Intuitional consciousness, 255 -- the superiority of, over the rational, 187 Intuitions and the lead of life, 191 -- -- -- Thinker, 27 -- free, mobile and formless, 166 -- the conceptualization of, 248 -- -- humility of, 165 -- -- nature of, 185 Intuitograms, as concepts, 248 Intuitograph as means of contacting the egopsychic consciousness by the Thinker, 10 -- as super-concepts, 255 -- the difficulty of transmitting, 315 Invariability, the vaunted, of the laws of mathesis, 37 Invariants, psychological, 24 Investigations, metageometrical, and the new sense-organs, 354 Involution, as antithesis of evolution, 10-11 -- kosmic involution, 226 -- of matter, 328 -- the movement of, 219 -- -- seven stages of, 208-12 Ions, creation of, 219 -- magnitude of a hydrogen ion, 225 J Judgments _a priori_, Kant on, 85-6 -- and the faculty _a priori_, 190-1 -- -- zones of affinity, 124 -- based upon a replica of consciousness, 205 -- no trustworthy, can be predicated upon fragmentary knowledge, 282 -- of the intellect, 302 -- the lessening of error in, 256 -- -- more complex the more at variance with the nature of things, 75 -- -- synthesis of, 257-8 -- valid judgments long delayed, 170-1 Judicative power of mathematics, 180 Justification for a multi-dimensional quality in space, 262 -- of four-dimensionality, 176 Justification of sense-deliveries by one another, 76 -- -- the existence of the fourth dimension, 125 K Kant, 85, 181, 182, 322 -- and the faculty of thinking, 261 -- -- -- idea of space, 322-3 -- influence of, on the hyperspace movement, 49-50 -- on the nature of things, 119 -- -- space as an intuition, 115 Kathekos, 233-4 -- as chaos, 266 -- -- symbol of Chaos-Theos-Kosmos, 11-12 -- symbology of, 234 Kathekosis, _note_, 227 Kathekosity, fringe of, 229 -- rock-bound coast of, 267 -- significance of, 12 Kathekotic consciousness, 272 -- period, 209 Key to the mysteries of nature, the fourth dimension as, 131 Keyser, Cassius Jackson, and freedom of the mind, 33 -- -- -- on attitude of metageometricians, 71 -- -- -- -- dimensionality, 94-5 -- -- -- -- four-dimensionality of space, 142-3 -- -- -- -- generability of hyperspace, 144 Klein, Felix, 12, 54-5, 66-7 Knowledge, all, relative, 101 -- barrier to the certitude of the Thinker's, 186-7 -- fabric of, 196 -- hypothetical nature of, 189, _ff_ -- immeasurable realm of, laid bare by the telescope, 298 Knowledge, mathematical, apriority of, questioned, 37 -- nature of the non-Euclidean, superperceptual, 72 -- real, difficulties of acquiring, 325 -- related to the stream of life and to the shore of materiality, 323 -- relative, degrees exist for, 164 -- sphere of, 184 -- systematization of, 126 -- ultimate, consciousness as a barrier to, 207 -- unification of, 256