ex-xian

But the Stadium paradox depends on a limit. He divides length infinitly, that's exactly what a limit is.

It seems that Zeno mixes the continuous and the discrete and that's where the paradox comes from. He allows length to be continuous and compares it to a discrete concept of time.

[ December 23, 2002: Message edited by: xianseeker ]</p>

Mr. Sammi

One time I thought of a cute solution to Zeno's paradox. Let me alter the desk problem by putting a book on top of the desk. We now wish to touch the book by sucessive divisions of space AND mathematically it seems as if we never touch the book.

NOW try to get to the desk exactly where the book is lying, we will find we have to pass the book, we have to touch the book before we can get to the desk.

This means my solution is to want to go further, go past, go beyond, then we will surely pass what we wanted in the first place. (If I think of a glorious death, should I live a magnificent life?)

Generally speaking let X be the distance to traverse. It seems as if we cannot get to X by the sucessive halving of X. If we substitute X for X+1, we will find we will pass the original X, and reach our goal, while X+1 now seems out of reach.

Think Past.
Think Beyond.

* * *

The philosophical ramifications of Zeno and this method, if we can compare it with the divide-and-conquer method in AI, or the use of sub-goals IS quite significant. Zeno shows us that we cannot keep sub-dividing the problem until nothing is left, at some point, some work must be done. There is an atomic limit, a treshold after which the divide-and-conquer method becomes absurd.

I believe Zeno wanted humankind to realise the buck cannot always be passed around or divided into parcels and shared amoung the fools, at some point, the buck should stop being passed and responsibility should begin.


Sammi Na Boodie ()

Darth Dane

A more interesting thought mayhaps?


Lets take the atom (latin meaning indivisble) forget about quarks and such, the smallest is that which is indivisible.

Now between the atoms there is space, what is this space made of?

A supertanker (Huge ship, weighs a lot...) is comprised of atoms. As a thought experiment, scientists imagined that if you pressed all atoms so close to eachother that they touched, the ship would fill up less space than a pea, probably infinitely less...but weigh the same. The same is true the other way around. We can enlarge the space bewteen atoms, and make the ship even bigger than it is, infinitely bigger. We realize that we can continue to enlarge the space, indefinately. Since everything is dependant on the space bewtween it's atoms, and the atoms define the space. The atoms and the space is together the ship. If atoms (or quarks or whatever, oh and atom means indivisible) is the smallest thing there is, how can there be space between them?

Atoms define Space
Space defines Atoms

Both point to eachother and define eachother, but are inherently different.

But of what is space made?




DD - Touch Spliff

Liquidrage

The Planck length is about 1.6 x 10-35 m.

Once your fractions reach this length, there is no difference between them once the boundry is reached. And the next fraction and the one after that and the one after that, etc.

So, eventually you would hit this length and "half" would become meaningless.
But this does not invalidate the concept of "infiinity" any more then saying I have 3 apples invalidates that concept. It does appear to invalidate applying infinity to your scenario however.

Liquidrage

Science in still trying to figure out your last question.

For example, string theory starts with tiny 1-dimensional strings. Which means it cannot be a truely fundamental theory since it is built upon a pre-existing framework of 1-dimensional space.

Where as LQG (Loop Quantum Gravity) is attempting to create a theory using spin-networks (pure numbers) that would give rise to the dimensions themselves. In this case LQG could be said to be a fundamental theory.

I'm not saying LQG is correct. It may not be. But if it does turn out to be correct (in some form) it would be fundamental and answer where "space" comes from.
Where as if some variant of string theory turns out to be factual, it still would not answer your question completely.

Darth Dane

The fact that it is being said that there isn´t any difference, is only an established convention, with no real hold in reality, due to the fact that we seem not to be able to go deeper down in the scale of things.

That which is smaller than the smallest must be that which connects them both.





DD - Touchy Spliff

Liquidrage

I think it has a hold in relaity.

Trying to confine a particle (any particle) to a region smaller then the Planck length will cause a gravitational collapse.

Darth Dane

Edit:

Yes it would be to difficult to harness all the energy for that, but some scientists say that that is what happened at the big bang




DD - Touched Spliff