eint schlagen. As science aims only to classify, predict and control phenomena, it has no absolute philosophic certainty except as a logical interpretation of the empirical facts of man's experience, and of the relative limitations of mathematical deduction and physical induction it has been well said that "the former breaks down on the subtlety of nature, the latter on its imperceptibility." Galileo's telescope, Leeuwenhoek's microscope, Lavoisier's balance, Kirchhoff's spectroscope, are doubtless of more practical value, but certainly not of more scientific importance than formal and symbolic logic, the calculus, determinants, quaternions, vector analysis or the improved formulation of dynamics. Without induction, it is true, no new facts; but without deductive methods there could be no interpretation of these facts, nor would scientists have the means of predicting other facts which go beyond experience, or of controlling phenomena. Yet an authority so open-minded as Professor Huxley, who seems to have confused mathematical methods with the scholastic reasoning and bigotry which opposed the great cause he championed, seldom lost an opportunity to say hard things about the science "which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." In Professor Sylvester's brilliant and memorable reply to some of Huxley's after-dinner denunciations, "the most eloquent of mathematicians" retorted upon his adversary that his chaffing might have been more guarded "had his speech been made before instead of after dinner," and went on to show that the maligned science employs not only imagination and invention, but observation and experiment at need. Even mathematicians, Sylvester pointed out, occasionally make discoveries, as witness Eisenstein's discovery of invariants, which was happened upon by purely physical observation "just as accidentally and unexpectedly as M. du Chaillu might meet a gorilla in the country of the Fantees." The touchstone of the matter lies in the one really telling remark that Huxley made about it, viz., that mathematics will not yield correct results if applied to erroneous data. The advance of modern science is largely bound up with the perfection of instruments of precision, and we have learned from the teaching of Lord Kelvin and the writings of Poincaré to recognize that mathematical
- "Lectures on the Method of Science," Oxford, 1905, 12.
- Huxley, "Lay Sermons," New York, 1871, 168.
- Ibid., 66.
- Nature, London, 1869-70, I., 237.
- Ibid., 238.
- "Mathematics may be compared to a mill of exquisite workmanship which grinds you stuff to any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat flour from peascods, so pages of formulae will not get a definite result out of loose data." Huxley, "Aphorisms and Reflections," London, 1907, 93.