Just How Unreasonable is the Effectiveness of Mathematics?

2018 ◽  
Author(s):  
Otávio Bueno ◽  
Steven French
Keyword(s):  
Mathematical Structures ◽  
Eugene Wigner ◽  
Applicability Of Mathematics ◽  
Unreasonable Effectiveness ◽  
Species Specific ◽  
Special Circumstances

Eugene Wigner famously challenged philosophers to account for ‘the unreasonable effectiveness of mathematics’. Mark Steiner responded that mathematics is essentially species specific and thus the strategies involved in its applicability are, at their core, anthropocentric. This chapter tackles Steiner’s claims and suggests that the mystery he sees in mathematics’ applicability can be dispelled by adopting a kind of optimistic attitude with regard to the variety of mathematical structures that are typically made available in any given context. This suggests applying mathematics is simply a matter of finding a structure to fit the phenomena in question. However, as Wilson notes, mathematics is more ‘rigid’ than this attitude assumes and certain ‘special circumstances’ must obtain for it to be brought into contact with physics. We suggest that it is via certain idealizations that these circumstances are constructed and the mystery of the applicability of mathematics is dispelled.

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 Machines, Logic and Quantum Physics

2000 ◽  
Vol 6 (3) ◽  
pp. 265-283 ◽  
Author(s):  
David Deutsch ◽  
Artur Ekert ◽  
Rossella Lupacchini
Keyword(s):  
Quantum Physics ◽  
A Priori ◽  
Physical Reality ◽  
Physical World ◽  
Empirical Science ◽  
Physical Sciences ◽  
Mathematical Structures ◽  
Eugene Wigner ◽  
The Universe ◽  
Modern Status

§1. Mathematics and the physical world. Genuine scientific knowledge cannot be certain, nor can it be justified a priori. Instead, it must be conjectured, and then tested by experiment, and this requires it to be expressed in a language appropriate for making precise, empirically testable predictions. That language is mathematics.This in turn constitutes a statement about what the physical world must be like if science, thus conceived, is to be possible. As Galileo put it, “the universe is written in the language of mathematics”. Galileo's introduction of mathematically formulated, testable theories into physics marked the transition from the Aristotelian conception of physics, resting on supposedly necessary a priori principles, to its modern status as a theoretical, conjectural and empirical science. Instead of seeking an infallible universal mathematical design, Galilean science usesmathematics to express quantitative descriptions of an objective physical reality. Thus mathematics became the language in which we express our knowledge of the physical world — a language that is not only extraordinarily powerful and precise, but also effective in practice. Eugene Wigner referred to “the unreasonable effectiveness of mathematics in the physical sciences”. But is this effectiveness really unreasonable or miraculous?Numbers, sets, groups and algebras have an autonomous reality quite independent of what the laws of physics decree, and the properties of these mathematical structures can be just as objective as Plato believed they were (and as Roger Penrose now advocates).

scholarly journals On the Logic of Being and Wigner's Astonishment Regarding the Applicability of Mathematics

2020 ◽  
Vol 2 (1) ◽  
pp. 31-32
Author(s):  
Gordon E Mullings
Keyword(s):  
Nobel Prize ◽  
Logical Possibility ◽  
Possible World ◽  
Physical Sciences ◽  
Eugene Wigner ◽  
Applicability Of Mathematics

The Nobel Prize winning Physicist, Eugene Wigner, famously posed a powerful challenge (1960) by asking why is mathematics so effective, especially in the physical sciences. It is possible that the reason for the effectiveness of mathematics is not because mathematics is in any way causative, but instead because mathematics studies the structure of logical possibility and constraint. When plugged into a possible world, mathematics gives us the tools to analyze the logically possible outcomes. Therefore, when a possible world that is expressed mathematically sufficiently aligns with reality, mathematics becomes effective at expressing relationships and outcomes.

Imaging molecules adsorbed onto electrodes under potential control by scanning probe microscopy

1991 ◽  
Vol 49 ◽  
pp. 376-377 ◽  
Author(s):  
N.J. Tao ◽  
J.A. DeRose ◽  
P.I. Oden ◽  
S.M. Lindsay
Keyword(s):  
Surface Charge ◽  
Environmental Effects ◽  
Scanning Probe Microscopy ◽  
Statistical Significance ◽  
Electrochemical Methods ◽  
Surface Structures ◽  
Scanning Probe ◽  
Potential Control ◽  
Afm Imaging ◽  
Special Circumstances

Clemmer and Beebe have pointed out that surface structures on graphite substrates can be misinterpreted as biopolymer images in STM experiments. We have been using electrochemical methods to react DNA fragments onto gold electrodes for STM and AFM imaging. The adsorbates produced in this way are only homogeneous in special circumstances. Searching an inhomogeneous substrate for ‘desired’ images limits the value of the data. Here, we report on a reversible method for imaging adsorbates. The molecules can be lifted onto and off the substrate during imaging. This leaves no doubt about the validity or statistical significance of the images. Furthermore, environmental effects (such as changes in electrolyte or surface charge) can be investigated easily.

Electron Microscopy in the Study of Natural Phytoplankton Assemblages

1985 ◽  
Vol 43 ◽  
pp. 620-623
Author(s):  
Linda Sicko-Goad
Keyword(s):  
Electron Microscopy ◽  
Aquatic Environment ◽  
Size Range ◽  
Physical Parameters ◽  
Specific Information ◽  
Phytoplankton Assemblages ◽  
Phytoplankton Productivity ◽  
Ecosystem Effects ◽  
Time Of Year ◽  
Species Specific

Although the use of electron microscopy and its varied methodologies is not usually associated with ecological studies, the types of species specific information that can be generated by these techniques are often quite useful in predicting long-term ecosystem effects. The utility of these techniques is especially apparent when one considers both the size range of particles found in the aquatic environment and the complexity of the phytoplankton assemblages.The size range and character of organisms found in the aquatic environment are dependent upon a variety of physical parameters that include sampling depth, location, and time of year. In the winter months, all the Laurentian Great Lakes are uniformly mixed and homothermous in the range of 1.1 to 1.7°C. During this time phytoplankton productivity is quite low.

64: Rapid, Species-Specific Detection of Uropathogens from Clinical Urine Specimens Using an Electrochemical Microsensor Array

2005 ◽  
Vol 173 (4S) ◽  
pp. 18-18
Author(s):  
Joseph C. Liao ◽  
Mitra Mastali ◽  
David A. Haake ◽  
Bernard M. Churchill
Keyword(s):  
Specific Detection ◽  
Species Specific ◽  
Urine Specimens

Suicide-Related Crimes in Contemporary European Criminal Laws

Crisis ◽  
1997 ◽  
Vol 18 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Ilkka Henrik Mäkinen
Keyword(s):  
Suicide Prevention ◽  
Suicide Mortality ◽  
Legal Systems ◽  
Cultural Attitudes ◽  
Public Opinions ◽  
Suicide Rates ◽  
Narrow Scope ◽  
National Affair ◽  
Attitudes Towards Suicide ◽  
Special Circumstances

This article describes suicide-related penal legislation in contemporary Europe, and analyzes and relates the results to cultural attitudes towards suicide and to national suicide rates. Data were obtained from 42 legal entities. Of these, 34 have penal regulations which - according to definition - chiefly and directly deal with suicide. There are three main types of act: aiding suicide, abetting suicide, and driving to suicide. The laws vary considerably with regard to which acts are sanctioned, how severely they are punished, and whether any special circumstances such as the motive, the result, or the object can make the crime more serious. Various ideologies have inspired legislation: religions, the euthanasia movement, and suicide prevention have all left their mark. There are some cases in which neighboring legal systems have clearly influenced laws on the topic. However, the process seems mostly to have been a national affair, resulting in surprisingly large discrepancies between European legal systems. The laws seem to reflect public opinions: countries which punish the crimes harder have significantly less permissive cultural attitudes towards suicide. Likewise, suicide rates were significantly higher in countries with a narrow scope of criminalization and milder punishments for suicide-related crimes. The cultural and normative elements of society are connected with its suicide mortality.

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