The Clockwork Universe Part 23

42 The question of whether vacuums could exist spurred long, angry debates. The invention of the air pump did not settle the debate, in the view of Leibniz and some others, because even if a jar no longer contained The question of whether vacuums could exist spurred long, angry debates. The invention of the air pump did not settle the debate, in the view of Leibniz and some others, because even if a jar no longer contained air air it might still contain some more ethereal fluid. Leibniz and Descartes both maintained that the very notion of a vacuum was nonsensical-how could there be a place containing nothing at all, when the meaning of the word it might still contain some more ethereal fluid. Leibniz and Descartes both maintained that the very notion of a vacuum was nonsensical-how could there be a place containing nothing at all, when the meaning of the word place place is "the location where something happens to be"? Newton and Pascal insisted just as vehemently that vacuums were real. Descartes contended, cattily, that the only vacuum was in Pascal's head. is "the location where something happens to be"? Newton and Pascal insisted just as vehemently that vacuums were real. Descartes contended, cattily, that the only vacuum was in Pascal's head.

43 If the first block were 1 inch thick, the next inch, then , , 1/5, and so on, the tower If the first block were 1 inch thick, the next inch, then , , 1/5, and so on, the tower would would climb infinitely high (although it would rise excruciatingly slowly). climb infinitely high (although it would rise excruciatingly slowly).

44 A sequence A sequence may may attain its goal. The sequence 1, 1, 1,... has the number 1 as its limit. But a "typical" sequence draws ever nearer to its goal without actually touching it. The sequence .9, .99, .999,... never reaches its limit, which is the number 1. attain its goal. The sequence 1, 1, 1,... has the number 1 as its limit. But a "typical" sequence draws ever nearer to its goal without actually touching it. The sequence .9, .99, .999,... never reaches its limit, which is the number 1.

45 Gilbert and Sullivan's Major-General knew it well, along with much else. "About binomial theorem I'm teeming with a lot o' news / With many cheerful facts about the square of the hypotenuse." Gilbert and Sullivan's Major-General knew it well, along with much else. "About binomial theorem I'm teeming with a lot o' news / With many cheerful facts about the square of the hypotenuse."

46 Unbeknownst to Leibniz, the English mathematician and astronomer Thomas Harriot had been the first to discuss binary numbers, decades before. But Harriot never published any of his work, and his papers went unseen until the late 1700s. It turns out that Harriot had recorded a number of other firsts as well; Harriot turned a telescope to the sky a few weeks before Galileo did. Unbeknownst to Leibniz, the English mathematician and astronomer Thomas Harriot had been the first to discuss binary numbers, decades before. But Harriot never published any of his work, and his papers went unseen until the late 1700s. It turns out that Harriot had recorded a number of other firsts as well; Harriot turned a telescope to the sky a few weeks before Galileo did.

47 Sometimes the right notation can even hint at a deep, surprising insight. Simply using decimal notation, and then adding column by column, suggests that 1 + .1 + .01 + .001 +... = 1.11111... , and not infinity. Sometimes the right notation can even hint at a deep, surprising insight. Simply using decimal notation, and then adding column by column, suggests that 1 + .1 + .01 + .001 +... = 1.11111... , and not infinity.

48 Most people "know" not just that an apple fell but that it bonked Newton on the head. Most people "know" not just that an apple fell but that it bonked Newton on the head.

49 Another exotic import, tea, had arrived at about the same time, although coffee caught on first. On September 25, 1660, Pepys wrote in his diary that "I did send for a cup of tee (a China drink) of which I never had drank before." Another exotic import, tea, had arrived at about the same time, although coffee caught on first. On September 25, 1660, Pepys wrote in his diary that "I did send for a cup of tee (a China drink) of which I never had drank before."

50 The statement The statement if a planet travels in an ellipse if a planet travels in an ellipse, then it follows an inverse-square law then it follows an inverse-square law is different from the statement is different from the statement if a planet follows an inverse-square law if a planet follows an inverse-square law, then it travels in an ellipse. then it travels in an ellipse. It might have been that one was true but the other was not. It might have been that one was true but the other was not. If someone owns a dog If someone owns a dog, then he owns a pet then he owns a pet is true; is true; if someone owns a pet if someone owns a pet, then he owns a dog then he owns a dog is not. In this case it was clear to Newton (though bewilderingly obscure to others) that if one statement was true, the other had to be true as well. is not. In this case it was clear to Newton (though bewilderingly obscure to others) that if one statement was true, the other had to be true as well.

51 Sixteen hundred years before Newton, Plutarch wrote that Archimedes grew so absorbed in his thoughts that he "would often forget his food and neglect his person" and have to be "carried by absolute violence to bathe." Sixteen hundred years before Newton, Plutarch wrote that Archimedes grew so absorbed in his thoughts that he "would often forget his food and neglect his person" and have to be "carried by absolute violence to bathe."

52 In time, this bewilderment died away. Darwin noted impatiently that, although his critics demanded that he explain where intelligence and awareness come from, n.o.body demanded a similar account of gravity. "Why is thought being a secretion of brain more wonderful than gravity a property of matter?" he asked. In time, this bewilderment died away. Darwin noted impatiently that, although his critics demanded that he explain where intelligence and awareness come from, n.o.body demanded a similar account of gravity. "Why is thought being a secretion of brain more wonderful than gravity a property of matter?" he asked.

53 The debate over whether we should look at scientists' characters and motives, or if it is only their findings that matter, continues today. "Science doesn't work because we're all nice," a NASA climatologist declared in November 2009, in the midst of a dispute over global warming. "Newton may have been an a.s.s, but the theory of gravity still works." The debate over whether we should look at scientists' characters and motives, or if it is only their findings that matter, continues today. "Science doesn't work because we're all nice," a NASA climatologist declared in November 2009, in the midst of a dispute over global warming. "Newton may have been an a.s.s, but the theory of gravity still works."