Measurement of hyperspaces, the science of,73Measurements, space determined by the number of,61— systems of space,91Measurer of space,n-dimensionality as a,296-7Mecanique Analytique,50-1,321Mechanics of matter, the passage from, to the dynamics of life,326— to biogenetics, the passage from357— the turning from, to biogenetics,322,ffMechanism, the doctrine of, due to analytics,40Memories, stored in the omnipsyche,258Men as gods,289Mental evolution, determinative period of,31— — elaborative period of,31-32— — formative period of,31Mentality, inner mysteries of creative,91— infantile out-feelings of the,336— the principle of,210,ffMentalities, the adaptation of phenomena to,184Mentograph, the,121— the basis of intellectual consciousness,13Mesozoic man and his environments,347-8Metageometrical investigations and the new sense-organs,354Metageometricians 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,263Metageometry, as a stepping stone,238— defined,13— Riemann, the father of,63— the fabric of,66Metamorphosis of matter by life,328— of the monopyknon,214Metamorphotic stage of space-genesis,228Metaphysician, the preserves of, usurped by mathematicians,141Meta-self as medium of kosmic consciousness,13,217Methods of the ego,344— scientific, and the ample explication of phenomena,154Mikrokosmic consciousness,270Mind, 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,224Mind-principle, the quintopyknon as the basis of,221,ffMirrors, three, and the hypercube,136-8Mobility, life as,264Molecule, the four-dimensional, Newcomb on,159Monadic phase of evolution,210-1Moneron and man, the gulf between,28Monopyknon, the,213,216Monopyknosis, defined,17,208-10,218Monstrosities, mathetic,202Moods of the kosmos,311Morphogeny,13,233-4Morphons, the creation of,219Motility, the scope of,131Movement, forward, in knowledge,336— hyperspace as an evolutionary,44-68— — influence of Kant on,49-50— of life in chaos,307Multi-dimensional quality of space, justification for,262Multiplication of hypotheses,118Mutuality, intuition as promoter of,301,ffMysteries, inner, of creative mentality,91— kosmic, low-lying plains of,239--- of life and mind,326— — the sciences and the four-space operator,131Mystery, kosmic, the revelation of, foreshadowed in manifold,77— of reaction,167-8— — space decreases as copes of consciousness increases,273,ffNn-Coördinates,203n-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,158n-Space, imperceptibility of,94Nasir-Eddin,46,53Natural symbols, ideas as,126Nature, representative, of things,119— the vacuum-stillness of,339Naughttounity, consciousness registers from,165Near-truth,300,ff— as variation from criterion of truth,324— based upon partial knowledge,14— space-curvature as a,306— space-manifold as a,318Nebulosity,267Necessity, as a bulwark of geometry,77-8Nerve-body, the,349Neurogram,14Neurograph, the Thinker's scrutiny of,190Neurographical communications,244Newcomb, Simon,14-5,66— — and the four-dimensional molecule,159— — on the fourth dimension,125Non-Euclideans and the meaning of dimension,97— — things as they actually are,71— dilemma of,86— meaning of the term,69— results obtained by,88Non-manifestation, as antithesis of manifestation,106— and manifestation,206Non-methodic advancement of human consciousness,299Non-spatiality, cut off from spatiality,266Norm, as a value assigned by the intellect,167— consciousness as a,15;161-202— of life, found by synthesis,300— — the natural geometry,263Note, the dominant, of communality,301Notions of space, triple presentations to the consciousness,72Number, as a phase of kosmogenesis,309— numbers as infinitesimals of unity,41Numericity of being,309OObjects and ideas,126-7— passage of, into the fourth dimension,130— of study, identification of consciousness with,189Obliquity, perceptual, of metageometricians,102Obscurantism, mathetic,154Occultist and the scientist,350Omnipsyche,265— as agency of kosmic consciousness,258— — neglected factor of evolution,259— defined,15One-space represented by a line,134Ontogeny recapitulates phylogeny,27,334Order, kosmic, the difference between, and hyperspace,143— mathematical, discovered by the intellect,261— the fiat of,208— the totality of,265Orderliness,266Organ, determined by function to be performed,336Organs broken up by life into special parts,343— the evolution of,188Orthodoxy of mathematics,34Outcome of new adjustments,256Out-feelings of the Thinker, infantile,336Outlook, the spiritualization of our mental,40PPapyrus, a hieratic,44Parallel-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,47Parallels, convergence of,80— infinity of, through a given point,70— meet at infinity,88— theory of,47-9Passage from mechanics to biogenetics,357— from mechanics to dynamics,326— from three-space to four-space,292-3— of mathetic contrivances,241— of space,16,297Pathway of life, sinuosities in,330Patterns of the intellect, ready-made,166Pentagrammaton of space,237Perceptibility in the Thinker, the faculty of,188Perception, domain of, and the sensible world,19— inner organs of,352— replaced by conception,255Percepts, and the ego,244Period, chaomorphogenic,208,ff— determinative,61-5— kathekotic,210Perisophical nature of analytics,320,ffPerisophism, a,300Permissibility of mathetic license, unlimited,38Perpendicularity,132,177— of lines in the four-space,130Phantasy and reality, line of demarkation between,173— the world of,146Phantom-ideal, the,277Phase of the world age, evolutionary,209Phenomena, 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,154Phenomenal, the inverse of realism,278Philosophy and the criterion of truth,323-4— regeneration of,358— systems of, and zones of affinity,124Phosphorescence, dim, added to the unilluminated pool of sense-consciousness by the intuition,26Phylogeny and ontogeny,334— represented in ontogeny,27Physical as embodiment of all possibilities,227— phenomena as space-activities,229Physicality, the principle of,210,ffPhysics of the brain,292Piproportion, significance of,311-2Pickering on space-curvature,279Pineal gland, energized by the pituitary body,348-9— — the,344,ff— — not a vestigal organ,354Pituitarial awakening, general results of,355-8Pituitary body and the Thinker,351— — as an organ,344-352— — C. De M. Sajous on,345— — hypertrophy of,347— — location of,246— — the,344,ffPlane, 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,212Planes, a cube as a succession of,148-9Plasm, kosmic, strivings of,215— psychic,260— the differentiation of,214Plato,322— and the divine geometry,193,237— — — shadow consciousness,281— on God as geometrizer,181— — ideas,34Play, sensuous, of the intellect,295Plenum, space as a,230— the universe as a,107Poincairé,90Point, an infinity of parallels through a given,70— as generating element,144— position of,132— succession of points, a line as,148Polarity between concrete and abstract,294-5Ponderability, as property of hyperspace,63Popularization of the fourth dimension,128— of the non-Euclidean geometry,66-7Possibilities in the world of hyperspace,129— of four-space, the marvelous,130Postulate-systems, the multiplication of,85Powers of mind, not attained at one and the same time,334Pralaya,213— as kosmic quietude,17Predicates, all mathematical, not justified by the phenomenal,128Principle, ensouling,214-5Printing press, the invention of, and the laws of psychogenesis,30Problem, the fourth dimension as a transcendental,140Procedure, the involved, of arriving at hyperspace notions,73Process, evolution a continuous,327— space as a dynamic,307Proclus,83Profundities, kosmic, and hyperspace,156Progression eastward terminates at the west,306Proof of rotation about a plane,146-151Propagation of intuitographs, difficulty of,315Propositions, geometric, subjunctive quality of,38Pseudosphere and the shape of space,70— as basis of Beltrami's calculations,17— the nature of,64-5Psychics of consciousness,292— transmuted,260Psychogenesis, alchemy of,225— kosmic,272— laws of, and the printing press,30,116Psychogenesis, mind's place in,123— outgrown phase of,302— outstanding facts of,131Psychogeny, defined,17Ptolemy,45,52,83Publicist, the mathematical, and the duodim,128— the non-Euclidean,146Pyknon as a kosmic principle,212— — basis of space-genesis,17Pyknosis,212— and involution,210,231— as a metamorphotic process,214— the seven processes of,17,294QQuality, dimension as commensurable,140Quantities, algebraic, cannot represent space,125-7Quantity, consciousness as a tri-space,172Quartodim,18,134Quartodimensionality,292Quartopyknosis,17,208-10Quartopyknotic, principle as basis of spirituality,228Quintopyknon,220Quintopyknosis and thea priori,223— meaning of,17,208-10Quintopyknotic principle as basis of mentality,228RRace, humanity to evolve a new,358— resplendent,338Rajah-Tamas,220Rajah Yoga,357Rational, valueless when unsanctioned by the intuition,187Reaction, as a mystery,167-8Real, Thinker as a part of the,201Realism 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,172Realities, abstractionizing,144,294— incomprehensible to the intellect,126— innermost, of things,356— lesser give way to greater,195— natural symbolism of,