4 ms·

Xeno's Paradox

LogicHoleFlaw 17y ago
Gah, Zeno's Paradox. A professor tried to stump the class with that one in an introductory philosophy course I took. I then proceeded to introduce him the fundamental principles of calculus with respect to limits. I think I threw in some snark about how this was the difference between mathematicians and philosophers - mathematicians actually find solutions! Then scientists ensure they apply to reality, and engineers make them useful.
- jordyhoyt 17y ago
  Then, I'm afraid, you're missing the point of the paradox. There are a few stories (improperly called "paradoxes") attributed to Zeno: http://en.wikipedia.org/wiki/Zeno%27s_paradoxes http://en.wikipedia.org/wiki/Zeno%27s_paradoxes You're probably thinking of The Dichotomy. This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Further, very interesting reading: http://www.mathpages.com/rr/s3-07/3-07.htm http://www.mathpages.com/rr/s3-07/3-07.htm Math just gave us a way of coming up with the obvious answer, it does not describe the nature of the universe, which is what the philosophy was attempting.
  - 321abc 17y ago
    Also, just because a bunch of puny humans manage to convince each other that the world must be a certain way doesn't mean it actually is.
    - joeyo 17y ago
      That depends on what your meaning of the word 'is' is.
  - ewjordan 17y ago
    This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Actually, neither story proves either claim, which is apparent since there are rigorously defined and perfectly self consistent mathematical theories for each case. Philosophers just don't like them because they involve actual mathematical definitions, so they hide their heads in the sand and pretend they don't exist. From that Wikipedia article, a quote from Russell: Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned. In other words, it's very easy to argue that infinite processes, continuous space, or motion in space don't make any sense if you can't be bothered to learn how they're rigorously defined in the mathematical theory you're arguing about. And FWIW, philosophy may have been attempting to describe the nature of the universe, but I can't come up with a single example of an actual physical result that's come from the field. You may argue that math and physics sprung from philosophy, but realize that those two disciplines provide most of philosophy's harshest detractors these days. And as far as retroactive claims that if people had listened to Zeno we might have stumbled upon special relativity earlier? (from the second link) Flat out bull poopy. The "inconsistencies" that special relativity resolves have nothing to do with classical mechanics at all, they have to do with E+M, and without a well tested and reliable E+M theory and the Michelson-Morley experiment to directly show us that the speed of light is constant regardless of motion we would have dismissed relativity theory as far too strange to be true (which, amusingly enough and in spite of massive evidence to the contrary, is a claim I've heard straight from the mouth of a tenured philosophy professor at an Ivy League school). An infinite speed of light would lead to a perfectly valid classical mechanics, albeit one that we could (now) prove is wrong, and there's nothing more logically consistent about either relativity or quantum mechanics that would have led us to either one without strenuous experimentation and Real Science.
- dfranke 17y ago
  The problem with philosophers is not that they can't find solutions, it's that they're incapable of rejecting bad ones. There are plenty of good ideas in philosophy, but you can't pick them out from the flood stupid ones without thinking everything through from square one on your own. Hence the reason that millenia later we're still here debating Zeno, while physicists no longer have to bother giving much thought to 100-year-old rejected theories. A university dean approaches the chair of the Physics department and tells him, "Look, we really need to talk your budget. Every year it's particle accelerator this and supercomputer that. You're bleeding the college dry. Why can't you be more like the Math department? All they ever ask us for is pencils and chalkboards and wastebaskets. Or better yet, why can't you be like the Philosophy department? They don't even ask for wastebaskets!"

Xeno's Paradox

Gah, Zeno's Paradox. A professor tried to stump the class with that one in an introductory philosophy course I took. I then proceeded to introduce him the fundamental principles of calculus with respect to limits. I think I threw in some snark about how this was the difference between mathematicians and philosophers - mathematicians actually find solutions! Then scientists ensure they apply to reality, and engineers make them useful.

jordyhoyt 17y ago
Then, I'm afraid, you're missing the point of the paradox. There are a few stories (improperly called "paradoxes") attributed to Zeno: http://en.wikipedia.org/wiki/Zeno%27s_paradoxes http://en.wikipedia.org/wiki/Zeno%27s_paradoxes You're probably thinking of The Dichotomy. This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Further, very interesting reading: http://www.mathpages.com/rr/s3-07/3-07.htm http://www.mathpages.com/rr/s3-07/3-07.htm Math just gave us a way of coming up with the obvious answer, it does not describe the nature of the universe, which is what the philosophy was attempting.
- 321abc 17y ago
  Also, just because a bunch of puny humans manage to convince each other that the world must be a certain way doesn't mean it actually is.
  - joeyo 17y ago
    That depends on what your meaning of the word 'is' is.
- ewjordan 17y ago
  This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Actually, neither story proves either claim, which is apparent since there are rigorously defined and perfectly self consistent mathematical theories for each case. Philosophers just don't like them because they involve actual mathematical definitions, so they hide their heads in the sand and pretend they don't exist. From that Wikipedia article, a quote from Russell: Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned. In other words, it's very easy to argue that infinite processes, continuous space, or motion in space don't make any sense if you can't be bothered to learn how they're rigorously defined in the mathematical theory you're arguing about. And FWIW, philosophy may have been attempting to describe the nature of the universe, but I can't come up with a single example of an actual physical result that's come from the field. You may argue that math and physics sprung from philosophy, but realize that those two disciplines provide most of philosophy's harshest detractors these days. And as far as retroactive claims that if people had listened to Zeno we might have stumbled upon special relativity earlier? (from the second link) Flat out bull poopy. The "inconsistencies" that special relativity resolves have nothing to do with classical mechanics at all, they have to do with E+M, and without a well tested and reliable E+M theory and the Michelson-Morley experiment to directly show us that the speed of light is constant regardless of motion we would have dismissed relativity theory as far too strange to be true (which, amusingly enough and in spite of massive evidence to the contrary, is a claim I've heard straight from the mouth of a tenured philosophy professor at an Ivy League school). An infinite speed of light would lead to a perfectly valid classical mechanics, albeit one that we could (now) prove is wrong, and there's nothing more logically consistent about either relativity or quantum mechanics that would have led us to either one without strenuous experimentation and Real Science.
dfranke 17y ago
The problem with philosophers is not that they can't find solutions, it's that they're incapable of rejecting bad ones. There are plenty of good ideas in philosophy, but you can't pick them out from the flood stupid ones without thinking everything through from square one on your own. Hence the reason that millenia later we're still here debating Zeno, while physicists no longer have to bother giving much thought to 100-year-old rejected theories. A university dean approaches the chair of the Physics department and tells him, "Look, we really need to talk your budget. Every year it's particle accelerator this and supercomputer that. You're bleeding the college dry. Why can't you be more like the Math department? All they ever ask us for is pencils and chalkboards and wastebaskets. Or better yet, why can't you be like the Philosophy department? They don't even ask for wastebaskets!"