Bandwidth: How Mathematics, Physics, And Chemistry Constrain Society

Contents
Foreword
Preface and Acknowledgements
About the Author
List of Variables
0. Spoiler Alert
1. Measurement
	1.1 Words and Equations
	1.2 Decisions, Decisions
	1.3 Validation: Carbon Dioxide
2. Correlation vs. Causation
	2.1 Causality and Correlation
	2.2 Extrapolation Is Dangerous
	2.3 Least Squares Linear Regression
	2.4 Correlation Coefficient
	2.5 Equal Spacing Simplification
	2.6 Linearizing Nonlinear Functions
3. Noise
	3.1 Shot Noise
	3.2 Error Propagation
	3.3 Other Noise Sources
	3.4 Significant Figures
4. Signal
	4.1 Spectrophotometry
	4.2 Dithizone Determination of Lead
	4.3 ICP-Mass Spectrometry
	4.4 Direct Assay of Lead in Water by ICP-MS
	4.5 Correlated Noise Example
	4.6 Summary
5. Uncertainty — Quantum and Classical
	5.1 Quantum Uncertainty
	5.2 Classical Bandwidth Uncertainty
	5.3 Classical Nonlinear Uncertainty
6. Sampling
	6.1 Granularity
	6.2 Aliased Sampling
	6.3 Human Perceptual Limits
7. Bandwidth
	7.1 Language and Information
	7.2 Accelerated Communication
	7.3 Someone, Everyone, or No One Knows
8. Detection Limit
	8.1 The NMR Approach
	8.2 The LC-MS Approach
	8.3 What Does “Zero” Mean?
	8.4 Bias and Offsets
9. Dynamic Range
	9.1 Titration
	9.2 Derivatization
10. Potential Wells
	10.1 Forces and Wells
	10.2 Multiple Wells
	10.3 Parametrized Wells
	10.4 Migrating Between Subwells
	10.5 Connecting Wells to Bandwidth
11. Nonlinearity, Complexity, Chaos
	11.1 Wrestling with Rössler
	11.2 Poincaré, Lorenz, and Chaos, Oh My!
	11.3 Self-Organization
12. Markov Processes and Renormalization
	12.1 Phase Transitions and the Renormalization Group
13. Neural Networks
	13.1 Perceptrons and Their Uses, With a Side of Immunoassay
	13
.2 Skeptical View of Neural Networks
14. Qualitative, Quantitative, Triage
	14.1 The Danger of Uncritical Quantitation
	14.2 Decisions, Decisions, Decisions
15. Doug Hofstadter Got It Right: The Gödel Theorem
	15.1 Formal Systems Have Limitations
	15.2 Simple Problems Can Take Forever to Solve
	15.3 Getting Outside Our Potential Well
16. Mental Zoom Lens
	16.1 Zooming Between Scales
	16.2 Lost Information, Overwhelming Complexity
	16.3 Endless Frontier?
	16.4 Information Renormalization
17. Theology and Religion
	17.1 Purpose in Prospect and Retrospect
	17.2 Conventional Approaches, Unconventional Expressions
	17.3 Dichotomies
	17.4 Ethical Evolution?
	17.5 Freedom
	17.6 Conscience and Consciousness
18. Politics, Business, and Law in Light of Mathematical Concepts
	18.1 Scientists as Politicians
	18.2 Law
	18.3 Choices
	18.4 Overwhelmed
	18.5 Dunning-Kruger and Information Flow
	18.6 Tunnel Vision
	18.7 Too Much, Too Little
	18.8 Money as Information
19. Research and Freedom in Light of Mathematical Concepts
	19.1 Big Science Appears
	19.2 Challenges to a Potential Well Dweller
	19.3 Other Potential Wells Appear
	19.4 A Disquieting Conclusion
Appendix 1 Laser Pointer/Drinking Glass Colorimeter
Appendix 2 Human Relationships as an Iterated Map
Appendix 3 Calculus in Five Pages
Notes and Literature Citations
Index