellectuality, 307

- -materiality, 307

- -spatiality, 307

- -Theos-Kosmos, 215, 233-4, 237

- - - a triglyph symbolizing kathekos, 11-2

Character of the universe, fixed by consciousness, 162

Characteristics, changes in the, of reality, 169

- fourth dimensional, of the ether, 157

- minds of similar, fall into zones of affinity, 124

- of non-Euclidean space, 72-3

Chasm, kosmic, between the real and the ideal, 107

Chemists, speculative, and the ourth dimension, 155

Chrism, sacred, of creative mentality, 91

Circle, significance of process of squaring, 109

Circle, the symbology of, 309

Circuits, closed, our interests as, 167

Clairaudience, 352

Clairvoyance, 352

Clairvoyant perception, 349

Clause, enabling, of metageometry, 76-7

Clavius, Christoph, 46, 52, 83

Clifford, 66

Code, psychic, for systematizing cognitions, 190-1

Cognition, instantaneous, organ of, 258

- intimacies of direct, 205

- the method of, 186-8

Cognitions, intuitive, 145, 192-3

- psychic code for systematizing, 190-1

Commensurable quality, dimension as, 140

Communal consciousness, 270, ff

Communalization and the intuition, 301

Conarium, the, 345

Conceivability and evolution of mind, 24

- ultimate range of, 278

Conceiving, power of, derived from sense-experience, 26

Concept, as a shadow, 119

- the hyperspace, gradual rise of, 27-8

Conception and awareness, 120

- every, based upon prior experience, 25

- freedom, the, of the mind from, 28

Conceptions, symbolic, dependence placed upon, 147

Concepts, and the Thinker, 244

- intuitograms as, 248

- quality of, dependent upon sense-experience, 26

Concepts, the perception of, 255

Conceptual, related to the objective, 291

- the, and mathematicians, 71

Conceptualization, the act of, 4

- the power of, dependent upon evolution of mind, 25

Conclusions, mathetic, complex dependence of, 37

Concrete hewn into shape by the intellect, 295

Congruency, the, between intellect and the universe, 319, ff

Congruity, the, between concepts and objects, 120

Connection, the, traced out between reality and object, 126

Co-originality of things, 303

Consciousness and kosmos, graph representing, 271

- - the character of the sensible world, 166

- - - wake of life, 205

- - time, 224

- angularity of, 120

- a priori, 185

- a replica of, and judgments, 205

- as a scale, 165

- - barrier to ultimate knowledge, 207

- - determinant of dimension, 145

- - life, 295

- - variable quantity, 171

- attachment of, to the order of becoming, 305

- dawn of, and dimension, 179

- degrees of, 162

- deprived of the validity of notions, 314

- evolution of, 250

- expansion of, 164, 272

- extended, 89-90

- focus of, 290

Consciousness and the planes of the kosmos, 163

- fragmentary view of, 260

- freedom of, in the genus homo, 332

- habitation of, 278

- higher, and art, 181

- - planes of, 178

- history of, 298-9

- identification of, with objects, 189-90

- intuitional, 255

- keyed to the entire range of reality, 167-8

- kinds of, 270, ff

- kosmic, Elysian fields of, 235

- of the primitive man, 253

- organ of, 184, ff; 90

- psychics of, 292

- raised from the sensuous to the conceptual, 72

- recipient of truths from dual sources, 26

- sensible world as instrument of, 199

- triple presentation of notions of space to, 72

- turned inward, 283

- unification of the states of, 192

- youthful, of mankind, 122

Consequences, the science of, 85

Considerations, mathematical, and reality, 128

Consistency, kosmic, 174

- self, of hyperspatial hypotheses, 67

- the criterion of geometry, 86

- - inconsistence of, 173

- - metageometrician curtailed by, 85

Construction, idealized, cannot be objectified, 144, 276

- ideal, the meaning of, 4

- mental, trafficking in, 154

Consubstantiality of intellectuality and spatiality, 331, ff

Continuity of the psychic plasm, 260

Contrivances, mathetic, the passing of, 241

Convergence of parallel lines, 315

Convolutions, duplex, 146

Co?rdinates, as spatial determinants, 203

- of hyperspace, 94, 97, 99, 115-6

- systems of, 301, ff

- three, 132, 232

Copolarity of ideas and objects, 127

Corpora quadrigemina, 345

Corpuscular orbits of particles, 152

Cosmos, significance of, 4

Creation, impregnated screen of, 232

Creations, the, of the intellect, 173

Criterion of geometry as consistency and convenience, 86

- - truth, 323-4

Crookes, 344

Cube, as succession of planes, 148

- generation of the, 144

- illustrated, 133

- the generating, 134

Curiosities, analytic, energy spent in elaborating misappropriated, 39

Current, electric, as component in the fourth dimension, 153

Curvature of space, the doctrine of, formulated by Riemann, 5

- - - valid element in the notion of, 305

- the measure of, 61

Curved space and metageometricians, 316

D

D'Alembert, note, 51

Dante, 181

Darwin, 181

Day, the Great Kosmic, 213

De Tilly, 66

Death, as fourth dimensional unity, 159

- of the intellect, 195

Decrement of the diametrical ratio to the circumference of circle, 312

Deeps, fearful, of kosmic mind, 71, 91

Definition, apotheosis of, 77-8

- as an arbitrary determination, 100

- the deification of, 37

Degrees of realism, 164-5

Deiform, basic idea of the, 5

Demarkation between reality and phantasy, the line of, 173

Deposits of life, 173

Descartes, 322

Designs, cut out in materiality by life, 264

Details, the power to dispose of innumerable, 303

Determinations, geometrical, the necessity of, inheres in logical deductions, 78

- the factors of conscious, 162

Determinative period of mental development, 31

Development of the intuitive faculty, future, 188

Diacritics of life, 286

Diameter, the ratio of, to the circumference, 311-2

Difference between concept and thing, 121-2

- between mathematical and perceptual space, 120

- between the ideal and the actual is dynamic, 108

Differential, among minds, 124

Difficulty of imagining the fourth dimension, 90

- of propagating an intuition, 315

Difficulties in the acquisition of real knowledge, 325

- of hyperspace, the logical, 139-41

Dilemma of metageometricians, 97-8

Dimension, a distinct stage in psychogenesis, 27

- - system of space measurement, 5

- and analysis, 163

- - D'Alembert, note, 51

- - the action of a tartrate in, 156

- as an arbitrary contrivance, 262

- - - assemblage of elements, 93

- - direction, 140

- - extent, 98

- - lying near the surface of things, 159-60

- - space, 96

- current definitions of, 98-100

- denied legitimate anchorage, 265

- determined by consciousness, 145

- does not explain spiritualism, 155

- evolution of the fourth, 44

- fourth, direction of, 134

- as "jack of all trades," 156

- impossible to actualize, 124

- key, to non-Euclidean geometry, 90

- movement of a plane into, 147-8

- no motion of material masses into, 125

- not a priori, 116

- proof of the existence of the fourth, 136

Dimensionality, and the intellect, 200

- as dependent upon the will of the investigator, 95

Dimensionality, conception of, purely conventional, 92

- logical difficulties which beset, 97

- of perceptual space, 72

- - space, the four, 142-3

Dimensions, four, no basis in consciousness for, 172

- piled upon one another, 300

- vanity, the, of segmenting space into many, 299

Direction as dimension, 99

Disappointment with the sensible world, 120-1

Discoveries, metageometrical, as excrescences of mental unfoldment, 131

- never the result of methodic reflection, 29-30

Disorder, the edict of, and space, 230

Disorderliness, the fringe of, 277

Dispossessal of the intellect by the intuition, 195

Dissimilarities, besetment of, 291

Distinctions, between conceptual and perceptual space, fundamental, 73-5

Diversity, a result of the fragmentative tendency of life, 6

- as transfinite quantity, 42

Divinity, prize of, won by the intellect, 43

Duadic phase of evolution, 210-1

Duodim, defined, 6; 128, 129, 134, 177

- consciousness, 163

Duopyknon, 212, 213

- the meaning of, 6

Duopyknosis, 208-10, 218

- as a stage in the evolution of space, 6

Duration and space, 224

- eternal, 234

Dynamic appearance, space as, 104, 107

Dynamism, of the intellect, functional, 303

E

Earth, the nebulous youth of, 335

- a new, 358

East effloresces as West, 306

Ego, the, 270

- and percepts, 244

- as sovereign, 244

- Thinker's dependence upon, 245

- - treatment of, 246

Egopsyche, 265

- as an agency of self-consciousness, 258

- defined, 7

Egos, compared to choppy sea, 256-7

Egypt, birth-place of geometry, 44

Eisenlohr, 44

Elaborative period of the non-Euclidean geometry, 66-70

- - of mental development, 31-32

Element of evolution, basal, 259

Elements of the non-Euclidean geometry, 79-80

Elephant and blind men, 257

Ellis, Wilmot E., on ether as four-dimensional, 157-9

Embrace of direct cognition, 205

Engenderment of space, 260

Ensoulment of the world-plasm, 329

Entities, hyperspace, and the phenomenal world, 128-130

Enumeration, reformation of the system of, 38

Enveilment of consciousness, 273-4

Environment, artificial and natural, 162

Epiphysis, the, 345

Equidistantial, described by hyperspatial perpendicular, 80

Essence, elemental, as world-plasm, 329

Ether as possessing fourth dimensional characteristics, 157

Ethics recast in a new mold, 358

Euclid, 46, 70, 83, 263

- and the parallel-postulate, 45

- never-dying elements of, 53

Evidences, mathematical, exemplifies intellectual evolution, x

- the vanity of fragmentary, 204

Evolution, a continuous process, 327

- and the norms of reality, 175

- basal element of, 259

- commencement of, 232-3

- intellectual, forward movement of, 184

- kosmic, vicissitudes of, 215

- laws of, govern mind, 28

- mental, results of, 122

- of faculties, synchronous with evolution of matter, 332

- - material characteristics of the earth, 335

- - organs, time required for, 188

- preparation of the field of, 218

Exaltation of matter into spirit, 329

Examples of new perceptive evidences, 341-3

Existence on a higher plane, states of, 162

Experience, corroborative testimony of, denied hyperspace, 263

- prior, and conception, 25

Experiences, spatial, systematization of, 78

Extension, space as an unbounded, 61

Extra-spatiality, degraded into spatiality, 261

Extravaganza, mathematical, and the fourth dimension, 156

Eyes, as Roentgen rays, 353

F

Fact-mass, 289

Factors of conscious determinations, 162

- four, of the criterion of truth, 324-5

Facts as facets of truth, 284

- attempts to reform, 304

- logic as symbolism of, 287

- - the modeler of, 288

Faculties, dual derivation of, 162

- evolution of, synchronous with evolution of material qualities, 332, ff

- extended, 239

- foreshadowed by the hyperdimensional, 131

- higher, man must win his way to, 357

- new faculties evidenced by four-space, 24-29

- rudimentary nature of, 341, ff

- the source of, 349

Faculty and the intellect, 247, ff

- as transmissible character, 251

- determined by function, 336

- greatly extended, 117

- higher than the intellect, 126

- I-making, self-consciousness as, 243

- intuitive, 185

- of perception in higher worlds, 353

- - awareness, the awakening of, 89-91

- overshadowed by the intellect, 188

- of perception in higher worlds, 353

- rudimentary condition of, 192, ff

Faculty, outcropping of, 249-51

Failure of efforts to justify the objective existence of four-space, 125-6

Failures at solving the parallel-postulate, outcome of, 48, 83

Faith, dispossessed by knowledge, 358

Fay, mathetic, 160

Fechner, 39

Finity and unboundedness of space, 76

Flammarion, Camille, 341-2, 344

Flexity, as property of hyperspace, 63

Flexure, space as a, 305

Fluxional, between sense objects and ideal representations, 122-3

Fluxion, psychic, as difference between memory image and object, 7-8; 122

Focus of consciousness, 163, 290

- - the intellect, 310

Fohat, and the creation of morphons, 219

- as creative energy, 213

- Creator, 8

Fohatic energy, 226

Form, as vehicle of life, 330

- definition of, 8

- driven back over the path of its genesis, 327

- pure, cannot exist in nature, 294

- the idealty of, 110

- the universe not a pure, 108

Formative period of mental development, 31

- - of non-Euclidean geometry, 55

Formula, eight different alcohols from one, 155

Four-dimensionality, justification of, 176

Four-space, a curiosity of analytics, 40

- and Riemann, 27

- as a divertisement, 175

- consciousness does not act in the, 172

- existence of, denied, 171-2

- movement of matter in, 157

- reality of, glibly proclaimed, 154

- the, 8, 240

- - denizens of, 353

- - domain of, 154

- - study of, 124

- use of analogies to popularize, 128

Fourth dimension, analogical reasoning of, 177-9

- as a transcendental problem, 140

- - an attitude of the intellect, 200

- electric current as a component in, 153

- imaginability of, 106-7

- Simon Newcomb on, 125

Fragmentariness of the intellectual method, 164

Fragmentary view of the universe, 260

Fragmentation, tendency to, 296

- harks back to cell-division, 301

Freedom, a new, 338

- determined by absence of bonds, 280

- mathematical, 60

- mental, 66-7

- now dawning for the mind, 32

- of consciousness in genus homo, 332

- regal freedom of the mind, 118

- three degrees of, 125

- unrealizable, for the Thinker, 255

Fringe, chaogenetic, 308, 309

- of disorderliness, 257

- - kathekosity, 229

Frischauf, 66

Full, the universe as a, 310

Function determines faculty, 336

Functions back of latent faculties, indefinite, 343

- cellular and histologic, 253

Functioning, instinctive, of the intellect, 289

Fundamentals, totality of, kosmic, 265

G

Gamut of realism, 169

Gauge, awareness as a, 161-202

Gauss, Charles Frederick, 8-9, 56-8, 59, 174

- - - as formulator of the non-Euclidean geometry, 57

Geminos of Rhodes, 45, 52

Generability, as property of space, 62

- of hyperspace, Keyser on, 144

- - space by lines, 143

Generation, the, of the hypercube, 134

- of the hypertetrahedron, 135-6

Genesis, of space, 211, 227, ff

- - the earth, its nebulous youth, 335

- - - form, 327

- - - sensible world, 167

Genus homo, freedom of consciousness in, 332

Geometricity, 266

Geometries, non-Euclidean, based upon a negation of the latent geometrism, 262-3

- three possible, 54

Geometrism, engenderment of, 262

- established by life, 264

- kosmic geometrism, establishment of, 231

- latent, 257

- native geometrism of space, 262

- rediscovered by the intellect, 9-10

Geometrism, the basis of, 237, 261

Geometry, anti-Euclidean, 69

- and the study of magnitudes in space, 203

- artificial, 262-4

- a two-fold, 59

- breakdown of, 266

- determinative period of the non-Euclidean, 61-4

- diverse systems of, 323

- Euclid's Elements of, 53-4

- formal bulwarks of, 77-9

- Imaginary Geometry, The, 60

- natural geometry, 261

- Plato and the divine geometry, 193

- possible systems of, 174

- radical essence of pure, 85

Geometry, non-Euclidean, at variance with the parallel-postulate, 83-5

- - based upon a misconception, 91

- - determined by qualitative differences, 140

- - elaborative period of, 66-70

- - first published treatise on, 60

- - formative period of, 55

- - the final issue of, 88-9

- - growth and development of, 92

- - invalidation of, 174

- - key to, 90

- Lambert's Non-Euclidean geometry, note, 51

- - popularization of, 66-7

- - Schweikart's treatise on, 59

- - self-consistence of, 57

- - some elements of, 79-80

- - superperceptual knowledge of, 72

Geometry, non-Legendrean, 70

- symbolic, and commensurable quality, 145

Gerling, as correspondent of Gauss, 58

Germ-plasm, continuity of, 260

Giantism, 347

Glimpse, a, of the reality of space, 314

Glorification of the flesh, 227

Groups, transformation, discovery of, 30

Guide-posts to a new domain, 273, 277

Gulf, interposed between manifestation and non-manifestation, 206

H

Halley, memoir of, mastered by La Grange, 50

Halstead, G. B., note, 49, 66; note, 79

Heindel, Max, note, 353

Helmholtz, 39, 66

Hewer, the, of the concrete, the intellect as, 295

Hinton, C. H., 154

- on the fourth dimension, 153

History, the, of mind, three great epochs of, 31-32

Homogeneity, the, of realism, 165

Hoüel, J., 60, 66

Hudson, 344

Humanity and the exalting power of life, 331, ff

Hypercube, boundaries of, and mirrors, 136-9

- the generation of, 134, 145

Hyperdimensional, as a prophecy of new faculties, 131

Hyperspace, 175

- a monument to the intellect, 356

- and the involved procedure of arriving at a recognition of its relations, 73

- and the passage thither, 293, ff

Hyperspace as a figurative mountain-peak, 200

- - - movement, 44-68

- - an all-powerful something, 160

- - - idealized construction, 10

- - evidence of new faculties, 24

- - ignes fatuii, 154

- - illusion, 202

- a symbol of higher consciousness, 180-4

- concept of, as an evolutionary quantity, 44-5

- confounded with real space, 91

- creation of, 335

- denied the corroborative testimony of experience, 263

- direction of, baffling to mathematicians, 146

- discovery of, a sign of mental evolution, 180

- domain of, a fairy-land, 239

- magnitudes of, the non-sensuous, 72

- mysterious hiding place in, 129

- the logical difficulties of, 139-141

- the six pillars of, 62-3

Hyperspatiality as the toys of childhood, 241

Hypertetrahedron, the, 135

Hypertrophy of the pituitary body, 347

Hypervolume, the, 134

Hypothesis, a superfoetated, 141

- four-space, utility of, 129; 154

Hypotheses, admissibility of, 118

- incompatibility of the non-Euclidean, 67; 71

- Riemannian, 80

- solution of, Bolyai, 31

Hyslop, James H., on the logical difficulties of hyperspace, 139-141

I

Icosahedron, examination of the, 285

Ideal, and the real, kosmic chasm between, 107

- perceptual value of, 275, ff

Ideas and words as symbols, 126-7

- Malebranche on, 222

- realism of, 24-35

- the symbolism of, 205

Identification of consciousness with being, 205-6

- with the objects of study, 189-90

Identity of things-in-themselves, 353

Ignes fatuii and hyperspaces, 154

Illustration of plane-rotation, 148-150

- - the tesseract, 133

Images, totality of, recoils upon us, 167

Imaginability of the fourth dimension, 90, 106-7

Imagination, premises of, the mathematical, 146

Impossibility of plane-rotation, the structural, 151-3

Impressions, the symbolism of, neurographic, 186

Impulse, the satisfaction of the original creative, 310-1

Incomprehensibility of reality to the intellect, 126

Incongruity, life estranged by a radical, 325

Individual as space, 223

Ineptitude of intellectual determinations for vitality, 314

Infinite, interpreted in the terms of the finite, 82

Infinitesimals of unity, numbers as, 41

Infinity as a process, 109

- of becomings, 234

Infinity of parallels through a given point, 70

- - space, a capital illusion, 195

- the concept of, 277

- - innate dread of, 103

- - relativity of, 194

Influence of abstract thought, 33

- - Kant on the non-Euclidean geometry, 49-50

- - La Grange, 51-2

- - the intellect, 315

Infundibulum, the, 345

Inner organs of perception, 352

Innermost, the, realities of things, 356

Insouciance of the geometer, 96, 294

Instant-exposure and intellect, 311

Instrument, intellect likened to a color-bearing, 313

- for the measurement of the passage of space, 297

- of consciousness, the sensible world as, 199

- - life, form as an, 328

Integers, as fractional parts of unity, 41

Intellect and its domination of the intuition, 333

- - - final union with the space-mind, 194

- - - topography, 312

- - spatiality, 263

- - the deposits of life, 173

- - - designs cut by life in materiality, 264

- - - dictum of Sensationalists, 26

- - - instant-exposure, 311

- - - intuitive faculty, 247, ff

- - - prize of divinity, 43

- as a color-bearing instrument, 313-4

- - - searchlight, 168

Intellect as a fashioner of phenomena, 199, ff

- - hewer of the concrete, 295

- - sole interpretative agency, 166-7

- automatism of, 253, 338

- cannot seize life, 282

- crowned by a diadem of gold, 338

- dominated by the intuition, 250

- fashioned for matter only, 231

- follows in the grooves of logic, 294

- hyperspace as a monument to, 356

- in the field of vitality, ix

- its aptitude for starts and stops, 292, 302

- - instinctive tendency to fragmentate, 296

- quality, determined by mathematics, 337

- makes for individuality, 252

- misses the ceaselessness of life, 201

- modus vivendi of, its influence upon knowledge, 184

- the constitution of, 291

- - cut and mode of, 167

- - focus of, 310

- - illusion of, 246

- - illusionary character of, 323

- - incomprehensibility of reality to, 126

- - instinctive functioning of, 289

- - judgments of, 302

- - moods of, 202

- - predominating tendency in, 320-1

- - scientific tendence of, 165-6

- - struggle of, against dispossessal, 195

- unsuited to deal with reality, 322, ff

Intellectuality and reality, 304

- - spatiality, consubstantial, 331

Intellectuality as co-extensive with spatiality and materiality, 236

- the source of, 260

- - Thinker makes his own, 242

Intelligence and automatism, 253, ff

- the Thinker as a pure, 243

- transfinite intelligence and the degrees of realism, 164

Intent, the kosmic, of the intellect, 326

Interests, the sphere of our, as closed circuits, 167

Interior, the great, 290

Interiority of being, 290

Interpretation, the standards of, vary as consciousness varies, 171

Interstices of materiality, 264

Intuition and brotherhood, 252

- - communalization, 301

- - the riddle of spatiality, 325

- as dispossessor of the intellect, 195

- cannot be served by mathematics, 337

- dominated by the intellect, 333

- held in abeyance, 338, ff

- its domination of the intellect, 250

- the development of a spatial, not absurd, 145

- - need of a sympathetic attitude towards, 249

- - results of the development of, 357

Intuitional consciousness, 255

- the superiority of, over the rational, 187

Intuitions and the lead of life, 191

- - - Thinker, 27

- free, mobile and formless, 166

- the conceptualization of, 248

- - humility of, 165

- - nature of, 185

Intuitograms, as concepts, 248

Intuitograph as means of contacting the egopsychic consciousness by the Thinker, 10

- as super-concepts, 255

- the difficulty of transmitting, 315

Invariability, the vaunted, of the laws of mathesis, 37

Invariants, psychological, 24

Investigations, metageometrical, and the new sense-organs, 354

Involution, as antithesis of evolution, 10-11

- kosmic involution, 226

- of matter, 328

- the movement of, 219

- - seven stages of, 208-12

Ions, creation of, 219

- magnitude of a hydrogen ion, 225

J

Judgments a priori, Kant on, 85-6

- and the faculty a priori, 190-1

- - zones of affinity, 124

- based upon a replica of consciousness, 205

- no trustworthy, can be predicated upon fragmentary knowledge, 282

- of the intellect, 302

- the lessening of error in, 256

- - more complex the more at variance with the nature of things, 75

- - synthesis of, 257-8

- valid judgments long delayed, 170-1

Judicative power of mathematics, 180

Justification for a multi-dimensional quality in space, 262

- of four-dimensionality, 176

Justification of sense-deliveries by one another, 76

- - the existence of the fourth dimension, 125

K

Kant, 85, 181, 182, 322

- and the faculty of thinking, 261

- - - idea of space, 322-3

- influence of, on the hyperspace movement, 49-50

- on the nature of things, 119

- - space as an intuition, 115

Kathekos, 233-4

- as chaos, 266

- - symbol of Chaos-Theos-Kosmos, 11-12

- symbology of, 234

Kathekosis, note, 227

Kathekosity, fringe of, 229

- rock-bound coast of, 267

- significance of, 12

Kathekotic consciousness, 272

- period, 209

Key to the mysteries of nature, the fourth dimension as, 131

Keyser, Cassius Jackson, and freedom of the mind, 33

- - - on attitude of metageometricians, 71

- - - - dimensionality, 94-5

- - - - four-dimensionality of space, 142-3

- - - - generability of hyperspace, 144

Klein, Felix, 12, 54-5, 66-7

Knowledge, all, relative, 101

- barrier to the certitude of the Thinker's, 186-7

- fabric of, 196

- hypothetical nature of, 189, ff

- immeasurable realm of, laid bare by the telescope, 298

Knowledge, mathematical, apriority of, questioned, 37

- nature of the non-Euclidean, superperceptual, 72

- real, difficulties of acquiring, 325

- related to the stream of life and to the shore of materiality, 323

- relative, degrees exist for, 164

- sphere of, 184

- systematization of, 126

- ultimate, consciousness as a barrier to, 207

- unification of, 256

Kosmogenesis, the latent geometrism of, 264

- - scope of, 237

Kosmometer, the, 297

Kosmos, and consciousness, graph representing, 271

- arrangements of the contents of, 317-8

- in a state of becoming, 265

- magnitude of, 308

- moods of, 311

- space as the consistence of, 239

- see Cosmos, 12

L

Labor, division of, between the tuitional and the intuitional faculties, 193-4

- mathematical labors, significance of, 176

La Grange, Joseph Louis, 12,

39, 50-3, 321, 322

- - - - and the parallel-postulate, 51-2

Lambert, John, 58

- - and the theory of parallels, 48-9

Language, the passing of, 357

Legendre, 70

Leibnitz' dictum, 26

Leonard rays, 336

License, mathematic, permissibility of, 38

Lie, Sophus, 12, 67

- - and transformation groups, 30

Life, analysis incapable of dealing with, 319

- and consciousness as one, 224

- - form rooted in pyknosis, 214, 328

- - the fourth dimension, 172

- - - inaptitude of mathematics for, 179

- - - power to create, 297

- as agent of creation, 343

- - creative agent, 264

- - expression, 303

- - vassal of materiality, 329-30

- causative agencies in prolonging, 123

- current of, as engendering element, 331

- deposits of, and the intellect, 173

- estranged by a radical incongruity, 325

- exalting power of, and humanity, 331, ff; 342

- exhibition of its remains, 282

- flow of, 265, 297

- form as an instrument of, 328

- indescribable signs of, 219

- infinitive action of, 327

- intellect has no aptitude for, 231

- intuitive, values of, x

- larger life of the Thinker, 196

- lead of, followed by intuition, 191

- limits of, fixed by consciousness, 198, ff

- most solid facts of, as shadows, 195

- motility of, admits of endless variations, 35

Life, movement of chaos in, 307

- passage of, 201

- passage through spatiality, 288

- power to manipulate, 303

- recurrent movement of, 307

- totality of egoic, 243

- undulations in the current of, 329

- uniqueness of, 41

- wake of, and consciousness, 205, 288

Life-cycle, evolutionary results of the, 259

Life-stream, the, 278

Light, polarized, and the fourth dimension, 156

- consciousness as a spreading, 168

Light-years and space, 278

Limits, the sphere of, consciousness as, 163

Line, as generating element, 144

- the straight, a curved, 76

Lineage of every principle runs back to monopyknosis, 213

Lines, perpendicularity of, in four space, 130

Lobachevski, 55, 60, 66, 87

Lodge, Sir Oliver, 340-1; 344

Logic as architect, 118

- conventional forms of, 262

- data of, 286

- intellect follows in the grooves laid out by, 294

- miracle power of, over facts, 288-9

- rules of, allowability under, 163

- - - the game of, 164

- as symbolism of facts, 287

Logos and the limits of space, 193

- being of, 218

- body of being of, 214

- consciousness of, 204

- creative, 12, 213

- the, 216-7

Lorenz, 83

Luther, Martin, 181

M

Magnitudes, geometry, a study of, 203

- non-sensuous, of hyperspace, 72

Makrokosmic consciousness, 270

Malebranche, N., 222; see note

Manifestation and non-manifestation, 206

Manifold, finite, though unbounded, 70

- manufactured by the analyst, 77

- the, 61-2, 172

Manifoldness, analytical manifoldnesses, as mental excitants, 89-90

- as a conventional construction, 262

- - an intuition, 318

- of space, as a near-truth, 317

Manning, 82, 157

- and maneuvers in the fourth dimension, 152

Manvantara, 213, 228-9, 232

- as evolution and involution combined, 13

Mask, logic as a, 288-9

Mass-termini, of lines, 236

Mastery of life over matter, 330

- of the sensible world, 196-7

Materiality as a deposit of life, 295

- - consubstantial with spatiality, 331, ff

- becoming spatialized, 261

- characteristics of, 260

- engendered by kosmic mind, 261

- engenderment of, 294

- interpenetrative with spirituality, 236

- interstices of, 264

- neglect of, 320

Materiality, shore of, 323

- transmuted into spirituality, 328

Mathematicians and the definition, 37

- - - limitations of consciousness, 178

- - - phenomenal world, 118-9

- as prophets, 336

- respected by humanity, 337

- the gods of mathesis, 84

Mathematics, a determinant of the quality of the intellect, vii

- and the criterion of truth, 323

- - - kosmic intent of the intellect, 326

- as symbology, 184

- Euclidean, 140

- fails when it encounters life, 337

- its inaptitude for life, 179

- - kingdom yielded to kinetics, 358

- possesses no judicative power over life, 180

- the orthodoxy of, 34

Mathesis, and conceptional space, 203

- conduct of the intellect in the field of, vii

- definition of, 13

- domain of, as origin of fourth dimension, 130

- gods of, 84

- marvelous domain of, 118

- realm of, not submissive to laws of sensible space, 34

- things of, as emblems of kosmic forces, 239

- world of, 67, 127

Matter and mind, syncretization of, 299

- appulses of life against, 328

- as a deposit of life, 330

- honeycombs of, 339

Matter metamorphosed by life, 328

- mind as wedded to, 249

- movement of, in four-space, 157

- qualities of, and faculties, 332

- seven planes of, 212

- spiritualization of, as end of evolution, 327

- totality of, acted upon by totality of life, 328

- unity of, with space, 260

- universum of, 261

Matutinal ceremonials of creation, 221

Measurability, as property of space, 62-3

Measurement of hyperspaces, the science of, 73

Measurements, space determined by the number of, 61

- systems of space, 91

Measurer of space, n-dimensionality as a, 296-7

Mecanique Analytique, 50-1, 321

Mechanics of matter, the passage from, to the dynamics of life, 326

- to biogenetics, the passage from 357

- the turning from, to biogenetics, 322, ff

Mechanism, the doctrine of, due to analytics, 40

Memories, stored in the omnipsyche, 258

Men as gods, 289

Mental evolution, determinative period of, 31

- - elaborative period of, 31-32

- - formative period of, 31

Mentality, inner mysteries of creative, 91

- infantile out-feelings of the, 336

- the principle of, 210, ff

Mentalities, the adaptation of phenomena to, 184

Mentograph, the, 121

- the basis of intellectual consciousness, 13

Mesozoic man and his environments, 347-8

Metageometrical investigations and the new sense-organs, 354

Metageometricians and hyperspace, 238

- - proof of rotation about a plane, 149-151

- - the curved space, 316

- - - fourth dimension, 145

- - - key to the mysteries of nature, 131

- baffled by the direction of hyperspace, 146

- dilemma of, 97-8

- eschew sense-data, 73-4

- Keyser on the attitude of, 71

- perceptual obliquity of, 102

- - seed thought of, 182

- turned to idealized constructions, 263

Metageometry, as a stepping stone, 238

- defined, 13

- Riemann, the father of, 63

- the fabric of, 66

Metamorphosis of matter by life, 328

- of the monopyknon, 214

Metamorphotic stage of space-genesis, 228

Metaphysician, the preserves of, usurped by mathematicians, 141

Meta-self as medium of kosmic consciousness, 13, 217

Methods of the ego, 344

- scientific, and the ample explication of phenomena, 154

Mikrokosmic consciousness, 270

Mind, amenability of, to the evolutionary movement, 28-32

- and freedom from conception, 28

- - - - problems of physical existence, 32

- - the new freedom, 33

- as vehicle of life, 285-6

- - wedded to matter, 249

- coevalism of, and space, 240

- consubstantial with space, 239-40

- divine, of the kosmos, 176

- evolution of, and conceivability, 24

- of the duodim, 128

- powers of, not attained simultaneously, 334

- profound influence of hyperspace on the, 91

- space as progenitor of, 224

- three great epochs of the history of, 30-31

- tuitional, the limitations of, 192-3

- the unity of, with space, 224

Mind-principle, the quintopyknon as the basis of, 221, ff

Mirrors, three, and the hypercube, 136-8

Mobility, life as, 264

Molecule, the four-dimensional, Newcomb on, 159

Monadic phase of evolution, 210-1

Moneron and man, the gulf between, 28

Monopyknon, the, 213, 216

Monopyknosis, defined, 17, 208-10, 218

Monstrosities, mathetic, 202

Moods of the kosmos, 311

Morphogeny, 13, 233-4

Morphons, the creation of, 219

Motility, the scope of, 131

Movement, forward, in knowledge, 336

- hyperspace as an evolutionary, 44-68

- - influence of Kant on, 49-50

- of life in chaos, 307

Multi-dimensional quality of space, justification for, 262

Multiplication of hypotheses, 118

Mutuality, intuition as promoter of, 301, ff

Mysteries, inner, of creative mentality, 91

- kosmic, low-lying plains of, 239

--- of life and mind, 326

- - the sciences and the four-space operator, 131

Mystery, kosmic, the revelation of, foreshadowed in manifold, 77

- of reaction, 167-8

- - space decreases as copes of consciousness increases, 273, ff

N

n-Co?rdinates, 203

n-Dimensionality, as a phase of geometry, 300

- - property of intellectuality, 269

- - quality of conceptual space, 14

- irreconcilable with perceptual space, 156

- no justification for, 235

- not surprising that the intellect fell upon, 296, ff

- predicates concerning, 158

n-Space, imperceptibility of, 94

Nasir-Eddin, 46, 53

Natural symbols, ideas as, 126

Nature, representative, of things, 119

- the vacuum-stillness of, 339

Naught to unity, consciousness registers from, 165

Near-truth, 300, ff

- as variation from criterion of truth, 324

- based upon partial knowledge, 14

- space-curvature as a, 306

- space-manifold as a, 318

Nebulosity, 267

Necessity, as a bulwark of geometry, 77-8

Nerve-body, the, 349

Neurogram, 14

Neurograph, the Thinker's scrutiny of, 190

Neurographical communications, 244

Newcomb, Simon, 14-5, 66

- - and the four-dimensional molecule, 159

- - on the fourth dimension, 125

Non-Euclideans and the meaning of dimension, 97

- - things as they actually are, 71

- dilemma of, 86

- meaning of the term, 69

- results obtained by, 88

Non-manifestation, as antithesis of manifestation, 106

- and manifestation, 206

Non-methodic advancement of human consciousness, 299

Non-spatiality, cut off from spatiality, 266

Norm, as a value assigned by the intellect, 167

- consciousness as a, 15; 161-202

- of life, found by synthesis, 300

- - the natural geometry, 263

Note, the dominant, of communality, 301

Notions of space, triple presentations to the consciousness, 72

Number, as a phase of kosmogenesis, 309

- numbers as infinitesimals of unity, 41

Numericity of being, 309

O

Objects and ideas, 126-7

- passage of, into the fourth dimension, 130

- of study, identification of consciousness with, 189

Obliquity, perceptual, of metageometricians, 102

Obscurantism, mathetic, 154

Occultist and the scientist, 350

Omnipsyche, 265

- as agency of kosmic consciousness, 258

- - neglected factor of evolution, 259

- defined, 15

One-space represented by a line, 134

Ontogeny recapitulates phylogeny, 27, 334

Order, kosmic, the difference between, and hyperspace, 143

- mathematical, discovered by the intellect, 261

- the fiat of, 208

- the totality of, 265

Orderliness, 266

Organ, determined by function to be performed, 336

Organs broken up by life into special parts, 343

- the evolution of, 188

Orthodoxy of mathematics, 34

Outcome of new adjustments, 256

Out-feelings of the Thinker, infantile, 336

Outlook, the spiritualization of our mental, 40

P

Papyrus, a hieratic, 44

Parallel-postulate and the surface of a sphere, 70

- as basis of non-Euclidean geometry, 54

- - stated by Euclid, 55

- - - - Lobachevski, 55

- - - - Manning, 82

- failures to demonstrate, 48, 82-3

- in the Elements of Euclid, 16

- Saccheri's proof of, 47

Parallels, convergence of, 80

- infinity of, through a given point, 70

- meet at infinity, 88

- theory of, 47-9

Passage from mechanics to biogenetics, 357

- from mechanics to dynamics, 326

- from three-space to four-space, 292-3

- of mathetic contrivances, 241

- of space, 16, 297

Pathway of life, sinuosities in, 330

Patterns of the intellect, ready-made, 166

Pentagrammaton of space, 237

Perceptibility in the Thinker, the faculty of, 188

Perception, domain of, and the sensible world, 19

- inner organs of, 352

- replaced by conception, 255

Percepts, and the ego, 244

Period, chaomorphogenic, 208, ff

- determinative, 61-5

- kathekotic, 210

Perisophical nature of analytics, 320, ff

Perisophism, a, 300

Permissibility of mathetic license, unlimited, 38

Perpendicularity, 132, 177

- of lines in the four-space, 130

Phantasy and reality, line of demarkation between, 173

- the world of, 146

Phantom-ideal, the, 277

Phase of the world age, evolutionary, 209

Phenomena, efforts to explain, on the basis of the fourth dimension, 129

- fashioned by the intellect, 199

- fragmentary interpretation of, 302

- mind's method of apprehending, 186

- physical phenomena amply explained by scientific methods, 154

Phenomenal, the inverse of realism, 278

Philosophy and the criterion of truth, 323-4

- regeneration of, 358

- systems of, and zones of affinity, 124

Phosphorescence, dim, added to the unilluminated pool of sense-consciousness by the intuition, 26

Phylogeny and ontogeny, 334

- represented in ontogeny, 27

Physical as embodiment of all possibilities, 227

- phenomena as space-activities, 229

Physicality, the principle of, 210, ff

Physics of the brain, 292

Pi proportion, significance of, 311-2

Pickering on space-curvature, 279

Pineal gland, energized by the pituitary body, 348-9

- - the, 344, ff

- - not a vestigal organ, 354

Pituitarial awakening, general results of, 355-8

Pituitary body and the Thinker, 351

- - as an organ, 344-352

- - C. De M. Sajous on, 345

- - hypertrophy of, 347

- - location of, 246

- - the, 344, ff

Plane, as generating element, 144

- movement of, into the fourth dimension, 147

- realism appears to be divided into, 164

- rotation about a, 130, 146-151

- the seven planes of matter, 212

Planes, a cube as a succession of, 148-9

Plasm, kosmic, strivings of, 215

- psychic, 260

- the differentiation of, 214

Plato, 322

- and the divine geometry, 193, 237

- - - shadow consciousness, 281

- on God as geometrizer, 181

- - ideas, 34

Play, sensuous, of the intellect, 295

Plenum, space as a, 230

- the universe as a, 107

Poincairé, 90

Point, an infinity of parallels through a given, 70

- as generating element, 144

- position of, 132

- succession of points, a line as, 148

Polarity between concrete and abstract, 294-5

Ponderability, as property of hyperspace, 63

Popularization of the fourth dimension, 128

- of the non-Euclidean geometry, 66-7

Possibilities in the world of hyperspace, 129

- of four-space, the marvelous, 130

Postulate-systems, the multiplication of, 85

Powers of mind, not attained at one and the same time, 334

Pralaya, 213

- as kosmic quietude, 17

Predicates, all mathematical, not justified by the phenomenal, 128

Principle, ensouling, 214-5

Printing press, the invention of, and the laws of psychogenesis, 30

Problem, the fourth dimension as a transcendental, 140

Procedure, the involved, of arriving at hyperspace notions, 73

Process, evolution a continuous, 327

- space as a dynamic, 307

Proclus, 83

Profundities, kosmic, and hyperspace, 156

Progression eastward terminates at the west, 306

Proof of rotation about a plane, 146-151

Propagation of intuitographs, difficulty of, 315

Propositions, geometric, subjunctive quality of, 38

Pseudosphere and the shape of space, 70

- as basis of Beltrami's calculations, 17

- the nature of, 64-5

Psychics of consciousness, 292

- transmuted, 260

Psychogenesis, alchemy of, 225

- kosmic, 272

- laws of, and the printing press, 30, 116

Psychogenesis, mind's place in, 123

- outgrown phase of, 302

- outstanding facts of, 131

Psychogeny, defined, 17

Ptolemy, 45, 52, 83

Publicist, the mathematical, and the duodim, 128

- the non-Euclidean, 146

Pyknon as a kosmic principle, 212

- - basis of space-genesis, 17

Pyknosis, 212

- and involution, 210, 231

- as a metamorphotic process, 214

- the seven processes of, 17, 294

Q

Quality, dimension as commensurable, 140

Quantities, algebraic, cannot represent space, 125-7

Quantity, consciousness as a tri-space, 172

Quartodim, 18, 134

Quartodimensionality, 292

Quartopyknosis, 17, 208-10

Quartopyknotic, principle as basis of spirituality, 228

Quintopyknon, 220

Quintopyknosis and the a priori, 223

- meaning of, 17, 208-10

Quintopyknotic principle as basis of mentality, 228

R

Race, humanity to evolve a new, 358

- resplendent, 338

Rajah-Tamas, 220

Rajah Yoga, 357

Rational, valueless when unsanctioned by the intuition, 187

Reaction, as a mystery, 167-8

Real, Thinker as a part of the, 201

Realism and its degrees, 164-5, 279

- - the Thinker, 315

- as life, 286

- consciousness as touch-stone of, 168

- found in the direction inverse to the phenomenal world, 278

- homogeneity of, 165

- illusionary nature of, 36

- infinite gamut of, 36

- its degrees and the states of consciousness, 197

- new scope of, bewilders the mind, 170-1

- not of mathematical import, 290

- of concepts and the sensible world, 40

- - the domain of mathesis, 33-4

- psychological quality of, 285

- the thread of, 169

- three dimensional scope of, 172

Realities, abstractionizing, 144, 294

- incomprehensible to the intellect, 126

- innermost, of things, 356

- lesser give way to greater, 195

- natural symbolism of, 128

- our, non-existent to beings on spirit-levels, 35

- shaped upon conventional models, 294

- supersensuous, 180

Reality, as life and consciousness, 173

- barrier to the cognition of, 189, ff, 273

- comprehension of, 165, 303

- current of, 322

- defined as life, 18

- flow of, 319

- flowing stream of, 124

- myriad ways of presenting itself, 287

- naked contact with, 193

- not an inscrutable quantity, 194

- obscured, 302

- of the four-space glibly asserted, 154

- thread of, 200

- universum of, 127

Realms, supersensuous, 338

Re-becoming, life and consciousness as a, 257

Reciprocity of consciousness and realism, 197-8

- of the manifest and the unmanifest, 217

Recoil of images upon us, 167-8

Reflexive development of the intellect, 254

Relativity of all knowledge, 101

Religion and realism, 170

- the changes in, 358

Remains of life exhibited to the intellect, 283

Remaking of moods by the intellect, 201

Replica of consciousness as basis of judgments, 205

Representation, sensuous, compared with a shadow, 119-120

Research, improvement in the methods of, 125

Reservoir, psychic, of evolution, 260

Residuum, the unexplained, 157-8

Revelational impressions, 29

Riddle of spatiality and the intuition, 325

Riemann, G. F. B., 18, 19, 54, 66-7, 87

- and a limited space, 108-9

- - the curvature of space, 5

- - - determinative period, 65

- - finite space, 103

- - - four-space, 27

- - - manifold, 317

- as inventor of the manifold, 86

- on the bases of geometry, 61-4

Roentgen rays, 336

Rotation about a line, 147-8

- about a plane, 146-151

- - - - illustrated, 148-50

- intra-corpuscular, 152

Rudimentary organs, vague functions lying back of, 343

Rule in the evolution of faculties, 333

S

Saccheri, Girolamo, 47-8, 52, 83

Sajous, C. De M., on the pituitary body, 345

Schematism, the suitability of the present, 320-1

Schweikart, Ferdinand Karl, 19, 66, 69

- on the non-Euclidean geometry, 58-60

Science Absolute of Space, 60

Science and reality, 170-1

- no longer empirical, 358

- skeptical attitude of, 349

Scientist, method of the, opposed to the analyst, 84-5

Scopographic impressions, 19, 190

Screen, the impregnated, of creation, 232

Sea, choppy, and egos, 256-7

Search, the path of, for spatial understanding, 278

Seb, the god, 215

Sects, coplanar, 79

Self and the immensity of space, 223

- of the universe, 217

- the kosmic, 278

Self-consciousness, 270

- and space, 223

- as I-making faculty, 243

- determination of, 302

Self-consistency, 173

Sella turcica, the, 345

Semi-Euclidean geometry, the, 70

Sensationalists on the intellect, 26

Sense-data, spurned by the metageometrician, 73

Sense-delivery, one, justified by the other, 76

- symbolism of, 203-4

Sense-knowledge, the sphere of, extended, 339-40

Senses, the answer of, to new needs, 332

Sensible world, as domain of perception, 19

Sensographic impressions, as perceptions, 19

Senso-mechanisms of the intellect, 165

Sentience, the principle of, 210, ff

Septopyknon, the, 227

Septopyknosis, as kosmic materiality, 18, 208-10

Septopyknotic, the, principle,

228

Seven planes of matter, 212

Sextopyknon, the, 209

Sextopyknosis, defined as kosmic sensibility, 18, 208-10

Sextopyknotic, as emotional principle, 228

Shadow likened to a sense presentation, 119

Shadowgraphs, 281

Silences, nature's great, 339

Similitude of agent and principle, 243-6

Sinuosities in the pathway of life, 330

Socrates, 322

Solitariness of intellectual testimony, 76

Space and edict of disorder, 230

- - four-dimensional entities, 128-130

Space and quartopyknons, 219-20

- - self-consciousness, 223

- - the idealized construction, 144

- as a dynamic process, 216

- - all-mother, 229-30

- - an assemblage of spheres, 143

- - becoming, 195

- - boundary of another space, 49-50

- - consistence of the kosmos, 239

- - curved, 164

- - dynamic appearance, 228, 307

- - eldest born of kathekosis, 215

- - engendered product of life, 308, ff

- - evolution, 226, ff

- - finite extension, 62, 106

- - generable quantity, 103

- - infinite continuum, 70

- - intuitional concept, 225

- - kosmic order, 265, 267

- - nether pole of non-manifestation, 207-8

- - path of life, 293-4

- - pseudosphere, 70

- - sheer roominess, 115

- - system of co?rdinates, 99

- - unbounded extension, 61

- best study of, the consciousness, 269

- conceptual, as basis of non-Euclidean geometry, 72

- - fundamentally distinct from perceptual, 72-75

- elliptical, 67

- engenderment of, 260

- essential nature of, 212

- fabric of, the, lends itself to measurement, 99-100

- four-, 8

- fractionalized space, 296

- foundations of, 221

- four-dimensional, 41

- Paul Carus on, 354

- fourth dimension of, efforts at making it thinkable, 125

- generability of, by lines, 143

- genesis of, 227, ff

- geometric, purely formal construction, 75-6

- limits of and the Creative Logos, 193

- manifoldness of, 77

- mind and, the coevalism of, 240

- mystery of, 278, ff

- nature of, answered to by mind, 198-9

- nether pole of non-manifestation, 207-8

- non-Euclidean, the characteristics of, 72-3

- not a pure form, 110

- passage of, 16

- path of search for, must be Thinker-ward, 278

- perceptual, irreconcilable with the fourth dimension, 156

- possible curvature of, and the non-Euclidean geometry, 76-7

- primeval, and tridimensionality, 236

- problem of devising a, 87-8

- psychological nature of, 305

- real, confounded with hyperspace, 91

- Riemann on the curvature of, 5

- the unity of, 224

- - - - with matter, 260

Space-activities, as chemism and physicism, 229-30

Space-center, the, 306-7

Space-consciousness, 225

- as a direct process, 224

- mergence of, with the individual consciousness, 195

Space-curvature, as an arbitrary construction, 262

- as near-truth, 306

- nature of, 279

- no need for, 237

- translation of, in terms of the intellect, 315

Space-forms, the construction of, 74

Space-genesis, 20, 232, 233

- alphabet of, 237

- completion of, 226

- norm of, 174

- pyknon as a basis of, 17

- symbolism of, 208, ff, 235

Space-manifold, the, 279

Space-measurement, and reality, Euclid's system of, 96

- systems of, 201

Space-mind and archeological evidences, 193

- - knowledge, 187

- - the Thinker, 253, 272

- attainment of, 225, 231

- granaries of, 235

- the realization of, 238

Space-process, the, 305

Space-realities, hyperspace as a stepping stone to, 238

Spark, the omnipsyche as a, 258

Spatiality and the intellect, 263-4

- consubstantial with materiality, 20, 331, ff

- cut-off from non-spatiality, 266

- interpenetrative with materiality, 236

- nonconformity of, with logic, 164

- riddle of, and the intuition, 325

-, rise of, 180

- Thinker's outlook in, 316

- world of nascent, 232

Spencer, Herbert, 322

Spinoza, 322

Spiritism, the phenomena of, 154

Spiritualists, the claim of, regarding the fourth dimension, 154-5

Spirituality, materiality transmuted into, 328

- principle of, 210, ff

- seeds of, 221

Spiritualization of the flesh, 227

- - man's mental outlook, 40

- - matter, the end of evolution, 327

Squares, the form of, in the non-Euclidean geometry, 59

St. Marie, Flye, 66

Stage of pyknosis, 208, ff

-, quartopyknotic, 219, ff

Stanley, Hiram M., on space as dynamism, 104-7

States, the two, of consciousness; one unaware of the other, 192

Straight, a, determined by two points, 79

Stuff, etherealized four-dimensional, 160

Sum, angular, 79

- triangular, less than two right angles, 59

Superconcepts, as intuitographs, 255

Superconceptual, as the intuitional, 20

Superperception and automatism of the intellect, 20

Superperceptual, the, 74

Superunodim, the, 177

Swedenborg, 180, 184

Symbol, psychic, and the brain, 190

- words as symbols of ideas, 126-7

Symbolism of life, 286

- - neurographical impressions, 186

- - realities, 128

- - sense-deliveries, 204

- - space-genesis, 208, ff

Symbology, depicting planes of consciousness, 270

- of mathematical knowledge, 203, ff

Synchronous evolution of faculties and properties of matter, 332

Syncretization of mind and matter, 299

Synthesis and the norm of reality, 300

Synthetic school of geometry, 56

T

Tactographic impressions, 190

Tartrate and a component in the fourth dimension, 156-7

Task of mental evolution, the supreme, 169

Taurinus, 56-7, 69

Telescope, its effect upon consciousness, 298

Tendence, intellect as scientific, 165-6

Tendencies, destined to flower as faculties, 89-91, 332

Tendency to fragmentate, the intellect and, 296

Tesseract as represented by Carus, 136-8

- illustrated, 133

- the, 20, 145

- the elements of, 135

- the four co?rdinates of, 132

Testimony of the intellect, incapable of comparison, 76

Tetragrammaton, the, 308

Tetrahedron, the, 135

Thalamencephalon, the, 345

Thales, 44

Theory of knowledge, 290

Thingness of objects and the impossibility of comprehending, 122

Things, the dual nature of, 119

- - value of, 161

Things-in-themselves, the identity of, 353

Thinkability of the fourth dimension, 125

Thinker as a pure intelligence, 184, 248

- - engenderer of the intellect, 291

- - principal to the ego, 243, ff

- - six times removed from the sensible world, 201

- - the source of the intuition, 26

- and concepts, 244

- - his approach to the kosmic mind, 202, 223

- - - larger life, 196

- - - treatment of the ego, 246

- - - of sense-impressions, 74-5

- - realism, 315

- - space, 193

- - a segment of reality, 171

- the, and the amplitude of the degrees of realism, 198, 270

- and the barriers of consciousness, 207

- - - brotherhood of man, 301

- - - degrees of realism, 175

- - - manipulation of concepts, 255

- - - nature of space, 268

- - - neurograph, 190

- - - new faculty, 335

- - - perceptive faculty, 188

- - - pituitary body, 351

- defined as the spiritual man, 21

- his consciousness and the ether, 280

- - dependence upon the ego, 245

- - method of contacting the external world, 189-191

- - outlook upon the universe of spatiality, 242

Thinker, his schematism of cognitive powers, 206

- - sphere of awareness, 283

- the difference between, and the intellectuality, 256

- - evolutionary needs of, 336

- - upreaching yearnings of, 336

Thinker-ward, space must be sought in a direction, 278

Thinking, abstract, elevating influence of, 33

Thought, prolonged abstract, benefits of, 249

Time, as an aspect of consciousness, 224

- divested of timeliness, 279

Todhunter, 46

Tool, fashioning, life as a, 264

Topography of the intellect, 312

Touchstone, consciousness as a, 168

Tracery of connection between ideas and objects, 126

Trafficking in mental constructions, 154

Transcendental, the realm of, and mathematicians, 142

Transfinite as a limit, 122, 216

Transfinity, 21-2

Tree-reality, 126

Triadic phase of evolution, 210-1

Triangles, angular sum of, 78, 88

Tridim, the, 22, 129, 134, 147, 177

Tridimension, the, 147

Tridimensionality and primeval space, 236

- and the space-mind, 193

- a quality of perceptual space, 22

- mastery of the phenomena of, 172

- the sufficiency of, 198

Tripyknon, the, 212, 213

Tripyknosis, 17, 208-10, 219

Truth compared with facts, 288

- criterion of, 5, 323-4

- facets of, 284

- kinds of, 324

- logic does not illuminate, 287-8

Tuitive, the, and the intuitive faculties, 192-3

U

Ultima Thule, the, 207

Unbounded, the, as a finite extension, 70

Undulations, three, in the current of life, 329

Unfoldment, mental, and metageometrical discoveries, 131

Uni-circle, the, 308

Unification of all knowledge, 256

Uniqueness of real space, 95

Unitariness of all existences, 241

Unity, as end of analysis, 42

- death as a fourth dimensional, 159

- kosmic, integers as fractional parts of, 41

- of mind and space, 224, 230

- the new realization of, 225

Universality, geometric, based upon the formal character of assumptions, 77-8

Universe, a glorified, 226, 268

- as a full, 308

- - - plenum, 107

- and the seven planes of matter, 212

- character of, fixed by consciousness, 162

- limited and conditioned, 127

- not a pure form, 108

- the perfected, and the circle, 310

- - theory of the mechanical origin of, due to analytics, 40

- unity in the, 301-2

Universum of appearance, 187

- of life and consciousness, 257

Universum of reality, 127

- - space, 269

Unknowable as a symbol, 194

- the darkness which shuts out the, 207

Unodim, the, 129, 134, 176-7

- - consciousness, 163

- defined, 22

Upraisement of matter, 329

Upspringing of a new faculty, 333

V

Vacuum-stillness of nature, 339

Validity of mathematical conclusions, 101

Value assigned by the intellect to the sensible world, 167

- assumptional, vitiating influence of, 163

- - of the ideal, 275

Vanity of fragmentary evidences, 204

- of intellectual method,

325, ff

- - segmenting space into many dimensions, 299

Vassal, life as the, of materiality, 329

Vehicle of life, form as, 330

- - - mind as, 286

Vicissitudes of kosmic evolution, 215

Vision, the inner, 356

W

Wachter, 69

Wallis, John, 46, 83

Weismann, note, 260

Words, as symbols of ideas, 126-7, 204

World and the child mind, 121

- as instrument of consciousness, 199, 298

- fabric of, and geometrism, 261

- impossibility of objectifying the fourth dimension in the perceptual, 124

- of phantasy, conditions of, identified with sensible realm, 146

- phenomenal, and hyperspace entities, 128-130

- sensible, as a carpet, 196

- the domain of a perception, 19

- - genesis of, 167

World-plasm, kathekotic, 267

- as elemental essence, 329

Y

Yoga, Rajah, 357

Youth of the earth, the nebulous, 335

Z

Zollner, and the claims of the spiritualists, 154

Zones of Affinity, 22, 124

Zoometer, the, 297

FOOTNOTES:

[1] Vide Popular Science Monthly, vol. 78, p. 554, 1911.

[2] Vide New York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79, G. B. Halstead on Lambert's Non-Euclidean Geometry.

[3] Prolegomena, Kant, p. 37, Trans. by J. P. Mahaffy and J. H. Bernard.

[4] In 1754 D'Alembert (1717-1783) published an article in the famous old Encyclopedia edited by Diderot and himself on Dimension. In this article the idea of the fourth dimension is dwelt upon at length. The view which he expressed in this article, of course, served greatly to popularize the conception among the learned men of the day, and owing to the close relationship existing between D'Alembert and La Grange, it is not surprising that the latter should have been very much enamored of the idea.

[5] Vide Nature, Vol. VIII, pp. 14-17; 36, 37 (1873); also Mathematical Papers, pp. 65-71.

[6] Mathematics, by C. J. Keyser, Adrian Professor of Mathematics, Columbia University.

[7] The science of pure mathematics is perhaps indebted to no one in so great a degree as to George Bruce Halstead, formerly of the University of Texas, whose labors in connection with the popular exposition of the non-Euclidean geometry have been most untiring and effectual. Vide Popular Astronomy, Vol. VII and VIII, 1900, Dr. G. B. Halstead.

[8] Note.-M may be any point on the line BA indefinitely produced.

[9] Vide Non-Euclidean Geometry, p. 91.

[10] Vide Nature, Vol. XLV, 1892.

[11] Vide Monist, Vol. XVI, 1896, Mathematical Emancipations.

[12] Vide Monist, Vol. XIX, p. 402 (1909).

[13] Philosophical Review, Vol. VII (1898).

[14] Vide Foundations of Mathematics, p. 107.

[15] Vide Foundations of Mathematics, p. 42.

[16] Vide Science, Vol. VII, p. 2, No. 158, 1898.

[17] Vide Foundations of Mathematics, pp. 93-94.

[18] Vide Philosophical Review, Vol. V, 1896, p. 352, et. seq.

[19] Vide Monist, Vol. XVI, 1896, Mathematical Emancipations.

[20] Vide Fourth Dimension, Simply Explained, edited by H. P. Manning, p. 28.

[21] Vide Fourth Dimension, p. 75, C. H. Hinton.

[22] Q. v., p. 242, edited by H. P. Manning.

[23] Vide Science, Vol. VII, 158, 1898, p. 4.

[24] See Fig. 18.

[25] Vide Recherche, Chap. VII, also Philosophical Review, V. 15, p. 401.-Malebranche.

[26] Kathekosis (from Chaos-Theos-Kosmos) is to evolution what "chaogeny" is to involution. It is the end of evolution, but also the beginning of involution, and in the latter function is known as "chaogeny." See diagram No. 17.

[27] See The Germ Plasm; A Theory of Heredity, by A. Weissman.

[28] Figure 20.

[29] See pp. 338, 341.

[30] See Unknown, p. 485, et. seq.

[31] Rosicrucian Cosmo-Conception, p. 477, Max Heindel

[32] Foundations of Mathematics, p. 90.

Transcriber's Notes

Variations in spelling, punctuation and hyphenation have been retained except in obvious cases of typographical errors. Inconsistencies between the text and index have been resolved in favour of the text.

Duplication of the sub title (The Mystery of Space) betwen the table of contents and the introduction has been removed.