The Paradox of Infinity

Wait... I haven't been able to find a username to register yet... :bugeye:

Please Register or Log in to view the hidden image!

 

Log in or Sign up to hide all adverts.

Ok... here it is...

Please Register or Log in to view the hidden image!

 

Log in or Sign up to hide all adverts.

What? Explain your graph.

 

Log in or Sign up to hide all adverts.

i don't understand the graph...or the argument to be honest. but what he's saying is the half of the equation before the = is infinite while the sum will be decidedly finite because each consecutive term becomes less and less as the series continues ie 1/2>1/4, 1/4>1/8, 1/8>1/16 and so on.

Please Register or Log in to view the hidden image!

...

Please Register or Log in to view the hidden image!

1/2 + 1/4=3/4 + 1/8=7/8 + 1/16=15/16 etc., etc...hummmm...
seems that the eventual answer would come out to be (x-1)/x...what does that mean?

 

Truth,
"Oh. Wow. You answered your own quesiton, haven't ya? "

So you think things can be infinitely small, large, fast, etc.? Can you think of a scenario where this is not the case? Call it a thought experiment...

My hunch tells me there are limits due to the basic properties of space-time in our universe. For instance, if you tried to cut something planck length in half, you would wind up with planck length. Simply cannot be done. Course, I could be wrong.

 

Umm... tell me where half of the expression is in 1/2 + 1/4 + 1/8 + ...

Like maybe he means (1/2 + 1/8 + 1/32 + ...) + (1/4 + 1/16 + 1/64 + ...)?

Well the limit of (x-1)/x at x=infinity is 1.

 

You can't escape the problem that easily. The problem is that Zeno's premises lead to a static universe. The concept presented of illusory motion is self-defeating; you can't have even the illusion of motion unless something changes to create the illusion of motion and something exists in time to perceive this illusory change. The problem of stasis is a recurring one regarding concepts of infinity.

Irrelevant. It doesn't change the distance. All it means is that you can (theoretically / mathematically) divide a unit into an infinite number of sub-units.

If you're adding halves here your graph is wrong, it should be a curve not a straight line. Each proceeding fraction is smaller than the next and your curve should round off and never reach the limit... it doesn't just go shooting off to infinity.

If you're just adding all real numbers I don't understand the point because it has nothing to do with measuring distance.

The problem in the real world is that as you proceed into quantum distances position, momentum, and causality become uncertain. Essentially the whole thing blurs out in quantum indeterminacy. In this case, the Universe is quantized, there is no such thing as infinite divisibility and the mathematical concept of an infinite number of dimensionless points is simply a fallacy.

~Raithere

 

Change is constant.

That's not the point of the graph. The graph shows a picture of infinity. The point of the graph is that finity is a whole and infinity is the relationship between the parts and the whole. When the whole is undevided, there are no parts. That is one side of the graph. When the whole is "completely" divided, you get other side of the graph- infinite number of parts, with no whole. That also shows a relationship between nothingness an infinity, and how infinite parts can add to a whole. Also take into account that the whole is defined by you. You define the object in question. For instance, you could define the object as a computer and take a look at the parts of the computer.

Everything has distance. Even 1/1000mm...

Quanta IS infinitely divisible.

 

No.

Well, read my explanation on Plack lenght somewhere in this thread!

Please Register or Log in to view the hidden image!

 

Have you actually seen something that small? You are thinking abstractly, not reality. I think math is more like "in theory this or that exists" but does that have to apply to reality? No.

There is a shape, called Gabriel's horn. It has an infinite surface area and infinite length, but it's volume is finite. Where can I find one of these in reality? And you cannot argue that it is non-constructable because it is, in math. Just like "the smallest length." In math, it can be constructed such that the distance between 0 and 1 can be infinitely divisible, but does that have to apply to reality? Just like Gabriel's horn, not necessarily.

 

Agreed. Not sure how you reconcile the two ideas though, perhaps you were being sarcastic about Zeno.

I'm not sure what your getting at here. The terms "parts" and "whole" are problematic. It sounds like you're equating the concept of infinity with the idea of unity.

Nevermind.

No, they're not. That's the point of the theory. It means that even if distance is theoretically infinitely divisible anything you might use to measure the distance (e.g. matter or energy) is restricted to certain indivisible values.

http://en.wikipedia.org/wiki/Quanta

~Raithere

 

I wasn't being sarcastic.

Given the existance of infinity, infinity would be the whole while finity would be the parts.

By definition (from the site):
"In physics, a quantum refers to an indivisible and perhaps elementary entity. "

That's brilliant. You don't know what it is so you call it a name. Then you use your tools to determine what is it. What are those tools? The Planck units. And as I said earlier, the Plack units don't give us absolute limits- they gives us a limitation of our understanding. Beyond those numbers, we simply cannot understand, our brains cannot process it. So basicaly, when we look at a black hole, we don't say that it doesn't exist and there is nothing in it- we say that we are simply unable to understand it due to a limitation of our own subjective capacity of understanding. So the quantum is the smallest particle we are capable of understanding.

 

Then how do you reconcile change with a static universe?

Problem is we don't know if anything is infinite.

It's not a limit of comprehension it appears to be a physical limitation. A quanta is the smallest unit of energy that seems to exist. You can't get half a photon; you either have a photon or you don't.

~Raithere

 

Which static universe?

We can infer it from philosophical reasoning and logic.

It is a limit of comprehension. The Plack lenght, for instance, is based purely on the ability (or rather inability) of black holes to hold information.

What energy are you talking about? Do you consider space-time energy?

Huuumm... maybe...
What's the size of a photon?

 

Well if you are serious about Zeno's paradox as being true (which it isn't), then it IMPIES a static universe. You are implying the Zeno was correct AND that the universe is in constant motion. Both cannot be true, they are contradictory.

 

he wrote: 1/2 + 1/4 + 1/8...= infinity. bear with me here.

Please Register or Log in to view the hidden image!

the equation wasn't in quotations and each successive fraction was half of its predecessor. i was only trying to add it up to a point so i could see where it was going and it seemed to end up as 1/x + 1/(x*2) + 1/(x*4) + 1/(x*8) + etc...= (x - 1)/x...have i just totally made an ass of myself or did you follow where i was going?

Please Register or Log in to view the hidden image!

 

:bugeye:
i was pretty good at highschool math and didn't go on to take college math. i'm a mechanic. sue me. but if you would be so kind as to explain how infinity minus 1 (possible?) over infinity equals 1?

Please Register or Log in to view the hidden image!

 

(x-1)/x

(1-1)/1 = 0
(2-1)/2 = 1/2
(3-1)/3 = 2/3
(4-3)/4 = 3/4
(1000-1)/1000 = 999/1000

See how it get's closer to one?

Infinity - any number = infinity.
infinity - infinity = undefined
infinity*0 = undefined
...

 

You could also do this:

(x-1)/x = 1 - 1/x

As the magnitude of x gets bigger, the magnitude of 1/x gets smaller and smaller every time... all the way to zero.

 

To me, unmeasurable does not necessarily equate to infinite. The distance between point A and point B is finite in that the distance has boundaries... with the boundaries being point A and point B. An infinite universe has no boundaries but there are finite distances between points in the universe.