The End of Infinity.

I have a question regarding infinity.

If infinity means that something can have absolutely no end, ever, can someone tell me how this would work:

Lets say you are holding a metal bar (or anything long). You hold one end in your hand but the other extends for infinity in the other direction. Would this bar have infinite length? It does go on for infinity but it also has an end?

My brain can't wrap itself around this and its quite annoying me

If you held a hoola hoop, you could follow it's length hand over hand to infinity. If there is such a thing as infinity, I imagine that it not so much as goes on forever as much as it eventually turns back upon itself.

[Edited on 6-4-2004 by Jonna]

But a hola hoop doesnt have infinite length, you can follow it for infinity but you have to keep going over the same part.

How can the bar I mentioned loop back onto itself? It not a loop there is one end and it is straight.

If you can hold an end of it, it is not infinite. Its like a line. Draw a line on a peice of paper, and it is a line segment, not a true line. A true line has no ends. So, if you can see an end, it has one and therefore isn't infinite.

As far as imagining a circle. A circle is not infinite. Yes, you could take infinite time in our perception to keep running your eyes around it. Or running your hands around it. That still does not make the circle infinite. The circle has an outer boundry and a center. The outside circumference has a length.

Infinity is not something a human can truly understand. Everything we can see or imagine is finite. People feel that they can comprehend this term. Which, as a word, it is easily comprehensible. Infinity itself is not though. People who think they understand infinity do not have a full concept of what it really is. They imagine finite things in there mind and construe them as infinite.

So, you are not out of line being confused by it.

[Edited on 4/6/2004 by Seapeople]

Originally posted by Faceless
Lets say you are holding a metal bar (or anything long). You hold one end in your hand but the other extends for infinity in the other direction. Would this bar have infinite length? It does go on for infinity but it also has an end?

My solution would be to say that it only has one end. You can never reach the other end and therefore it doesn't exist. It's like asking how much infinity is? Does it stop at 10000000? Ofcourse it doesn't, you will never find the end of infinity and you will have never find the end of the bar.
This may seem strange, but it's all theoretical correct and in real life you can of course never make a infinite length metal bar. A situation with a one-ended bar will never occur.

Seapeople, I think it's really possible to understand infinity. You just need to describe it mathematically. The normal infinity we talk about is aleph0. This is the total amount of integer numbers and also the amount of rational numbers. It behaves as follows:

aleph0 + x = aleph0
aleph0*x = aleph0

(2^aleph0 = aleph1

Now it becomes strange, because aleph1 is actually larger than normal infinity. It's the total amount of real numbers. Really interesting, but I guess it isn't really what we're talking about.)

[Edited on 6-4-2004 by amantine]

Originally posted by Faceless
But a hola hoop doesnt have infinite length, you can follow it for infinity but you have to keep going over the same part.

What is length? It is a dimension of space and everything in space exists in a time so you would never really go over the same part twice. Have you ever heard the old saying "You can never step in the same stream twice"? This is because everything exists in a space at a time. You may have the same 'area' of space, but it is not the same space without the proper corralation of the same time.

May not be the answer you want, but it is an answer.

Originally posted by Jonna

Originally posted by Faceless
But a hola hoop doesnt have infinite length, you can follow it for infinity but you have to keep going over the same part.

What is length? It is a dimension of space and everything in space exists in a time so you would never really go over the same part twice. Have you ever heard the old saying "You can never step in the same stream twice"? This is because everything exists in a space at a time. You may have the same 'area' of space, but it is not the same space without the proper corralation of the same time.

May not be the answer you want, but it is an answer.

This is true, but you still have to take into account that it is the act of running your hand around the circle that could go on forever, not the circle. It is the act of moving your eyes over the circle that can go on forever, not the circle.

[Edited on 4/6/2004 by Seapeople]

Originally posted by amantine
My solution would be to say that it only has one end. You can never reach the other end and therefore it doesn't exist.

Such a theoretical one-ended bar would be akin to a ray. It has one fixed, finite point and a line that extends into infinity.

Some fun ideas to play with are the philosophies of Zeno of Elea.

www.mlahanas.de...

The solutions to these are now known, but there are still some quite mindbending concepts to think through there.

Originally posted by amantine
A situation with a one-ended bar will never occur.

[Edited on 6-4-2004 by amantine]

But neither will a situation with a no ended bar.

Thanks for the explanations but I still dont get it. If the bar has one end and also extends for infinity in the other direction would the end you are hold be the end of infinity? or the begining?

Originally posted by Seapeople
It is the act of moving your eyes over the circle that can go on forever, not the circle.

As I stated, I do not believe that infinity (something without end) exists in the way that it seems to be normally perceived.

Well, maybe the best way to say this is like this.

Infinity was a term created by a person to name something he couldnt understand. Therefore, the term is not intended to be understood. People try and try to figure it out. Our minds can't comprehend it either because we are limited or it does not exist.

Originally posted by Kano
Some fun ideas to play with are the philosophies of Zeno of Elea.

www.mlahanas.de...

The solutions to these are now known, but there are still some quite mindbending concepts to think through there.

OMG I have a headache trying to wrap my pea brain around Zeno's paradoxes. Very cool, though. I will try reading it again when I have total quiet time in my house (never) Seriously, I will definitely give it another try. Thanks for the link

Anyone that has studied electronics or physics, knows that all energies manifest themselves in different waves, the most common one in the known universe is a sine wave. We can see sine waves using oscilloscopes, and you will see it as a positive alternation and a negative alternation. Like a wave going up and the same wave in the oposite direction.

One cycle of a sine wave is made up of both alternations, and we also know that we see it in this waveform, through an oscilloscope, only to be able to make measuraments. But in itself a sinewave is a circle. This tells us that the most common energies, manifest themselves in a circle and spread out. Much like when you drop a pebble in a pond.

It is safe to say that infinite, is like the line in a circle, but that circle only represents one universe. So infinity will be an infinite number of these circles. Many of them interact and blend with each other, much like what happens in the allegory of the pebble and the pond.

There are theories which state that we think there are multiverses, not only the one we see with our powerful telescopes. It is a theory, but, one that can be demonstrated through mathematics.

If I remember correctly it was Physicist Paul Davies the one who has been able to demonstrate that there are 13 different dimensions, not five like most people think. And that's only what we have been able to demonstrate until a few years ago.

Mind you, it was only through mathematical equations that he was able to demonstrate this.

[Edited on 6-4-2004 by Muaddib]

Originally posted by Muaddib
If I remember correctly it was Physicist Paul Davies the one who has been able to demonstrate that there are 13 different dimensions, not five like most people think. And that's only what we have been able to demonstrate until a few years ago.

If I remember right, those smaller dimensions curl back to themselves, according to string theory (if I'm not mistaken). If you traveled a straight line in those dimensions, you will eventually reach back to the exact place you first were.

Comparable to the hoola hoop mentioned earlier.

[Edited on 6-4-2004 by TheBandit795]

Originally posted by Muaddib
If I remember correctly it was Physicist Paul Davies the one who has been able to demonstrate that there are 13 different dimensions, not five like most people think. And that's only what we have been able to demonstrate until a few years ago.

You are probably refering to his book 'God and the new physics'. Good book! I'd suggest it.

Possible bandit, unless one universe is touching another and you end up on another universe.

Hermes trimegistus explained in his emerald tablet.
"That which is above is from that which is below, and that which is below is from that which is above, working the miracles of one."

Or as is known in metaphysic circles, "as is above so below."

Just like we can say that atoms, (electrons, protons, neutrons) are the microcosmo, and galaxies are the macrocosmo, but universes are also a macrocosmo.

Atoms act much like galaxies, which in turn are a mirror image of how multiverses are. Of course, the last part is still just a theory, since we can only see one universe.

Originally posted by 23rd_Degree

Originally posted by amantine
My solution would be to say that it only has one end. You can never reach the other end and therefore it doesn't exist.

Such a theoretical one-ended bar would be akin to a ray. It has one fixed, finite point and a line that extends into infinity.

If you were holding the end (0) and it extended forever (all positive real numbers), then your first equation is incorrect for sure.
aleph0 + x = aleph0
If x is a point on the bar, then x should = all real numbers. A negative number would be behind you and not on the bar. Zero is easier understood as where you are standing next to the infinity bar, not the end. After all, numbers are only useful if relationsionship to something.

Originally posted by icelid
If you were holding the end (0) and it extended forever (all positive real numbers), then your first equation is incorrect for sure.
aleph0 + x = aleph0
If x is a point on the bar, then x should = all real numbers. A negative number would be behind you and not on the bar. Zero is easier understood as where you are standing next to the infinity bar, not the end. After all, numbers are only useful if relationsionship to something.

That is a bit strange indeed. You are wrong when you say my equation is wrong, because I ment with x a random number.

aleph0 U x = aleph0, because the cardinality stays the same. You can match up the parts of the set aleph0 U x and the set aleph. It is even true that aleph0 U [aleph0] = aleph0. Sometimes the set aleph U [aleph0] is also called aleph0+1, but this is not the same as aleph1. What are infinite and transfinite numbers?. The rules for working with transfinite numbers.

You got me doubting the size of the set that describes the infinite bar. Is it aleph0 or aleph1? It doesn't matter of the math rules, but it is something interesting to discuss. I think aleph0 is the best, because the planck length stops the universe from being a continuum. If the rod is in a pure mathematical environment I think it's length is aleph1, because the rod contains all real numbers, not just the natural or rational numbers.

To faceless, it would be like counting from 0 to infinity. You will never reach the other end. The end of the bar is probably best described as the beginning of infinity.

originally posted by faceless
My brain can't wrap itself around this and its quite annoying me

You are not alone. The subject of infinity brings even the most seasoned scientist to a halt. It is difficult to understand something you can not experience with one of your senses. Everything around you is in relation to finite measurements. You were born on a certain day. You have been going to school for x years. France was a dominant country years ago. (Although this approaches infinity) Infinity is more of a useful math tool than a concrete idea. Still, it is fun to study this topic, so keep going and don't let being puzzled stop you from doing research on the idea.

One of my favorite discussions on infinity is found here.
Let us imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are full. When a new guest arrives asking for a room, the proprietor apologizes, "Sorry, all the rooms are full." But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are full. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. "But of course!" says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3,.........

This goes on into a discussion that discusses infinity related to time, and how is it impossible to have an infinite past. If the past was infinite, that is an unmeasurable amount of time, then we would never arrive at the present moment. The state of the universe would be forever approaching this moment where you read this post, but it would never happen. I could go on about this subject forever, but then, you would never get to the next post.

Enjoy.


[Edited on 6-4-2004 by dbates]