Gerling, as correspondent of Gauss, 58_The mystery of space

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

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

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

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

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

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

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_-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

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

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

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

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

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

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

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

Up-raisement of matter, 329

Upspringing of a new faculty, 333

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

Wachter, 69

Wallis, John, 46, 83

Weissman, _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

Yoga, Rajah, 357

Youth of the earth, the nebulous, 335

Zollner, and the claims of the spiritualists, 154

Zones of Affinity, 22, 124

Zoometer, the, 297

Transcriber's Notes

Variations in spelling, punctuation and hyphenation have been retained

except in obvious cases of typographical errors. Inconsistencies

between the text and index have been resolved in favour of the text.

Duplication of the sub title (The Mystery of Space) on consecutive

pages has been removed.

Italics are shown thus _italic_.

In the five cases where illustrations could be realistically rendered

using only text symbols this has been done.

End of Project Gutenberg's The Mystery of Space, by Robert T. Browne