World Famous Comics: Zeno's Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time
Zeno's Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time
By: Joseph Mazur Publisher: Plume Average Rating: Binding: Paperback Label: Plume Number of Items: 1 Number of Pages: 272 Publication Date: March 25, 2008
Product Description: The fascinating story of an ancient riddle—and what it reveals about the nature of time and space
Three millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno’s Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs—but through it all, the paradox of motion remains.
Run faster than Achilles!, and perhaps the book won't overtake you and you won't have to buy it.
I purchased this product some time ago, but didn't feel up to the task of reviewing it. What for? Who heeds bad revs?
It's a bad (or rather, unworthy of its theme), bad book all right. I'll be brief:
1) Its exposure of philosophy is superficial and biased (I don't have the space here to give examples, but trust me).
2) It's repetitive. For example, the stadium paradox is covered at least thrice: in page 4 of the Introduction (where it's stated that Aristotle exposed it as based on a fallacy); in pp. 29/31, where Mazur gives Zeno his due; and in page 41/42, where the book says Aristotle failed to understand the nature of the paradox. The other paradoxes (especially the arrow) are also analized several times.
3) It's incoherently written. For example, in page 132, Mazur writes "The arrow paradox also requires an understanding of limits as a mathematical model for instantaneous velocity, which calculus treats as a derivative, an instrument that creates limits of average changes in a dependent variety in small intervals on an independent variable. The model here is to view each point on the arrow's trajectory as though it were a limit of a sequence of rational numbers on the number line, so the arrow's path is assured a persistent even flow of space in the continuity of time. In effect it assumes, quite correctly, that all numbers on the number line are convergent sequences of rational numbers". Half a page (in the book's oversize font) completely wasted. And don't you think that a reader who understands what "convergent sequences of rational numbers" means would also know what is a real number?
4) Mazur manages to be at the same time irrelevant, at the limit of his knowledge, and a provider of meaningless detail. Now hear this (p. 196)!: "The quantum mechanics story began when a German physicist named Max Karl Ernst Ludwig Planck asked why subatomic particles radiate a blue light when they travel through a non vacuum-medium faster than the speed of light in that medium". Why, Mr. Mazur, methought Cerenkov radiation was discovered much later. What Planck (what would have happened had he had only three names?) was looking for was a way to avoid the so called "ultraviolet catastrophe" in the black body radiation formula.
Bear in mind that each of these examples could be multiplied almost indefinitely. On the other hand, nothing on supertasks, or the legitimacy of conflating the geometrical and the real number continua, or the conceptual resemblance between Zeno's paradoxes and Kant's antinomies, and the question these place on the possibility of a represtation-based understanding of Nature; ... .
Do you think I'm unfair? But Mazur strikes me as intellectually dishonest in the same sense as Lacan when he equated, before an innocent crowd of bewildered and awed disciples, the phallus with i, the unity of imaginary numbers.
In short, if you think that the story of math and physics consists of knowing that in 1586 Stevin, Maurice & alia often met at a tavern where "water, dripping from cracks in its massive stone walls, kept [it] cool and damp. Candles and torch sconces provided moderate light in the windowless room. An intoxicating smell of fermenting spirits seeped from a whiskey and brandy distillery next door. Beer was cheap", and that they "would often sit together at a long sticky oak table coated with layers of sugars dried from decades of beer spills" (pp. 68/69), or that Dirichlet's names were Johann Peter Gustav Lejeune (p. 116), then you'll learn a lot from this book.
In any other case, avoid this travesty.
dialectic Fun to see this book. The subject is still alive.
For someone not acquainted with Zeno's paradoxes, here is a book by a contemporary author, supported by a contemporary publisher, for a contemporary audience. But the subject is ancient, having been discussed by authors since Aristotle. And as might be expected, an older literature is certainly available for those who would like to learn more of the details.
I have just one critique. I would've preferred a healthier skepticism about Plato-- especially where Plato uses second-hand sources about Parmenides, Zeno, and Socrates. Aristotle said the "forms" were from Plato, not from Socrates. So when reading, for example, Socrates' story of the cave, because of Aristotle's warning I try to strip away what might be suspect as Plato's and instead look underneath for a basic story that Socrates might actually have told. The basic story of the cave seems to be that only through "dialectic" can you get out of the cave of darkness to see what you really are. To me Plato's writings also seem inaccurate about "dialectic." Whatever "dialectic" is, I know for sure that you are not going to get out of the cave of darkness to see what you really are by participating in dialectic with me. And based on what Aristotle said, I don't think you could've gotten out of the cave of darkness to see what you really are by dialectic with Plato. It seems to me that only dialectic with Socrates could have guided you out of the cave of darkness to see what you really are. Socrates must have had a gift for dialectic that could guide a person out of the cave.
For the reader of this book, the relevance is that Aristotle seems to have credited Zeno with inventing dialectic, which somehow must have involved the paradoxes. Zeno was a student of Parmenides, so it seems to me that it was Parmenides who had the gift for dialectic that could guide a person out of the cave, and most likely not Zeno. Though perhaps, by using his paradoxes as tools, Zeno was trying to help Parmenides. Due to the lack of texts so much is left to the imagination that it almost seems better suited to poetry or creative story telling. Here's one attempt...
Parmenides had the gift for dialectic that could guide a person out of the cave of darkness to see the truth. But Zeno didn't have that gift, and Plato didn't have that gift. When Parmenides died, Socrates somehow inherited that gift for dialectic from him. More than just a recording of words and thoughts (as in Plato's writing), dialectic that can guide you out of the cave involves non-verbal communication such as tone of voice, tempo, stress, pitch, intonation, prosody, as well as eye contact, facial expression, hand movements, body language, the sound of laughter, the sound of "ahas," human touch, and so on and so on-- none of which can be captured in written texts (like Plato's).
The paradoxes would have come into play something like this--
Zeno is talking with a person about the truth to which Parmenides had guided him.
(Parmenides' poem tells of a journey to a door that opens, where you meet truth. Rather than "true" in the sense of something that has an opposite-- i.e., "false"-- the truth in Parmenides' poem is a goddess. And just as with a goddess, truth can be admired for its beauty, truth has a presence of being that can be experienced, and truth can take you into love. In Parmenides poem, truth is not just something with an opposite, as in the sense of "true" or "false." Rather, truth is something that exists. It exists inside of you. And at the end of a journey with Parmenides as your guide, there is a door . . .)
To the reasoning mind-- perhaps a mind granting ultimate authority to written texts and therefore only to those ideas available through written words-- the journey that Parmenides describes by analogy might be a logical impossibility. And here is where Zeno might usefully have employed his paradoxes as an attempt to help.
Not to undertake the journey with Parmenides as a guide into the truth he describes would be like Achilles listening to a very clever tortoise describe the paradox of the race, and as a result give up trying without even approaching the starting line. In Zeno's paradox of the race, the tortoise is like one's own reasoning mind-- a reasoning mind, as all minds are, limited in its scope just to ideas and concepts expressible in written texts and rhetorics. But dialectic (it seems from the poem) takes a willing human being into the realm of the heart.
So in the story a conversation occurs with a person who reasons that the journey in Parmenides' poem is logically impossible. And in response Zeno says something like this:
"My friend, the tortoise is clever-- clever beyond belief. But don't listen to it. In spite of the ideas of defeat that Achilles faced when it spun its paradoxes to him, he knew in his heart that he could win the race. All he had to do was try. So for this journey, my friend, like Achilles all you need to do is to make the effort. Follow your heart. It thirsts for fulfillment, and it will tell you what you need to know."
Rather than use a departed and imagined Socrates or Parmenides to advance his own agenda (as Plato seems to have done), Zeno was trying to help a person get through logical skepticism and doubt of the reasoning mind when listening to Parmenides, live.
In such a story Mark Twain had it right. History doesn't repeat itself. It's just that, on occasion, it rhymes.
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