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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George Allen and Unwin. The World of Mathematics.
These waves—the familiar electromagnetic waves—were eventually detected by the German physicist Heinrich Hertz in a series of mathematicw conducted in the late s. Evolution has primed humans to think mathematically. The New Zealander-American mathematician Vaughan Jones detected an unexpected relation between knots and another abstract branch of mathematics known as von Neumann algebras.
Isn’t this absolutely amazing? Would they now be one piece and both speed up? 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. Retrieved 16 October In order to be able to develop something like a periodic table of the elements, Thomson had to be able to classify knots—find out which different knots are possible.
Retrieved from ” https: In some cases it may even be useful to consider the attainment which is possible at the level of the intelligence of some other species. Mario Livio’s book Is God a Mathematician?
Suppose that a falling body broke into two pieces. He concludes his paper with the same question with which he began:. Communications on Pure and Applied Mathematics.
In other words, physicists and mathematicians thought that knots were viable models for atoms, and consequently they enthusiastically engaged in the mathematical study of knots.
So knot theory emerged from an attempt to explain physical reality, then it wandered into eigner abstract realm of pure mathematics—only to eventually return to its ancestral origin. Biology was now the study of information stored in DNA — strings of four letters: It follows the lives and thoughts of some of the greatest mathematicians in history, and attempts to explain the “unreasonable effectiveness” of mathematics. Another oft-cited example is Maxwell’s equationsderived to model the elementary electrical and magnetic phenomena known as of the mid 19th century.
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only effectuveness mathematical properties that we can discover.
It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind’s capacity to divine them.
However, then came the surprising passive effectiveness of mathematics. By a remarkably circular twist of history, knots are now found to provide answers in string theory, our present-day best effort to understand the constituents of matter!
Differential geometry Matheematics analysis Harmonic analysis Functional analysis Operator theory. In what follows I will describe a wonderful example of the continuous interplay between active and passive effectiveness.
There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
Sciences reach a point where they become mathematized. When a effextiveness 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
When are two pieces one? Wigner’s work provided a fresh insight into both physics and the philosophy of mathematicsand has been fairly often cited in the academic literature on the philosophy of physics and of mathematics. From Wikipedia, the free encyclopedia.
In other words, at least some of the laws of nature are formulated in directly applicable mathematical terms. The passive effectiveness, on the other hand, refers to cases in which abstract mathematical theories had been developed with absolutely no applications in mind, only to turn out decades, or sometimes centuries later, to be powerfully predictive physical models.
At first blush, you may think that the minimum number of crossings in a knot could serve as such an invariant. This particular need sparked a great interest in the mathematical theory of knots.
In particular, string theorists Hirosi Ooguri and Cumrun Vafa discovered that the number of complex topological structures that are formed when many strings interact is related to the Jones polynomial. 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? Inthe American mathematician James Waddell Alexander discovered an algebraic expression known as the Alexander polynomial that uses the arrangement of crossings to label the knot.
What is it that gives mathematics such incredible powers? 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: Peter Woita theoretical physicist, believes that this conflict exists in string theorywhere very abstract models may be impossible to test in any foreseeable experiment.
Unreasonable effectiveness |
The Jones polynomial distinguishes, for instance, even between knots and their mirror images figure 3for which the Alexander polynomials were identical. There are actually two facets to the effectvieness effectiveness,” one that I will call active and another that I dub passive. New Directions in the Philosophy of Science.
The lesson from this very brief history of knot theory is remarkable. Cambridge Journal of Economics.
Recall that Thomson started to study knots because he was searching for a theory of atoms, then considered to be the most basic constituents of matter. Later, Hilary Putnam explained these “two miracles” as being necessary consequences of a realist but not Platonist view of the philosophy of mathematics. Still, even without any other application in sight, the mathematical interest in knot theory continued at that point for its own sake. These equations also describe radio waves, discovered eutene David Edward Hughes inaround the time of James Clerk Maxwell ‘s death.