Bandwidth How Mathematics Physics and Chemistry Constrain Society 1st Edition by Alexander Scheeline, Susan Avery ISBN 9789811237874 9811237875

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ISBN 10: 9811237875
ISBN 13: 9789811237874
Author: Alexander Scheeline, Susan Avery

The physical sciences and mathematics are extraordinarily useful in explaining the material world. People and society are constrained by physical reality, but we are often unclear on what constraints are absolute, which may be relative, and those that are simply a matter of taste. Bandwidth explains how limitations in the movement and perception of information constrain human behavior, cognition, interaction, and perspective. How fast can we learn? How much? Why are habits and biases unavoidable? Why is the common statement “any nation that can land people on the moon surely can …” frequently wrong? Using equations and physical models, Bandwidth describes constraints which, in part, explain political, economic, religious, and personal frictions. Aspects considered include: how much information can one human absorb in a lifetime? How far does a process of perturbation propagate? How do specialization or generalization, critical thinking or belief, influence what people accomplish? Throughout, equations are used to compactly express ideas, illustrating why mathematical economy of expression accelerates communication and deeper understanding. The critical impacts of uncertainty, fluctuations, or noise, and their implications for law and society, are emphasized.

Bandwidth How Mathematics Physics and Chemistry Constrain Society 1st Edition Table of contents:

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

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Tags: Alexander Scheeline, Susan Avery, Bandwidth, Mathematics Physics, Chemistry Constrain Society