353

Ignes fatuii and hyperspaces, 154

Illustration of plane-rotation, 148-150

— — the tesseract, 133

Images, totality of, recoils upon us, 167

Imaginability of the fourth dimension, 90, 106-7

Imagination, premises of, the mathematical, 146

Impossibility of plane-rotation, the structural, 151-3

Impressions, the symbolism of, neurographic, 186

Impulse, the satisfaction of the original creative, 310-1

Incomprehensibility of reality to the intellect, 126

Incongruity, life estranged by a radical, 325

Individual as space, 223

Ineptitude of intellectual determinations for vitality, 314

Infinite, interpreted in the terms of the finite, 82

Infinitesimals of unity, numbers as, 41

Infinity as a process, 109

— of becomings, 234

Infinity of parallels through a given point, 70

— — space, a capital illusion, 195

— the concept of, 277

— — innate dread of, 103

— — relativity of, 194

Influence of abstract thought, 33

— — Kant on the non-Euclidean geometry, 49-50

— — La Grange, 51-2

— — the intellect, 315

Infundibulum, the, 345

Inner organs of perception, 352

Innermost, the, realities of things, 356

Insouciance of the geometer, 96, 294

Instant-exposure and intellect, 311

Instrument, intellect likened to a color-bearing, 313

— for the measurement of the passage of space, 297

— of consciousness, the sensible world as, 199

— — life, form as an, 328

Integers, as fractional parts of unity, 41

Intellect and its domination of the intuition, 333

— — — final union with the space-mind, 194

— — — topography, 312

— — spatiality, 263

— — the deposits of life, 173

— — — designs cut by life in materiality, 264

— — — dictum of Sensationalists, 26

— — — instant-exposure, 311

— — — intuitive faculty, 247, ff

— — — prize of divinity, 43

— as a color-bearing instrument, 313-4

— — — searchlight, 168

Intellect as a fashioner of phenomena, 199, ff

— — hewer of the concrete, 295

— — sole interpretative agency, 166-7

— automatism of, 253, 338

— cannot seize life, 282

— crowned by a diadem of gold, 338

— dominated by the intuition, 250

— fashioned for matter only, 231

— follows in the grooves of logic, 294

— hyperspace as a monument to, 356

— in the field of vitality, ix

— its aptitude for starts and stops, 292, 302

— — instinctive tendency to fragmentate, 296

— quality, determined by mathematics, 337

— makes for individuality, 252

— misses the ceaselessness of life, 201

— modus vivendi of, its influence upon knowledge, 184

— the constitution of, 291

— — cut and mode of, 167

— — focus of, 310

— — illusion of, 246

— — illusionary character of, 323

— — incomprehensibility of reality to, 126

— — instinctive functioning of, 289

— — judgments of, 302

— — moods of, 202

— — predominating tendency in, 320-1

— — scientific tendence of, 165-6

— — struggle of, against dispossessal, 195

— unsuited to deal with reality, 322, ff

Intellectuality and reality, 304

— — spatiality, consubstantial, 331

Intellectuality as co-extensive with spatiality and materiality, 236

— the source of, 260

— — Thinker makes his own, 242

Intelligence and automatism, 253, ff

— the Thinker as a pure, 243

— transfinite intelligence and the degrees of realism, 164

Intent, the kosmic, of the intellect, 326

Interests, the sphere of our, as closed circuits, 167

Interior, the great, 290

Interiority of being, 290

Interpretation, the standards of, vary as consciousness varies, 171

Interstices of materiality, 264

Intuition and brotherhood, 252

— — communalization, 301

— — the riddle of spatiality, 325

— as dispossessor of the intellect, 195

— cannot be served by mathematics, 337

— dominated by the intellect, 333

— held in abeyance, 338, ff

— its domination of the intellect, 250

— the development of a spatial, not absurd, 145

— — need of a sympathetic attitude towards, 249

— — results of the development of, 357

Intuitional consciousness, 255

— the superiority of, over the rational, 187

Intuitions and the lead of life, 191

— — — Thinker, 27

— free, mobile and formless, 166

— the conceptualization of, 248

— — humility of, 165

— — nature of, 185

Intuitograms, as concepts, 248

Intuitograph as means of contacting the egopsychic consciousness by the Thinker, 10

— as super-concepts, 255

— the difficulty of transmitting, 315

Invariability, the vaunted, of the laws of mathesis, 37

Invariants, psychological, 24

Investigations, metageometrical, and the new sense-organs, 354

Involution, as antithesis of evolution, 10-11

— kosmic involution, 226

— of matter, 328

— the movement of, 219

— — seven stages of, 208-12

Ions, creation of, 219

— magnitude of a hydrogen ion, 225


J

Judgments a priori, Kant on, 85-6

— and the faculty a priori, 190-1

— — zones of affinity, 124

— based upon a replica of consciousness, 205

— no trustworthy, can be predicated upon fragmentary knowledge, 282

— of the intellect, 302

— the lessening of error in, 256

— — more complex the more at variance with the nature of things, 75

— — synthesis of, 257-8

— valid judgments long delayed, 170-1

Judicative power of mathematics, 180

Justification for a multi-dimensional quality in space, 262

— of four-dimensionality, 176

Justification of sense-deliveries by one another, 76

— — the existence of the fourth dimension, 125


K

Kant, 85, 181, 182, 322

— and the faculty of thinking, 261

— — — idea of space, 322-3

— influence of, on the hyperspace movement, 49-50

— on the nature of things, 119

— — space as an intuition, 115

Kathekos, 233-4

— as chaos, 266

— — symbol of Chaos-Theos-Kosmos, 11-12

— symbology of, 234

Kathekosis, note, 227

Kathekosity, fringe of, 229

— rock-bound coast of, 267

— significance of, 12

Kathekotic consciousness, 272

— period, 209

Key to the mysteries of nature, the fourth dimension as, 131

Keyser, Cassius Jackson, and freedom of the mind, 33

— — — on attitude of metageometricians, 71

— — — — dimensionality, 94-5

— — — — four-dimensionality of space, 142-3

— — — — generability of hyperspace, 144

Klein, Felix, 12, 54-5, 66-7

Knowledge, all, relative, 101

— barrier to the certitude of the Thinker's, 186-7

— fabric of, 196

— hypothetical nature of, 189, ff

— immeasurable realm of, laid bare by the telescope, 298

Knowledge, mathematical, apriority of, questioned, 37

— nature of the non-Euclidean, superperceptual, 72

— real, difficulties of acquiring, 325

— related to the stream of life and to the shore of materiality, 323

— relative, degrees exist for, 164

— sphere of, 184

— systematization of, 126

— ultimate, consciousness as a barrier to, 207

— unification of, 256

Kosmogenesis, the latent geometrism of, 264

— — scope of, 237

Kosmometer, the, 297

Kosmos, and consciousness, graph representing, 271

— arrangements of the contents of, 317-8

— in a state of becoming, 265

— magnitude of, 308

— moods of, 311

— space as the consistence of, 239

— see Cosmos, 12


L

Labor, division of, between the tuitional and the intuitional faculties, 193-4

— mathematical labors, significance of, 176

La Grange, Joseph Louis, 12, 39, 50-3, 321, 322

— — — — and the parallel-postulate, 51-2

Lambert, John, 58

— — and the theory of parallels, 48-9

Language, the passing of, 357

Legendre, 70

Leibnitz' dictum, 26

Leonard rays, 336

License, mathematic, permissibility of, 38

Lie, Sophus, 12, 67

— — and transformation groups, 30

Life, analysis incapable of dealing with, 319

— and consciousness as one, 224

— — form rooted in pyknosis, 214, 328

— — the fourth dimension, 172

— — — inaptitude of mathematics for, 179

— — — power to create, 297

— as agent of creation, 343

— — creative agent, 264

— — expression, 303

— — vassal of materiality, 329-30

— causative agencies in prolonging, 123

— current of, as engendering element, 331

— deposits of, and the intellect, 173

— estranged by a radical incongruity, 325

— exalting power of, and humanity, 331, ff; 342

— exhibition of its remains, 282

— flow of, 265, 297

— form as an instrument of, 328

— indescribable signs of, 219

— infinitive action of, 327

— intellect has no aptitude for, 231

— intuitive, values of, x

— larger life of the Thinker, 196

— lead of, followed by intuition, 191

— limits of, fixed by consciousness, 198, ff

— most solid facts of, as shadows, 195

— motility of, admits of endless variations, 35

Life, movement of chaos in, 307

— passage of, 201

— passage through spatiality, 288

— power to manipulate, 303

— recurrent movement of, 307

— totality of egoic, 243

— undulations in the current of, 329

— uniqueness of, 41

— wake of, and consciousness, 205, 288

Life-cycle, evolutionary results of the, 259

Life-stream, the, 278

Light, polarized, and the fourth dimension, 156

— consciousness as a spreading, 168

Light-years and space, 278

Limits, the sphere of, consciousness as, 163

Line, as generating element, 144

— the straight, a curved, 76

Lineage of every principle runs back to monopyknosis, 213

Lines, perpendicularity of, in four space, 130

Lobachevski, 55, 60, 66, 87

Lodge, Sir Oliver, 340-1; 344

Logic as architect, 118

— conventional forms of, 262

— data of, 286

— intellect follows in the grooves laid out by, 294

— miracle power of, over facts, 288-9

— rules of, allowability under, 163

— — — the game of, 164

— as symbolism of facts, 287

Logos and the limits of space, 193

— being of, 218

— body of being of, 214

— consciousness of, 204

— creative, 12, 213

— the, 216-7

Lorenz, 83

Luther, Martin, 181


M

Magnitudes, geometry, a study of, 203

— non-sensuous, of hyperspace, 72

Makrokosmic consciousness, 270

Malebranche, N., 222; see note

Manifestation and non-manifestation, 206

Manifold, finite, though unbounded, 70

— manufactured by the analyst, 77

— the, 61-2, 172

Manifoldness, analytical manifoldnesses, as mental excitants, 89-90

— as a conventional construction, 262

— — an intuition, 318

— of space, as a near-truth, 317

Manning, 82, 157

— and maneuvers in the fourth dimension, 152

Manvantara, 213, 228-9, 232

— as evolution and involution combined, 13

Mask, logic as a, 288-9

Mass-termini, of lines, 236

Mastery of life over matter, 330

— of the sensible world, 196-7

Materiality as a deposit of life, 295

— — consubstantial with spatiality, 331, ff

— becoming spatialized, 261

— characteristics of, 260

— engendered by kosmic mind, 261

— engenderment of, 294

— interpenetrative with spirituality, 236

— interstices of, 264

— neglect of, 320

Materiality, shore of, 323

— transmuted into spirituality, 328

Mathematicians and the definition, 37

— — — limitations of consciousness, 178

— — — phenomenal world, 118-9

— as prophets, 336

— respected by humanity, 337

— the gods of mathesis, 84

Mathematics, a determinant of the quality of the intellect, vii

— and the criterion of truth, 323

— — — kosmic intent of the intellect, 326

— as symbology, 184

— Euclidean, 140

— fails when it encounters life, 337

— its inaptitude for life, 179

— — kingdom yielded to kinetics, 358

— possesses no judicative power over life, 180

— the orthodoxy of, 34

Mathesis, and conceptional space, 203

— conduct of the intellect in the field of, vii

— definition of, 13

— domain of, as origin of fourth dimension, 130

— gods of, 84

— marvelous domain of, 118

— realm of, not submissive to laws of sensible space, 34

— things of, as emblems of kosmic forces, 239

— world of, 67, 127

Matter and mind, syncretization of, 299

— appulses of life against, 328

— as a deposit of life, 330

— honeycombs of, 339

Matter metamorphosed by life, 328

— mind as wedded to, 249

— movement of, in four-space, 157

— qualities of, and faculties, 332

— seven planes of, 212

— spiritualization of, as end of evolution, 327

— totality of, acted upon by totality of life, 328

— unity of, with space, 260

— universum of, 261

Matutinal ceremonials of creation, 221

Measurability, as property of space, 62-3