Chapter XX (part 1)

p. 243 CHAPTER XX The sense of infinity. The Neophyte's first ordeal. An intolerable sadness. The loss of everything real. What would an animal feel on becoming a man? The transition to the new logic. Our logic as founded on the observation of the laws of the phenomenal world. Its invalidity for the study of the world of noumena. The necessity for another logic. Analogy between the axioms of logic and of mathematics. TWO MATHEMATICS. The mathematics of real magnitudes (infinite and variable): and the mathematics of unreal, imaginary magnitudes (finite and constant). Transfinite numbers—numbers lying beyond INFINITY. The possibility of different infinities. THERE is in existence an idea which a man should always call to mind when too much subjugated by the illusions of the reality of the unreal , visible world in which everything has a beginning and an end. It is the idea of infinity, the fact of infinity. In the book A New Era of Thought —concerning which I have had already much to say—in the chapter "Space the Scientific Basis of Altruism and Religion," Hinton says: . . . When we come upon infinity in any mode of our thought, it is a sign that that mode of thought is dealing with a higher reality than it is adapted for, and in struggling to represent it, can only do so by an infinite number of terms (of realities of a higher order). Truly what is infinity, as the ordinary mind represents it to itself? It is the only reality and at the same time it is the abyss, the bottomless pit into which the mind falls, after having risen to heights to which it is not native. Let us imagine for a moment that a man begins to feel infinity in everything: every thought, every idea leads him to the realization of infinity. This will inevitably happen to a man approaching an understanding of a higher order of reality. But what will he feel under such circumstances? p. 244 He will sense a precipice, an abyss everywhere, no matter where he looks; and experience indeed an incredible horror, fear and sadness, until this fear and sadness shall transform themselves into the joy of the sensing of a new reality. ". . . An intolerable sadness is the very first experience of the Neophyte in occultism. . . ." says the author of Light on the Path . We have already examined into the manner in which a two-dimensional being might approach to a comprehension of the third dimension. But we have never asked ourselves the question: what would it feel , beginning to sense the third dimension, beginning to be conscious of "a new world" environing it? First of all, it would feel astonishment and fright—fright approaching horror; because in order to find the new world it must lose the old one. _____ Let us imagine the predicament of an animal in which flashes of human understanding have begun to appear. What will it sense first of all? First of all, that its old world, the world of the animal , its comfortable, habitual world, the one in which it was born, to which it has become accustomed, and which it imagines to be the only real one, is crumbling away and falling all around it. Everything that before seemed real, becomes false, delusive, fantastic, unreal. The impression of the unreality of all its environment will be very strong. Until such a being shall learn to comprehend the reality of another, higher order, until it shall understand that behind the crumbling old world one infinitely more beautiful and new is opening up, considerable time will necessarily pass. And during all this time, a being in whom this new consciousness is in process of unfoldment must pass from one abyss of despair to another, from one negation to another. It must repudiate everything around itself.