In the preceding section attention was called to the fact that every point p of the straight line produces a separation of the same into two portions such that every point of one portion lies to the left of every point of the other. I find the essence of continuity in the converse, i. e., in the following principle: "If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions." ...every one will at once grant the truth of this statement; the majority of my readers will be very much disappointed in learning that by this commonplace remark the secret of continuity is to be revealed.
Richard DedekindRelated topics
attention commonplace continuity fall find following grant learning left line once point second secret straight truth lies pointsRelated quotes
If my history lesson has done nothing else, it should have reminded you that, during any given period in the evolving history of physics, the prevailing, main line, climate of opinion was likely as not to be wrong, as seen in the light of later developments. And yet, in those earlier times, with relatively few individuals involved, change did occur, but slowly... What is fundamentally different in the present day situation in high energy physics is that large numbers of workers are involved, with corresponding pressures to conformity and resistance to any deflection in direction of the main stream, and that the time scale of one scientific generation is much too long for the rapid pace of experimental discovery. I also have a secret fear that new generations may not necessarily have the opportunity to become familiar with dissident ideas.
Julian Schwinger
A line cannot control pictorial space absolutely. A line may flow freely in and out space, but cannot independently create the phenomenon of push and pull necessary to plastic creation. Push and pull are expanding and contracting forces which are activated by carriers in visual motion. Planes are the most important carriers, lines and points less so.. .the picture plane reacts automatically in the opposite direction to the stimulus received; thus action continues as long as it receives stimulus in the creative process. Push answers with pull and pull with push. ... At the end of his life and the height of his capacity Cézanne understood color as a force of push and pull. In his pictures he created an enormous sense of volume, breathing, pulsating, expanding, contracting through his use of colors.
Hans Hofmann
I realise that 2008 will be an important test for Russia, and not an easy one. At the same time, the Constitution of the Russian Federation states that the President, the head of state, is elected for four years through direct secret ballot and cannot stay in office for more than two consecutive terms.
I am not indifferent of course to the question of who will take in their hands the destiny of the country I have devoted my life to serving. But if each successive head of state were to change the Constitution to suit them, we would soon find ourselves without a state at all. I think that Russia's different political forces are sufficiently mature to realise their responsibility to the people of the Russian Federation. In any case, the person who receives the votes of the majority of Russian citizens will become the President of the country.
Vladimir Putin
If Christ were to walk in this world today, do you know what would happen to Him? He would be placed in a mental institution and given psycho-therapy, just as would His Saints. The world would crucify Him today just as it did 2000 years ago, for the world has not learned a thing, except more devious forms of hypocrisy. And what would happen if, in one of my classes at the university, I would one day tell my students that all the learning of this world is of no importance beside the duty of worshipping God, accepting the God-man who died for our sins, and preparing for the life of the world to come? They would probably laugh at me, and the university officials, if they found out, would fire me-for it is against the law to preach the Truth in our universities. We say that we live in a Christian society, but we do not: we live in a society.
Seraphim Rose
The line of cleavage drawn on principle and conduct in public affairs is never in any healthy community identical with the line of cleavage between creed and creed or between class and class. On the contrary, where the community life is healthy, these lines of cleavage almost always run nearly at right angles to one another. It is eminently necessary to all of us that we should have able and honest public officials in the nation, in the city, in the state. If we make a serious and resolute effort to get such officials of the right kind, men who shall not only be honest but shall be able and shall take the right view of public questions, we will find as a matter of fact that the men we thus choose will be drawn from the professors of every creed and from among men who do not adhere to any creed.
Theodore Roosevelt