-- 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