The quantum theory, as it is now constituted, presents us with a very great challenge, if we are at all interested in such a venture, for in quantum physics there is no consistent notion at all of what the reality may be that underlies the universal constitution and structure of matter. Thus, if we try to use the prevailing world view based on the notions of particles, we discover that the 'particles' (such as electrons) can also manifest as waves, that they move discontinuously, that there are no laws at all that apply in detail to the actual movements of individual particles and that only statistical predictions can be made about large aggregates of such particles. If on the other hand we apply the world view in which the world is regarded as a continuous field, we find that this field must also be discontinuous, as well as particle-like, and that it is as undermined in its actual behaviour as is required in the particle view of relation as a whole.
David BohmRelated topics
field find great large matter move now quantum thus try universal use venture view well Laws presentsRelated quotes
Had it merely called to our attention the existence and exact nature of certain fundamental gaps in economic theory, the Theory of Economic Behavior by von Neumann and Morgenstern would have been a book of outstanding importance. But it does more than that. It is essentially constructive: where existing theory is considered to be inadequate, the authors put in its place a highly novel analytical apparatus designed to cope with the problem.
It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy. The applicability to games proper (chess and poker) is obvious from the title. Moreover, the book is of considerable interest from a purely mathematical point of view.
Leonid Hurwicz
As for the Republicans - how can one regard seriously a frightened, greedy, nostalgic huddle of tradesmen and lucky idlers who shut their eyes to history and science, steel their emotions against decent human sympathy, cling to sordid and provincial ideals exalting sheer acquisitiveness and condoning artificial hardship for the non-materially-shrewd, dwell smugly and sentimentally in a distorted dream-cosmos of outmoded phrases and principles and attitudes based on the bygone agricultural-handicraft world, and revel in (consciously or unconsciously) mendacious assumptions (such as the notion that real liberty is synonymous with the single detail of unrestricted economic license or that a rational planning of resource-distribution would contravene some vague and mystical 'American heritage'...) utterly contrary to fact and without the slightest foundation in human experience? Intellectually, the Republican idea deserves the tolerance and respect one gives to the dead.
H. P. Lovecraft
The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without any conflict in the results. It is only from the philosophical point of view that objections have been raised. They bear on certain ways of reasoning peculiar to analysis and set theory. These modes of reasoning were first systematically applied in giving a rigorous form to the methods of the calculus. [According to them, ] the objects of a theory are viewed as elements of a totality such that one can reason as follows: For each property expressible using the notions of the theory, it is [an] objectively determinate [fact] whether there is or there is not an element of the totality which possesses this property. Similarly, it follows from this point of view that either all the elements of a set possess a given property, or there is at least one element which does not possess it.
Paul Bernays
We have to live and move and have our being in ahimsa, even as Hitler does in himsa. It is the faith and perseverance and single-mindedness with which he has perfected his weapons of destruction that commands my admiration. That he uses them as a monster is immaterial for our purpose. We have to bring to bear the same single-mindedness and perseverance in evolving our ahimsa. Hitler is awake all the 24 hours of the day in perfecting his sadhana. He wins because he pays the price. His inventions surprise his enemies. But it is his single-minded devotion to his purpose that should be the object of our admiration and emulation. Although he works all his waking hours, his intellect is unclouded and unerring. Are our intellects unclouded and unerring? A mere belief in ahimsa or the charkha will not do. It should be intelligent and creative. If intellect plays a large part in the field of violence, I hold that it plays a larger part in the field of non-violence.
Mahatma Gandhi
Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, - a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.
William John Macquorn Rankine