AAbeyance, higher faculties held in, until lower are fully developed, 334— intuition kept in,338,ffAbility, to sense the inaudible and the invisible,342Absolute, no room for the,101Abstract thought, invigorating power of,33,40Abstractions, realizing,144,294Absurdity, analysis inevitably ends in an,319-20Acrobatics, mathetic,146Acromegaly,347Action, automatic, of the intellect,253-4— engendering, of life on the form,330Activities, space, as physical and chemical phenomena,229-30Actualities of the physical world pushed over into the conceptual,119Actuality imperceptible to the intellect,126Adaptability of life,330— — mathematical laws,37-39Adaptation, purpose of,327-8Adaptations made by an organism,162Additional freedom bestowed by higher faculties,334Affinity, zones of,22,124Agency, interpretative, intellect as an,166-7Agent, ego as an, of the Thinker,243,ff— engendering, life as an,331— of creation, life as an,343Ahmes, an Egyptian priest,44Alchemy of psychogenesis,225Alcohols, eight different, from one formula,155Algebraic quantities and space,125-7Allowability of the rules of logic,163Aloofness, the, of scientific dogmatism,340Alphabet of space-genesis,237— the geometric,193Amenability of mind to the laws of evolution,28-31Analogies, use of, to popularize the four-space,128-9Analogy, difference between two processes illustrated by,74Analysis incapable of dealing with life,319— the manifold, the fiat of,77Analyst and the manufacture of the space-manifold,77— disregards the conformity of the nature of things,84Analytics and the mechanical origin of the universe,40-1— perisophical nature of,320,ff— the four-space, a curiosity of,40Anchorage, fourth dimension denied,265Angularity of consciousness,120Answer of the senses to new needs,332— the, of consciousness to realism,97Anti-Euclidean geometry,69Apotheosis of the definition,78Apparatus, man's perceptive,357Apparent vassalage of life,329-30Appearance, dynamic, space as,104-7Appetences, materialistic, of empiricists,340Appulses of life against matter,328Appurtenances of materiality,331A priori,185,ff— — knowledge,110-5Aprioriness,112,116Apriority, the principle of,113,223Arbitrariness of the common mensurative quantities,41Archeological evidences,332Archimedes,70Aristotle,322Arrangement of the contents of the kosmos,317-8Art and the criterion of truth,323— — — higher consciousness,181— evidences of new faculties in the field of,335Assemblage of mathetic contrivances,335Assumptions, category of,189— procedure based upon, disadvantages of,163At-one-ment,224,252,270— defined as the end of evolutionary activity,1Attachment of the consciousness to the order of becoming,305Attainment, the difficulty of, by the intellectual method,206— of space-consciousness,225Attitude, the need of a more liberal,340— towards things spatial,306Audital nerves, notes that transcend the grasp of,355Aura, pulsating,348Automatism of the intellect,253,ff;338Avenues of knowledge opened to inner perceptive faculties,353Awakening of the faculty of awareness in a new domain,90— — — pituitary body and the pineal gland,353— pituitarial, general results of,355-8Awareness, 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,274,283BBaltzer,66Barrier, the, to the Thinker's certitude,186-8Barriers, freedom determined by absence of,280Becoming, endless labyrinth of,220— the kosmos, in a state of,265— the order of,305Becomings, infinity of,234Becquerel rays,336Being, identification of consciousness with,205— kathekotic,210Being, the interiority of,290— the numericity of,309— the range of, co-extensive with reality,168Beings, discarnate,154Beltrami, Eugenio,1-2,63-5,66-7— — and the manifold,317— — and the pseudosphere,64-5Besiegement of matter by life,329-30Bessel, on geometry as incomplete,58Bewilderment, new realities cause,169-70— of the mind,182Biogenetics, passage from mechanics to,357— turning to, from mechanics,322Birth, as a fourth dimensional process,159Blind men and the elephant,257Bolyai, Janos,2-3,46,60,66,83,87Boundaries of a hypercube,136-8Brain, the physics of,292Brain-consciousness,184,186— standards of,190Brotherhood, and the tendencies of the Thinker's consciousness,301— the keynote of the intuition,252Bulwarks, the formal, of geometry,77-9CCarpet, the sensible world as a,196Carus, Paul, on four-dimensional space,254— — on metageometricians,102— — on space,110— — on the representation of the tesseract,136-7Cayley,3-4,54-5,66-7Cell-activity as a performancea priori,114Cell-colony,250,301Cell-consciousness as an aposterioristic phenomenon,185Centers, pyknotic,232Certainty, geometric, the basis of,77-8— of mathetic conclusions, provisional,37Chaogenic period of involution,208,ffChaogeny,231,233— the evolution of chaos into order,4— the laboratory of,193Chaomorphogeny, defined,4,231-2Chaos, as egg-plasm,265— duration of,268— movement of life in,307— shores of,307Chaos-geometricity,307— -intellectuality,307— -materiality,307— -spatiality,307— -Theos-Kosmos,215, 233-4,237— — — a triglyph symbolizing kathekos,11-2Character of the universe, fixed by consciousness,162Characteristics, 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,72-3Chasm, kosmic, between the real and the ideal,107Chemists, speculative, and the ourth dimension,155Chrism, sacred, of creative mentality,91Circle, significance of process of squaring,109Circle, the symbology of,309Circuits, closed, our interests as,167Clairaudience,352Clairvoyance,352Clairvoyant perception,349Clause, enabling, of metageometry,76-7Clavius, Christoph,46,52,83Clifford,66Code, psychic, for systematizing cognitions,190-1Cognition, instantaneous, organ of,258— intimacies of direct,205— the method of,186-8Cognitions, intuitive,145,192-3— psychic code for systematizing,190-1Commensurable quality, dimension as,140Communal consciousness,270,ffCommunalization and the intuition,301Conarium, the,345Conceivability and evolution of mind,24— ultimate range of,278Conceiving, power of, derived from sense-experience,26Concept, as a shadow,119— the hyperspace, gradual rise of,27-8Conception and awareness,120— every, based upon prior experience,25— freedom, the, of the mind from,28Conceptions, symbolic, dependence placed upon,147Concepts, and the Thinker,244— intuitograms as,248— quality of, dependent upon sense-experience,26Concepts, the perception of,255Conceptual, related to the objective,291— the, and mathematicians,71Conceptualization, the act of,4— the power of, dependent upon evolution of mind,25Conclusions, mathetic, complex dependence of,37Concrete hewn into shape by the intellect,295Congruency, the, between intellect and the universe,319,ffCongruity, the, between concepts and objects,120Connection, the, traced out between reality and object,126Co-originality of things,303Consciousness 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,290Consciousness and the planes of the kosmos,163— fragmentary view of,260— freedom of, in thegenus 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,122Consequences, the science of,85Considerations, mathematical, and reality,128Consistency, kosmic,174— self, of hyperspatial hypotheses,67— the criterion of geometry,86— — inconsistence of,173— — metageometrician curtailed by,85Construction, idealized, cannot be objectified,144,276— ideal, the meaning of,4— mental, trafficking in,154Consubstantiality of intellectuality and spatiality,331,ffContinuity of the psychic plasm,260Contrivances, mathetic, the passing of,241Convergence of parallel lines,315Convolutions, duplex,146Coördinates, as spatial determinants,203— of hyperspace,94,97,99,115-6— systems of,301,ff— three,132,232Copolarity of ideas and objects,127Corpora quadrigemina,345Corpuscular orbits of particles,152Cosmos, significance of,4Creation, impregnated screen of,232Creations, the, of the intellect,173Criterion of geometry as consistency and convenience,86— — truth,323-4Crookes,344Cube, as succession of planes,148— generation of the,144— illustrated,133— the generating,134Curiosities, analytic, energy spent in elaborating misappropriated,39Current, electric, as component in the fourth dimension,153Curvature of space, the doctrine of, formulated by Riemann,5— — — valid element in the notion of,305— the measure of,61Curved space and metageometricians,316DD'Alembert,note,51Dante,181Darwin,181Day, the Great Kosmic,213De Tilly,66Death, as fourth dimensional unity,159— of the intellect,195Decrement of the diametrical ratio to the circumference of circle,312Deeps, fearful, of kosmic mind,71,91Definition, apotheosis of,77-8— as an arbitrary determination,100— the deification of,37Degrees of realism,164-5Deiform, basic idea of the,5Demarkation between reality and phantasy, the line of,173Deposits of life,173Descartes,322Designs, cut out in materiality by life,264Details, the power to dispose of innumerable,303Determinations, geometrical, the necessity of, inheres in logical deductions,78— the factors of conscious,162Determinative period of mental development,31Development of the intuitive faculty, future,188Diacritics of life,286Diameter, the ratio of, to the circumference,311-2Difference between concept and thing,121-2— between mathematical and perceptual space,120— between the ideal and the actual is dynamic,108Differential, among minds,124Difficulty of imagining the fourth dimension,90— of propagating an intuition,315Difficulties in the acquisition of real knowledge,325— of hyperspace, the logical,139-41Dilemma of metageometricians,97-8Dimension, 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,