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 Coördinates, 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-Coördinates, 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 coördinates, 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 coördinates 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

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