Manifold Quotes - page 3
The main object of study in differential geometry is, at least for the moment, the differential manifolds, structures on the manifolds (Riemannian, complex, or other), and their admissible mappings. On a manifold the coordinates are valid only locally and do not have a geometric meaning themselves.
Shiing-Shen Chern
The peace that passeth understanding is that which comes when the pain is not relieved, which subsists in the midst of the painful situation, suffusing it, which springs out of the pain itself, which shimmers on the crest of the wave of pain, which is the spear of frustration transfigured into the shaft of light. It is upon those we love that we must anchor ourselves spiritually in the last moments. The sense of interconnectedness with them stands out vividly by way of contrast at the very moment when our mortal connection with them is about to be dissolved. And the intertwining of our life with theirs, the living in the life that is in them, is but a part of our living in the infinite manifold of the spiritual life. The thought of this, as apprehended, not in terms of knowledge, but in immediate experience, begets the peace that passeth understanding. And it is upon the bosom of that peace that we can pass safely out of the realm of time and space.
Felix Adler
There is no lack of diagnoses of the manifold ills that beset the international order, coherent and even convincing diagnoses by foremost think tanks, universities and outstanding individual researchers all over the world. Obstacles to an improved world order are evident, but remedies do not materialize. Is it because the real power no longer resides in States and Governments but rather in the economy, the intelligence community, the military-industrial and financial-industrial complexes, which are neither democratic nor transparent and operate impervious to reasons other than power or profit? The answers are complex and require further research, which may contribute to future reports on the vast menu of General Assembly resolution 67/175.
Alfred de Zayas
In a stroke of imaginative genius our understanding of consciousness was radically transformed, but in an entirely unexpected way. Critical clues came from diffuse nerve nets and, even more extraordinarily, plant neurobiology. Banished forever was the idea that the brain alone was the seat of consciousness. Rather, it is an 'antenna' embedded in a hyperdimensional matrix. The depths of reality are only now being uncovered, but now the springs of imagination, intuition, abstraction and even pre-cognition are revealed. What was once called the unreasonable effectiveness of mathematics was simply a clue to a superbly structured universe where mind is an integral component, instantiated at the big bang or maybe even before? Future exploration offers dizzying prospects, but we are not the first to venture forth. Far in advance of the emergence of human consciousness, innumerable galactic civilisations had slipped into what we now call the Mortimer Manifold.
Simon Conway Morris
If the miser reaches the point of sacrificing his health, his pleasures, and even his very honesty for the love of his money, shall we not succeed in learning to love so noble an aim as intellectual work sufficiently to make us sacrifice our laziness for a few hours every day? ... Should not our young people therefore spend at least five hours a day at their work-table in order to assure for themselves, both now and in the future, the manifold joys of intellectual culture?
Jules Payot
In classical Newtonian physics there was a clear understanding of 'what reality is'. Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in 'the present'. Often it is stated that three dimensional space and one dimensional time have been substituted by four dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that what is 'present', cannot be retained. Is reality then the four dimensional manifold of relativity theory? And if so, what is then the meaning of 'change in time'?
Diederik Aerts
If speculation tends thus to a terrific unity, in which all things are absorbed, action tends directly back to diversity. The first is the course or gravitation of mind the second is the power of nature. Nature is manifold. The unity absorbs, and melts or reduces. Nature opens and creates. These two principles reappear and interpenetrate all things, all thought the one, the many.
Ralph Waldo Emerson
The validity of demonstrably wrong law cannot conceivably be justified. However, any answer to the question of the purpose of law other than by enumerating the manifold partisan views about it has proved impossible- and it is precisely on that impossibility of any natural law, and on that alone, that the validity of positive law may be founded. At this point relativism, so far only the method of our approach, enters our system as a structural element.
Ordering their living together cannot be left to the legal notions of the individuals who live together, since these different human beings will possibly issue contradictory directions. Rather, it must be uniformly governed by a transindividual authority. Since, however, in the relativistic view of reason and science are unable to fulfill that task, will and power must undertake it. If no one is able to determine what is just, somebody must lay down what is to be legal.
Gustav Radbruch
