"Motion is impossible" claims modern Zeno

[A.T.]

So we must say that continuous motion has a special quality that is a "sum greater than its parts", so to speak.

No, it has nothing to with motion being special. You can divide any number like that. An it's not greater than the sum of its parts.

 

[thinkandmull]

Than we are faced with the same paradox as Zeno's Arrow paradox. I think motion is "one step ahead" of matter so to speak. I don't know how else to say it. When you cross a finite segment, you pass over infinite points, and there is no final step. There are no discrete "one two three" steps to take and then wow! you are at your destination. I'm thinking that motion must be more mysterious, something about it that we are not getting straight from math, but can understand better with physics

 

[PeroK]

Than we are faced with the same paradox as Zeno's Arrow paradox. I think motion is "one step ahead" of matter so to speak. I don't know how else to say it. When you cross a finite segment, you pass over infinite points, and there is no final step. There are no discrete "one two three" steps to take and then wow! you are at your destination. I'm thinking that motion must be more mysterious, something about it that we are not getting straight from math, but can understand better with physics

My steps are about 1m, so if I have to travel 3m, then it is "one, two, three" and I'm at my destination.

I never thought much of Zeno's paradox, I must admit. Here's my version:

The hare starts 1m behind the tortoise.
The hare starts 1m behind the tortoise.
The hare starts 1m behind the tortoise ...

Ergo, the hare never even moves let alone catches the tortoise.

 

[Dale]

Since I am using a line's quality as the bases for my understanding this, no I am not sure what a limit would be for infinite numbers or steps

This is the thing that you need to learn then. Once you have understood the limit of an infinite sum of real numbers then the mapping from the real numbers to a line is trivial.

As far as the infinite sum goes, this is actually straightforward. If you have $\sum _{n=1}^k \frac{1}{2^n}$ then you can fairly easily convince your self (simply by writing it out for a few small values of $k$) that the answer is $1-2^{-k}$. As $k$ becomes larger and larger the sum gets closer and closer to 1. In fact, you can specify any arbitrary $0<\epsilon<<0.5$ and calculate the $k$ necessary to make the sum closer to 1 than $\epsilon$. This is what it means to have a limit. The limit of any finite series is less than 1, but as the finite series gets arbitrarily large the sum gets arbitrarily close to 1. So the infinite sum is equal to 1.

Please start with this website and think and mull it over a bit:
http://www.math.utah.edu/~carlson/teaching/calculus/series.html

 

[A.T.]

...so to speak. I don't know how else to say it.

Use math.