Chapter X: The Media of New Perceptive Faculties (2)

CAYLEY, A., vide _Science_, Vol. IX, pp. 59-63:
_Amer. Math. Mo._, Vol. II, pp. 102-106.
_Amer. Math. Mo._, Vol. VI, pp. 59-65.
_Review of Reviews_, June, 1895, pp. 693-694.

CLASS BOOK OF NON-EUCLIDEAN GEOMETRY:
Vide _Science_, XIII, pp. 462-465.

CORNHILL MAGAZINE (n.s.):
Vol. XXXVII, pp. 647-665, C. H. BRYAN, on the Fourth Dimension.

EASY NON-EUCLID:
_Monist_, XIX, pp. 399-402.

EDUCATIONAL REVIEW:
November, 1902, issue, pp. 346, et seq.

EUCLID'S PARALLEL-POSTULATE, by JOHN W. WITHERS.

FLATLAND, by A. SQUARE.

FOUNDATIONS OF GEOMETRY:
_Science_, Vol. VI, pp. 487-491.

FOUNDATIONS OF MATHEMATICS, by PAUL CARUS.

FOURTH DIMENSION:
By HERMAN SCHUBERT, C. H. HINTON, CLAUDE BRAGDON.

FOURTH DIMENSION, SIMPLY EXPLAINED:
Edited by H. P. MANNING.

FOURTH DIMENSION:
_Cornhill Magazine_, n.s., Vol. XXXVII, pp. 647-665, by C. H. BRYAN.

FOURTH DIMENSION, THE RIDDLE OF:
H. A. BRUCE, in _Scientific American Supplement_, Vol. LXVI, p. 146.

GEOMETRY, FOUNDATIONS OF, by O. VEBLEN:
_Popular Science Monthly_, Vol. LXVIII, pp. 21, et seq.

GEOMETRY, LOBACHEVSKI'S:
_Theory of Parallels_, trans. by GEO. BRUCE HALSTED.

GEOMETRY, NON-EUCLIDEAN:
_American Mathematical Monthly_, Vol. VII, pp. 123-133.

GEOMETRY, NON-EUCLIDEAN, REPORT ON PROGRESS IN:
Reprinted from _Science_, n. s., Vol. X, No. 251, pp. 545,
et seq., by GEO. BRUCE HALSTED.

GEOMETRY, NON-EUCLIDEAN, THESIS ON:
By M. L. GERARD.

GEOMETRY, NON-EUCLIDEAN:
By ROBERTO BONOLA, trans. by H. S. CARSLAW, University of
Sydney, N.S.W.

GEOMETRY, NON-EUCLIDEAN:
JULIAN LOWELL COOLIDGE, pp. 46, et seq.

GEOMETRY, NON-EUCLIDEAN:
By H. P. MANNING.

GEOMETRY, Space and, in Light of Physiologic, Psychologic and
Physical Inquiry, vide _Open Court_, 1906, by E. MACH.

HALSTED, GEORGE BRUCE:
Cayley, A., Biog. of, vide _Amer. Math. Mo._, Vol. II, p. 102.
Four-fold Space in Two-fold Time, vide _Science_, Vol. XIX, p. 319.
Hoüel, Biog. of, _American Math. Mo._, Vol. IX, pp. 99-101.
Lambert's Non-Euclidean Geometry, vide _N. Y. Math. Soc. Bull._,
Vol. III, p. 79.
Lobachevski, N., Biog. of, vide _Amer. Math. Mo._, Vol. II,
pp. 137-139; _Open Court_, Vol. XIII, pp. 411-415.
Message of Mathematics to Natural and Rational Theology, vide
_Hibbert's Journal_, Vol. VII, 1809.
Non-Euclidean Geometry, Inevitable, vide _Monist_, Vol. IV, p. 483.
Non-Euclidean Geometry, Historical and Expository, _American
Mathematical Monthly:_
Vol. I, pp. 70-72; 112-115; 149-152; 188-195; 222-223; 259-260;
301-303; 345-346; 378-379; 421-423 (1894).
Vol. II, pp. 10; 42-43; 67-69; 108-109; 144-145; 181-214;
256-257; 309-313; 346-348 (1895).
Vol. III, pp. 13-14; 35-36; 67-69; 109; 132-133 (1896).
Vol. IV, pp. 10; 77-79; 101-102; 170-171; 200; 247-249; 269-270;
307-308 (1897).
Vol. V, pp. 1-2; 67-69; 127; 218; 290-291 (1898).
_Review of Reviews_, Vol. II, 1895, pp. 693-694.
Space, New Ideas About, _Popular Science Monthly_, Vol. XI, p. 364.

HELMHOLTZ, H., _On Origin and Meaning of Geometric Axioms:_
_Vide Mind_, Part I, No. 3, July, 1876. For replies and discussions
of the above, vide _Nature_, JEVONS, Vol. IV, p. 481; J. L. TUPPER,
_Nature_, Vol. V, p. 202; HELMHOLTZ, in _Academy_, Vol. III, p. 52;
_Mind_, Part II, April, 1878.

HERMATHENA, Vol. XIII, pp. 491, et seq., 1906.

HIGHER SPACE, A PRIMER OF, by CLAUDE BRAGDON.

INGLEBY, C. M.:
A Non-Mathematical Criticism of a Part of Professor Clifford's
Lecture on "Curved Space," _Macmillan's Magazine_, October, 1872;
also _Nature_, Vol. VII, 1873.

JOURNAL OF MATHEMATICS, AMERICAN:
Vol. I, pp. 262, 276, 384, 386; HALSTED (1878).

JOUR. PHILOS., PSYCHOL. AND SCIENTIFIC METHODS:
Vol. VI, pp. 617, et seq.

KANT, EMMANUEL, trans. by FRED. PAULSEN.

KANT, EMMANUEL, _Prolegomena_, trans. by J. P. MAHAFFY and
J. H. BERNARD, pp. 35-39.

LAMBERT, BIOGRAPHY OF:
_American Math. Mo._, Vol. II, pp. 209-211.

LIE, SOPHUS:
_Science_, Vol. IX, pp. 447-448.

LOBACHEVSKI, N.:
_Open Court_, Vol. XII, pp. 411-415,
_Amer. Math. Mo._, Vol. II, pp. 137-139.

LONDON, EDINBURGH AND DUBLIN PHILOSOPHICAL MAGAZINE:
Vol. V, series 6, p. 559.

MATHEMATICS, FOUNDATIONS OF: PAUL CARUS.

MATHEMATICAL PAPERS OF CHICAGO CONGRESS, p. 92.

MATHEMATICAL PAPERS, pp. 55-71.

MATHEMATICS (a brochure):
By C. J. KEYSER, Adrian Professor of Mathematics, Columbia Univ.

MATHEMATICS, HIGHER:
Edited by MANSFIELD MERRIAM and ROBERT S. WOOD, 1902, pp. 508,
et seq.

MATHEMATICS, SPIRITUAL SIGNIFICANCE OF:
C. J. KEYSER, reprinted from Columbia Univ. _Quar._, December, 1911.

MEMORIAL VOLUME OF SCIENTIFIC PAPERS:
Pub. by Univ. of St. Andrews, pp. 3-45, D. M. Y. SOMERVILLE.

MIND (Magazine):
Vol. I, 1876, pp. 303, et seq. J. N. P. LAND.
Vol. II, 1877, p. 40, J. N. P. LAND.
Vol. IX, pp. 522, et seq. 1900.

MONIST (Magazine):
Vol. II, pp. 50, 321, PAUL CARUS.
Vol. IV, 1894, Articles by G. B. HALSTED and J. DELBOEUF.
Vol. VI, 1895, HERMAN SCHUBERT.
Vol. VII, G. B. HALSTED, on Saccheri.
Vol. XIII, pp. 80-102; 218-234.
Vol. XIV, Article by E. MACH.
Vol. XV, p. 127, PAUL CARUS.
Vol. XVI, 1906, p. 433, DAVID P. ABBOTT.
Idem, 1906, p. 65, C. J. KEYSER, on _Mathematical Emancipations_.

NATURE (Magazine):
Vol. VIII, pp. 8, 14-17, 36-37 (1873).
Vol. XV, pp. 533-537 (1877).
Vol. XLV, P. 404 (1891).

NEWCOMB'S PHILOSOPHY OF HYPERSPACE:
_Science_, Vol. VII, p. 212.

NEW YORK MATH. SOC. BULLETIN:
Vol. III, p. 79 (1893), F. S. WOOD on _Forms of Non-Euclidean
Space_.

OPEN COURT (Magazine):
Vol. XVI, pp. 513-521.
Vide December, 1913 edition, p. 757.

PHILOSOPHY OF MATHEMATICS, by PAUL CARUS.

PHILOSOPHICAL REVIEW:
Vol. V, 1896, p. 175, F. C. S. SCHILLER.
Idem, p. 357, J. H. HYSLOP.
Vol. VII, p. 615.
Vol. X, pp. 113, 229, 314, 375, 488, 579, 583.
Vol. XII, p. 493.

POPULAR SCIENCE MONTHLY:
No. 66 (1905), pp. 639-646.
Vol. LXVII, pp. 639, et seq.
Vol. LXVIII, pp. 21, et seq.
Vol. LXXVIII. p. 554 (1911), SAMUEL MOFFAT WEYER.

POPULAR ASTRONOMY:
Vols. VII and VIII (1900), G. B. HALSTED.
Vol. XVIII, pp. 42, et seq. (1910), W. H. PICKERING.
Vol. LXXV, p. 179, W. W. PAYNE, on _Attraction and Figure of the
Earth_.
Vide No. 84 (1901), pp. 187-190.

POPULARIZATION, THE, OF NON-EUCLIDEAN GEOMETRY:
_Amer. Math. Mo._, Vol. VIII, pp. 31-35.

PSYCHOLOGICAL BULLETIN:
Vol. VIII, p. 22 (1911).

QUEEN'S QUARTERLY:
Vol. XX, pp. 431-446, A. L. CLARK (1913).

REVUE GENERALE DES SCIENCES:
No. 23, trans. _Nature_, Vol. XLV, 1892.

ROYAL ASTRONOMICAL SOCIETY PROCEEDINGS:
Vol. XVI, pp. 80-85.

ROYAL SOCIETY PROCEEDINGS, LONDON:
Obituary Notices of Deceased Fellows, Vol. XVI, p. 69 (1867-68).

ROYAL SOCIETY OF N. S. W. JOURNAL AND PROCEEDINGS:
Vol. XXXV, p. 243 (1902), G. H. KNIBBS.

SCIENCE (Magazine):
Vol. III (new series), No. 58, 1896.
Vol. VI, pp. 487-491 (1897).
Vol. VII, pp. 1-7, _Philosophy of Hyperspace_, S. NEWCOMB.
Idem, p. 861 (1898).
Vol. XIII, pp. 462-465.
Vol. XIV (new series), pp. 711-712, G. B. HALSTED.
Vol. XIX, pp. 401-413.
Vol. XX, pp. 353-456, JOSIAH ROYCE.
Vol. XXII, pp. 270-271.
Vol. XXXV, No. 906 (1912).
Vol. XXXVII, pp. 885, et seq., C. J. KEYSER, on _Concerning the
Figure of the Universe of Space_.

SCIENCE ET L'HYPOTHESE, R. POINCARÉ.

SCIENTIFIC AMERICAN SUPPLEMENT:
Vol. LXVI, pp. 14-16 (1908).

SCIENTIFIC ROMANCES, C. H. HINTON.

THOUGHT, NEW ERA OF, C. H. HINTON.

WESTMINSTER REVIEW:
Vol. CLII, pp. 675, et seq.

ZOLLNER, J. C. F., _On Space of Four Dimensions_:
_Quar. Jour. of Science_, Vol. VIII (1878), pp. 227-237.

INDEX

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, 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, 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

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, 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