A Quote by Georg C. Lichtenberg
In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.
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This harmony that human intelligence believes it discovers in nature - does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that which is common to several thinking beings, and could be common to all; this common part, we will see, can be nothing but the harmony expressed by mathematical laws.
We feel certain that the extraterrestrial message is a mathematical code of some kind. Probably a number code. Mathematics is the one language we might conceivably have in common with other forms of intelligent life in the universe. As I understand it, there is no reality more independent of our perception and more true to itself than mathematical reality.
When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as well to express them so -- translating them out of their hieroglyphics that we might also work upon them by experiment?
Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
Our common language is English. And our common task is to ensure that our non-English-speaking children learn this common language.
So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality.
This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.
Law grows, and though the principles of law remain unchanged, yet (and it is one of the advantages of the common law) their application is to be changed with the changing circumstances of the times. Some persons may call this retrogression, I call it progression of human opinion.
Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.
In animation, what's wonderful is that when you start to work with multiple nationalities, the common language becomes a visual language rather than a spoken language, which blends beautifully with the art form.
We have found that companies need to speak a common language because some of the suggested ways to harness disruptive innovation are seemingly counterintuitive. If companies don't have that common language, it is hard for them to come to consensus on a counterintuitive course of action.
You are frightened of everything. You call it caution. You call it common sense. You call it practicality. You call it playing the odds, but that's only because you're afraid to call it by its real name, and its real name is fear.
We are all American. If we believe that we are Americans, if we believe that what binds us together is what we have in common, then it must include the common language, and that common tongue is English.
We should replace bilingual education with immersion in English so people learn the common language of the country and they learn the language of prosperity, not the language of living in a ghetto.
Great art speaks a language which every intelligent person can understand. The people who call themselves modernists today speak a different language.
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