scholarly journals Cosmology and Hilbert's sixth problem

2020 ◽  
pp. 43-49
Author(s):  
Milan Cirkovic
Keyword(s):  
Open Problem ◽  
Mathematical Physics ◽  
Mathematical Structures ◽  
David Hilbert ◽  
Physical Cosmology ◽  
As If ◽  
New Millennium

There have been tantalizing indications from many quarters of physical cosmology that we are living in the multiverse - a huge set of cosmological domains ("universes"). What is the structure of this larger whole is an entirely open problem on the interface between physics and metaphysics. A goal of the present paper is to draw attention to the connection between this problem and an old and celebrated puzzle in mathematical physics. Among the unresolved problems David Hilbert posed in 1900 as a challenge for the dawning century, none is more philosophically controversial than the Sixth Problem, requiring the axiomatization of physical theories. In the new century and the new millennium, this problem has remained a challenge, usually swept under the rug as "not belonging to mathematics" (as if that impacts its epistemical status) or simply "unresolved". Recent radical ontological/cosmological hypothesis of Max Tegmark, identifying mathematical and physical structures, might shed some new light onto this allegedly antiquated subject: it might be the case that the problem has already been solved, insofar we have formalized mathematical structures! While this can be seen as "cutting the Gordian knot" rather than patiently resolving the issue, we suggest that there are several advantages to taking Tegmark's solution seriously, notably in the domain of (future) physics of the observer.

scholarly journals Thin-layer solutions of the Helmholtz equation

2020 ◽  
pp. 1-15
Author(s):  
J. R. OCKENDON ◽  
R. H. TEW
Keyword(s):  
Wave Propagation ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Open Problem ◽  
High Frequency ◽  
Mathematical Structure ◽  
Mathematical Physics ◽  
Thin Layers ◽  
Frequency Wave ◽  
High Frequency Wave

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

‘The emergency which has arrived’: the problematic history of nineteenth-century British algebra – a programmatic outline

1994 ◽  
Vol 27 (3) ◽  
pp. 247-276 ◽  
Author(s):  
Menachem Fisch
Keyword(s):  
Nineteenth Century ◽  
Scientific Revolution ◽  
Coming Of Age ◽  
Mathematical Physics ◽  
John Herschel ◽  
History Of ◽  
As If ◽  
Second Coming

More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’.

scholarly journals Introduction

2000 ◽  
Vol 10 (2) ◽  
pp. 97-98 ◽  
Author(s):  
M. BARR ◽  
P. J. SCOTT ◽  
R. A. G. SEELY
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Physics ◽  
75Th Birthday ◽  
Small Sample ◽  
The Other ◽  
Significant Feature ◽  
Mathematical Structures ◽  
Theory Of Computing ◽  
Computing Science ◽  
Small Conference

On December 5, 1997, a small conference was held at McGill on the occasion of Jim Lambek's 75th birthday. Subsequently it was decided to publish two volumes of papers contributed in his honour to mark this occasion: this issue of Mathematical Structures in Computer Science is one of the volumes; the other is Volume 6 of the journal Theory and Applications of Categories. At the December 1997 conference, a brief biographical essay was presented by Michael Barr and appears in the TAC volume. However, we wish to make some further remarks here.Jim completed his Ph.D. at McGill under Hans Zassenhaus in 1950, and has remained at McGill since then. But it is of interest to note that Jim wrote two theses: the second involved biquaternions in mathematical physics, and so foreshadows a significant feature of his career: Jim has consistently shown a remarkable range of interests, from physics to linguistics, from algebra to logic, from the history and philosophy of mathematics to the theory of computing science (although he never touches a computer, to this day!). Let us just review a small sample of his more than 100 published papers.

Poincaré’s Mathematical Creations in Search of the ‘True Relations of Things’

2018 ◽  
Author(s):  
Connemara Doran
Keyword(s):  
Physical Theory ◽  
Mathematical Physics ◽  
Metric Geometry ◽  
Henri Poincaré ◽  
Mathematical Structures ◽  
Space And Time ◽  
Pure Mathematics ◽  
Quantum Phenomena

How did the vast corpus of mathematical innovation of Henri Poincaré (1854–1912) engage the rationale, and impact the fate, of the notion of the ether in physics? Poincaré sought the ‘true relations’ that adhere in the phenomena—relations that persist irrespective of the choice of a metric geometry and a change in physical theory. This chapter traces how Poincaré embedded utterly new geometries and topological intuitions at the heart of pure mathematics, mathematical physics and philosophy. It demonstrates that Poincaré had no ownership of the physicists’ ether concept and that he viewed the ether as neither necessary nor necessarily a hindrance for further advance. Poincaré attended to the profound and subtle needs regarding space and time within physics by creating profound and subtle mathematics to capture the ‘true relations’, of spacetime. Poincaré thereby rendered the physicists’ ether superfluous while also creating mathematical structures for gravitational and quantum phenomena.

scholarly journals Categorical properties of intuitionistic fuzzy groups

2021 ◽  
Vol 27 (4) ◽  
pp. 55-70
Author(s):  
P. K. Sharma ◽  
◽  
Chandni ◽  
Keyword(s):  
Category Theory ◽  
Abelian Category ◽  
Mathematical Physics ◽  
Theoretical Computer Science ◽  
Contravariant Functor ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
Intuitionistic Fuzzy ◽  
Categorical Properties ◽  
The Relationship

The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.

scholarly journals Universes as big data

2021 ◽  
Author(s):  
Yang-Hui He
Keyword(s):  
Machine Learning ◽  
Data Science ◽  
Mathematical Physics ◽  
Theoretical Physics ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Physics First ◽  
Mathematical Structures ◽  
Starting Point ◽  
Computer Scientists

In this paper, we briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi–Yau landscape — accumulated by the collaboration of physicists, mathematicians and computer scientists over the last four decades — as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories. In parallel, we discuss the program in machine-learning mathematical structures and address the tantalizing question of how it helps doing mathematics, ranging from mathematical physics, to geometry, to representation theory, to combinatorics and to number theory.

Improvement of an artificial test substrate technique for evaluation of em immunocytochemical labeling

1987 ◽  
Vol 45 ◽  
pp. 762-763
Author(s):  
G. D. Gagne ◽  
M. F. Miller
Keyword(s):  
Bovine Serum Albumin ◽  
Serum Albumin ◽  
Bovine Serum ◽  
Artificial Substrate ◽  
Chemical Fixation ◽  
As If

We recently described an artificial substrate system which could be used to optimize labeling parameters in EM immunocytochemistry (ICC). The system utilizes blocks of glutaraldehyde polymerized bovine serum albumin (BSA) into which an antigen is incorporated by a soaking procedure. The resulting antigen impregnated blocks can then be fixed and embedded as if they are pieces of tissue and the effects of fixation, embedding and other parameters on the ability of incorporated antigen to be immunocyto-chemically labeled can then be assessed. In developing this system further, we discovered that the BSA substrate can also be dried and then sectioned for immunolabeling with or without prior chemical fixation and without exposing the antigen to embedding reagents. The effects of fixation and embedding protocols can thus be evaluated separately.

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