Measurement of hyperspaces, the science of, 73

Measurements, space determined by the number of, 61

— systems of space, 91

Measurer of space, n-dimensionality as a, 296-7

Mecanique Analytique, 50-1, 321

Mechanics of matter, the passage from, to the dynamics of life, 326

— to biogenetics, the passage from 357

— the turning from, to biogenetics, 322, ff

Mechanism, the doctrine of, due to analytics, 40

Memories, stored in the omnipsyche, 258

Men as gods, 289

Mental evolution, determinative period of, 31

— — elaborative period of, 31-32

— — formative period of, 31

Mentality, inner mysteries of creative, 91

— infantile out-feelings of the, 336
— the principle of, 210, ff

Mentalities, the adaptation of phenomena to, 184

Mentograph, the, 121

— the basis of intellectual consciousness, 13

Mesozoic man and his environments, 347-8

Metageometrical investigations and the new sense-organs, 354

Metageometricians and hyperspace, 238

— — proof of rotation about a plane, 149-151

— — the curved space, 316

— — — fourth dimension, 145

— — — key to the mysteries of nature, 131

— baffled by the direction of hyperspace, 146

— dilemma of, 97-8

— eschew sense-data, 73-4

— Keyser on the attitude of, 71

— perceptual obliquity of, 102

— — seed thought of, 182

— turned to idealized constructions, 263

Metageometry, as a stepping stone, 238

— defined, 13

— Riemann, the father of, 63

— the fabric of, 66

Metamorphosis of matter by life, 328

— of the monopyknon, 214

Metamorphotic stage of space-genesis, 228

Metaphysician, the preserves of, usurped by mathematicians, 141

Meta-self as medium of kosmic consciousness, 13, 217

Methods of the ego, 344

— scientific, and the ample explication of phenomena, 154

Mikrokosmic consciousness, 270

Mind, amenability of, to the evolutionary movement, 28-32

— and freedom from conception, 28

— — — — problems of physical existence, 32

— — the new freedom, 33

— as vehicle of life, 285-6

— — wedded to matter, 249

— coevalism of, and space, 240

— consubstantial with space, 239-40

— divine, of the kosmos, 176

— evolution of, and conceivability, 24

— of the duodim, 128

— powers of, not attained simultaneously, 334

— profound influence of hyperspace on the, 91

— space as progenitor of, 224

— three great epochs of the history of, 30-31

— tuitional, the limitations of, 192-3

— the unity of, with space, 224

Mind-principle, the quintopyknon as the basis of, 221, ff

Mirrors, three, and the hypercube, 136-8

Mobility, life as, 264

Molecule, the four-dimensional, Newcomb on, 159

Monadic phase of evolution, 210-1

Moneron and man, the gulf between, 28

Monopyknon, the, 213, 216

Monopyknosis, defined, 17, 208-10, 218

Monstrosities, mathetic, 202

Moods of the kosmos, 311

Morphogeny, 13, 233-4

Morphons, the creation of, 219

Motility, the scope of, 131

Movement, forward, in knowledge, 336

— hyperspace as an evolutionary, 44-68

— — influence of Kant on, 49-50

— of life in chaos, 307

Multi-dimensional quality of space, justification for, 262

Multiplication of hypotheses, 118

Mutuality, intuition as promoter of, 301, ff

Mysteries, inner, of creative mentality, 91

— kosmic, low-lying plains of, 239

--- of life and mind, 326

— — the sciences and the four-space operator, 131

Mystery, kosmic, the revelation of, foreshadowed in manifold, 77

— of reaction, 167-8

— — space decreases as copes of consciousness increases, 273, ff


N

n-Coördinates, 203

n-Dimensionality, as a phase of geometry, 300

— — property of intellectuality, 269

— — quality of conceptual space, 14

— irreconcilable with perceptual space, 156

— no justification for, 235

— not surprising that the intellect fell upon, 296, ff

— predicates concerning, 158

n-Space, imperceptibility of, 94

Nasir-Eddin, 46, 53

Natural symbols, ideas as, 126

Nature, representative, of things, 119

— the vacuum-stillness of, 339

Naught to unity, consciousness registers from, 165

Near-truth, 300, ff

— as variation from criterion of truth, 324

— based upon partial knowledge, 14

— space-curvature as a, 306

— space-manifold as a, 318

Nebulosity, 267

Necessity, as a bulwark of geometry, 77-8

Nerve-body, the, 349

Neurogram, 14

Neurograph, the Thinker's scrutiny of, 190

Neurographical communications, 244

Newcomb, Simon, 14-5, 66

— — and the four-dimensional molecule, 159

— — on the fourth dimension, 125

Non-Euclideans and the meaning of dimension, 97

— — things as they actually are, 71

— dilemma of, 86

— meaning of the term, 69

— results obtained by, 88

Non-manifestation, as antithesis of manifestation, 106

— and manifestation, 206

Non-methodic advancement of human consciousness, 299

Non-spatiality, cut off from spatiality, 266

Norm, as a value assigned by the intellect, 167

— consciousness as a, 15; 161-202

— of life, found by synthesis, 300

— — the natural geometry, 263

Note, the dominant, of communality, 301

Notions of space, triple presentations to the consciousness, 72

Number, as a phase of kosmogenesis, 309

— numbers as infinitesimals of unity, 41

Numericity of being, 309


O

Objects and ideas, 126-7

— passage of, into the fourth dimension, 130

— of study, identification of consciousness with, 189

Obliquity, perceptual, of metageometricians, 102

Obscurantism, mathetic, 154

Occultist and the scientist, 350

Omnipsyche, 265

— as agency of kosmic consciousness, 258

— — neglected factor of evolution, 259

— defined, 15

One-space represented by a line, 134

Ontogeny recapitulates phylogeny, 27, 334

Order, kosmic, the difference between, and hyperspace, 143

— mathematical, discovered by the intellect, 261

— the fiat of, 208

— the totality of, 265

Orderliness, 266

Organ, determined by function to be performed, 336

Organs broken up by life into special parts, 343

— the evolution of, 188

Orthodoxy of mathematics, 34

Outcome of new adjustments, 256

Out-feelings of the Thinker, infantile, 336

Outlook, the spiritualization of our mental, 40


P

Papyrus, a hieratic, 44

Parallel-postulate and the surface of a sphere, 70

— as basis of non-Euclidean geometry, 54

— — stated by Euclid, 55

— — — — Lobachevski, 55

— — — — Manning, 82

— failures to demonstrate, 48, 82-3

— in the Elements of Euclid, 16

— Saccheri's proof of, 47

Parallels, convergence of, 80

— infinity of, through a given point, 70

— meet at infinity, 88

— theory of, 47-9

Passage from mechanics to biogenetics, 357

— from mechanics to dynamics, 326

— from three-space to four-space, 292-3

— of mathetic contrivances, 241

— of space, 16, 297

Pathway of life, sinuosities in, 330

Patterns of the intellect, ready-made, 166

Pentagrammaton of space, 237

Perceptibility in the Thinker, the faculty of, 188

Perception, domain of, and the sensible world, 19

— inner organs of, 352

— replaced by conception, 255

Percepts, and the ego, 244

Period, chaomorphogenic, 208, ff

— determinative, 61-5

— kathekotic, 210

Perisophical nature of analytics, 320, ff

Perisophism, a, 300

Permissibility of mathetic license, unlimited, 38

Perpendicularity, 132, 177

— of lines in the four-space, 130

Phantasy and reality, line of demarkation between, 173

— the world of, 146

Phantom-ideal, the, 277

Phase of the world age, evolutionary, 209

Phenomena, efforts to explain, on the basis of the fourth dimension, 129

— fashioned by the intellect, 199

— fragmentary interpretation of, 302

— mind's method of apprehending, 186

— physical phenomena amply explained by scientific methods, 154

Phenomenal, the inverse of realism, 278

Philosophy and the criterion of truth, 323-4

— regeneration of, 358

— systems of, and zones of affinity, 124

Phosphorescence, dim, added to the unilluminated pool of sense-consciousness by the intuition, 26

Phylogeny and ontogeny, 334

— represented in ontogeny, 27

Physical as embodiment of all possibilities, 227

— phenomena as space-activities, 229

Physicality, the principle of, 210, ff

Physics of the brain, 292

Pi proportion, significance of, 311-2

Pickering on space-curvature, 279

Pineal gland, energized by the pituitary body, 348-9

— — the, 344, ff

— — not a vestigal organ, 354

Pituitarial awakening, general results of, 355-8

Pituitary body and the Thinker, 351

— — as an organ, 344-352

— — C. De M. Sajous on, 345

— — hypertrophy of, 347

— — location of, 246

— — the, 344, ff

Plane, as generating element, 144

— movement of, into the fourth dimension, 147

— realism appears to be divided into, 164

— rotation about a, 130, 146-151

— the seven planes of matter, 212

Planes, a cube as a succession of, 148-9

Plasm, kosmic, strivings of, 215

— psychic, 260

— the differentiation of, 214

Plato, 322

— and the divine geometry, 193, 237

— — — shadow consciousness, 281

— on God as geometrizer, 181

— — ideas, 34

Play, sensuous, of the intellect, 295

Plenum, space as a, 230

— the universe as a, 107

Poincairé, 90

Point, an infinity of parallels through a given, 70

— as generating element, 144

— position of, 132

— succession of points, a line as, 148

Polarity between concrete and abstract, 294-5

Ponderability, as property of hyperspace, 63

Popularization of the fourth dimension, 128

— of the non-Euclidean geometry, 66-7

Possibilities in the world of hyperspace, 129

— of four-space, the marvelous, 130

Postulate-systems, the multiplication of, 85

Powers of mind, not attained at one and the same time, 334

Pralaya, 213

— as kosmic quietude, 17

Predicates, all mathematical, not justified by the phenomenal, 128

Principle, ensouling, 214-5

Printing press, the invention of, and the laws of psychogenesis, 30

Problem, the fourth dimension as a transcendental, 140

Procedure, the involved, of arriving at hyperspace notions, 73

Process, evolution a continuous, 327

— space as a dynamic, 307

Proclus, 83

Profundities, kosmic, and hyperspace, 156

Progression eastward terminates at the west, 306

Proof of rotation about a plane, 146-151

Propagation of intuitographs, difficulty of, 315

Propositions, geometric, subjunctive quality of, 38

Pseudosphere and the shape of space, 70

— as basis of Beltrami's calculations, 17

— the nature of, 64-5

Psychics of consciousness, 292

— transmuted, 260

Psychogenesis, alchemy of, 225

— kosmic, 272

— laws of, and the printing press, 30, 116

Psychogenesis, mind's place in, 123

— outgrown phase of, 302

— outstanding facts of, 131

Psychogeny, defined, 17

Ptolemy, 45, 52, 83

Publicist, the mathematical, and the duodim, 128

— the non-Euclidean, 146

Pyknon as a kosmic principle, 212

— — basis of space-genesis, 17

Pyknosis, 212

— and involution, 210, 231

— as a metamorphotic process, 214

— the seven processes of, 17, 294


Q

Quality, dimension as commensurable, 140

Quantities, algebraic, cannot represent space, 125-7

Quantity, consciousness as a tri-space, 172

Quartodim, 18, 134

Quartodimensionality, 292

Quartopyknosis, 17, 208-10

Quartopyknotic, principle as basis of spirituality, 228

Quintopyknon, 220

Quintopyknosis and the a priori, 223

— meaning of, 17, 208-10

Quintopyknotic principle as basis of mentality, 228


R

Race, humanity to evolve a new, 358

— resplendent, 338

Rajah-Tamas, 220

Rajah Yoga, 357

Rational, valueless when unsanctioned by the intuition, 187

Reaction, as a mystery, 167-8

Real, Thinker as a part of the, 201

Realism and its degrees, 164-5, 279

— — the Thinker, 315

— as life, 286

— consciousness as touch-stone of, 168

— found in the direction inverse to the phenomenal world, 278

— homogeneity of, 165

— illusionary nature of, 36

— infinite gamut of, 36

— its degrees and the states of consciousness, 197

— new scope of, bewilders the mind, 170-1

— not of mathematical import, 290

— of concepts and the sensible world, 40

— — the domain of mathesis, 33-4

— psychological quality of, 285

— the thread of, 169

— three dimensional scope of, 172

Realities, abstractionizing, 144, 294

— incomprehensible to the intellect, 126

— innermost, of things, 356

— lesser give way to greater, 195

— natural symbolism of,