According to what Xeno said about measuring and motion. Something can't travel to somewhere without first travelling half-way. 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.

I'm sorry, but I don't see where you explained how Xeno is a quack.

To me, this is a very important critique of our view of space as being continuous.  The problem is that we don't know what happens at the Planck length.  My opinion on this is that it is a scientific concept (not mathematical), and thus, I accept space as being continuous on the fact that the statement has yet to be falsified.

Instead of saying before you can move one unit, you have to move a half unit...

But is that first part wrong?  If so, how?

Patrick wrote:

Because 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.

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.

...but that wouldn't make a measurement from 0 to 1 = 0.5.

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?

I'm not even sure why you're talking about measurements being equal to something.

I guess I really don't understand that either.

But the argument is against continuous space, not whether or not you can travel.

Ricky wrote:

Patrick wrote:

Because 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.

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.

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.

mathsyperson wrote:

I 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.

Zeno liked to make up things that used apparently sound mathematics and yet that were clearly false, to annoy all the mathematicians of the time. A more famous example is of the tortoise and the athlete, although the reasoning used is kind of similar.

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.

It would help if we knew what space and length is.

I defined Space as "The region in which objects exist.", and Length as "Distance. How far from end to end." in the math dictionary.

(If anyone else would like to offer concise definitions better than those, please do.)

hmm...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.

the universe cant be continuous, or else we run into this paradox, where any division of distance can be reduced to .000...1. obviously a paradox. therefore, space must be discrete, which is the only other logical logical possibility. a sort of proof by contradiction of the discreteness of the universe. as mentioned before, the plank length is the discrete unit of space, just like the quanta is the discrete unit of energy...which was discovered by max planck. this in itself leads to interesting physical conclusions, but also mathematical ones. yay!

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.

A more accurate statement is "which is the only other possibility, that I can think of".

Perhaps movement is discrete and space is continuous.  Perhaps space is continuous but acts with very weird properties on the small scale.  Actually, we already know the 2nd is true.

The list goes on...

i mean, the discrete space theory of the plank length is accepted, right?

I've never even heard of a non-philosophical based discrete space theory.  That is, one which comes out of actual physics instead of mind-experiments.  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.