# Possible Solution To Zeno's Paradox? Breakthrough or Rubbish? **URL:** \ **Category:** Great Debates\ **Created:** [August 8, 2003, 12:44pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817 "2003-08-08T12:44:01Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Bosda\_Di\_Chi\_of\_Tricor](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bosda_di_chi_of_tricor/32/16845_2.png) [@Bosda\_Di\_Chi\_of\_Tricor](https://boards.straightdope.com/u/Bosda_Di_Chi_of_Tricor)\ **Post date:** [August 8, 2003, 12:44pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/1 "2003-08-08T12:44:01Z")
[http://story.news.yahoo.com/news?tmpl=story&cid=96&ncid=753&e=10&u=/space/20030807/sc\_space/newtheoryoftimerattleshallsofscience](http://story.news.yahoo.com/news?tmpl=story&cid=96&ncid=753&e=10&u=/space/20030807/sc_space/newtheoryoftimerattleshallsofscience) Does he have something? Or is it just looney trash? ---
**Author:** ![Aro](https://avatars.discourse-cdn.com/v4/letter/a/b3f665/32.png) [@Aro](https://boards.straightdope.com/u/Aro)\ **Post date:** [August 8, 2003, 1:11pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/2 "2003-08-08T13:11:47Z")
I don’t know about this guy, but can someone explain why Zeno’s Paradox (especially the one about _“Achilles and the tortoise”_) is considered a paradox at all? From my reading, what he thinks is an ‘infinite’ number is really an infinitely regressing number with a fixed fractional value. 1 + 0.1 + 0.01 + 0.001…etc. does not become infinitely large. Rather it becomes 10/9. It always seemed to me that Zeno completely mistook the concept of a number or distance ‘infinitely increasing’ in his ideas. Of course, it is quite possible it is I who is mistaken. ---
**Author:** ![biqu](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@biqu](https://boards.straightdope.com/u/biqu)\ **Post date:** [August 8, 2003, 1:16pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/3 "2003-08-08T13:16:27Z")
[Already covered in GQ.](http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=202417) ---
**Author:** ![biqu](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@biqu](https://boards.straightdope.com/u/biqu)\ **Post date:** [August 8, 2003, 1:21pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/4 "2003-08-08T13:21:13Z")
When I tacked a link to this article onto a [thread in CCC](http://boards.straightdope.com/sdmb/showthread.php?postid=3791680#post3791680), **Chronos** replied: > [@](#): > > I’m puzzled here. If this guy is so smart, why is he spending so much effort solving puzzles that were already solved much more cleanly and easily by Newton? Next week, why doesn’t he figure out a solution to the puzzle of retrgrade motion of the planets, based on a complicated set of crystalline spheres? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [August 8, 2003, 1:21pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/5 "2003-08-08T13:21:22Z")
Some issues: Technically, those aren’t Zeno’s Paradoxes. Zeno’s Paradox involves an arrow in flight: at any point in time, the arrow at at a point in space, so the arrow’s flight is really just a sequence of points. Regarding “Zeno’s Paradoxes”: The solution seems obvious, now. Space may be infinitely subdivisible (at least in mathematics), but so is time, and there’s a one-to-one correspondence between space and time. ---
**Author:** ![monstro](https://avatars.discourse-cdn.com/v4/letter/m/ba9def/32.png) [@monstro](https://boards.straightdope.com/u/monstro)\ **Post date:** [August 8, 2003, 2:11pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/6 "2003-08-08T14:11:29Z")
whooshy whoosh whoosh ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 8, 2003, 3:27pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/7 "2003-08-08T15:27:40Z")
> [@](#): > > \*Originally posted by TVAA \* > **Technically, those aren’t Zeno’s Paradoxes. Zeno’s Paradox involves an arrow in flight: at any point in time, the arrow at at a point in space, so the arrow’s flight is really just a sequence of points.** There are four paradoxes of motion that are generally attributed to Zeno of Elea. You can read about them and their context [here](http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Zeno_of_Elea.html). ---
**Author:** ![Bippy\_the\_Beardless](https://avatars.discourse-cdn.com/v4/letter/b/ac8455/32.png) [@Bippy\_the\_Beardless](https://boards.straightdope.com/u/Bippy_the_Beardless)\ **Post date:** [August 8, 2003, 7:59pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/8 "2003-08-08T19:59:42Z")
I can’t find any scientific web sites mentioning this guy. Is he a fake, is that what **monstro** is whooshing about? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [August 8, 2003, 8:15pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/9 "2003-08-08T20:15:48Z")
Fascinating. I vaguely remember being told that most of Zeno’s paradoxes came from his students and were only attributed to him. Although, I wonder now how we supposedly found this out… In any case: to return to the OP, this guy just seems like a loon. Zeno’s Paradox(es) were dealt with a long time ago. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 8, 2003, 8:22pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/10 "2003-08-08T20:22:40Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*In any case: to return to the OP, this guy just seems like a loon. Zeno’s Paradox(es) were dealt with a long time ago. \*\* I’ll agree with that, although I’ve never seen a resolution to the arrow paradox that I really like. I also wonder what exactly the ancients found puzzling about the stadium paradox. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 8, 2003, 8:29pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/11 "2003-08-08T20:29:31Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*In any case: to return to the OP, this guy just seems like a loon. Zeno’s Paradox(es) were dealt with a long time ago. \*\* I’ll agree with that, although I’ve never seen a resolution to the arrow paradox that I really like. I also wonder what exactly the ancients found puzzling about the stadium paradox. ---
**Author:** ![monstro](https://avatars.discourse-cdn.com/v4/letter/m/ba9def/32.png) [@monstro](https://boards.straightdope.com/u/monstro)\ **Post date:** [August 8, 2003, 8:52pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/12 "2003-08-08T20:52:52Z")
**Bippy** , whooshy = everything in this thread goes right over my head whoosh whoosh = I wish I had taken logic in college. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [August 9, 2003, 2:46am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/13 "2003-08-09T02:46:21Z")
Knowing about Symbolic Logic probably wouldn’t help, **monstro** , except possibly as a mental exercise to become more practiced in logical thought. Thinking well takes practice, but virtually everyone can learn to do it. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [August 9, 2003, 7:38am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/14 "2003-08-09T07:38:25Z")
Vorlon > [@](#): > > Space may be infinitely subdivisible (at least in mathematics), but so is time, and there’s a one-to-one correspondence between space and time. [Neither space nor time](http://www.physlink.com/Education/AskExperts/ae281.cfm) is infinitely subdivisible. > [@](#): > > Thinking well takes practice, but virtually everyone can learn to do it. Best of luck with your endeavor. ---
**Author:** ![biqu](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@biqu](https://boards.straightdope.com/u/biqu)\ **Post date:** [August 9, 2003, 8:09am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/15 "2003-08-09T08:09:06Z")
> [@](#): > > _Originally posted by Libertarian_ > [Neither space nor time](http://www.physlink.com/Education/AskExperts/ae281.cfm) is infinitely subdivisible. **Chronos** says [we don’t know either way](http://boards.straightdope.com/sdmb/showthread.php?postid=3761213#post3761213). > [@](#): > > _Originally posted by Chronos_ > The whole misunderstanding of the Planck scales is a minor pet peeve of mine. We don’t know that you can’t divide up space finer than the Planck length. In fact, we know precious little at all about what happens at the Planck length. That’s just what the Planck scale is: It’s a back-of-the-envelope estimate of the scale at which our current theories break down. > > The problem, basically, is this. We have General Relativity, which involves the constants G (Newton’s gravitational constant) and c (the speed of light), and which works very well. We also have quantum mechanics, which involves the constants hbar (Planck’s quantum of action) and c, and which also works very well. So long as we’re in a situation where only one of those theories applies (which is everything we have any experimental experience with at all), we’re fine: We apply one theory, ignore the other, and get an answer. > > But if we squish all three of those constants together in the right way, we get a unit of length (squish them slightly differently, and you can get a time, or mass, or energy, or most any other sort of unit). If we’re working with something with about that size, then both GR and QM will be significant simultaneously. Except that GR and QM don’t really seem to play well together. Surely, there’s some way of explaining what happens in such situations, but we have no idea what it is. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [August 9, 2003, 9:22am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/16 "2003-08-09T09:22:58Z")
I certainly recognize the eminent authority of Chronos in the field of physics, and therefore admit my error. What I should have said is that the assertion, “Space may be infinitely subdivisible (at least in mathematics), but so is time…,” is not known to be true. Perhaps the assertor will admit his error as well — anything is possible. ---
**Author:** ![kambuckta](https://avatars.discourse-cdn.com/v4/letter/k/53a042/32.png) [@kambuckta](https://boards.straightdope.com/u/kambuckta)\ **Post date:** [August 9, 2003, 10:27am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/17 "2003-08-09T10:27:02Z")
Seeing as space and time ARE mathematical constructs, there is no reason why they should not be infinitely divisible. Or am I missing something here? ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [August 9, 2003, 12:04pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/18 "2003-08-09T12:04:04Z")
Obviously you can imagine a space/time continuously or discretely. Maths uses both on occasion. The question is, what is the universe? For an up-to-the-minute report, read the other thread 🙂 ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [August 9, 2003, 9:24pm UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/19 "2003-08-09T21:24:23Z")
In classical models of time and space, they are indeed infinitely divisible. (It’s just the Cartesian coordinate system in four dimensions.) It may or may not be the case that modern physics implies a universe that is actually digital, not analog, but it’s far from clear (the Planck length may or may not be the most basic unit, even assuming it’s the smallest unit we can ever measure). **Libertarian** : I will once again appeal to your better instincts and beg you to cease spreading ignorance on these boards. There’s more than enough in the world already – we don’t need to help it propagate. ---
**Author:** ![astorian](https://avatars.discourse-cdn.com/v4/letter/a/ad7895/32.png) [@astorian](https://boards.straightdope.com/u/astorian)\ **Post date:** [August 10, 2003, 4:53am UTC](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817/20 "2003-08-10T04:53:17Z")
Anyone who’s had two days of calculus class should be able to “solve” Zeno’s paradox, and tell you the precise moment at which the tortoise will be overtaken. [Next page](https://boards.straightdope.com/t/possible-solution-to-zenos-paradox-breakthrough-or-rubbish/193817.md?page=2)