“Carefully observe oneself and one's situation, carefully observe others, and carefully observe one's environment”

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book III, Chapter I, Sec. 1

Vol. I, Ch. 10, as translated by R. B. Haldane
The World as Will and Representation (1819; 1844; 1859)
Context: Correct and accurate conclusions may be arrived at if we carefully observe the relation of the spheres of concepts, and only conclude that one sphere is contained in a third sphere, when we have clearly seen that this first sphere is contained in a second, which in its turn is contained in the third. On the other hand, the art of sophistry lies in casting only a superficial glance at the relations of the spheres of the concepts, and then manipulating these relations to suit our purposes, generally in the following way: — When the sphere of an observed concept lies partly within that of another concept, and partly within a third altogether different sphere, we treat it as if it lay entirely within the one or the other, as may suit our purpose.

Source: Persecution and the Art of Writing (1952), How to Study Spinoza's Theologico-Political Treatise, p. 144

Introduction à l'Étude de la Médecine Expérimentale (1865)

Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954)
Context: It will seem a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

Source: The Rise of Endymion (1997), Chapter 34 (p. 701)

Saanen, Switzerland (5 August 1973)
1970s
Context: Now, one sees all that by observing, by being aware, watching, one is aware of all this. Then out of that awareness you see there is no division between the observer and the observed. It is a trick of thought which demands security. Please don't madam, please. And by being aware it sees the observer is the observed, that violence is the observer, violence is not different from the observer. Now how is the observer to end himself and not be violent? Have you understood my question so far? I think so. Right? The observer is the observed, there is no division and therefore no conflict. And is the observer then, knowing all the intricacies of naming, linguistically caught in the image of violence, what happens to that violence? If the observer is violent, can the observer end, otherwise violence will go on? Can the observer end himself, because he is violent? Or what reality has the observer? Right sir? Is he merely put together by words, by experience, by knowledge? So is he put together by the past? So is he the past? Right? Which means the mind is living in the past. Right? obviously. You are living in the past. Right? No? As long as there is an observer there must be living in the past, obviously. And all our life is based on the past, memories, knowledge, images, according to which you react, which is your conditioning, is the past. And living has become the living of the past in the present, modified in the future. That's all, as long as the observer is living. Now does the mind see this as a truth, as a reality, that all my life is living in the past? I may paint most abstract pictures, write the most modern poems, invent the most extraordinary machinery, but I am still living in the past.