The Mystery of Space: A Study of the Hyperspace Movement in the Light of the Evolution of New Psychic Faculties and an Inquiry Into the Genesis and Essential Nature of Space

Paul, 1919 - 395 sider
Mathematics is the biometer of intellectual evolution. Hence, the determination of the status quo of the intellect at any time can be accomplished most satisfactorily by applying to it the rigorous measure of the mathematical method. The intellect has but one true divining rod and that is mathematics. By day and by night it points the way unerringly, so long as it leads through materiality; but, falteringly, blindly, fatally, when that way veers into the territory of vitality and spirituality. Wherefore, when we have wished to ascertain the real status of the intellect, as well as its limitations, tendencies, possibilities, we have turned to its conduct in the field of mathesis where it is least trammeled in its ingressive and egressive motivations because of the natural and easy accommodation which is offered for intellectual movement. Whether there are signs of moribundity or symptomatic evidences of marked growth or of a termination of intellectual regnancy, or whatever may be the occasion for the examination, no surer index than the mathematical may be found for the purpose. Full logical justification is, therefore, claimed for the choice of mathematical evidences to test the assumption that a new era of conscious mental conquest is opening for the vanguard of humanity and sequently for the human family.

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Side 52 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 47 - ... immediately on intuition, and indeed on pure and a priori intuition, because it is apodeictically certain. That we can require a line to be drawn to infinity (in indefinitum) , or that a series of changes (for example, spaces traversed by motion) shall be infinitely continued, presupposes a representation of space and time, which can only attach to intuition, namely, so far as it in itself is bounded by nothing, for from concepts it could never be inferred.
Side 14 - If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.
Side iii - The mystery of space. A study of the hyperspace movement in the light of the evolution of new psychic faculties and an inquiry into the genesis and essential nature of space.
Side 31 - Let the words of my mouth, and the meditation of my heart, be acceptable in thy sight, O Lord, my strength, and my redeemer.
Side 339 - The boundary between the two states — the known and the unknown — is still substantial, but it is wearing thin in places; and like excavators engaged in boring a tunnel from opposite ends, amid the roar of water and other noises, we are beginning to hear now and again the strokes of the pickaxes of our comrades on the other side.
Side ii - Indeed, the domain of the senses in Nature is almost infinitely small in comparison with the vast region accessible to thought which lies beyond them. From a few observations of a comet, when it comes within the range of his telescope, an astronomer can calculate its path in regions which no telescope can reach; and in like manner, by means of data furnished in the narrow world of the senses, we make ourselves at home in other and wider worlds, which...
Side 31 - ... in them it lives ever joyously, sustained by an unfailing sense of infinite freedom.
Side 57 - There is a two-fold geometry — a geometry in the narrower sense, the Euclidean, and an astral science of magnitude. "The triangles of the latter have the peculiarity that the sum of the three angles is not equal to two right angles. "This presumed, it can be most rigorously proven: (a) That the sum of the three angles in the triangle is less than two right angles. "(b) That this sum becomes ever smaller, the more content the angle...
Side 1 - I can not say more, only so much: that from nothing I have created another wholly new world. All that I have hitherto sent you compares to this only as a house of cards to a castle.

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