128— our, non-existent to beings on spirit-levels,35— shaped upon conventional models,294— supersensuous,180Reality, 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,127Realms, supersensuous,338Re-becoming, life and consciousness as a,257Reciprocity of consciousness and realism,197-8— of the manifest and the unmanifest,217Recoil of images upon us,167-8Reflexive development of the intellect,254Relativity of all knowledge,101Religion and realism,170— the changes in,358Remains of life exhibited to the intellect,283Remaking of moods by the intellect,201Replica of consciousness as basis of judgments,205Representation, sensuous, compared with a shadow,119-120Research, improvement in the methods of,125Reservoir, psychic, of evolution,260Residuum, the unexplained,157-8Revelational impressions,29Riddle of spatiality and the intuition,325Riemann, 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,61-4Roentgen rays,336Rotation about a line,147-8— about a plane,146-151— — — — illustrated,148-50— intra-corpuscular,152Rudimentary organs, vague functions lying back of,343Rule in the evolution of faculties,333SSaccheri, Girolamo,47-8,52,83Sajous, C. De M., on the pituitary body,345Schematism, the suitability of the present,320-1Schweikart, Ferdinand Karl,19,66,69— on the non-Euclidean geometry,58-60Science Absolute of Space,60Science and reality,170-1— no longer empirical,358— skeptical attitude of,349Scientist, method of the, opposed to the analyst,84-5Scopographic impressions,19,190Screen, the impregnated, of creation,232Sea, choppy, and egos,256-7Search, the path of, for spatial understanding,278Seb, the god,215Sects, coplanar,79Self and the immensity of space,223— of the universe,217— the kosmic,278Self-consciousness,270— and space,223— as I-making faculty,243— determination of,302Self-consistency,173Sella turcica, the,345Semi-Euclidean geometry, the,70Sensationalists on the intellect,26Sense-data, spurned by the metageometrician,73Sense-delivery, one, justified by the other,76— symbolism of,203-4Sense-knowledge, the sphere of, extended,339-40Senses, the answer of, to new needs,332Sensible world, as domain of perception,19Sensographic impressions, as perceptions,19Senso-mechanisms of the intellect,165Sentience, the principle of,210,ffSeptopyknon, the,227Septopyknosis, as kosmic materiality,18,208-10Septopyknotic, the, principle,228Seven planes of matter,212Sextopyknon, the,209Sextopyknosis, defined as kosmic sensibility,18,208-10Sextopyknotic, as emotional principle,228Shadow likened to a sense presentation,119Shadowgraphs,281Silences, nature's great,339Similitude of agent and principle,243-6Sinuosities in the pathway of life,330Socrates,322Solitariness of intellectual testimony,76Space and edict of disorder,230— — four-dimensional entities,128-130Space 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,260Space-activities, as chemism and physicism,229-30Space-center, the,306-7Space-consciousness,225— as a direct process,224— mergence of, with the individual consciousness,195Space-curvature, as an arbitrary construction,262— as near-truth,306— nature of,279— no need for,237— translation of, in terms of the intellect,315Space-forms, the construction of,74Space-genesis,20,232,233— alphabet of,237— completion of,226— norm of,174— pyknon as a basis of,17— symbolism of,208,ff,235Space-manifold, the,279Space-measurement, and reality, Euclid's system of,96— systems of,201Space-mind and archeological evidences,193— — knowledge,187— — the Thinker,253,272— attainment of,225,231— granaries of,235— the realization of,238Space-process, the,305Space-realities, hyperspace as a stepping stone to,238Spark, the omnipsyche as a,258Spatiality 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,232Spencer, Herbert,322Spinoza,322Spiritism, the phenomena of,154Spiritualists, the claim of, regarding the fourth dimension,154-5Spirituality, materiality transmuted into,328— principle of,210,ff— seeds of,221Spiritualization of the flesh,227— — man's mental outlook,40— — matter, the end of evolution,327Squares, the form of, in the non-Euclidean geometry,59St. Marie, Flye,66Stage of pyknosis,208,ff—, quartopyknotic,219,ffStanley, Hiram M., on space as dynamism,104-7States, the two, of consciousness; one unaware of the other,192Straight, a, determined by two points,79Stuff, etherealized four-dimensional,160Sum, angular,79— triangular, less than two right angles,59Superconcepts, as intuitographs,255Superconceptual, as the intuitional,20Superperception and automatism of the intellect,20Superperceptual, the,74Superunodim, the,177Swedenborg,180,184Symbol, psychic, and the brain,190— words as symbols of ideas,126-7Symbolism of life,286— — neurographical impressions,186— — realities,128— — sense-deliveries,204— — space-genesis,208,ffSymbology, depicting planes of consciousness,270— of mathematical knowledge,203,ffSynchronous evolution of faculties and properties of matter,332Syncretization of mind and matter,299Synthesis and the norm of reality,300Synthetic school of geometry,56TTactographic impressions,190Tartrate and a component in the fourth dimension,156-7Task of mental evolution, the supreme,169Taurinus,56-7,69Telescope, its effect upon consciousness,298Tendence, intellect as scientific,165-6Tendencies, destined to flower as faculties,89-91,332Tendency to fragmentate, the intellect and,296Tesseract as represented by Carus,136-8— illustrated,133— the,20,145— the elements of,135— the four coördinates of,132Testimony of the intellect, incapable of comparison,76Tetragrammaton, the,308Tetrahedron, the,135Thalamencephalon, the,345Thales,44Theory of knowledge,290Thingness of objects and the impossibility of comprehending,122Things, the dual nature of,119— — value of,161Things-in-themselves, the identity of,353Thinkability of the fourth dimension,125Thinker 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,242Thinker, his schematism of cognitive powers,206— — sphere of awareness,283— the difference between, and the intellectuality,256— — evolutionary needs of,336— — upreaching yearnings of,336Thinker-ward, space must be sought in a direction,278Thinking, abstract, elevating influence of,33Thought, prolonged abstract, benefits of,249Time, as an aspect of consciousness,224— divested of timeliness,279Todhunter,46Tool, fashioning, life as a,264Topography of the intellect,312Touchstone, consciousness as a,168Tracery of connection between ideas and objects,126Trafficking in mental constructions,154Transcendental, the realm of, and mathematicians,142Transfinite as a limit,122,216Transfinity,21-2Tree-reality,126Triadic phase of evolution,210-1Triangles, angular sum of,78,88Tridim, the,22,129,134,147,177Tridimension, the,147Tridimensionality and primeval space,236— and the space-mind,193— a quality of perceptual space,22— mastery of the phenomena of,172— the sufficiency of,198Tripyknon, the,212,213Tripyknosis,17,208-10,219Truth compared with facts,288— criterion of,