The triangles that we can measure are not large enough... to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe: ...a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space... from this outside point of view we might be able to perceive the curvature of the three-dimensional world.
Willem de SitterRelated topics
able curvature dimension enough given kind large might measure outside point real relativity space study three view wayRelated quotes
We have looked first at man with his vanities and greed and his problems of a day or a year; and then only, and from this biased point of view, we have looked outward at the earth he has inhabited so briefly and at the universe in which our earth is so minute a part. Yet these are the great realities, and against them we see our human problems in a different perspective. Perhaps if we reversed the telescope and looked at man down these long vistas, we should find less time and inclination to plan for our own destruction.
Rachel Carson
The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid Kantorovich
After experience had taught me that all the usual surroundings of social life are vain and futile; seeing that none of the objects of my fears contained in themselves anything either good or bad, except in so far as the mind is affected by them, I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else: whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness.
Baruch Spinoza
If every day a man takes orders in silence from an incompetent superior, if every day he solemnly performs ritual acts which he privately finds ridiculous, if he unhesitatingly gives answers to questionnaires which are contrary to his real opinions and is prepared to deny his own self in public, if he sees no difficulty in feigning sympathy or even affection where, in fact, he feels only indifference or aversion, it still does not mean that he has entirely lost the use of one of the basic human senses, namely, the sense of humiliation.
Václav Havel
The man who has struggled bravely with the passions of the body, has fought ably against unclean spirits, and has expelled from his soul the conceptual images they provoke, should pray for a pure heart to be given him and for a spirit of integrity to be renewed within him (cf. Ps. 51:10). In other words, he should pray that by grace he may be completely emptied of evil thoughts and filled with divine thoughts, so that he may become a spiritual world of God, splendid and vast, wrought from moral, natural and theological forms of contemplation.
Maximus the Confessor