If A=B then A-B=0

hence why dx is proportional to dt... i already said everything you did. =)

O ya. I knew that. I was just testing you, to show my interior knowlege.
It's superior not interior.
Uh, ya.

Yes but you used mainly math and did something no one during his time period could. You disproved the paradox by showing why it doesn't work. I went a little deeper and explained the flaw in the logic the seemed to work. That being he was considering motion without taking into account time.

hence dt. t in dt is time, unless i'm measuring... uh.. teslas.

I never said you didn't mention time, you saw and exploited that weakness in the argument. What you did not do was say anything at all about that weakness. You simply stated that the math doesn't work out, and did that by introducing a variable that wasn't in the original problem without explaining why. Basically, you used mathmatical know how to see a logical hole without actually having to do the logic.

I on the other hand spotted where he went wrong. As in Zeno never consider the effect of speed and thereby time. You jumped straight to equations of motion sidestepping the problem of having to add in the abstract nature of time by making it abstract. Then used unrelated math rules to show why it works, which is actually how a lot of things are down. This took into account the base underlying flaw of Zeno's logic but never really stated outwardly.

I took the less traveled route and found why logic the seemingly worked in words didn't work out mathmatically. That being he Zeno wasn't thinking of motion in the same way we understand it, and he was negelecting time entirely. The merit of your way is that we get the answer and disprove the paradox but you miss a bit of the reasoning behind it. Like the fundementally different ways you and he treated motion. Indeed, after I said something you became quite aware of his missing consideration of time. However, I highly doubt when you were constructing that mathmatical proof you were thinking, or at least you weren't aware you were thinking, that since he had not considered the time it would take to cover the distance he had made an error.

It could be that you did notice the lack of time and from there luanched into the math proof with abstract rules. That suggests that you found the logic no quite enough to completely prove the point, which it most certainly does. Math is a powerfull tool for getting answers but the greatest minds have always reasoned their way through a problem. Einstein hated math and because of that we have general relativity, which absurdly enough is unbearably math intensive. Special relativity and relativity in general grew from thought expierments and the math fell into place later. Einstein was simply able to intuitively handle abstract concepts that today we have to simplify into math.

In short trust in the force Luke(Sorry really bad joke). If the logic works then trust it. If your unsure check it with the math but don't use the math as a reason for the logic. If the math works there has to be a nonmathmatical logical reason for it. Finding the reason is the real challenge, and is the path to truly understanding something.

I'd take that apart piece by piece, but its rather obvious that math (especially in this instance) is logic. Math is just the logical extension of patterns. So basically you're just wasting time rehashing what i put down with a grand total of 5 characters ( dx/dt )

more importantly, you seem to have forgotten that i said
Ta-Dah! you've been repeating what i've been saying all along =D
next time, if my post has like 5 lines, be sure not to skip 2 thru 4.

Logic yes but weak logic that uses rules actually exterior to the problem. Notice how you had to use an intergration then invoked L'Hopital's rule as a final proof to your math proof. If you go back in time and try to use that on Zeno's he'd look at you like you were crazy.

That's just rude as you seem to have skipped all this from my post.

Let's take a look at what you posted.

Implicit in that is everything I said but no where do you actually come out and state it. That is the power of math and it's weakness. Anyone can do the math with a little training but understanding the logic buried there is another story. So as I said before you introduced time but never said why it had to be there or anything about it not being in the original problem. Basically, you showed how the paradox doesn't work; while I dug in a bit and found the why. You used propieties of numbers, equations, and mathmatical operators basically going outside the problem for the tools that answer the question. My way stays completely with the intrinsic properties of the problem and gives a solid explination of why the math works out and what was missing.

If you really can't see the difference between the logic used in math and good old reasoning then no argument I make will sway you. Indeed, the only argument you'd really trust would contain math and I'm sorry but I can't show you the difference mathmatically. (Which another reason why its better to use reasoning type logic as much as possible. It just has more uses.)

Oh and to clarify the point a bit. With math you can end up with correct answers that make no sense at all. Like the wave particle duality of light and all other particles. When this was proven with math everyone was at a loss as to how a particle could be a wave. That is until someone took the step and said it's not the particle that's waving but the probility of finding it at a location. That insight was no where in the math and was a quantitatively proven later with math, but not before the quantitative leap using reasoning.

Incorrect, i said exactly what the weakness was, and that was....
The only difference is that you didn't like the fact that i used math. Seriously, this isn't a big deal, you're just pretty much beating on a drum that doesn't exist. Saying that using math to describe a problem gives an incomplete view is totally correct, but not when i caps lock-ed the most important part in text.

If i had set up the infinite sum, changed it into an integral from 0 to infinity, and evaluated whether or not the time taken was finite or infinite, then fine, you'd be perfectly justified in saying that my math didn't talk about the weakness inherant in the paradox. Did i do that? No.

Basically, you're making this a bigger issue than it is; you repeated what i said... no biggie. If you have any real beef with that, i'm sad to say i'm going to ignore you, because creating a rivalry here is totally useless, especially when the paradox has already been nicely debunked. To me, this thread is pretty much closed.

You've managed to completely misinterpert everything I said. The dispute is not over the content so much as how you pharsed in. In that regard you were correct in saying I didn't like the math. I personally love to do math but I know that it is inherently difficult to form a clear mental picture straight from math. I don't care that you said everything I said. The entire point of me saying it again was to make more apperant want went wrong. Saying: Says aboslutely nothing at all about how or why time is centeral to the paradox, unless you are really good with the math and can imediately see the physical reasoning behind it. (Sorry to say most people can't.) It says what is happening with respect to time but it doesn't describe why you can't consider motion without time. Nor does it say anything about Zeno not considering time intially. Our difference of opinion is purley ontological and semantical but that doesn't make it any less important. So really you mentioned the central issue of the paradox in passing but you never said anything about why it was central or even that it was central.

Oh and yes you did pass over it slightly be using the math you did and saying that but not nearly deep enough to really get at the core reason. That reason being Zeno was trying to describe motion without using time not just that he never said anything about time.

As for simply ignoring me that is plain inconsiderate and rude, more so than flaming in my opinion. When someone flames the due it through lack of inteligence but for an otherwise inteligent person to close out another person trying to have a reasonable desicussion because of a difference of opinion, no matter how insignificant either side thinks that difference is, smacks of arogance. I've been perfectly civil in trying to explain the very subtle difference between what you said and what I said and being dismissive is not flattering. As my argumentative writing teacher would say, you must treat all oponents fairly and evenly, not dismissing any out of hand; doing so will not change the minds of those dismissed and will weaken your case in the eyes of even those you treated fairly. Not to mention it makes it seem like you think your opinion and interpertation is more valid than anyone elses while providing absolutely no proof either way.