Difference between revisions of "Chapter 73: 706-713"
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'''Sir William Johnson'''<br> | '''Sir William Johnson'''<br> | ||
See page [http://masondixon.pynchonwiki.com/wiki/index.php?title=Chapter_54:_525-541#Page_532 532]. | See page [http://masondixon.pynchonwiki.com/wiki/index.php?title=Chapter_54:_525-541#Page_532 532]. | ||
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| + | '''Zeno's Paradox'''<br> | ||
| + | Zeno of Elea (ca. 490 BC? – ca. 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Betrand Russell has described as "immeasurably subtle and profound"... This seems to be a reference to the paradox of Achilles and the Tortoise: Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox. From [http://en.wikipedia.org/wiki/Zeno%27s_paradoxes WIKI] | ||
==Page 707== | ==Page 707== | ||
Revision as of 09:54, 9 November 2009
Contents
Page 706
Sir William Johnson
See page 532.
Zeno's Paradox
Zeno of Elea (ca. 490 BC? – ca. 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Betrand Russell has described as "immeasurably subtle and profound"... This seems to be a reference to the paradox of Achilles and the Tortoise: Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox. From WIKI
Page 707
When they happen across an Adventurer from Mexico, and the ancient City he has discover'd beneath the Earth..."
Yet another reference to Hollow Earth theory. See p.548.
