The mystery of space

by Robert T. Browne

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]
Relativity of all knowledge, [101]
Religion and realism, [170]
— the changes in, [358]
Remains of life exhibited to the intellect, [283]
Remaking of moods by the intellect, [201]
Replica of consciousness as basis of judgments, [205]
Representation, sensuous, compared with a shadow, [119]-[120]
Research, improvement in the methods of, [125]
Reservoir, psychic, of evolution, [260]
Residuum, the unexplained, [157]-[8]
Revelational impressions, [29]
Riddle of spatiality and the intuition, [325]
Riemann, G. F. B., [18], [19], [54], [66]-[7], [87]
— and a limited space, [108]-[9]
— — the curvature of space, [5]
— — — determinative period, [65]
— — finite space, [103]
— — — four-space, [27]
— — — manifold, [317]
— as inventor of the manifold, [86]
— on the bases of geometry, [61]-[4]
Roentgen rays, [336]
Rotation about a line, [147]-[8]
— about a plane, [146]-[151]
— — — — illustrated, [148]-[50]
— intra-corpuscular, [152]
Rudimentary organs, vague functions lying back of, [343]
Rule in the evolution of faculties, [333]
S
Saccheri, Girolamo, [47]-[8], [52], [83]
Sajous, C. De M., on the pituitary body, [345]
Schematism, the suitability of the present, [320]-[1]
Schweikart, Ferdinand Karl, [19], [66], [69]
— on the non-Euclidean geometry, [58]-[60]
Science Absolute of Space, [60]
Science and reality, [170]-[1]
— no longer empirical, [358]
— skeptical attitude of, [349]
Scientist, method of the, opposed to the analyst, [84]-[5]
Scopographic impressions, [19], [190]
Screen, the impregnated, of creation, [232]
Sea, choppy, and egos, [256]-[7]
Search, the path of, for spatial understanding, [278]
Seb, the god, [215]
Sects, coplanar, [79]
Self and the immensity of space, [223]
— of the universe, [217]
— the kosmic, [278]
Self-consciousness, [270]
— and space, [223]
— as I-making faculty, [243]
— determination of, [302]
Self-consistency, [173]
Sella turcica, the, [345]
Semi-Euclidean geometry, the, [70]
Sensationalists on the intellect, [26]
Sense-data, spurned by the metageometrician, [73]
Sense-delivery, one, justified by the other, [76]
— symbolism of, [203]-[4]
Sense-knowledge, the sphere of, extended, [339]-[40]
Senses, the answer of, to new needs, [332]
Sensible world, as domain of perception, [19]
Sensographic impressions, as perceptions, [19]
Senso-mechanisms of the intellect, [165]
Sentience, the principle of, [210], ff
Septopyknon, the, [227]
Septopyknosis, as kosmic materiality, [18], [208]-[10]
Septopyknotic, the, principle, [228]
Seven planes of matter, [212]
Sextopyknon, the, [209]
Sextopyknosis, defined as kosmic sensibility, [18], [208]-[10]
Sextopyknotic, as emotional principle, [228]
Shadow likened to a sense presentation, [119]
Shadowgraphs, [281]
Silences, nature's great, [339]
Similitude of agent and principle, [243]-[6]
Sinuosities in the pathway of life, [330]
Socrates, [322]
Solitariness of intellectual testimony, [76]
Space and edict of disorder, [230]
— — four-dimensional entities, [128]-[130]
Space and quartopyknons, [219]-[20]
— — self-consciousness, [223]
— — the idealized construction, [144]
— as a dynamic process, [216]
— — all-mother, [229]-[30]
— — an assemblage of spheres, [143]
— — becoming, [195]
— — boundary of another space, [49]-[50]
— — consistence of the kosmos, [239]
— — curved, [164]
— — dynamic appearance, [228], [307]
— — eldest born of kathekosis, [215]
— — engendered product of life, [308], ff
— — evolution, [226], ff
— — finite extension, [62], [106]
— — generable quantity, [103]
— — infinite continuum, [70]
— — intuitional concept, [225]
— — kosmic order, [265], [267]
— — nether pole of non-manifestation, [207]-[8]
— — path of life, [293]-[4]
— — pseudosphere, [70]
— — sheer roominess, [115]
— — system of coördinates, [99]
— — unbounded extension, [61]
— best study of, the consciousness, [269]
— conceptual, as basis of non-Euclidean geometry, [72]
— — fundamentally distinct from perceptual, [72]-[75]
— elliptical, [67]
— engenderment of, [260]
— essential nature of, [212]
— fabric of, the, lends itself to measurement, [99]-[100]
— four-, [8]
— fractionalized space, [296]
— foundations of, [221]
— four-dimensional, [41]
— Paul Carus on, [354]
— fourth dimension of, efforts at making it thinkable, [125]
— generability of, by lines, [143]
— genesis of, [227], ff
— geometric, purely formal construction, [75]-[6]
— limits of and the Creative Logos, [193]
— manifoldness of, [77]
— mind and, the coevalism of, [240]
— mystery of, [278], ff
— nature of, answered to by mind, [198]-[9]
— nether pole of non-manifestation, [207]-[8]
— non-Euclidean, the characteristics of, [72]-[3]
— not a pure form, [110]
— passage of, [16]
— path of search for, must be Thinker-ward, [278]
— perceptual, irreconcilable with the fourth dimension, [156]
— possible curvature of, and the non-Euclidean geometry, [76]-[7]
— primeval, and tridimensionality, [236]
— problem of devising a, [87]-[8]
— psychological nature of, [305]
— real, confounded with hyperspace, [91]
— Riemann on the curvature of, [5]
— the unity of, [224]
— — — — with matter, [260]
Space-activities, as chemism and physicism, [229]-[30]
Space-center, the, [306]-[7]
Space-consciousness, [225]
— as a direct process, [224]
— mergence of, with the individual consciousness, [195]
Space-curvature, as an arbitrary construction, [262]
— as near-truth, [306]
— nature of, [279]
— no need for, [237]
— translation of, in terms of the intellect, [315]
Space-forms, the construction of, [74]
Space-genesis, [20], [232], [233]
— alphabet of, [237]
— completion of, [226]
— norm of, [174]
— pyknon as a basis of, [17]
— symbolism of, [208], ff, [235]
Space-manifold, the, [279]
Space-measurement, and reality, Euclid's system of, [96]
— systems of, [201]
Space-mind and archeological evidences, [193]
— — knowledge, [187]
— — the Thinker, [253], [272]
— attainment of, [225], [231]
— granaries of, [235]
— the realization of, [238]
Space-process, the, [305]
Space-realities, hyperspace as a stepping stone to, [238]
Spark, the omnipsyche as a, [258]
Spatiality and the intellect, [263]-[4]
— consubstantial with materiality, [20], [331], ff
— cut-off from non-spatiality, [266]
— interpenetrative with materiality, [236]
— nonconformity of, with logic, [164]
— riddle of, and the intuition, [325]
—, rise of, [180]
— Thinker's outlook in, [316]
— world of nascent, [232]
Spencer, Herbert, [322]
Spinoza, [322]
Spiritism, the phenomena of, [154]
Spiritualists, the claim of, regarding the fourth dimension, [154]-[5]
Spirituality, materiality transmuted into, [328]
— principle of, [210], ff
— seeds of, [221]
Spiritualization of the flesh, [227]
— — man's mental outlook, [40]
— — matter, the end of evolution, [327]
Squares, the form of, in the non-Euclidean geometry, [59]
St. Marie, Flye, [66]
Stage of pyknosis, [208], ff
—, quartopyknotic, [219], ff
Stanley, Hiram M., on space as dynamism, [104]-[7]
States, the two, of consciousness; one unaware of the other, [192]
Straight, a, determined by two points, [79]
Stuff, etherealized four-dimensional, [160]
Sum, angular, [79]
— triangular, less than two right angles, [59]
Superconcepts, as intuitographs, [255]
Superconceptual, as the intuitional, [20]
Superperception and automatism of the intellect, [20]
Superperceptual, the, [74]
Superunodim, the, [177]
Swedenborg, [180], [184]
Symbol, psychic, and the brain, [190]
— words as symbols of ideas, [126]-[7]
Symbolism of life, [286]
— — neurographical impressions, [186]
— — realities, [128]
— — sense-deliveries, [204]
— — space-genesis, [208], ff
Symbology, depicting planes of consciousness, [270]
— of mathematical knowledge, [203], ff
Synchronous evolution of faculties and properties of matter, [332]
Syncretization of mind and matter, [299]
Synthesis and the norm of reality, [300]
Synthetic school of geometry, [56]
T
Tactographic impressions, [190]
Tartrate and a component in the fourth dimension, [156]-[7]
Task of mental evolution, the supreme, [169]
Taurinus, [56]-[7], [69]
Telescope, its effect upon consciousness, [298]
Tendence, intellect as scientific, [165]-[6]
Tendencies, destined to flower as faculties, [89]-[91], [332]
Tendency to fragmentate, the intellect and, [296]
Tesseract as represented by Carus, [136]-[8]
— illustrated, [133]
— the, [20], [145]
— the elements of, [135]
— the four coördinates of, [132]
Testimony of the intellect, incapable of comparison, [76]
Tetragrammaton, the, [308]
Tetrahedron, the, [135]
Thalamencephalon, the, [345]
Thales, [44]
Theory of knowledge, [290]
Thingness of objects and the impossibility of comprehending, [122]
Things, the dual nature of, [119]
— — value of, [161]
Things-in-themselves, the identity of, [353]
Thinkability of the fourth dimension, [125]
Thinker as a pure intelligence, [184], [248]
— — engenderer of the intellect, [291]
— — principal to the ego, [243], ff
— — six times removed from the sensible world, [201]
— — the source of the intuition, [26]
— and concepts, [244]
— — his approach to the kosmic mind, [202], [223]
— — — larger life, [196]
— — — treatment of the ego, [246]
— — — of sense-impressions, [74]-[5]
— — realism, [315]
— — space, [193]
— — a segment of reality, [171]
— the, and the amplitude of the degrees of realism, [198], [270]
— and the barriers of consciousness, [207]
— — — brotherhood of man, [301]
— — — degrees of realism, [175]
— — — manipulation of concepts, [255]
— — — nature of space, [268]
— — — neurograph, [190]
— — — new faculty, [335]
— — — perceptive faculty, [188]
— — — pituitary body, [351]
— defined as the spiritual man, [21]
— his consciousness and the ether, [280]
— — dependence upon the ego, [245]
— — method of contacting the external world, [189]-[191]
— — outlook upon the universe of spatiality, [242]
Thinker, his schematism of cognitive powers, [206]
— — sphere of awareness, [283]
— the difference between, and the intellectuality, [256]
— — evolutionary needs of, [336]
— — upreaching yearnings of, [336]
Thinker-ward, space must be sought in a direction, [278]
Thinking, abstract, elevating influence of, [33]
Thought, prolonged abstract, benefits of, [249]
Time, as an aspect of consciousness, [224]
— divested of timeliness, [279]
Todhunter, [46]
Tool, fashioning, life as a, [264]
Topography of the intellect, [312]
Touchstone, consciousness as a, [168]
Tracery of connection between ideas and objects, [126]
Trafficking in mental constructions, [154]
Transcendental, the realm of, and mathematicians, [142]
Transfinite as a limit, [122], [216]
Transfinity, [21]-[2]
Tree-reality, [126]
Triadic phase of evolution, [210]-[1]
Triangles, angular sum of, [78], [88]
Tridim, the, [22], [129], [134], [147], [177]
Tridimension, the, [147]
Tridimensionality and primeval space, [236]
— and the space-mind, [193]
— a quality of perceptual space, [22]
— mastery of the phenomena of, [172]
— the sufficiency of, [198]
Tripyknon, the, [212], [213]
Tripyknosis, [17], [208]-[10], [219]
Truth compared with facts, [288]
— criterion of,

[5], [323]-[4]
— facets of, [284]
— kinds of, [324]
— logic does not illuminate, [287]-[8]
Tuitive, the, and the intuitive faculties, [192]-[3]
U
Ultima Thule, the, [207]
Unbounded, the, as a finite extension, [70]
Undulations, three, in the current of life, [329]
Unfoldment, mental, and metageometrical discoveries, [131]
Uni-circle, the, [308]
Unification of all knowledge, [256]
Uniqueness of real space, [95]
Unitariness of all existences, [241]
Unity, as end of analysis, [42]
— death as a fourth dimensional, [159]
— kosmic, integers as fractional parts of, [41]
— of mind and space, [224], [230]
— the new realization of, [225]
Universality, geometric, based upon the formal character of assumptions, [77]-[8]
Universe, a glorified, [226], [268]
— as a full, [308]
— — — plenum, [107]
— and the seven planes of matter, [212]
— character of, fixed by consciousness, [162]
— limited and conditioned, [127]
— not a pure form, [108]
— the perfected, and the circle, [310]
— — theory of the mechanical origin of, due to analytics, [40]
— unity in the, [301]-[2]
Universum of appearance, [187]
— of life and consciousness, [257]
Universum of reality, [127]
— — space, [269]
Unknowable as a symbol, [194]
— the darkness which shuts out the, [207]
Unodim, the, [129], [134], [176]-[7]
— — consciousness, [163]
— defined, [22]
Upraisement of matter, [329]
Upspringing of a new faculty, [333]
V
Vacuum-stillness of nature, [339]
Validity of mathematical conclusions, [101]
Value assigned by the intellect to the sensible world, [167]
— assumptional, vitiating influence of, [163]
— — of the ideal, [275]
Vanity of fragmentary evidences, [204]
— of intellectual method, [325], ff
— — segmenting space into many dimensions, [299]
Vassal, life as the, of materiality, [329]
Vehicle of life, form as, [330]
— — — mind as, [286]
Vicissitudes of kosmic evolution, [215]
Vision, the inner, [356]
W
Wachter, [69]
Wallis, John, [46], [83]
Weismann, note, [260]
Words, as symbols of ideas, [126]-[7], [204]
World and the child mind, [121]
— as instrument of consciousness, [199], [298]
— fabric of, and geometrism, [261]
— impossibility of objectifying the fourth dimension in the perceptual, [124]
— of phantasy, conditions of, identified with sensible realm, [146]
— phenomenal, and hyperspace entities, [128]-[130]
— sensible, as a carpet, [196]
— the domain of a perception, [19]
— — genesis of, [167]
World-plasm, kathekotic, [267]
— as elemental essence, [329]
Y
Yoga, Rajah, [357]
Youth of the earth, the nebulous, [335]
Z
Zollner, and the claims of the spiritualists, [154]
Zones of Affinity, [22], [124]
Zoometer, the, [297]

FOOTNOTES:

[1] Vide Popular Science Monthly, vol. 78, p. 554, 1911.

[2] Vide New York Mathematical Society Bulletin, Vol. III, 1893-4, p. 79, G. B. Halstead on Lambert's Non-Euclidean Geometry.

[3] Prolegomena, Kant, p. 37, Trans. by J. P. Mahaffy and J. H. Bernard.

[4] In 1754 D'Alembert (1717-1783) published an article in the famous old Encyclopedia edited by Diderot and himself on Dimension. In this article the idea of the fourth dimension is dwelt upon at length. The view which he expressed in this article, of course, served greatly to popularize the conception among the learned men of the day, and owing to the close relationship existing between D'Alembert and La Grange, it is not surprising that the latter should have been very much enamored of the idea.

[5] Vide Nature, Vol. VIII, pp. 14-17; 36, 37 (1873); also Mathematical Papers, pp. 65-71.

[6] Mathematics, by C. J. Keyser, Adrian Professor of Mathematics, Columbia University.