Just as mathematics was not always equally valued in antiquity, so, and much more so, after the Renaissance of learning, it was variously exalted or despised. Giordano Bruno satirised the abuse of it, and said that without physical science "to be able to calculate and measure, to understand geometry and perspective, is but a pastime of ingenious fools," and warned his readers against confusing mathematical "signs" and real "causes": "a reflected or direct ray, an acute or obtuse angle, a perpendicular, incident or straight line, a greater or smaller are of a circle, such and such an aspect, are mathematical circumstances and not natural causes. To play with geometry is one thing, to prove by means of nature is another. It is not lines and angles that make the fire more or less hot, but near and far situations, short and long spaces of time."[41] Campanella flatly denied Aristotle's assertion of the superiority of mathematics to physical science, declaring that its alleged purity was really weakness (_debilitas_), its simplicity was inability to include more things (_plura accipere_), its universality a contradiction against the nature of true science which is always of particulars (_de singularibus_), its demonstrative method by signs not by causes (_per signa, non per causas_); and finally that it is not a science investigated for its own sake and is valueless unless it is applied to physical matters (_nisi applicentur physicis rebus_).[42] Bacon is of the same opinion, that mathematics taken by itself is useless, and is useful only as an "auxiliary science," a "great appendix" to the physical sciences.[43] These definitions and restrictions, and others like them, might have yielded as a conclusion the entirely instrumental and practical character of mathematical science: but the conclusion was not drawn, so far as I know; and Bacon himself considered mathematics as in itself too exclusively and uselessly theoretical. "For since," he goes on in the passage above quoted, "it is a fact of human nature, no doubt to the great detriment of science, that it rejoices in the open plains of generalities, so to speak, rather than in the forests and closes of the particular, no discovery is more pleasant and gratifying than mathematics wherewith to sate this love of wandering and of meditation."