The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Interdisciplinary Science Reviews (Impact Factor: 0.3). 08/2011; 36(3):209-213. DOI: 10.1179/030801811X13082311482537
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Available from: Steve Russ, Aug 13, 2015
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    • "Contemporary physical theory arises from the " unreasonable effectiveness of mathematics " (Wigner, 1960). Fundamental symmetries evolve then cool to elicit contents' phase transitions and observables whose mirror images should be identical. "
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    ABSTRACT: Gravitation theories allow isotropic or chiral vacuum backgrounds in the massed sector. Atomic mass distribution quantitative parity divergence can be calculated to large volumes in periodic crystals. It is shown that a parity Eötvös experiment opposing single crystal solid spheres of enantiomorphic space groups P3121 and P3221 quartz may empirically falsify isotropic vacuum and the Equivalence Principle without contradicting prior (achiral) observations in any venue at any scale, and should be performed.
    Preview · Article · Dec 2010
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    • "We now arrive at a crucial point; numerous authors refer to the " great stability and reliability " of Mathematics, which would need to be accounted for. And there is the customary and pre-scientific astonishment before the " unreasonable effectiveness of Mathematics " , an exceedingly famous title for a quite modest article, (Wigner, 1960) (but why did such a great thinker as Wigner not find more profound examples to support his thesis? Wigner's article, which everybody quotes – due to its so very effective and memorable title – and which very few read, presents examples that are not astounding). "
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    ABSTRACT: The foundation of Mathematics is both a logico-formal issue and an epistemological one. By the first, we mean the explicitation and analysis of formal proof principles, which, largely a posteriori, ground proof on general deduction rules and schemata. By the second, we mean the investigation of the constitutive genesis of concepts and structures, the aim of this paper. This “genealogy of concepts”, so dear to Riemann, Poincaré and Enriques among others, is necessary both in order to enrich the foundational analysis with an often disregarded aspect (the cognitive and historical constitution of mathematical structures) and because of the provable incompleteness of proof principles also in the analysis of deduction. For the purposes of our investigation, we will hint here to a philosophical frame as well as to some recent experimental studies on numerical cognition that support our claim on the cognitive origin and the constitutive role of mathematical intuition.
    Full-text · Article · Apr 2010 · Topoi
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    • "I wish here to discuss some aspects of extreme mathematical realism, and of Tegmark's proposal in particular, and point out what seem to me to be several problematic issues at the foundations of it. Far from swinging to the other, constructivist extreme (which, most scientists will agree, is clearly contradicted by the impressive success of science, and of mathematics' role in it [8]), I will advocate for an intermediate position. This consists essentially in the (mildly anti-Platonic) acceptance that mathematics is, at least in part, a human construction, without denying that its impressive success in science indicates that there is more to the relation between mathematics and reality than merely the fact that we use the former to describe the latter. "
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    ABSTRACT: I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this--at first sight purely philosophical--difference in point of view.
    Preview · Article · May 2009 · Foundations of Physics
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