-- a monument to the intellect, 356 -- and the involved procedure of arriving at a recognition of its relations, 73 -- and the passage thither, 293, _ff_ Hyperspace as a figurative mountain-peak, 200 -- -- -- movement, 44-68 -- -- an all-powerful something, 160 -- -- -- idealized construction, 10 -- -- evidence of new faculties, 24 -- -- _ignes fatuii_, 154 -- -- illusion, 202 -- a symbol of higher consciousness, 180-4 -- concept of, as an evolutionary quantity, 44-5 -- confounded with real space, 91 -- creation of, 335 -- denied the corroborative testimony of experience, 263 -- direction of, baffling to mathematicians, 146 -- discovery of, a sign of mental evolution, 180 -- domain of, a fairy-land, 239 -- magnitudes of, the non-sensuous, 72 -- mysterious hiding place in, 129 -- the logical difficulties of, 139-141 -- the six pillars of, 62-3 Hyperspatiality as the toys of childhood, 241 Hypertetrahedron, the, 135 Hypertrophy of the pituitary body, 347 Hypervolume, the, 134 Hypothesis, a superfoetated, 141 -- four-space, utility of, 129; 154 Hypotheses, admissibility of, 118 -- incompatibility of the non-Euclidean, 67; 71 -- Riemannian, 80 -- solution of, Bolyai, 31 Hyslop, James H., on the logical difficulties of hyperspace, 139-141 I Icosahedron, examination of the, 285 Ideal, and the real, kosmic chasm between, 107 -- perceptual value of, 275, _ff_ Ideas and words as symbols, 126-7 -- Malebranche on, 222 -- realism of, 24-35 -- the symbolism of, 205 Identification of consciousness with being, 205-6 -- with the objects of study, 189-90 Identity of things-in-themselves, 353 _Ignes fatuii_ and hyperspaces, 154 Illustration of plane-rotation, 148-150 -- -- the tesseract, 133 Images, totality of, recoils upon us, 167 Imaginability of the fourth dimension, 90, 106-7 Imagination, premises of, the mathematical, 146 Impossibility of plane-rotation, the structural, 151-3 Impressions, the symbolism of, neurographic, 186 Impulse, the satisfaction of the original creative, 310-1 Incomprehensibility of reality to the intellect, 126 Incongruity, life estranged by a radical, 325 Individual as space, 223 Ineptitude of intellectual determinations for vitality, 314 Infinite, interpreted in the terms of the finite, 82 Infinitesimals of unity, numbers as, 41 Infinity as a process, 109 -- of becomings, 234 Infinity of parallels through a given point, 70 -- -- space, a capital illusion, 195 -- the concept of, 277 -- -- innate dread of, 103 -- -- relativity of, 194 Influence of abstract thought, 33 -- -- Kant on the non-Euclidean geometry, 49-50 -- -- La Grange, 51-2 -- -- the intellect, 315 Infundibulum, the, 345 Inner organs of perception, 352 Innermost, the, realities of things, 356 _Insouciance_ of the geometer, 96, 294