Math and Human Behavior

Math 250Pre-May Seminar

Axioms of Human Behavior All are created equal Knowledge and beliefs arise from

senses Behavior determined by enjoyment

of pleasure, avoidance of pain Human nature shaped by culture &

environment All act according to self interest

Jeremy Bentham (1748-1832) A “codifying

animal” Luckless in

romance Anti church/state

alliance Anti monarchy Anti packed juries Maximize pleasure,

minimize pain

Jeremy Bentham (1748-1832) Moral Calculus Cost-Benefit Analysis Democracy and Universal Suffrage Utilitarianism

John Locke (1632-1704) Tabula Rasa Rights Social Contract Limited

Government

Declaration of Independence

When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

Declaration of Independence

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are Life, Liberty and the pursuit of Happiness. That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, That whenever any Form of Government becomes destructive of these ends, it is the right of the people to alter or abolish it, and to institute new Government.

Thomas Malthus (1766-1834)

Rates of Growth:

Population vs. Production

Geometric vs. Arithmetic

David Ricardo (1772-1823) Supply and Demand

Raymond Pearl (1879-1940)and Lowell Reed (1886-

1966)

Rediscovery of Logistic Growth

John Graunt (1620-1674) and William Petty (1623-

1687)

Lambert Adolphe Jacques Quetelet (1796 –1874)

Vilfredo Pareto (1848-1923) Pareto Principle Power Laws

Vilfredo Pareto (1848-1923) Pareto Principle Power LawsDistribution of World GDP, 1989

Quintile of population IncomeRichest 20% 82.70%Second 20% 11.75%Third 20% 2.30%Fourth 20% 1.85%Poorest 20% 1.40%

Francis Galton (1822-1911)