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Measuring and Reasoning

Book Description

In Measuring and Reasoning, Fred L. Bookstein examines the way ordinary arithmetic and numerical patterns are translated into scientific understanding, showing how the process relies on two carefully managed forms of argument: • Abduction: the generation of new hypotheses to accord with findings that were surprising on previous hypotheses, and • Consilience: the confirmation of numerical pattern claims by analogous findings at other levels of measurement. These profound principles include an understanding of the role of arithmetic and, more importantly, of how numerical patterns found in one study can relate to numbers found in others. They are illustrated through numerous classic and contemporary examples arising in disciplines ranging from atomic physics through geosciences to social psychology. The author goes on to teach core techniques of pattern analysis, including regression and correlation, normal distributions, and inference, and shows how these accord with abduction and consilience, first in the simple setting of one dependent variable and then in studies of image data for complex or interdependent systems. More than 200 figures and diagrams illuminate the text. The book can be read with profit by any student of the empirical nature or social sciences and by anyone concerned with how scientists persuade those of us who are not scientists why we should credit the most important claims about scientific facts or theories.

Table of Contents

  1. Cover
  2. Halftitle
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Analytical Table of Contents
  8. Preface
  9. Epigraphs
  10. Part I. The Basic Structure of a Numerical Inference
    1. 1 Getting Started
      1. 1.1 Our Central Problem: What Is a Good Numerical Inference?
      2. 1.2 The Sinking of the Scorpion
      3. 1.3 Prospectus
    2. 2 Consilience as a Rhetorical Strategy
      1. 2.1 Continental Drift
      2. 2.2 E. O. Wilson’s View of Consilience
      3. 2.3 Some Earlier Critiques
      4. 2.4 The Issue of Heterogeneity
        1. Random Walks
      5. 2.5 The Graphics of Consilience
      6. Appendix 2.A Mathematics or Physics? Consilience and Celestial Mechanics
        1. 2.A.1 What Ellipses Are
        2. 2.A.2 What a Cosine Is
        3. 2.A.3 Changing Coordinate Systems
        4. 2.A.4 Newton’s Law of Gravitation
        5. 2.A.5 Another Change of Variable
        6. 2.A.6 Getting to Kepler’s First Law
        7. 2.A.7 Mathematics or Physics?
      7. 2.B Historical Note: From Weiss through Kuhn to This Book
    3. 3 Abduction and Strong Inference
      1. 3.1 Example: Global Warming Is Anthropogenic
        1. What is the Evidence?
      2. 3.2 That Hypothesis Wins That Is the Only One That Fits the Data
      3. 3.3 Numerical Inferences Are the Natural Home of Abductive Reasoning
      4. 3.4 Strong Inference
      5. 3.5 Summary of Part I
      6. Appendix 3.A: Update on the Rhetoric of Climate Change
  11. Part II. A Sampler of Strategies
    1. 4 The Undergraduate Course
      1. E4.1 John Snow on the Origin of Cholera
        1. E4.1.1 The Basic Abduction
        2. E4.1.2 Two Modern Analogues
      2. L4.1 The Logic and Algebra of Least Squares
        1. L4.1.1 Sums of Squares
        2. L4.1.2 Precision of Averages, and Weighted Averages
        3. L4.1.3 Least-Squares Fits to Linear Laws
        4. L4.1.4 Regression as Weighted Averaging
      3. E4.2 Millikan and the Photoelectric Effect
        1. E4.2.1 The Role of Lines; the Role of Certainty
        2. E4.2.2 The Unreasonable Effectiveness of Mathematics in the Natural Sciences
      4. L4.2 Galton’s Machine
        1. L4.2.1 The Large-Scale Pattern of Binomial Coefficients
        2. L4.2.2 Ratio of Chances of Heads to Its Maximum
        3. L4.2.3 Notation: The Normal Distribution
        4. L4.2.4 Other Origins of the Normal Distribution
        5. L4.2.5 The Role of the Normal Distribution in Statistics
        6. L4.2.6 Galton’s Quincunx; Regression Revisited
          1. Mathematical Interlude
        7. L4.2.7 Appendix to section L4.2: Stirling’s Formula
      5. E4.3 Jean Perrin and the Reality of Atoms
        1. E4.3.1 Multiple Routes to the Same Quantity
        2. E4.3.2 More Detail about Brownian Motion
        3. E4.3.3 The Maxwell Distribution Is Exact
      6. L4.3 Likelihood-Based Statistical Inference
        1. L4.3.1 Bayes’ Theorem
        2. L4.3.2 The Gauss–Laplace Synthesis
        3. L4.3.3 Significance Testing: Decisions about Theories
        4. L4.3.4 The Contemporary Critique
      7. E4.4 Ulcers Are Infectious
        1. E4.4.1 Chronicle of a Preposterous Proposition
        2. E4.4.2 Evolution of Koch’s Postulates
      8. L4.4 Avoiding Pathologies and Pitfalls
        1. L4.4.1 The Langmuir–Rousseau Argument
        2. L4.4.2 An Unflawed Example from Frank Livingstone
      9. E4.5 Consilience and the Double Helix
        1. E4.5.1 The Nature Version
        2. E4.5.2 The True Version
      10. L4.5 From Correlation to Multiple Regression
        1. L4.5.1 From Causation to Correlation
        2. L4.5.2 The Algebra of Multiple Regression: Three Interpretations
        3. L4.5.3 Three Special Cases of Multiple Regression
        4. L4.5.4 The Daunting Epistemology of Multiple Regression
      11. E4.6 On Passive Smoking
        1. E4.6.1 Passsive Smoking and Heart Attacks
        2. E4.6.2 Passive Smoking and Lung Cancer
      12. L4.6 Plausible Rival Hypotheses
      13. E4.7 Milgram’s Obedience Experiment
        1. E4.7.1 Calibration as Consilience
        2. E4.7.2 Critique of Pseudoquantitative Psychology
      14. E4.8 Death of the Dinosaurs
        1. E4.8.1 Both Kinds of Abductions
        2. E4.8.2 The 1992 Confirmation
          1. Interim Concluding Remark
  12. Part III. Numerical Inference for General Systems
    1. 5 Abduction and Consilience in More Complicated Systems
      1. 5.1 Analysis of Patterns in the Presence of Complexity
        1. 5.1.1 The Hertzsprung–Russell Diagram
        2. 5.1.2 The Ramachandran Plot
        3. 5.1.3 The Face of Fetal Alcohol Syndrome
        4. 5.1.4 Preliminary Comments Suggested by the Preceding Examples
      2. 5.2 Abduction and Consilience in General Systems
        1. 5.2.1 Abduction and Consilience in a More General Context
        2. 5.2.2 More Advanced Schemes for Data
        3. 5.2.3 Models for Randomness Complement Our Models for Order
        4. 5.2.4 A Concluding Comment
      3. 5.3 Information and Information-Based Statistics
        1. 5.3.1 Information as a Mathematical Quantity
        2. 5.3.2 From Information to Numerical Inference
        3. 5.3.3 An Example
      4. 5.4 A Concluding Comment
    2. 6 The Singular-Value Decomposition: A Family of Pattern Engines for Organized Systems
      1. 6.1 The Hyperbolic Paraboloid
      2. 6.2 The Singular-Value Decomposition
        1. 6.2.1 The SVD Theorem and Its Role in the Description of Organized Complexity
        2. 6.2.2 Example: Viremia in Monkeys Exposed to SIV
      3. 6.3 Principal Components Analysis
        1. 6.3.1 Geometry of the Variation of Axes of an Ellipsoid
        2. 6.3.2 Under What Circumstances Can PCA Make Sense? Pattern Spaces for Variables
        3. 6.3.3 Example
      4. 6.4 Partial Least Squares and Related Methods for Associations Among Multiple Measurement Domains
        1. 6.4.1 Path Analysis Revisited
        2. 6.4.2 Two-Block Partial Least Squares
        3. 6.4.3 Extensions and Modifications
      5. 6.5 Another Tableau: Dissimilarities as Primary Data
        1. 6.5.1 From Distances to Coordinates: The Underlying Theorem
        2. 6.5.2 Classification
        3. 6.5.3 Covariance Distance
      6. 6.6 Concluding Comment
    3. 7 Morphometrics, and Other Examples
      1. 7.1 Description by Landmark Configurations
      2. 7.2 Procrustes Shape Distance
      3. 7.3 Procrustes Shape Coordinates and Their Subspaces
      4. 7.4 Procrustes Form Distance
      5. 7.5 The Thin-Plate Spline in 2D and 3D
      6. 7.6 Semilandmarks: Representation and Information Content of Curving Form
        1. 7.6.1 Sliding One Single Landmark
        2. 7.6.2 Sliding Any Number of Coordinates
        3. 7.6.3 Organizing the Semilandmarks in Practice: Working from a Template
      7. 7.7 Putting Everything Together: Examples
        1. 7.7.1 Allometric Growth
        2. 7.7.2 Simplifications of Grids
        3. 7.7.3 Focusing on the Interesting Region
        4. 7.7.4 A Symmetry Curve in 3D, and a Classification It Drives
        5. 7.7.5 Bilateral Symmetry
        6. 7.7.6 Combinations of Linear Constraints
        7. 7.7.7 “Form and Function”: An Example from the Morphometrics of Strain
      8. 7.8 Other Examples
        1. 7.8.1 It Wasn’t Just Alcohol
        2. 7.8.2 Karl Pearson, Right or Wrong
        3. 7.8.3 Structured Factor Analysis, Guttman-Style, and the “Horseshoe”
        4. 7.8.4 A Cautionary Closing Remark: Beware Epig
  13. Part IV. What Is to Be Done?
    1. 8 Retrospect and Prospect
      1. 8.1 Abduction, Consilience, and the Psychosocial Structures of Science
      2. 8.2 Implications for Inference Across the Sciences
      3. 8.3 What, Then, IS to Be Done?
  14. References
  15. Index