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

— attachment of, to the order of becoming, 305

— dawn of, and dimension, 179

— degrees of, 162

— deprived of the validity of notions, 314

— evolution of, 250

— expansion of, 164, 272

— extended, 89-90

— focus of, 290



Consciousness and the planes of the kosmos, 163

— fragmentary view of, 260

— freedom of, in the genus homo, 332

— habitation of, 278

— higher, and art, 181

— — planes of, 178

— history of, 298-9

— identification of, with objects, 189-90

— intuitional, 255

— keyed to the entire range of reality, 167-8

— kinds of, 270, ff

— kosmic, Elysian fields of, 235

— of the primitive man, 253

— organ of, 184, ff; 90

— psychics of, 292

— raised from the sensuous to the conceptual, 72

— recipient of truths from dual sources, 26

— sensible world as instrument of, 199

— triple presentation of notions of space to, 72

— turned inward, 283

— unification of the states of, 192

— youthful, of mankind, 122

Consequences, the science of, 85

Considerations, mathematical, and reality, 128

Consistency, kosmic, 174

— self, of hyperspatial hypotheses, 67

— the criterion of geometry, 86

— — inconsistence of, 173

— — metageometrician curtailed by, 85

Construction, idealized, cannot be objectified, 144, 276

— ideal, the meaning of, 4

— mental, trafficking in, 154

Consubstantiality of intellectuality and spatiality, 331, ff

Continuity of the psychic plasm, 260

Contrivances, mathetic, the passing of, 241

Convergence of parallel lines, 315

Convolutions, duplex, 146

Coördinates, as spatial determinants, 203

— of hyperspace, 94, 97, 99, 115-6

— systems of, 301, ff

— three, 132, 232

Copolarity of ideas and objects, 127

Corpora quadrigemina, 345

Corpuscular orbits of particles, 152

Cosmos, significance of, 4

Creation, impregnated screen of, 232

Creations, the, of the intellect, 173

Criterion of geometry as consistency and convenience, 86

— — truth, 323-4

Crookes, 344

Cube, as succession of planes, 148

— generation of the, 144

— illustrated, 133

— the generating, 134

Curiosities, analytic, energy spent in elaborating misappropriated, 39

Current, electric, as component in the fourth dimension, 153

Curvature of space, the doctrine of, formulated by Riemann, 5

— — — valid element in the notion of, 305

— the measure of, 61

Curved space and metageometricians, 316


D

D'Alembert, note, 51

Dante, 181

Darwin, 181

Day, the Great Kosmic, 213

De Tilly, 66

Death, as fourth dimensional unity, 159

— of the intellect, 195

Decrement of the diametrical ratio to the circumference of circle, 312

Deeps, fearful, of kosmic mind, 71, 91

Definition, apotheosis of, 77-8

— as an arbitrary determination, 100

— the deification of, 37

Degrees of realism, 164-5

Deiform, basic idea of the, 5

Demarkation between reality and phantasy, the line of, 173

Deposits of life, 173

Descartes, 322

Designs, cut out in materiality by life, 264

Details, the power to dispose of innumerable, 303

Determinations, geometrical, the necessity of, inheres in logical deductions, 78

— the factors of conscious, 162

Determinative period of mental development, 31

Development of the intuitive faculty, future, 188

Diacritics of life, 286

Diameter, the ratio of, to the circumference, 311-2

Difference between concept and thing, 121-2

— between mathematical and perceptual space, 120

— between the ideal and the actual is dynamic, 108

Differential, among minds, 124

Difficulty of imagining the fourth dimension, 90

— of propagating an intuition, 315

Difficulties in the acquisition of real knowledge, 325

— of hyperspace, the logical, 139-41

Dilemma of metageometricians, 97-8

Dimension, a distinct stage in psychogenesis, 27

— — system of space measurement, 5

— and analysis, 163

— — D'Alembert, note, 51

— — the action of a tartrate in, 156

— as an arbitrary contrivance, 262

— — — assemblage of elements, 93

— — direction, 140

— — extent, 98

— — lying near the surface of things, 159-60

— — space,