Is God a Mathematician_ - Mario Livio [125]
Actually, Newton may have written that phrase: It is impossible to know for sure whether Newton meant this as an insult or not. R.K. Merton did find “on the shoulders of giants” to be a fairly common phrase by Newton’s time (Merton 1993).
In his reply to Hooke’s letter: Impressively, Newton’s entire correspondence has been collected in Turnbull, Scott, Hall, and Tilling 1959–77.
The feud between the two scientists: The feud is described in great detail in a few excellent biographies of Newton, including Westfall 1983, Hall 1992, and Gleick 2003.
looked like nothing but a collection: In an essay published in 1674, Hooke wrote about gravity that its “attractive powers are so much more powerful in operating, by how much nearer the body wrought upon is to their own centers.” Hence, while he had the correct intuition, he failed to describe it mathematically.
“We offer this work as the mathematical principles”: There are a number of excellent translations of Newton’s Principia, including Motte 1729 and Cohen and Whitman 1999 (see Newton 1729). The most accessible with helpful notes is Chandrasekhar’s 1995 edited version. The general concept of a law of gravity and its history is discussed extensively in Girifalco 2008, Greene 2004, Hawking 2007, and Penrose 2004.
even in his more experimentally based book on light: Newton 1730.
In his Memoirs of Sir Isaac Newton’s Life: Stukeley 1752. In addition to the full biographies, there are small books describing certain episodes in the life of Newton or his relatives. Among these I note De Morgan 1885 and Craig 1946.
Irrespective of whether the mythical event: In his biography of Newton, David Brewster wrote in 1831: “The celebrated apple tree, the fall of one of the apples of which is said to have turned the attention of Newton to the subject of gravity, was destroyed by wind about four years ago; but Mr. Turnor [the proprietor of Newton’s house in Woolsthorpe] has preserved it in the form of a chair.” Brewster 1831.
It may have all started in Newton’s youth: A good description of Newton’s studies of mathematics is given in Hall 1992.
“And the same year [1666] I began”: The memorandum is in the Portsmouth Collection. There are other documents suggesting that Newton did indeed think of the inverse square law of gravity during the plague years. See Whiston 1753, for example.
For reasons that are not entirely clear: For a general discussion of the reasons for the delay in Newton’s announcement of the law of gravitation see Cajori 1928 and Cohen 1982. In the next section I summarize what I regard as the two most convincing suggestions as to what the reasons might have been.
“In 1684 Dr Halley came”: De Moivre was recalling here what Newton had described to him.
Some even speculate that he: This is suggested by Cohen 1982, to name just one source.
In his address at the bicentenary: Glaisher 1888.
For Newton, the world’s very existence: In Principia he says about God: “He is omnipresent not only virtually but also substantially…He is all eye, all ear, all brain, all arm, all force of sensing, of understanding, and of acting.” In a manuscript from the early 1700s, purchased at Sotheby’s in 1936 and exhibited in Jerusalem in 2007, Newton used the biblical book of Daniel to calculate the date for the apocalypse. In case you are worried, he reached the conclusion that he saw no reason for “its [the world] ending sooner” than 2060.
The validity of the cosmological, teleological: For excellent recent discussions of the history of these arguments and an assessment of their logical soundness, see Dennett 2006, Dawkins 2006, and Paulos 2008.
This type of logical maneuvering: See Dennett 2006, Dawkins 2006, Paulos 2008.
Chapter 5. Statisticians and Probabilists: The Science of Uncertainty
The branch of mathematics called calculus: Extremely accessible descriptions of calculus and its applications can be found in Berlinski 1996, Kline 1967, and Bell 1951. Somewhat more technical, but truly excellent is Kline 1972.
were members