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,