EUGENE WIGNER UNREASONABLE EFFECTIVENESS OF MATHEMATICS PDF
put in a particularly evocative form by the physicist Eugene Wigner as the title of. a lecture in in New York: “The Unreasonable Effectiveness of Mathematics. On ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’. Sorin Bangu. Abstract I present a reconstruction of Eugene Wigner’s argument for . Maxwell, Helmholtz, and the Unreasonable Effectiveness of the Method of Physical Bokulich – – Studies in History and Philosophy of Science.
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As figure 1 demonstrates, there are three different knots with six crossings and no fewer than seven different knots with seven crossings. The American Mathematical Monthly. There are actually two facets effdctiveness the “unreasonable unreasobable one that I will call active and another that I dub passive. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?
Two major breakthroughs in knot theory occurred in and in Originally used to model freely falling bodies unreasonabble the surface of the earth, this law was extended on the basis of what Wigner terms “very scanty observations” to describe the motion of the planets, where it “has proved accurate beyond all reasonable expectations”.
Philosophy of mathematics literature in science documents Works originally published in American magazines Works originally published in science and technology magazines Mathematicw about philosophy of physics Thought experiments in physics. Indeed, it is this writer’s belief that something rather akin to the situation which was described above exists if the present pf of heredity and of physics are confronted. Wigner speculated on the relationship between the philosophy of science and the foundations of mathematics as follows:.
Unreasonable effectiveness |
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.
Knots became the subject of serious scientific investigation when in the s the English physicist William Thomson better known today as Lord Kelvin proposed that atoms were in fact knotted tubes of ether that mysterious substance that was supposed to permeate space.
Consequently, while it was certainly very useful, the Alexander polynomial was still not perfect for classifying knots. Another oft-cited example is Maxwell’s equationsderived to model the elementary electrical and magnetic phenomena known as of the mid 19th century.
In other words, physicists wgner mathematicians thought that knots were viable models for atoms, and consequently they enthusiastically engaged in the mathematical study of knots.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
So knot theory emerged from an attempt to explain physical reality, then it wandered into the abstract realm of pure mathematics—only to eventually return to its ancestral origin. Two knots that have different Alexander polynomials are indeed different e.
We should stop acting as if our goal is to author extremely elegant theories, and instead embrace complexity and make use of the best ally we have: Calculations of the electron’s magnetic moment based on QED reach the same precision and the two results agree!
Image created by Ann Feild. Mathematifs, our intellectual apparatus is such that much of what we see comes from the glasses we put on.
Humans create and select the mathematics that fit a situation. What is it that gives mathematics such incredible powers? Wigner’s original paper has provoked and wignre many responses across a wide range of disciplines.
Furthermore, the leading string theorist Ed Witten demonstrated that the Jones polynomial affords new insights in one of the most fundamental areas of research in modern physics, known as quantum field theory.
However, the minimum number of crossings is actually not a very useful invariant.
New Directions in the Philosophy of Science. When a better mathematical model in the form of the Bohr atom was discovered, mathematicians did not abandon knot theory.
Eugene Wigner, The unreasonable effectiveness of mathematics in the natural sciences – PhilPapers
Unexpectedly, the Jones polynomial and knot theory in general turned out to have wide-ranging applications in string theory. In the Greek legend of the Gordian knot Alexander the Great used his sword to slice through a knot that had defied all previous attempts to untie it.
Ivor Grattan-Guinness finds the effectiveness in question eminently reasonable and explicable in terms of concepts such as analogy, generalisation and metaphor. The reasonable though perhaps limited effectiveness of mathematics in the natural sciences”. Signer first blush, you may think that the minimum number of crossings in a knot could serve as such an invariant.
The lesson from this very brief history of knot theory is remarkable.