Math and Graphs in History

1. Math and Graphs in History John V.C. Nye

2. Capitalism and Arithmetic • Frank Swetz studied how the use and teaching of mathematics was influenced by the switch from Roman to Arabic numerals in 15th century Europe • Traditional universities clung to Roman numerals • But arabic numerals allowed rapid, accurate computation

3. Advice in the 1400s • “…if the mathematical curriculum of the young man was to be confined to adding and subtracting, he could perhaps obtain instructions in a German university; but the art of multiplying and dividing, he continued, had been greatly developed in Italy which, in his opinion, was the only country where such advanced instruction could be obtained (Swetz, 1987, 14-15).”

4. An easy example • XCV / V=XIX (- II + XX + I) • MMCCCXXII / CCX=XI + XII/CCX (the remainder was XII)

5. Italians start first • Leonardo of Pisa learns and starts to promote Hindu-Arabic system starting in 1202 • Spread to counting houses and was helpful in pioneering double-entry bookkeeping • Other nations’ universities devalued arithmetic and calculation and focused on logic, rhetoric, and grammar • Italy was first nation to support lectures in algebra and to have a chair in computation

6. Rise of counting schools • Private schools to promote computational learning • Typical curriculum: multiplication, division, fractions, and information about local monetary systems • It took several centuries for the leading universities in Europe to adopt knowledge from the hindu-arabic system

7. Graphs and Statistics • Much of modern analysis is about combining numerical information with visual maps to help us SEE the connections

8. John Snow and Cholera • On August 31,1854 an outbreak of cholera in Soho, London led to the deaths of 127 in three days. Within a month 500 had died and most families fled the area. • He showed that cholera spread was tied to the location of a pump and contaminated water using a graph mapping statistical deaths

9. Old views of cholera • Early theories focused on “miasma in the atmosphere” • Nothing was done to contain cholera • Several tens of thousands of people died from 1831 to 1854 in England

10. Deaths from Cholera

11. Location of victims and exceptions • Clusters around water pump at broad street • Virtually no cases near the brewery where they didn’t drink the local water directly • Poland street warehouse, few cases but they had their own water

12. Pump Brewery

13. Economics and Economic History • Modern economics and modern economic history rose up with the development of improved mathematics and better statistical data

14. Simon Kuznets and GDP • During the Great Depression, Kuznets and a team at the National Bureau of Econ Research were tasked with creating overall measures of U.S. economy beginning in the 1930s. First report comes out in 1937

15. Major accomplishments • 1930s early GDP figures • 1940s national estimates to aid wartime planning; parallel measures in Europe • 1950s and 60; detailed measures to help with economic growth, planning, measures of personal income, input-output tables • 1960s and 1970s improved price indices for inflation

16. Early Quantitative Econ History • Initially descriptive • Minimal use of economic analysis • Big focus on Industrial Revolution but an overemphasis on individual technologies

17. Economics and History • By late 1950s more economists applying micro and macro theory and simple statistics to historical issues • Conrad and Meyer in 1958 published the first paper using statistical techniques to show that slavery was profitable in the United States South.

18. Cliometric Society • Began with an annual conference in 1960 bringing together young scholars using statistical and economic tools for the study of history • Early participants included Douglass North, William Parker, Robert Fogel, JRT Hughes, Alexander Gerschenkron, Lance Davis.

19. Early Work • Industrial Revolution • Ocean Shipping • Railroads • American Slavery • Internal and International Trade of the United States and Britain

20. Personal Research • Why The British Drink Beer Not Wine • Did Soviet Grandmasters Collude in Candidates’ Chess Tournaments? • Do Countries Systematically Falsify Economic Data? • Are Babies Born in the Year of the Dragon More Successful?