"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth." (Galileo Galilei, "The Assayer", 1623)
"Time is the order of existence of those things which are not simultaneous. Thus time is the universal order of changes when we do not take into consideration the particular kinds of change. Duration is magnitude of time. If the magnitude of time is diminished uniformly and continuously, time disappears into moment, whose magnitude is zero. Space is the order of coexisting things, or the order of existence for things which are simultaneous." (Gottfried W Leibniz, "Initium rerum Mathematicarum metaphysica", 1715)
"It is also only by virtue of the continual action of God upon us that we have in our soul the ideas of all things; that is to say, since every effect expresses its cause, the essence of our soul is a certain expression, imitation or image of the divine essence, thought, and will and of all the ideas which are comprised in God." (Gottfried W Leibniz, "Discourse on Metaphysics", 1686)
"There are two aspects of statistics that are continually mixed, the method and the science. Statistics are used as a method, whenever we measure something, for example, the size of a district, the number of inhabitants of a country, the quantity or price of certain commodities, etc. […] There is, moreover, a science of statistics. It consists of knowing how to gather numbers, combine them and calculate them, in the best way to lead to certain results. But this is, strictly speaking, a branch of mathematics." (Alphonse P de Candolle, "Considerations on Crime Statistics", 1833)
"The man who is guided by concepts and abstractions only succeeds by such means in warding off misfortune, without ever gaining any happiness for himself from these abstractions. And while he aims for the greatest possible freedom from pain, the intuitive man, standing in the midst of a culture, already reaps from his intuition a harvest of continually inflowing illumination, cheer, and redemption - in addition to obtaining a defense against misfortune. To be sure, he suffers more intensely, when he suffers; he even suffers more frequently, since he does not understand how to learn from experience and keeps falling over and over again into the same ditch." (Friedrich Nietzsche," On Truth and Lie in an Extra-Moral Sense", 1873)
"[…] the statistical prediction of the future from the past cannot be generally valid, because whatever is future to any given past, is in tum past for some future. That is, whoever continually revises his judgment of the probability of a statistical generalization by its successively observed verifications and failures, cannot fail to make more successful predictions than if he should disregard the past in his anticipation of the future. This might be called the ‘Principle of statistical accumulation’." (Clarence I Lewis, "Mind and the World-Order: Outline of a Theory of Knowledge", 1929)
"In time they [physicists] hoped to devise a model which would reproduce all the phenomena of physics, and so make it possible to predict them all. […] To-day we not only have no perfect model, but we know that it is of no use to search for one - it could have no intelligible meaning for us. For we have found out that nature does not function in a way that can be made comprehensible to the human mind through models or pictures. […] Although we can never devise a pictorial representation which shall be both true to nature and intelligible to our minds, we may still be able to make partial aspects of the truth comprehensible through pictorial representations or parables. As the whole truth does not admit of intelligible representation, every such pictorial representation or parable must fail somewhere. The physicist of the last generation was continually making pictorial representations and parables, and also making the mistake of treating the half-truths of pictorial representations and parables as literal truths." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)
"Above all, we see from these formulations how difficult it is when we try to push new ideas into an old system of concepts belonging to an earlier philosophy, or, to use an old metaphor, when we attempt to put new wine into old bottles. Such attempts are always distressing, for they mislead us into continually occupying with the inevitable cracks in the old bottles, instead of rejoicing over the new wine." (Werner K Heisenberg, "Physics and Philosophy: The Revolution in Modern Science", 1958)
"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)
"One cannot ‘invent’ the structure of an object. The most we can do is to patiently bring it to the light of day, with humility - in making it known, it is ‘discovered’. If there is some sort of inventiveness in this work, and if it happens that we find ourselves the maker or indefatigable builder, we are in no sense ‘making’ or ’building’ these ‘structures’. They have not waited for us to find them in order to exist, exactly as they are! But it is in order to express, as faithfully as possible, the things that we have been detecting or discovering, the reticent structure which we are trying to grasp at, perhaps with a language no better than babbling. Thereby are we constantly driven to ‘invent’ the language most appropriate to express, with increasing refinement, the intimate structure of the mathematical object, and to ‘construct’ with the help of this language, bit by bit, those ‘theories’ which claim to give a fair account of what has been apprehended and seen. There is a continual coming and going, uninterrupted, between the apprehension of things, and the means of expressing them by a language in constant state improvement [...].The sole thing that constitutes the true inventiveness and imagination of the researcher is the quality of his attention as he listens to the voices of things." (Alexander Grothendieck, "Récoltes et semailles –Rélexions et témoignage sur un passé de mathématicien", 1985)
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