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.

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.

scholarly journals On the Unusual Effectiveness of Logic in Computer Science

2001 ◽  
Vol 7 (2) ◽  
pp. 213-236 ◽  
Author(s):  
Joseph Y. Halpern ◽  
Robert Harper ◽  
Neil Immerman ◽  
Phokion G. Kolaitis ◽  
Moshe Y. Vardi ◽  
...  
Keyword(s):  
Computer Science ◽  
Laws Of Nature ◽  
Mathematical Formulation ◽  
Natural Sciences ◽  
Book Of Nature ◽  
Unreasonable Effectiveness ◽  
Empirical Law ◽  
Rational Explanation ◽  
Physical Phenomena ◽  
Logic In Computer Science

In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”

scholarly journals The Unreasonable Ubiquitousness of Quasi-Polynomials

10.37236/3750 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Kevin Woods
Keyword(s):  
General Class ◽  
Natural Sciences ◽  
Linear Inequalities ◽  
Boolean Operations ◽  
Natural Numbers ◽  
Ehrhart Theory ◽  
Presburger Arithmetic ◽  
Unreasonable Effectiveness ◽  
Polynomial Structure ◽  
Special Cases

A function $g$, with domain the natural numbers, is a quasi-polynomial if there exists a period $m$ and polynomials $p_0,p_1,\ldots,p_{m-1}$ such that $g(t)=p_i(t)$ for $t\equiv i\bmod m$. Quasi-polynomials classically - and "reasonably'' - appear in Ehrhart theory and in other contexts where one examines a family of polyhedra, parametrized by a variable $t$, and defined by linear inequalities of the form $a_1x_1+\cdots+a_dx_d\le b(t)$. Recent results of Chen, Li, Sam; Calegari, Walker; and Roune, Woods show a quasi-polynomial structure in several problems where the $a_i$ are also allowed to vary with $t$. We discuss these "unreasonable'' results and conjecture a general class of sets that exhibit various (eventual) quasi-polynomial behaviors: sets $S_t\subseteq\mathbb{N}^d$ that are defined with quantifiers ($\forall$, $\exists$), boolean operations (and, or, not), and statements of the form $a_1(t)x_1+\cdots+a_d(t)x_d \le b(t)$, where $a_i(t)$ and $b(t)$ are polynomials in $t$. These sets are a generalization of sets defined in the Presburger arithmetic. We prove several relationships between our conjectures, and we prove several special cases of the conjectures. The title is a play on Eugene Wigner's "The unreasonable effectiveness of mathematics in the natural sciences''.

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