353Ignes fatuiiand hyperspaces,154Illustration of plane-rotation,148-150— — the tesseract,133Images, totality of, recoils upon us,167Imaginability of the fourth dimension,90,106-7Imagination, premises of, the mathematical,146Impossibility of plane-rotation, the structural,151-3Impressions, the symbolism of, neurographic,186Impulse, the satisfaction of the original creative,310-1Incomprehensibility of reality to the intellect,126Incongruity, life estranged by a radical,325Individual as space,223Ineptitude of intellectual determinations for vitality,314Infinite, interpreted in the terms of the finite,82Infinitesimals of unity, numbers as,41Infinity as a process,109— of becomings,234Infinity of parallels through a given point,70— — space, a capital illusion,195— the concept of,277— — innate dread of,103— — relativity of,194Influence of abstract thought,33— — Kant on the non-Euclidean geometry,49-50— — La Grange,51-2— — the intellect,315Infundibulum, the,345Inner organs of perception,352Innermost, the, realities of things,356Insoucianceof the geometer,96,294Instant-exposure and intellect,311Instrument, 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,328Integers, as fractional parts of unity,41Intellect 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,168Intellect 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 vivendiof, 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,ffIntellectuality and reality,304— — spatiality, consubstantial,331Intellectuality as co-extensive with spatiality and materiality,236— the source of,260— — Thinker makes his own,242Intelligence and automatism,253,ff— the Thinker as a pure,243— transfinite intelligence and the degrees of realism,164Intent, the kosmic, of the intellect,326Interests, the sphere of our, as closed circuits,167Interior, the great,290Interiority of being,290Interpretation, the standards of, vary as consciousness varies,171Interstices of materiality,264Intuition 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,357Intuitional consciousness,255— the superiority of, over the rational,187Intuitions and the lead of life,191— — — Thinker,27— free, mobile and formless,166— the conceptualization of,248— — humility of,165— — nature of,185Intuitograms, as concepts,248Intuitograph as means of contacting the egopsychic consciousness by the Thinker,10— as super-concepts,255— the difficulty of transmitting,315Invariability, the vaunted, of the laws of mathesis,37Invariants, psychological,24Investigations, metageometrical, and the new sense-organs,354Involution, as antithesis of evolution,10-11— kosmic involution,226— of matter,328— the movement of,219— — seven stages of,208-12Ions, creation of,219— magnitude of a hydrogen ion,225JJudgmentsa priori, Kant on,85-6— and the facultya 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,170-1Judicative power of mathematics,180Justification for a multi-dimensional quality in space,262— of four-dimensionality,176Justification of sense-deliveries by one another,76— — the existence of the fourth dimension,125KKant,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,115Kathekos,233-4— as chaos,266— — symbol of Chaos-Theos-Kosmos,11-12— symbology of,234Kathekosis,note,227Kathekosity, fringe of,229— rock-bound coast of,267— significance of,12Kathekotic consciousness,272— period,209Key to the mysteries of nature, the fourth dimension as,131Keyser, 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,144Klein, Felix,12,54-5,66-7Knowledge, 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,298Knowledge, 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,256Kosmogenesis, the latent geometrism of,264— — scope of,237Kosmometer, the,297Kosmos, 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—seeCosmos,12LLabor, division of, between the tuitional and the intuitional faculties,193-4— mathematical labors, significance of,176La Grange, Joseph Louis,12,39,50-3,321,322— — — — and the parallel-postulate,51-2Lambert, John,58— — and the theory of parallels,48-9Language, the passing of,357Legendre,70Leibnitz' dictum,26Leonard rays,336License, mathematic, permissibility of,38Lie, Sophus,12,67— — and transformation groups,30Life, 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,35Life, 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,205,288Life-cycle, evolutionary results of the,259Life-stream, the,278Light, polarized, and the fourth dimension,156— consciousness as a spreading,168Light-years and space,278Limits, the sphere of, consciousness as,163Line, as generating element,144— the straight, a curved,76Lineage of every principle runs back to monopyknosis,213Lines, perpendicularity of, in four space,130Lobachevski,55,60,66,87Lodge, Sir Oliver,340-1;344Logic 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,287Logos and the limits of space,193— being of,218— body of being of,214— consciousness of,204— creative,12,213— the,216-7Lorenz,83Luther, Martin,181MMagnitudes, geometry, a study of,203— non-sensuous, of hyperspace,72Makrokosmic consciousness,270Malebranche, N.,222; seenoteManifestation and non-manifestation,206Manifold, finite, though unbounded,70— manufactured by the analyst,77— the,61-2,172Manifoldness, analytical manifoldnesses, as mental excitants,89-90— as a conventional construction,262— — an intuition,318— of space, as a near-truth,317Manning,82,157— and maneuvers in the fourth dimension,152Manvantara,213,228-9,232— as evolution and involution combined,13Mask, logic as a,288-9Mass-termini, of lines,236Mastery of life over matter,330— of the sensible world,196-7Materiality 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,320Materiality, shore of,323— transmuted into spirituality,328Mathematicians and the definition,37— — — limitations of consciousness,178— — — phenomenal world,118-9— as prophets,336— respected by humanity,337— the gods of mathesis,84Mathematics, 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,34Mathesis, 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,67,127Matter and mind, syncretization of,299— appulses of life against,328— as a deposit of life,330— honeycombs of,339Matter 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,261Matutinal ceremonials of creation,221Measurability, as property of space,62-3