Mathematical Explanation: A Pythagorean Proposal

2021 ◽  
Author(s):  
Samuel Baron
Keyword(s):  
Mathematical Explanation

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

The Effect of User Experience on Designing Interactive Tool: A Case Study of Learning Images Compression

2021 ◽  
Vol 9 (10) ◽  
pp. 1312-1320
Keyword(s):  
User Experience ◽  
Real Life ◽  
Mathematical Concept ◽  
Design Principles ◽  
Mathematical Explanation ◽  
Mathematical Concepts ◽  
Learning Platform ◽  
Learning Mathematics ◽  
The Common ◽  
Value Decomposition

Technology has significantly emerged in various fields, including healthcare, government, and education. In the education field, students of all ages and backgrounds turn to modern technologies for learning instead of traditional methods, especially under challenging courses such as mathematics. However, students face many problems in understanding mathematical concepts and understanding how to benefit from them in real-life. Therefore, it can be challenging to design scientific materials suitable for learning mathematics and clarifying their applications in life that meet the students’ preferences. To solve this issue, we designed and developed an interactive platform based on user experience to learn an advanced concept in the idea of linear algebra called Singular Value Decomposition (SVD) and its applicability in image compression. The proposed platform considered the common design principles to map between the provider in terms of clear mathematical explanation and the receiver in terms of matching good user experience. Twenty participants between the ages of 16 and 30 tested the proposed platform. The results showed that learning using it gives better results than learning traditionally in terms of the number of correct and incorrect actions, effectiveness, efficiency, and safety factors. Consequently, we can say that designing an interactive learning platform to explain an advanced mathematical concept and clarify its applications in real-life is preferable by considering and following the common design principles.

The Behavior of Number Concentration Tendencies for the Continuous Collection Growth Equation Using One- and Two-Moment Bulk Parameterization Schemes

2007 ◽  
Vol 46 (8) ◽  
pp. 1264-1274
Author(s):  
Jerry M. Straka ◽  
Katharine M. Kanak ◽  
Matthew S. Gilmore
Keyword(s):  
Growth Process ◽  
Number Concentration ◽  
Mathematical Explanation ◽  
Growth Equation ◽  
Parameterization Schemes ◽  
Distribution Shape ◽  
Bulk Parameterization

Abstract This paper presents a mathematical explanation for the nonconservation of total number concentration Nt of hydrometeors for the continuous collection growth process, for which Nt physically should be conserved for selected one- and two-moment bulk parameterization schemes. Where possible, physical explanations are proposed. The assumption of a constant no in scheme A is physically inconsistent with the continuous collection growth process, as is the assumption of a constant Dn for scheme B. Scheme E also is nonconservative, but it seems this result is not because of a physically inconsistent specification; rather the solution scheme’s equations simply do not satisfy Nt conservation and Nt does not come into the derivation. Even scheme F, which perfectly conserves Nt, does not preserve the distribution shape in comparison with a bin model.

scholarly journals Star Wars - an episodes battle

2020 ◽  
Vol 8 (6) ◽  
pp. 367-380
Author(s):  
Patrícia Nunes da Silva ◽  
Monica Almeida Gama ◽  
André Luiz Cordeiro dos Santos
Keyword(s):  
Mathematical Explanation ◽  
Star Wars ◽  
Market Experiment

Mlodinow (2008) proposed a crazy market experiment: to release the same film under two titles: Star Wars: Episode A and Star Wars: Episode B. Their marketing campaigns and distribution schedule are identical except by their titles on trailers and ads. He looks at the first 20,000 moviegoers and record the film they choose to see. He claims it is most probable the lead never changes, and it is 88 times more likely that one of the two films will be int the lead through all 20,000 customers than it is that the lead continuously seesaw. We present a detailed mathematical explanation for Mlodinow claims.

A Counterfactual Approach to Explanation in Mathematics

2019 ◽  
Vol 28 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Sam Baron ◽  
Mark Colyvan ◽  
David Ripley
Keyword(s):  
Scientific Explanation ◽  
Mathematical Explanation ◽  
Test Case ◽  
Mathematical Explanations ◽  
Counterfactual Theory ◽  
Explanatory Structure ◽  
Counterfactual Approach

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

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