scholarly journals “The Unreasonable Effectiveness of Mathematics”: Patterning of Patterns

2021 ◽  
Author(s):  
Serge Dolgikh
Keyword(s):  
Unreasonable Effectiveness

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals Eficácia sem razão [da matemática]

2016 ◽  
Vol 33 (2) ◽  
pp. 399
Author(s):  
Danny Augusto Vieira Tonidandel
Keyword(s):  
Natural Sciences ◽  
Unreasonable Effectiveness

http://dx.doi.org/10.5007/2175-7941.2016v33n2p399 Em 2003, o matemático Americano Alex Kasman (2003) escreveu um belo conto de “ficção matemática” intitulado “Unreasonable Effectiveness”, uma das várias respostas existentes ao clássico artigo de Wigner (1960) “The unreasonable effectiveness of mathematics in the natural sciences”. Na versão de Kasman, uma pesquisadora acaba, acidentalmente, descobrindo a resposta para a questão de como uma nova teoria encontra, em algum momento, uma utilidade prática na ciência. Isto é, como resultados abstratos, construídos sem quaisquer alicerces no “mundo real”, acabam se tornando tão úteis, mesmo em áreas completamente diversas? Neste artigo é proposta uma tradução comentada deste delicioso ensaio, tanto como proposta não convencional de experiência didática quanto uma reflexão sobre os rumos do desenvolvimento científico, propiciados pela Matemática e Física. Como objetivo secundário, procura-se trabalhar a motivação do estudante na busca por soluções não triviais para problemas científicos e filosóficos.

Conclusion

2021 ◽  
pp. 299-306
Author(s):  
William J. Talbott
Keyword(s):  
Real World ◽  
Human Mind ◽  
Epistemic Rationality ◽  
The Real ◽  
American Philosophy ◽  
Unreasonable Effectiveness

In this Conclusion, the author summarizes the main features of his theory of epistemic rationality and explains how his theory avoids commitment to any of the five presuppositions of the Proof Paradigm. He explains his new solution to the epistemological version of Berkeley’s puzzle. He recaps the real-world epistemological issues addressed by his theory. He concludes with some final thoughts, including a call to philosophers to reject both the presuppositions of the Proof Paradigm and the narrow scientism that characterizes so much of contemporary American philosophy. He urges us to replace that narrow scientism with a more expansive understanding of the human mind that can make sense of its “unreasonable effectiveness” in scientific and other inquiry.

Unreasonable Effectiveness

Math Horizons ◽  
2003 ◽  
Vol 10 (4) ◽  
pp. 29-31
Author(s):  
Alex Kasman
Keyword(s):  
Unreasonable Effectiveness

scholarly journals The Utterly Prosaic Connection between Physics and Mathematics

Philosophies ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 25
Author(s):  
Matt Visser
Keyword(s):  
Natural Sciences ◽  
Mathematical Entity ◽  
Eugene Wigner ◽  
Unreasonable Effectiveness ◽  
And Mathematics ◽  
The Universe

Eugene Wigner famously argued for the “unreasonable effectiveness of mathematics” as applied to describing physics and other natural sciences in his 1960 essay. That essay has now led to some 58 years of (sometimes anguished) philosophical soul searching—responses range from “So what? Why do you think we developed mathematics in the first place?”, through to extremely speculative ruminations on the existence of the universe (multiverse) as a purely mathematical entity—the Mathematical Universe Hypothesis. In the current essay I will steer an utterly prosaic middle course: Much of the mathematics we develop is informed by physics questions we are trying to solve; and those physics questions for which the most utilitarian mathematics has successfully been developed are typically those where the best physics progress has been made.

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