I. Bernard Cohen (1914–2003)

I was excited to find this short book in the stacks, but it ultimately fell flat as a whole. I enjoyed what the author set out to achieve: describing the many uses of numbers and some of the first (European) occurrences in the historical record. However, I finished the book craving more perspective on the significance and evolution of those changes in modern life.

The book is composed of many short chapters at first, but then concludes with two long chapters on Quetelet and Florence Nightingale. The focus seems to go from a critical analysis of numbers in society/politics, but then turns into biography. I wish the author had stayed focused on one or the other because both treatments are superficial. Surprisingly, computers -- humanity's number machines -- play a very small part of this book and are finally mentioned in the epilogue very cursorily.

While I'm very critical of the book overall, the things that shined were the historical anecdotes. Here are some highlights:
- p.19 — Egyptians were able to write large numbers in 3500 BCE
- p.19 — A description of how numbers can prove the feasibility of a reverse-engineered method thought to be used by Egyptians to build the pyramids.
- p.20 — Pyramids were tallest structure until Eiffel Tower
- p.29 — An account of census taking in the Bible: “Go number Israel and bring the number to David so that he might “know it”".
- p.30 — The mystery of the "sin" of census taking. Why did David sin by ordering a census and lead to death by plague of 70,000?
- p.28 — In the Bible, census takers were called “enumerators”.
- p.36 — The birth of modern science was based on direct confrontation of nature by experiment and obseration, but more importantly a dependence on the numbers (numerical measurement) of actual experience.
- p.37 — [For ancients prior to the Scientific Revolution] the goal of science was not to seek laws of nature expressed in terms of numbers or number-relations.
- p.46 — Leeuwenhoek makes a scale argument about sperm. He calculates that there's more sperm than the number of people the Earth can support.
- p.103 — The origin of the word statistics is from “statist” in Germany and is tied to politics.
- p.62 — Numerology is used to conveniently prove “evidence” against the papacy.
- p.101 — Lavoisier belived the “science of political economy” would cease to exist because all problems would be solved with no disagreements whatsoever using mathematics.
- p.97 — By 1800, it was the age of precision. In measuring time alone, there was an increase in precision of a factor of 200 compared to the 1 minute of arc in Tycho Brahe’s time.
- p.119 — Guerry’s use of the word “ordonnateur” may have led to the official French word for computer, “ordinateur”.
- The budget of crimes as statistics comes of age: “Society prepares the crime, and the guilty person is only the instrument”
- Charles Dickens was concerned about the use of averages to justify treatment of the common person. The use of an "average" justified bad working conditions.
- Joyce’s Ulysses was allowed to be published and distributed in the US based on Supreme Court Judge Woolsey’s decision that a person with “average sex instincts” would not be affected by the book. “L’homme moyen sensuel”. Already a ruling was based on an "average".
- p. 171 — The free will of admins (a scary thought). “For Nightingale, what mattered was the free will of administrators, who can choose whether to try to change the conditions that affect the way people act.”
- p. 173 — Nightingale wanted to "Bring mankind to perfection".
- p.174 — Nightingale believed that "Diagrams afford relief to the mind"

I was delighted to read some historical bits about one of my favorite scientists, James Clerk Maxwell. His wit came through when he satirized the British Association for the Advancement of Science (BAAS). “Ye British Asses, who expect to hear/ Ever some new thing.” (p. 149). A historical link is also unearthed between Maxwell and Quetelet. “The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet… there is an influence of the social sciences on the natural sciences.” (p.145).

This book awarded me some interesting ideas, but there are better books on the history of math and numbers, especially by Morris Kline. Read this if you are interested in historical anecdotes over understanding mathematical progress.… (more)