Alright this might be way out there, but I am going to say it anyways.

Frist my problem with the curent theroy on Points is that they have no size or shape. Or that thew size of a point is infinity small and large. Also they are shapeless. Another problem that I have is that there are an infinite amount of Points in one line segment. This seems unlikly for one obvious reason I will illistrate for you.

<-----o-o-o---o-------o-----------------o-------->
A F E D C B

Now, how do you go from point(o) A to point B? Well you first must pas through the middle or point C. Well how do you get there? Pass through point D (halfway). And how do you go there Through point E, but first F. If there are an infinite number of points in a line segement, then this will go on for eternity and make any movement immpossible. But since I can move, then this obviously is not correct.

How do these points make a line? You can't take a lot of something and make nothing can you?

But what if points did have size? Maybe not in 3 Deminsions or 2D. If points have a size of less that infinite but greater than zero, it would make movement possible, and lines would now logicialy be made.

Points might be of size, but a varing size, and be of underterminable size. But it was a "measureable size". something with-in the real numbers realm.

In lines the points could be all different sizes, and shapes. For congruent lines, the points doen't need to be the same size, but the big picture,the line needs to be the same size.

IN previous theroy, you may have an infinite number of points, and never have a line. But in my theroy, ANY two points make a line.

I have made revisions in the current rules of points, and I hope someone will disprove them. As I think of new rules and as people bring the up, I will post them here!

Hi Ender,

"If there are an infinite number of points in a line segement, then this will go on for eternity and make any movement immpossible. But since I can move, then this obviously is not correct."

An infinite number of infinitesimal steps can give a finite result. The concept of integration might resolve your problem.

Bye!

Crisp

I could be wrong, but don't points by definition have no properties other than location?

ok, there we go

-- -- -- -- -- --

with this line of 6 points it will take 6 times 2x time to move; let's say 12x.

- - - - - - - - - - - -

now it will take 12 times x time to move; also 12x.

when we go on like this til we have an infinite amount of infinite small points, it will take an infinite small amount of time to pass one point.
conclusion: we can move along the line....

(nice though btw, reminded me of the well-known hercules/turtle paradox, I guess everyone knows???)

something else:
a point only has position, no size.
a line only has position and length.
you can not compare these two is my opinion.

Well it will take some amount of time to get beyond them, that time shoukld be finite. Also suppose the points are infinitely large. Then by this logic, it should take an infinitly large amount of time to get by them.

The infinite size lets it grow big and small!

Crisp,
However I cannot take an infinite number of infintesimal steps!

Hi Ender,

"However I cannot take an infinite number of infintesimal steps!"

Can you take a finite number of infinitesimal steps ? Can you take an infinitesimal step ?

The problem with the ideas of infinity and infinitesimal are that they are not practically realisable. They are concepts for dealing with special situations that dont occur in real life

Bye!

Crisp

we can send an infinite radio signal (as in theory it will go on forever) with a finite travelling distance i.e. from a black hole

this reminds me of the paradox of Zeno ... or am I wrong?

the points theory is pure maths, isn't it? it's just some kind of concept in the world of maths

Ender,not exactly...when it takes some amount of time to get beyond them, it most mean they most have some size, and they aren't infinitely small anymore
It's indd the whole problem with finite and infinite, they can't really exist. (I think)
Like Crisp said:

Ender; you have stumbled upon something that is very true, I have my-self been working of a theory of this naature for quite some time now. In order to understand something of this nature we must introduce something called super-string-theory. This is quite a new subject yet it might be the key to this whole thing, (on a more broder note). Points do have size, yet that is in proportion to the plane on which it lies. points will always make up lines, and lines will make up planes, and planes will make up space. Super-string-theory, says that a point does have a definite size, yet its location is unknown, this is similar to quantum theory, in which we know that an atom contains electrons, yet the more specific we get into finding the location of the electron cloud the more assumable our answer will be and the more harder it is to find. This can be represented mathamaticly:

--Domain--
x=point 1
p=plane
s=space
n=infinite
-------------


f"(x < p < s)

=(x+x2+x3+x4...)=xn



S. Dalal

I'm not the only one going crazy...j/k

S. Dalal,

I an vaguly fimilar to super-string theroy. My knowledge only goes as far as Micho Kaku's <u>Hyperspace</u> goes.

I also was thinking that a point would be in proporting to a line, but i haven't been thinking of a plane, but it does make <b>some</b> sence!

here is one way of thinking about it.... take a point, it has no dinension


.


now double that, and draw a line



._______. now you have a line, 1 dimension



double it . .


. .

now you can draw a square (plane) having 2 dimensions


now double that, so you have two parralell planes. now you have a cube, 3 dimensions....


now if you can imagine what it would look like to double that, that would be one way of visualizing 4 dimensions

I think the best way to explain it would be to say that, since mathematical points have no size, any movement you make along a line *must* travel through an infinite number of points. Therefore, in a weird way, any movement along a line is going the same distance. Infinity plus Infinity gives you Infinity. Now, i'm not well versed in math, i'm taking calc this year, but thinking through the question logically thats the explanation i came up with.

Paradox of Zeno was a useless thread.

As for the infinite number of infinitesimal steps, I do believe that might be the way integration works...the number of steps reach infinity and the size of the steps (remember Riemann sums?) reach zero. Ender, I still don't get what you don't get.

man, next you'll be telling us that planes have mass.

Depending on the geometry, Ender, your assertion is correct. Depening on the geometry.