Customer Reviews

Zeno's Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time

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This is another book written in the same engaging formula, seen before in Mazur's other books. Besides the scientific facts, there is always a human element, and bits of trivia about the people that made these amazing discoveries. A fascinating mix of facts and literature, math and philosophy that draws you into a joyfully thought-provoking read.

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.

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. An older literature is certainly available for those who would like to learn more of the details.

Dialectic is the flow of peace from micro to macro in Plato's Republic: Book I

I do have a critique. I would've preferred a healthier skepticism about Plato, especially where Plato uses second-hand sources about Parmenides, Zeno, and Socrates. Courts of law disregard hearsay and here I would apply the same rationale. For example, Aristotle said the "forms" were from Plato, not from Socrates. So when reading 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. Plato's writings also seem inaccurate about "dialectic." Whatever "dialectic" is, I know you are not going to get out of the cave of darkness to see what you really are by participating in dialectic with me. 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, either. Only dialectic with Socrates could have guided you out of the cave of darkness to see what you really are.

Given these problems of partial information and hearsay, taking full account of context may help an interested reader. Socrates and Parmenides were of different times. Socrates followed Parmenides. And although our other main source about Socrates-- Xenophon-- was neither poet nor author like Plato, neither Xenophon nor Plato was in that closest circle of friends (those most intent in their practice of Socrates' message) who called Socrates "Master." But today for our information about Socrates we mostly rely on the writings of Plato and Xenophon, Plato is preferred to Xenophon, and neither was as attuned to Socrates' message as those who called Socrates Master. By comparison, Zeno seems to have heeded the message of Parmenides more closely than Plato heeded the message of Socrates. Rather than after he died, writing down the history of this amazing person who had tried to help them (as did Plato and Xenophon), Zeno constructed his paradoxes in order to help Parmenides in Parmenides' own lifetime. So it is a possibility that Zeno heard some feedback from Parmenides about his paradoxes and applied it, while it was impossible for Plato and Xenophon to get that kind of feedback from Socrates, who had died. From this point of view, Parmenides' message is the basic context for reading about Zeno.

Translating the Greek word "auto" into "self," Parmenides' most famous quote is "the self is for thinking and being." Thinking is a pragmatic tool for getting along in the world but does have limits. In Zeno's imagined race, by relying on thinking the clever tortoise could beforehand try to get Achilles to imagine that Achilles could never catch up from the head start being granted to the tortoise and so give up the race without even trying. Because before catching up, Achilles would always have to, first, get to an imagined midpoint between himself and the tortoise. But after reaching a midpoint, how could he ever get past another midpoint? The paradox imagined in the story comes from thinking that can't get beyond the imagined next midpoint. But recall that Parmenides said "the self is for thinking AND being." To win the actual race, all Achilles would have to do is Be what he is-- a human being with extreme physical capabilities. Simply by being the human being that he is, Achilles could win any race against a tortoise. Thinking does rule the imagination and without doubt works for many purposes. But as Zeno's story of the race illustrates, being what you are-- in the paradox, being a highly fit human being racing against a tortoise-- determines the real (not imagined) outcome.

The way it looks to me is that in their own time Parmenides and Socrates each had a gift for dialectic that could guide a person beyond thinking to be "the self" that truly-- beyond imagination and thought-- exists. In my own experience, that turns out to be the most interesting context for reading about Zeno. Maybe you will find it to be that way, too.