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You are not logged in. #1 20070103 07:50:53
Strange things about Xeno's ParadoxAccording to what Xeno said about measuring and motion. Something can't travel to somewhere without first travelling halfway. So this means that a measurement of 0 to 1 would be 0.5. This is not logical and this post is to explain what a quack Xeno was. 0 can be nothing and something. 0 #2 20070104 01:43:17
Re: Strange things about Xeno's Paradox
What you have to remember, is that Zeno was trained in argueing, not math(primarily anyway). Last edited by Patrick (20070104 01:44:18) #3 20070104 10:38:45
Re: Strange things about Xeno's Paradox
I'm sorry, but I don't see where you explained how Xeno is a quack. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20070104 22:56:19
Re: Strange things about Xeno's ParadoxWell, as I see it, Zeno of Elea(it's not Xeno) got this all wrong. Instead of saying before you can move one unit, you have to move a half unit, you should be saying when you move one unit you also move a half unit. #5 20070105 06:34:08
Re: Strange things about Xeno's Paradox
But is that first part wrong? If so, how? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20070105 06:59:38
Re: Strange things about Xeno's ParadoxBecause it's implying that moving a half unit is a seperate action from moving the whole unit. An action that has to be done on it's own and before the other. #7 20070105 09:10:33
Re: Strange things about Xeno's Paradox
Are you saying that to move a half unit, one must also move a full unit? Because if that isn't the case, then they are separate actions. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20070105 14:02:06
Re: Strange things about Xeno's ParadoxWell I agree that you have to move half a unit before you move one... but that wouldn't make a measurement from 0 to 1 = 0.5. #9 20070105 15:29:13
Re: Strange things about Xeno's Paradox
You lost me there. Is the measurement equal to 0.5? Or is whatever your measuring from 0 to 1 equal to whats at its median? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #10 20070105 18:04:20
Re: Strange things about Xeno's Paradox
That's what I was responding to #11 20070105 18:18:45
Re: Strange things about Xeno's ParadoxI guess I really don't understand that either. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #12 20070105 18:20:11
Re: Strange things about Xeno's ParadoxTo get from point a to point b you need to move half the distance there first. Then from there to b you need to move half the remaining distance and so on. So its a "Half the distance to the goal" thing that keeps repeating. The limit will be the goal point but it will never actually get there. Which I'm guessing is why Zeroface is calling him a quack. (Because we all know you can get there and move beyond it.) But his wording is still unclear. Last edited by mikau (20070105 18:29:00) A logarithm is just a misspelled algorithm. #13 20070105 18:47:03
Re: Strange things about Xeno's ParadoxBut the argument is against continuous space, not whether or not you can travel. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #14 20070105 19:16:49
Re: Strange things about Xeno's Paradoxaye, but i think he may have been using one to prove/disprove the other. I don't know. It was the first thing that ran through my head. A logarithm is just a misspelled algorithm. #15 20070106 05:59:35
Re: Strange things about Xeno's Paradox
Okay, you got me wrong there. I thought you would understand that all I was saying, was about the case where the goal was to move one unit. In that process, the half unit movement is a part of the full unit movement, not a seperate process. #16 20070106 08:15:31
Re: Strange things about Xeno's ParadoxI think Zeno is more clever than you're giving him credit for. He obviously didn't actually believe that his assertions were true  he just made them and then used the real world to contradict them. Hence it being called Zeno's paradox instead of Zeno's theorem. Why did the vector cross the road? It wanted to be normal. #17 20070106 09:18:15
Re: Strange things about Xeno's Paradox
Well, that's exactly my point! It doesn't really contradict the real world, or the world as we experience it anyway, because the premises are wrong. This is one of the things that can qualify a statement as a paradox, so Zeno succeded in making a paradox I guess. Though, I don't think it's of any importance to mathematics, only to the study of rethoric. #18 20070106 09:35:21
Re: Strange things about Xeno's ParadoxI'm sorry, I'm still not understanding. Which premise is the one which you are saying is wrong? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #19 20070106 12:21:44
Re: Strange things about Xeno's ParadoxIt would help if we knew what space and length is. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #20 20070106 13:26:56
Re: Strange things about Xeno's ParadoxI don't think the definitions are the problem. Just let space and length be as we naively think about them. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #21 20070320 14:53:30
Re: Strange things about Xeno's Paradoxhmm...i think that what zeno was referring to is that all change can be reduced to .0000...on to infinity...1. since the limit of this is zero, we can never move, hence the paradox. the problem with this is that all change cant in fact be reduced to .0000...1. which of course, leads us to the nature of the continuity of change. this leads us on to continuous functions on the complex plane, i think...or maybe im just a freshman who knows nothing. #22 20070320 15:08:57
Re: Strange things about Xeno's Paradoxo wait, i totally got it. #23 20070320 16:43:24
Re: Strange things about Xeno's Paradox
The bolded part is a logic fallacy known as a False Dilemma. You are forcing me to choose between X and Y, when in reality other choices such as Z exist. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #24 20070321 15:10:00
Re: Strange things about Xeno's Paradox
ah...you have got me thinking again. in fact, when i wrote that i almost put in the "that i can think of" part. of course, "those strange properties" that is, quantum physics (i think thats what you mean) dont mean the universe is continuous do they? i mean, the discrete space theory of the plank length is accepted, right? #25 20070321 15:22:13
Re: Strange things about Xeno's Paradox
I've never even heard of a nonphilosophical based discrete space theory. That is, one which comes out of actual physics instead of mindexperiments. The plank length is how much one has to "zoom in" until something known as quantum foam is observed. This is where space gets really weird and freaky and general relativity, which requires space to be nice and smooth, breaks down. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 