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
— attac

— — 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-

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, 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, 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, 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

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