"If we say there is a limit - the ultimate atom - then, as all size is comparative, we can imagine a being to whom this atom seems as large as an apple or even a house does to us; and we then find it quite unthinkable that this mass of matter should be in its nature absolutely indivisible even by an infinite force. It follows that all explanations of phenomena can only be partial explanations. They can inform us of the last change or the last series of changes which brought about the actual conditions now existing, and they can often enable us to predict future changes to a limited extent; but both the infinite past and the remote future are alike beyond our powers. Yet the explanations that the theory of evolution gives us are none the less real and none the less important, especially when we compare its teachings with the wild guesses or the total ignorance of the thinkers of earlier ages." (Alfred R Wallace, "Evolution", The Sun, 1900)
"The state of a system at a given moment depends on two things - its initial state, and the law according to which that state varies. If we know both this law and this initial state, we have a simple mathematical problem to solve, and we fall back upon our first degree of ignorance. Then it often happens that we know the law and do not know the initial state. It may be asked, for instance, what is the present distribution of the minor planets? We know that from all time they have obeyed the laws of Kepler, but we do not know what was their initial distribution. In the kinetic theory of gases we assume that the gaseous molecules follow rectilinear paths and obey the laws of impact and elastic bodies; yet as we know nothing of their initial velocities, we know nothing of their present velocities. The calculus of probabilities alone enables us to predict the mean phenomena which will result from a combination of these velocities. This is the second degree of ignorance. Finally it is possible, that not only the initial conditions but the laws themselves are unknown. We then reach the third degree of ignorance, and in general we can no longer affirm anything at all as to the probability of a phenomenon. It often happens that instead of trying to discover an event by means of a more or less imperfect knowledge of the law, the events may be known, and we want to find the law; or that, instead of deducing effects from causes, we wish to deduce the causes." (Henri Poincaré, "Science and Hypothesis", 1902)
"Ignorance is visited as sharply as willful disobedience - incapacity meets with the same punishment as crime. Nature’s discipline is not even a word and a blow, and the blow first; but the blow without the word. It is left to you to find out why your ears are boxed." (Thomas H Huxley, "Science and Education: A Liberal Education; and Where to Find It", 1904)
"Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality." (Henri Poincaré, "The Value of Science", Popular Science Monthly, 1906)
"The method of solving problems by honest confession of one’s ignorance is called Algebra." (Mary E Boole, "Philosophy and Fun of Algebra", 1909)
"Chance is only the measure of our ignorance." (Henri Poincaré, "The Foundations of Science", 1913)
"Whatever the progress of human knowledge, there will always be room for ignorance, hence for chance and probability." (Emile Borel, Le hasard [Chance], 1914)
"[…] science deals with but a partial aspect of reality, and there is no faintest reason for supposing that everything science ignores is less real than what it accepts. [...] Why is it that science forms a closed system? Why is it that the elements of reality it ignores never come in to disturb it? The reason is that all the terms of physics are defined in terms of one another. The abstractions with which physics begins are all it ever has to do with." (John W N Sullivan, "The Limitations of Science", 1915)
"Ignorance may find a truth on its doorstep that erudition vainly seeks in the stars." (George Iles, "Canadian Stories", 1918)
"In regions where our ignorance is great, occasional guesses are permissible." (Sir Oliver Lodge, "On the Supposed Weight and Ultimate Fate of Radiation", Philosophical Magazine Vol. 41, 1921)
"There are no rival hypotheses except the outworn and completely refuted idea of special creation, now retained only by the ignorant, the dogmatic, and the prejudiced." (Horatio H Newman, "Evolution, Genetics, and Eugenics", 1921)
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