As such it may describe instrumental theories with rigorous and enhancing contents that may be, or not, useful for our pratical goals.
What do you, fellow researchers, tell me about that?
TIA,
Marcos Wagner da Cunha
To start a discussion I suggest the following Wigner1s paper:
"The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
http://pt.scribd.com/doc/70089736/1960-Wigner-Unreasonable-Effectiveness-of-Mathematics-In-The-Natural-Sciences-Communications-in-Pure-and-Applied-Mathematics-Vol-13-No-I-Februa
Sans les mathématiques on ne pénètre point au fond de la philosophie.
Sans la philosophie on ne pénètre point au fond des mathématiques.
Sans les deux on ne pénètre au fond de rien. --- Leibniz
[Without mathematics we cannot penetrate deeply into philosophy.
Without philosophy we cannot penetrate deeply into mathematics.
Without both we cannot penetrate deeply into anything.]
"The basic lesson that I have learned from Godel is that mathematics is not a machine. Creativity is essential. And it is also mysterious. Just look at the ease with which rivers of beautiful mathematics owed from Euler's pen. Look at Ramanujan's remark that a goddess brought him ideas while he slept, and that no equation is worthwhile unless it expresses one of God's thoughts.1 Or, for that matter, look at Godel's faith that mathematicians can overcome the incompleteness theorem by intuiting new concepts and principles whenever this is needed for mathematics to advance. So it is high time for us to give up on static, formal mathematics and instead begin to study creativity and how ideas evolve."-Chaitin in http://library.nu/docs/CRELT3JQX1/Thinking%20about%20G%C3%B6del%20and%20Turing%3A%20Essays%20on%20Complexity%2C%201970-2007
http://library.nu/docs/CRELT3JQX1/Thinking%20about%20G%C3%B6del%20and%20Turing%3A%20Essays%20on%20Complexity%2C%201970-2007
"Davies asks what happens if we do not assume that the mathematical relations of the so-called laws of nature are the most basic level of description, but rather if information is regarded as the foundation on which physical reality is constructed. Davies suggests that instead of taking mathematics to be primar y, followed by physics and then information, the picture should be inverted in our explanatory scheme, so that we fi nd the conceptual hierarchy: information →laws of physics → matter." in
http://pt.scribd.com/doc/81329906/2010-Davis-Ed-m-Information-and-the-Nature-of-Reality-From-Physics-to-Metaphysics
http://pt.scribd.com/doc/81329906/2010-Davis-Ed-m-Information-and-the-Nature-of-Reality-From-Physics-to-Metaphysics
The Relation between Mathematics and Physics
Paul Dirac
"The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with remarkable success. This must be ascribed to some mathematical quality in Nature, a quality which the casual observer of Nature would not suspect, but which nevertheless plays an important role in Nature’s scheme.
One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various factors that make it up. The main aim of my talk to you will be to give you such an appreciation. I propose to deal with how the physicist’s views on this subject have been gradually modified by the succession of recent developments in physics, and then I would like to make a little speculation about the future."
http://www.scribd.com/doc/76276019/Dirac-The-Relation-Between-Mathematics-and-Physics-Proc-Roy-Soc-Edinburgh-1939
http://www.scribd.com/doc/76276019/Dirac-The-Relation-Between-Mathematics-and-Physics-Proc-Roy-Soc-Edinburgh-1939
I suppose you should not use this opportunity (ResearchGate site) to mention your bibliographic indications. In my opinion, to quote is NOT to think!
Why don't you try a short answer, by your own hand? Wouldn't it be much more feeding for our thought?
BTW, your quotes are very interesting. This is not the point of this complain.
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