Significance Quotes - page 6
Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i.e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.
Hans Reichenbach
The answer is in the problem, not away from the problem. I go through the searching, analysing, dissecting process, in order to escape from the problem. But, if I do not escape from the problem and try to look at the problem without any fear or anxiety, if I merely look at the problem - mathematical, political, religious, or any other - and not look to an answer, then the problem will begin to tell me. Surely, this is what happens. We go through this process and eventually throw it aside because there is no way out of it. So, why can't we start right from the beginning, that is, not seek an answer to a problem? - which is extremely arduous, isn't it? Because, the more I understand the problem, the more significance there is in it. To understand, I must approach it quietly, not impose on the problem my ideas, my feelings of like and dislike. Then the problem will reveal its significance. Why is it not possible to have tranquillity of the mind right from the beginning?
Jiddu Krishnamurti
A great chapter of the history of the world is written in the chalk. Few passages in the history of man can be supported by such an overwhelming mass of direct and indirect evidence as that which testifies to the truth of the fragment of the history of the globe, which I hope to enable you to read, with your own eyes, tonight.
Let me add, that few chapters of human history have a more profound significance for ourselves. I weigh my words well when I assert, that the man who should know the true history of the bit of chalk which every carpenter carries about in his breeches-pocket, though ignorant of all other history, is likely, if he will think his knowledge out to its ultimate results, to have a truer, and therefore a better, conception of this wonderful universe, and of man's relation to it, than the most learned student who is deep-read in the records of humanity and ignorant of those of Nature.
Thomas Henry Huxley
You see, the thing is, I've been in jams like this. The feeling is totally there among the musicians (and whoever else happens to be sitting around, whether they've paid for it or not, probably, and preferably, not). You are close to silence, Silence with a capital S. You are in tune with silence, the deepest sound of them all. Every sound, therefore, that you make, make with intention, sensitivity, and awareness, has a meaning, an ineffability, a significance. You are listening, Listening with a capital L. You hear what everyone else is doing; you do whatever is necessary, which is usually as little as possible. It has nothing to do with self-expression: it has to do with a group mind.
Robert Fripp
I rejoice to hear that you have begun Homer's Iliad; and have made so great a progress in Virgil. I hope you taste and love those authors particularly. You cannot read them too much: they are not only the two greatest poets, but they contain the finest lessons for your age to imbibe: lessons of honour, courage, disinterestedness, love of truth, command of temper, gentleness of behaviour, humanity, and in one word, virtue in its true significance.
William Pitt, 1st Earl of Chatham