On the Logic of Being and Wigner's Astonishment Regarding the 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.

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Just How Unreasonable is the Effectiveness of Mathematics?

10.1093/oso/9780198815044.003.0001 ◽

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.

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Machines, Logic and Quantum Physics

Bulletin of Symbolic Logic ◽

10.2307/421056 ◽

2000 ◽

Vol 6 (3) ◽

pp. 265-283 ◽

Cited By ~ 43

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).

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The Return of Pathological Science Accompanied by a Pinch of Replication

The Problem with Science ◽

10.1093/oso/9780197536537.003.0006 ◽

2021 ◽

pp. 109-130

Author(s):

R. Barker Bausell

Keyword(s):

Nobel Prize ◽

Cold Fusion ◽

Research Practice ◽

Physical Sciences ◽

Book Title ◽

The Road ◽

Pathological Science

No discussion of irreproducible science would be complete without at least a brief consideration of what happens when scientists go a step or two beyond questionable research practice (QRP)-driven research. So, continuing the metaphor of scientific journeys, Robert Park’s iconic book title, Voodoo Science: The Road from Foolishness to Fraud, encapsulates the interdisciplinary examples of what Irving Langmuir (a Nobel Prize recipient in chemistry) termed pathological science more than 65 years ago. The chapter discusses more recent examples of this phenomenon in some detail from both the physical sciences (cold fusion) and their sociobehavioral counterparts (the Daryl Bem psi episode). The latter (undoubtedly a virtual mentee of Joseph Banks Rhine whose exploits were exposed by Professor Langmuir) is given more prominence here because of its influence on the genesis of reproducibility crisis itself.

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Blackett Memorial Lecture, 1978. Fundamental research in India in the area of the physical sciences

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1979.0011 ◽

1979 ◽

Vol 365 (1721) ◽

pp. 145-160

Keyword(s):

Nobel Prize ◽

Royal Society ◽

Cosmic Radiation ◽

Memorial Lecture ◽

Physical Sciences ◽

Indian National Science Academy ◽

National Science ◽

Fundamental Research ◽

Science Academy

I consider it a great honour and privilege to have been invited to deliver the second Blackett Memorial Lecture organized under the joint sponsorship of the Royal Society and the Indian National Science Academy. I would like to express at the outset my gratitude to both Societies for providing me with this unique opportunity. It so happens that I have spent the last three decades of my life doing research in the field of cosmic radiation, a good fraction of which has been done with cloud chambers. Because of both these reasons, as you can easily imagine, I have been to a great extent personally influenced and inspired by P. M. S. (Lord) Blackett, whose pioneering and outstanding contributions in the field of cosmic radiation with counter controlled cloud chambers which brought him the Nobel Prize in 1948, are well known.

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Advances in ultramicrotomy for physical sciences applications

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149386 ◽

1993 ◽

Vol 51 ◽

pp. 710-711

Author(s):

G. McMahon ◽

T. Malis

Keyword(s):

Particle Surface ◽

Zeolite Catalysts ◽

Physical Sciences ◽

Pull Out ◽

Large Particles ◽

Novel Applications ◽

Metal Wires ◽

Frequent Problem ◽

Specific Orientation ◽

Diamond Knife

As with all techniques which are relatively new and therefore underutilized, diamond knife sectioning in the physical sciences continues to see both developments of the technique and novel applications.Technique Developments Development of specific orientation/embedding procedures for small pieces of awkward shape is exemplified by the work of Bradley et al on large, rather fragile particles of nuclear waste glass. At the same time, the frequent problem of pullout with large particles can be reduced by roughening of the particle surface, and a proven methodology using a commercial coupling agent developed for glasses has been utilized with good results on large zeolite catalysts. The same principle (using acid etches) should work for ceramic fibres or metal wires which may only partially pull out but result in unacceptably thick sections. Researchers from the life sciences continue to develop aspects of embedding media which may be applicable to certain cases in the physical sciences.

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