1st Edition

Mathematics for the Environment

By Martin Walter Copyright 2011
    678 Pages 54 B/W Illustrations
    by Chapman & Hall

    Mathematics for the Environment shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. These tools can then be used to understand and effectively deal with economic, environmental, and social issues. With elementary mathematics, the book seeks answers to a host of real-life questions, including:

    • How safe is our food and will it be affordable in the future?
    • What are the simple lessons to be learned from the economic meltdown of 2008–2009?
    • Is global climate change happening?
    • Were some humans really doing serious mathematical thinking 50,000 years ago?
    • What does the second law of thermodynamics have to do with economics?
    • How can identity theft be prevented?
    • What does a mathematical proof prove?

    A truly interdisciplinary, concrete study of mathematics, this classroom-tested text discusses the importance of certain mathematical principles and concepts, such as fuzzy logic, feedback, deductive systems, fractions, and logarithms, in various areas other than pure mathematics. It teaches students how to make informed choices using fundamental mathematical tools, encouraging them to find solutions to critical real-world problems.

    MATHEMATICS IS CONNECTED TO EVERYTHING ELSE
    Earth’s Climate and Some Basic Principles
    One of the Greatest Crimes of the 20th Century
    Feedback
    Edison’s Algorithm: Listening to Nature’s Feedback
    Fuzzy Logic, Filters, the Bigger Picture Principle
    Consequences of the Crime: Suburbia’s Topology
    A Toxic Consequence of the Crime
    Hubbert’s Peak and the End of Cheap Oil
    Resource Wars: Oil and Water
    The CO2 Greenhouse Law of Svante Arrhenius

    Economic Instability: Ongoing Causes
    Necessary Conditions for Economic Success
    The Mathematical Structure of Ponzi Schemes
    Dishonest Assessment of Risk
    One Reason Why Usury Should Again Be Illegal

    What Is Mathematics? More Basics
    The Definition of Mathematics Used in This Book
    The Logic of Nature and the Logic of Civilization
    Box-Flow Models
    Cycles and Scales in Nature and Mathematics
    The Art of Estimating

    We All Soak in a Synthetic Chemical Soup
    Thomas Latimer’s Unfortunate Experience
    What’s in the Synthetic Chemical Soup?
    Synthetic Flows and Assumptions
    The Flow of Information about Synthetic Flows
    You Cannot Do Just One Thing: Two Examples

    Mathematics: Food, Soil, Water, Air, Free Speech
    The "Hour Glass" Industrial Agriculture Machine
    Industrial Agriculture Logic vs. the Logic of Life
    Fast Foods, Few Foods, and Fossil Fuels
    Genetic Engineering: One Mathematical Perspective
    Toxic Sludge Is Good for You!
    Media Concentration
    Oceans: Rising Acidity and Disappearing Life
    Stocks, Flows and Distributions of Food
    My Definition of Food
    Choices: Central vs. Diverse Decision Making
    Correlations

    Mathematics and Energy
    How Much Solar Energy Is There?
    Solar Energy Is There, Do We Know How to Get It?
    Four Falsehoods
    Nuclear Power: Is It Too Cheap to Meter?
    Net Primary Productivity and Ecological Footprints
    NPP, Soil, Biofuels, and the Super Grid

    The Brower–Cousteau Model of the Earth
    How Heavily Do We Weigh upon the Earth?
    Mining and Damming: Massive Rearrangements
    Fish, Forests, Deserts, and Soil: Revisited
    The Cousteau–Brower Earth Model

    Fuzzy Logic, Sharp Logic, Frames, and Bigger Pictures
    Sharp (Aristotelian) Logic: A Standard Syllogism
    Measuring Truth Values: Fuzzy/Measured Logic
    Definitions, Assumptions and the Frame of Debate
    Humans in Denial — Nature Cannot Be Fooled — Gravity Exists
    The Bigger Picture Principle

    The Dunbar Number
    The Sustainability Hypothesis: Is It True?
    The Dunbar Number
    Public Relations, Political Power, and the Organization of Society
    Political Uses of Fear
    Confronting Fear (and Apathy): Organizing Your Community for Self-Preservation and Sustainability

    MATH AND NATURE: THE NATURE OF MATH
    One Pattern Viewed via Geometry and Numbers: Mathese
    The Square Numbers of Pythagoras
    The Language of Mathematics: Mathese
    A General Expression in Mathese: A Formula for Odd Numbers
    An Important Word in Mathese: Σ
    Sentences in Mathese: Equations with Σ and a Dummy Variable
    Induction, Deduction, Mathematical Research, and Mathematical Proofs
    What Is a Mathematical Proof?
    What Is a Deductive System?
    Originalidad es volver al Origen

    Axioms and Atoms
    Molecules and Atoms; the Atomic Number and the Atomic Mass Number of an Atom
    Scaling and Our First Two Axioms for Numbers
    Our First Axiom for Numbers
    Number 1: Its Definition, Properties, Uniqueness
    The Definition of Multiplicative Inverse
    Our Second Axiom for Numbers
    If … , Then … . Our First Proofs
    Return to the Problem: How Many Protons in One Gram of Protons?
    What Is a Mole? Scaling Up from the Atomic to the Human Scale

    Five More Axioms for Numbers
    Associativity, Identity, and Inverses for +
    Commutativity of + and *
    Distributivity

    What Patterns Can Be Deduced in Our Deductive System?
    Playing the Mathematics Game
    Rules for Playing the Mathematics Game
    The Usual Rules for Fractions Are Part of Our Deductive System
    Can You Tell the Difference between True and False Patterns?
    More Exercises

    ONE OF THE OLDEST MATHEMATICAL PATTERNS
    A Short Story and Some Numberless Mathematics
    Relations Defined as Collections of Ordered Pairs
    Symmetric Relations
    Transitive and Reflexive Relations
    Equivalence Relations
    Relations That Are Functions

    A Set of Social Rules for the Warlpiri People
    The Section Rule
    The Mother Relation Rules
    The Marriage Rules
    The Father Relation Rules
    Cultural Contexts in Which Mathematics Is Done

    COUNTING
    Counting Exactly
    Numeracy
    Counting Social Security Numbers among Other Things
    Permutations: Order Matters
    There Are n! Permutations of n Distinct Objects
    Counting Connections: Order Does Not Matter

    Equivalence Relations and Counting
    Using Equivalence Relations to Count
    Combinations: Order Does Not Matter
    Additional Counting Problems
    DNA Computing
    More Exercises

    BOX MODELS: POPULATION, MONEY, RECYCLING
    Some Population Numbers
    Counting People in the World
    A Fundamental Axiom of Population Ecology
    Counting People in the United States

    Basic Mathematical Patterns in Population Growth
    Schwartz Charts Are Box-Flow Models
    Our First Population Model: Simple Boxes and Flows
    Three Basic Operations: Addition, Multiplication, and Exponentiation
    Defining Logarithm Functions
    Computing Formulas for Doubling Times
    Natural Logarithms
    Logarithms to Any Base
    Further Study: More Complicated Models and Chaos Theory
    The World’s Human Population: One Box

    Box Models: Money, Recycling, Epidemics
    Some Obvious Laws Humans Continue to Ignore
    A Linear Multiplier Effect: Some Mathematics of Money
    Multiplier Effects Arising from Cycles: The Mathematics of Recycling
    A Simple Model of an Influenza Epidemic

    CHANCE: HEALTH, SURVEILLANCE, SPIES, AND VOTING
    Chance: Health and News
    If You Test HIV Positive, Are You Infected?
    Chance and the "News

    Surveillance, Spies, Snitches, Loss of Privacy, and Life
    Is Someone Watching You? Why?
    Living with a Police Escort?
    I’m Not Worried, I’ve Done Nothing Wrong

    Identity Theft, Encryption, Torture, Planespotting
    Encryption Mathematics and Identity Protection
    Extraordinary Rendition = Kidnapping and Torture
    Planespotting: A Self-Organizing Countermeasure the CIA Did Not Anticipate
    Bigger Pictures and the CIA

    Voting in the 21st Century
    Stealing Elections Is a Time Honored Tradition
    A Simple Solution Exists
    Two Modest Proposals

    ECONOMICS
    What Exactly Is Economics?
    It Takes the Longest Time to Think of the Simplest Things
    A Preview of Two Laws of Nature
    Three Kinds of Economists
    The Human Economy Depends on Nature’s Flows of Energy and Entropy
    Nature’s Services and Human Wealth: Important Calculations
    How We Treat Each Other: How We Treat Nature — The Tragedy of the Commons

    Mathematical Concepts and Economics
    Misapplied Mathematics
    New Mathematical Patterns: Self-Organizing Systems
    Finding a Niche: Habits and Habitats

    The Concept of Money
    Financial Wealth and Real Wealth
    Is Financial Collapse Possible Now?
    Follow the Money
    Are You Paying More or Less Than Your Fair Share of Taxes?
    Financial Growth vs. Fish Growth
    Fractional Reserve Banking: An Amazing Mathematical Trick

    Distributed vs. Centralized Control and Decision Making
    Farms: To Be Run by Few or by Many?
    Utilities: MUNI or Investor-Owned?
    Linux vs. Microsoft
    Medicine for People or for Profit or Both?
    A Little History
    An Example of the Need for Fuzzy Logic: The Definition of Poverty

    Energy and Thermodynamics
    Energy and the First Law of Thermodynamics
    The First Law of Thermodynamics
    Entropy and the Second Law of Thermodynamics
    Early Statements of the Second Law of Thermodynamics
    Algebraic Statement of the Second Law of Thermodynamics
    So What Is Entropy and Can We Measure It?
    Some Applications of the Second Law of Thermodynamics: Power Plants and Hurricanes
    Hiking up a Mountain
    Understanding Entropy with a Little Mathematics

    The Financial Mathematics of Loans, Debts, and Compound Interest
    Simple and Compound Interest: A Review
    How Much Does a Debt Really Cost You? Buying on Time and/or Installment Plans. Amortization. The Four Important Numbers: P, R, r, n
    Examples of Individual Debt: Rent-to-Own, Credit Cards, and Loans

    MEDIA LITERACY
    Information Flow in the 21st Century
    Investigative Journalism Requires Cash
    Thesis: The Range of Debate is Too Narrow Now
    Time Series Test and Multiple Source Test
    Measuring the Range of Debate
    Distractions and Illusions

    Media Literacy: Censorship and Propaganda
    Filters and Censors
    Censorship: External and Internal
    Conclusion and Epilog: Where Are the Adults?

    References

    Index

    Biography

    Martin Walter is a professor in the Department of Mathematics at the University of Colorado at Boulder. Dr. Walter is a Sloan, Woodrow Wilson, and National Science Foundation Fellow as well as a member of the American Mathematical Society and Mathematical Association of America. He has lectured or taught in various countries, including Japan, China, Poland, Romania, Australia, Belgium, Norway, Sweden, Denmark, England, Germany, India, Italy, Mexico, Puerto Rico, Canada, and Brazil.

    The book can be recommended to all those readers who are interested in applied mathematics as well as to those who do not think of themselves as mathematicians yet being interested in laws and relationships in which mathematics may be a helpful tool.
    —Herbert S. Buscher, Zentralblatt MATH 1211

    The book is heavily referenced … there are many detailed exercises designed to highlight how mathematics can be used to explain natural phenomena and human behavior and its consequences. … this book could serve as a text for courses in applied mathematics and a resource for study material in many other subject areas …
    MAA Reviews, July 2011

    "Recently I purchased Mathematics for the Environment and find it to be one of the most fascinating and comprehensive that I have ever encountered. Next semester I will be teaching a class on mathematical modeling for seniors in our department, and intend to use (with attribution of course) some of the examples and questions. Never have I seen such an eclectic set of topics in a single volume. Basically I am writing to thank you for it, and to say ‘Bravo’!"
    —John A. Adam, Ph.D., University Professor and Professor of Mathematics Department of Mathematics & Statistics Engineering & Computational Sciences Building Old Dominion University, Norfolk, Virginia, USA