A Quote by Werner Heisenberg
I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.
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Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.
The impossibility of separating the nomenclature of a science from the science itself, is owing to this, that every branch of physical science must consist of three things; the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact.
Modern man, seeking a middle position in the evaluation of sense impression and thought, can, following Plato , interpret the process of understanding nature as a correspondence, that is, a coming into congruence of pre-existing images of the human psyche with external objects and their behaviour. Modern man, of course, unlike Plato , looks on the pre-existent original images also as not invariable, but as relative to the development of a conscious point of view, so that the word "dialectic" which Plato is fond of using may be applied to the process of development of human knowledge.
Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefore objective in the sense that it can be unambiguously communicated in ordinary human language.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
Many of the products which create a modern standard of living are only the physical incorporations of ideas- not only the ideas of an Edison or a Ford but the ideas of innumerable anonymous people who figure out the design of supermarkets, the location of gasoline stations, and the million mundane things on which our material well-being depends. Societies which have more people carrying out physical acts and fewer people supplying ideas do not have higher standards of living. Quite the contrary.
When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as well to express them so -- translating them out of their hieroglyphics that we might also work upon them by experiment?
Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.
Neither is there figurative and non-figurative art. All things appear to us in the shape of forms. Even in metaphysics ideas are expressed by forms. Well then, think how absurd it would be to think of painting without the imagery of forms. A figure, an object, a circle, are forms; they affect us more or less intensely.
It seems that every practitioner of physics has had to wonder at some point why mathematics and physics have come to be so closely entwined. Opinions vary on the answer. ..Bertrand Russell acknowledged..'Physics is mathematical not because we know so much about the physical world, but because we know so little.' ..Mathematics may be indispensable to physics, but it obviously does not constitute physics.
The world of physics is essentially the real world construed by mathematical abstractions, and the world of sense is the real world construed by the abstractions which the sense-organs immediately furnish. To suppose that the "material mode" is a primitive and groping attempt at physical conception is a fatal error in epistemology.
We sift reality through screens composed of ideas . (And such ideas have their roots in older ideas.) Such idea systems are necessarily limited by language , by the ways we can describe them. That is to say: language cuts the grooves in which our thoughts move. If we seek new validity forms (other laws and other orders) we must step outside language.
Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.
Since man does not create physical matter, those who handle material objects in the production process are not producers in that sense. Economic benefits result from the transformation of matter in form, location, or availability (intellectually or temporally). It is these transformations that create economic benefits valued by consumers, and whoever arranges such transformations contributes to the value of things, whether his hands actually come into contact with physical objects or not.
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