On Observation (1850-1874)

"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space." (Charles Davies, "The Logic and Utility of Mathematics", 1850) 

"Every science consists in the coordination of facts; if the different observations were entirely isolated, there would be no science." (Auguste Comte, "Philosophy of Mathematics", 1851)

"In the fields of observation chance favors only the prepared mind." (Louis Pasteur, [Inaugural lecture], 1854)

"The progress of science has always been the result of a close interplay between our concepts of the universe and our observations on nature. The former can only evolve out of the latter and yet the latter is also conditioned greatly by the former. Thus, in our exploration of nature, the interplay between our concepts and our observations may sometimes lead to totally unexpected aspects among already familiar phenomena." (Tsung Dao Lee, [Nobel lecture for award received] 1957)

"When a power of nature, invisible and impalpable, is the subject of scientific inquiry, it is necessary, if we would comprehend its essence and properties, to study its manifestations and effects. For this purpose simple observation is insufficient, since error always lies on the surface, whilst truth must be sought in deeper regions." (Justus von Liebig," Familiar Letters on Chemistry", 1859) 

"Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer would always be in arrears, and were doomed forever to arrive at imperfect conclusion; but the power to perceive a law is equally rare in all ages of the world, and depends but little on the number of facts observed." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

"The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

"Exercising the right of occasional suppression and slight modification, it is truly absurd to see how plastic a limited number of observations become, in the hands of men with preconceived ideas." (Francis Galton, "Meteorographica" 1863)

"An anticipative idea or an hypothesis is, then, the necessary starting point for all experimental reasoning. Without it, we could not make any investigation at all nor learn anything; we could only pile up sterile observations. If we experiment without a preconceived idea, we should move at random […]" (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Men who have excessive faith in their theories or ideas are not only ill prepared for making discoveries; they also make very poor observations." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Observation is a passive science, experimentation an active science." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Only within very narrow boundaries can man observe the phenomena which surround him; most of them naturally escape his senses, and mere observation is not enough." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Facts can be accurately known to us only by the most rigid observation and sustained and scrutinizing skepticism […]" (James A Froude, Short Studies on Great Subjects Vol. 2, 1867)

"Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history."  (Lev N Tolstoy, “War and Peace”, 1867)

"Most, if not all, of the great ideas of modern mathematics have had their origin in observation." (James J Sylvester, A Plea for the Mathematician, Nature Vol. 1, 1869)

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts." (Louis Pasteur, "Étude sur la maladie des vers à soie", 1870)

"As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention." (James J Sylvester, "A Plea for the Mathematician", Nature Vol. 1, 1870)

"[Mathematics] is that [subject] which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"[…] wrong hypotheses, rightly worked from, have produced more useful results than unguided observation." (Augustus de Morgan, "A Budget of Paradoxes", 1872)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"Hence, even in the domain of natural science the aid of the experimental method becomes indispensable whenever the problem set is the analysis of transient and impermanent phenomena, and not merely the observation of persistent and relatively constant objects." (Wilhelm Wundt, "Principles of Physiological Psychology", 1874)

"Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show that its Method is the same: that, like other sciences, having observed or discovered properties, which it classifies, generalises, co-ordinates and subordinates, it proceeds to extend discoveries by means of Hypothesis, Induction, Experiment and Deduction." (George H Lewes, "Problems of Life and Mind: The Method of Science and its Application", 1874)

"When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. […] an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)