In enlisting the aid of reason in our quest for freedom, we shall be following in the footsteps of mathematicians and theoretical physicists. In their arduous and unflinching search after truth they have attained to a conception of the background of phenomena of far greater breadth and grandeur than that of the average religionist of to-day. As a mathematician once remarked to a neo-theosophist, "Your idea of the ether is a more material one than the materialist's own." Science has, however, imposed upon itself its own limitations, and in this connection these should be clearly understood. Science is that knowledge which can be gained by exact observation and correct thinking. If science makes use of any methods but these it ceases to be itself. Science has therefore nothing to do with morals: it gives the suicide his pistol, the surgeon his life-saving lance, but neither admonishes nor judges them. It has nothing to do with emotion: it exposes the chemistry of a tear, the mechanism of laughter; but of sorrow and happiness it has naught to say. It has nothing to do with beauty: it traces the movements of the stars, and tells of their constitution; but the fact of their singing together, and that "such harmony is in immortal souls," it leaves to poet and philosopher. The timbre, loudness, pitch, of musical tones, is a concern of science; but for this a Beethoven symphony is no better than the latest ragtime air from the music halls. In brief, science deals only with _phenomena_, and its gift to man is power over his material environment. MATHEMATICS The gift of pure mathematics, on the other hand, is primarily to the mind and spirit: the fact that man uses it to get himself out of his physical predicaments is more or less by the way. Consider for a moment this paradox. Mathematics, the very thing common sense swears by and dotes on, contradicts common sense at every turn. Common sense balks at the idea of _less than nothing_; yet the _minus_ quantity, which in one sense is less than nothing in that something must be added to it to make it equal to nothing, is a concept without which algebra would have to come to a full stop. Again, the science of quaternions, or more generally, a vector analysis in which the progress of electrical science is essentially involved, embraces (explicitly or implicitly) the extensive use of _imaginary_ or _impossible_ quantities of the earlier algebraists. The very words "imaginary" and "impossible" are eloquent of the defeat of common sense in dealing with concepts with which it cannot practically dispense, for even the negative or imaginary solutions of imaginary quantities almost invariably have some physical significance. A similar statement might also be made with regard to _transcendental_ functions.