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© 2015

On Meaningful Scientific Laws

  • This book gives many examples of applications

  • A "how to" book, which prepares the reader to transforming the problem of finding the scientific law relevant to a phenomenon into solving a functional equation problem

  • Closely related to, but essentially different from, dimensional analysis

Book

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Jean-Claude Falmagne, Christopher Doble
    Pages 1-9
  3. Jean-Claude Falmagne, Christopher Doble
    Pages 11-26
  4. Jean-Claude Falmagne, Christopher Doble
    Pages 27-46
  5. Jean-Claude Falmagne, Christopher Doble
    Pages 47-57
  6. Jean-Claude Falmagne, Christopher Doble
    Pages 59-78
  7. Jean-Claude Falmagne, Christopher Doble
    Pages 79-84
  8. Jean-Claude Falmagne, Christopher Doble
    Pages 85-103
  9. Jean-Claude Falmagne, Christopher Doble
    Pages 105-135
  10. Jean-Claude Falmagne, Christopher Doble
    Pages 137-154
  11. Jean-Claude Falmagne, Christopher Doble
    Pages 155-157
  12. Back Matter
    Pages 159-170

About this book

Introduction

The authors describe systematic methods for uncovering scientific laws a priori, on the basis of intuition, or "gedanken experiments". Mathematical expressions of scientific laws are, by convention, constrained by the rule that their form must be invariant with changes of the units of their variables. This constraint makes it possible to narrow down the possible forms of the laws. It is closely related to, but different from, dimensional analysis. It is a mathematical book, largely based on solving functional equations. In fact, one chapter is an introduction to the theory of functional equations.

Keywords

abstract axioms dimensional analysis functional equations invariance under transformations mathematical representations meaningfulness measurement scientific code

Authors and affiliations

  1. 1.Dept. Cognitive SciencesUniversity of California, Irvine School of Social SciencesIrvineUSA
  2. 2.MHE/ALEKS CorporationIrvineUSA

About the authors

Jean-Claude Falmagne is an emeritus professor of Cognitive Sciences at the University of California, Irvine. His research interests focus on the application of mathematics to educational technology, psychophysics, choice theory, and philosophy of sciences, in particular measurement theory.
Chris Doble is the Math Content Development Manager at MHE / ALEKS Corporation. Along with his focus on using technology in the teaching and learning of mathematics, he maintains academic interests and publishes in measurement theory and psychophysics.

Bibliographic information

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