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Wiley, thanks very much for the insightful and thorough answer. It was very educating and interesting.

One question though. Am I mistaken or did you just say I was right?!? [img]/phpBB/images/smiles/icon_eek.gif[/img]

(Dave shakes his head and mumbles the line from 2001 in his signature over and over.) [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

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On 2001-11-07 06:15, David Hall wrote:
Wiley, thanks very much for the insightful and thorough answer. It was very educating and interesting.

One question though. Am I mistaken or did you just say I was right?!? [img]/phpBB/images/smiles/icon_eek.gif[/img]

(Dave shakes his head and mumbles the line from 2001 in his signature over and over.) [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
I don't think he said that. You mentioned that you could see a mathematical paradox, but that it wasn't real because real movements aren't continuous. Wiley was specifically addressing that.

He's right. Mathematically speaking, all you're saying is, "here is an infinite series, where each point in the series gets closer to k, but no point in this series is k". Mathematically speaking, that's nice. But it's not a paradox.

There is a physical ramification of this as well. If, mathematically speaking, there's no a priori reason why this messes up your space, then physically speaking, there's no a priori reason why space can't have this topology.

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On 2001-11-06 18:49, Mr. X wrote:
Since Wiley isn't being very supportive of my wild claims, I'll just shut up! [img]/phpBB/images/smiles/icon_smile.gif[/img]
I still trying to decipher your claims. After that I may support them. If you're lucky. [img]/phpBB/images/smiles/icon_smile.gif[/img]

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On 2001-11-07 06:15, David Hall wrote:
Wiley, thanks very much for the insightful and thorough answer. It was very educating and interesting.

One question though. Am I mistaken or did you just say I was right?!? [img]/phpBB/images/smiles/icon_eek.gif[/img]

(Dave shakes his head and mumbles the line from 2001 in his signature over and over.) [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
I didn't say you were right, I said your analogy was sound. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Seriously, you're definitely on the right track. You recogonize there are two dimensions involved, space and time, which is the first and most important step in unravelling the paradox. Putting in terms of limits is just mathematical formalism.

And for the discrete case, you are right. If there is a minimum non-zero step size, Zeno's whole subdivision scheme fails.

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On 2001-11-07 11:18, Wiley wrote:
I still trying to decipher your claims. After that I may support them. If you're lucky. [img]/phpBB/images/smiles/icon_smile.gif[/img]
Oops! I knew it! Everyone always says I am talking gibberish and don't understand what I am talking about and keep nodding until I am done! [img]/phpBB/images/smiles/icon_smile.gif[/img]

I hate being misunderstood! [img]/phpBB/images/smiles/icon_frown.gif[/img] [img]/phpBB/images/smiles/icon_cry.gif[/img]

6. So the recent direction of this thread implies that infinity within a seeming paradox of the finite, and a completely empty vacuum are either equivalent entities, or similar entities, and are also mathematical postulates that don't actually exist in nature.

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Uh...
I don't know if I can draw anymore conclusions than:
The series of E(x/2*(1/2)^n) when n=0..infinity converges towards x where x would be the distance chosen. Taking an infinite number of steps as we would do in real life would equate to taking an infinite number of terms in the series.
Since abs(r)<1, since r=1/2 the series converge, and thanks to the handy dandy theorem on the convergence of geometric series we conclude the infinite series converges (as I previously said) towards x, the distance we had to go over. Hence the distance is finite and can therefore be crossed by an object with a finite speed warranting of course certain conditions ever so annoying and tedious to write that I will forego them here. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

Wiley Coyote here suggested something else. I forget what it is. [img]/phpBB/images/smiles/icon_smile.gif[/img] I just hope I can get Wiley's seal of approval on my wild claims!

I would also suggest that this is very feasible with time, as only a handful of things have to be changed and it yields the exact same converging series only different [img]/phpBB/images/smiles/icon_smile.gif[/img] but the same conclusion can be made. I mean different meaning, you know, what it means. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Note: E is summation, i.e. capital sigma.
Note2: My english is a little inelegant! Feel free to correct deficient syntax or incorrect use of words! Thank you!

<font size=-1>[ This Message was edited by: Mr. X on 2001-11-07 21:55 ]</font>

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Perhaps there has always been something and nothing, being the lack of existence, is an impossibility. I do not think that the lack of the existence of something can ever be proved, so I do not worry myself over such revolving-door questions and never put myself onto such a meaningless treadmill. You can prove that something exists. It is impossible to prove that nothing exists. So, do not sweat it...

ljbrs [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

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On 2001-11-07 20:10, ljbrs wrote:
Perhaps there has always been something and nothing, being the lack of existence, is an impossibility. I do not think that the lack of the existence of something can ever be proved, so I do not worry myself over such revolving-door questions and never put myself onto such a meaningless treadmill. You can prove that something exists. It is impossible to prove that nothing exists. So, do not sweat it...

ljbrs [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
That's a pretty strong point, methinks! [img]/phpBB/images/smiles/icon_smile.gif[/img]

10. On 2001-11-07 20:10, ljbrs wrote:
Perhaps there has always been something and nothing, being the lack of existence, is an impossibility. I do not think that the lack of the existence of something can ever be proved, so I do not worry myself over such revolving-door questions and never put myself onto such a meaningless treadmill. You can prove that something exists. It is impossible to prove that nothing exists. So, do not sweat it...

ljbrs [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_biggrin.gif[/img]
my brain hurts

11. Well reason thought can do that to you. jbrs is very good at well reasoned thought. [img]/phpBB/images/smiles/icon_smile.gif[/img]

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Are we talking about two different "nothings" here?

There is the mathematical and logical "nothing" which is just zero or the null set. Both of these are needed. The zero, for example, makes the number line continuous. Logically, the null set is just NOT ALL.

Both of these are "nothing" by definition.

The other "nothing" is the physical one which is not necessary and is really, really hard to prove. And as ljbrs says, we can't do anything about that so not to worry.

<font size=-1>[ This Message was edited by: David Simmons on 2001-11-08 13:36 ]</font>

13. On 2001-11-08 13:35, David Simmons wrote:
Are we talking about two different "nothings" here?

There is the mathematical and logical "nothing" which is just zero or the null set. Both of these are needed. The zero, for example, makes the number line continuous. Logically, the null set is just NOT ALL.

Both of these are "nothing" by definition.

The other "nothing" is the physical one which is not necessary and is really, really hard to prove. And as ljbrs says, we can't do anything about that so not to worry.

<font size=-1>[ This Message was edited by: David Simmons on 2001-11-08 13:36 ]</font>
Good points.

I'm thinking of an interesting analogy in music notation. (My field of artistic "mathematics.")

In music we have sharps, flats, and the natural sign, (among many other symbols.) The natural is sometimes referred to as the symbol that restores a note (or the key) to its former state. But this is not quite right. What the natural sign does is this: If a note is already sharp, followed by natural, the natural actually "flats" the sharp note. If the note is flat, followed by a natural, the natural "sharps" the note. So symbolically, the natural becomes a segregate sharp or flat.
Perhaps "nothing" in nature is akin to a natural sign. It becomes something else, without actually existing in and of itself.

And now, for an aspirin. [img]/phpBB/images/smiles/icon_eek.gif[/img]

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Ok, so who poked who in the what with a sharp what in the natural what now? [img]/phpBB/images/smiles/icon_smile.gif[/img]

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I know from where Wiley could start jumping up and down and hitting me upside the head with his baseball bat. Doh. Unfair, so unfair!

First I don't win an xbox then this!

[img]/phpBB/images/smiles/icon_cry.gif[/img] **Starts crying** [img]/phpBB/images/smiles/icon_cry.gif[/img]

<font size=-1>[ This Message was edited by: Mr. X on 2001-11-08 16:27 ]</font>

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On 2001-11-07 11:32, Wiley wrote:

I didn't say you were right, I said your analogy was sound. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Seriously, you're definitely on the right track. You recogonize there are two dimensions involved, space and time, which is the first and most important step in unravelling the paradox. Putting in terms of limits is just mathematical formalism.

And for the discrete case, you are right. If there is a minimum non-zero step size, Zeno's whole subdivision scheme fails.
Thanks Wiley (and Lusion, too). But to come clean, actually I realized what you really said. I was just being a little facetious there. [img]/phpBB/images/smiles/icon_biggrin.gif[/img] I'm just happy that I can even follow something of such a mathematical thread. (Couldn't follow any of the figures though. [img]/phpBB/images/smiles/icon_razz.gif[/img])

I even understand the reason there's no paradox in the continuous state. I suppose in my first post I should have said that I could see where a paradox "could" be seen, not that I could see one. Sorry.

Usually I'm pretty good at understanding basic concepts, but I'm not so good at the details, especially mathematical ones. From now on I'll leave it up to you brainy types to continue the discussions. [img]/phpBB/images/smiles/icon_biggrin.gif[/img] [img]/phpBB/images/smiles/icon_smile.gif[/img] [img]/phpBB/images/smiles/icon_razz.gif[/img]

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On 2001-11-08 13:35, David Simmons wrote:
Are we talking about two different "nothings" here?
...
The other "nothing" is the physical one which is not necessary and is really, really hard to prove. And as ljbrs says, we can't do anything about that so not to worry.
There is no "physical nothing". "Nothing" does not exist in some real, concrete sense. This doesn't have to be proven or disproven, for "nothingness" is not a thing such that it can possibly exist in a concrete sense. It's a lack of a thing. To treat "nothingness" as if it were really something, and therefore could possibly exist in some sense, is to commit a reification.

Now, vacuums are a different story--but, then again, vacuums aren't "nothing"--they're locations in space without matter in them, which is something. Maybe there are vacuums in space, when you grab a small enough piece of it--and maybe there aren't--and, just perhaps, it could be meaningless (eg, it could depend on exactly what you mean by matter). But there is no "nothingness" anywhere.

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You guys should find this interesting...

http://www.mathpages.com/rr/s3-07/3-07.htm

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I'll have to go through that in its entirety (uh, spelling and is that even a word?) if I want to outsmart Wiley! [img]/phpBB/images/smiles/icon_wink.gif[/img]

(Actually we're after the same point, but I'm attempting to come off better [img]/phpBB/images/smiles/icon_biggrin.gif[/img])

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On 2001-11-08 23:10, Lusion wrote:

There is no "physical nothing". "Nothing" does not exist in some real, concrete sense. This doesn't have to be proven or disproven, for "nothingness" is not a thing such that it can possibly exist in a concrete sense. It's a lack of a thing. To treat "nothingness" as if it were really something, and therefore could possibly exist in some sense, is to commit a reification.
Right. I used a poor choice of words in writing about a "physical nothing." I meant a space with nothing in it.

As for vacuums. I think that the ideal vacuum doesn't exist. But, I've been wrong before.

21. What a 'nothing' topic, or so me first thought. But as i suffered though the thread, started getting a 'glimpse' for a distinction.

There is a point in our universe, where nothing exists. But it does have a position in time and space, coordinates and nothing (SIC!) more.

What has always warped me noodle, is trying to think about the "edge" of the universe. More precisely, our 'bubble of a universe,' and the medium that defines such an edge. Without resorting to extra dimensions, started imaging the 'emptyness' of our universe at its 'edge,' adjacent to the 'emptyness' of this medium containing our universe...

Sorry, can't take it any further, it was an interesting sensation, a tickle. Doubt there any validity to it, but it was fun. Thanks.

22. On 2001-11-09 02:02, NubiWan wrote:
What a 'nothing' topic, or so me first thought. But as i suffered though the thread, started getting a 'glimpse' for a distinction.

There is a point in our universe, where nothing exists. But it does have a position in time and space, coordinates and nothing (SIC!) more.

What has always warped me noodle, is trying to think about the "edge" of the universe. More precisely, our 'bubble of a universe,' and the medium that defines such an edge. Without resorting to extra dimensions, started imaging the 'emptiness' of our universe at its 'edge,' adjacent to the 'emptiness' of this medium containing our universe...

Sorry, can't take it any further, it was an interesting sensation, a tickle. Doubt there any validity to it, but it was fun. Thanks.
The standard theory holds that there is no "edge", but rather that the observable universe is an expanding finite yet unbounded manifold. Space itself is expanding and the objects therein, such as galaxies, are all moving away from each other rather than from a central point. Beyond the observable, the universe could be infinite. (Nature is not obligated to follow our preconceived notions but also does leave tantalizing consistencies to follow in physics and astronomy.)

If the universe where like a conventional explosion with an edge and a central point from which matter, including us were expanding, this would be observable, but it is not observed.

Astronomer Ned Wright has an explanation here: http://www.astro.ucla.edu/~wright/infpoint.html

And he has interesting FAQs here: http://www.astro.ucla.edu/~wright/cosmology_faq.html

The BA has an article in this website about Universal Expansion: http://www.badastronomy.com/bitesize/accel2.html

I think in this thread and elsewhere I’ve read (not much else), the definition of “nothing” is very broad and includes philosophy as was pointed out by a previous poster. I was thinking much more confined within the observable universe. Along the lines of how much of a vacuum can there be? There might be something indirectly detectible which functions in the universe as a transitory entity that effects other things without being directly observed or even existing per say. (Now we’re out of the mainstream, so I guess it was OK to post the question here.) [img]/phpBB/images/smiles/icon_wink.gif[/img]

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On 2001-11-09 02:02, NubiWan wrote:
There is a point in our universe, where nothing exists. But it does have a position in time and space, coordinates and nothing (SIC!) more.
If it has attributes like position/coordinates then it is not nothing. You even called it "a point", which is clearly something, no matter how vague.

There is no such thing as a physical nothingness anywhere in the Universe.

24. As I understand it from a cosmological stance, there are three definitions of "universe":

1. the visible - that which we can observe
2. the universe - all that exists in this particular spacetime "bubble" that we find ourselves within, created with the BB
3. the Universe - all that is

The 'observable' universe is the same as the 'visible' one. It expands only with our ability to extend our "sight" or detection. We now *know* that the fabric of space is and will continue, to expand, accelerating actually. Barring technological advances, the 'observable universe' will be thinning out, over time less stars and galaxies will be 'visible' to us. Some theories suggest that an infinite number of these "bubble universes" were, and perhaps still are being, created. However we don't have and may never have, methods to actually know this, the very laws of physics may be 'different' within others of these bubble universes. To save wear and tear on me little noodle, have confined my universe to our bubble.

So there is a center most certainly, to our observable universe, the point where those observations are made. And the distinction that occured to me while reading thought this thread was;

There is a point within our universe, but at its "edge," where nothing exists, having nothing but a position in time and space, mere coordinates. Adjacent to a point within the 'emptyness' of this medium containing our universe, this point would not have any such coordinates.

A flight of fancy, of course, but found it entertaining. You said there is no "edge" to the universe, so how do you explain or measure, its "expansion?"

<font size=-1>[ This Message was edited by: NubiWan on 2001-11-09 13:24 ]</font>

25. There is no edge to the surface of a balloon as you inflate it, yet it expands.

26. Well there most certainly is an edge to an expanding balloon, the skin of the balloon itself.

27. I referred to the surface of the balloon, which is a 2-dimensional manifold in 3-space.

The balloon's surface has no edge: you can move over the surface forever without reaching a limit.

In this model universe, any 1- or 2-dimensional object on the surface of the balloon will see all other such objects receding as the balloon expands. The more distant the object is, the faster it moves away. (Of course, in this model, the light by which s/he sees those distant objects is also constrained to the surface of the balloon.)

Since you're seeing this from the godlike perspective of a higher dimension (3-space), you can see that the balloon is really a 3-dimensional object, and you wonder why the poor critters on the balloon don't just go "up" or "down" and escape their surface. But that's cheating. They're restricted to their 2-dimensional universe, just as we are to our 3-dimensional one.

Of course, myriad science fiction stories depend on the notion that one day we might find hyperdimensional shortcuts through our universe, the equivalent of a balloon-critter going "through the balloon" to reach another point on the surface. So far, however, that's just fiction.

I hope this is clear; if not, maybe I (or someone else) can think of some other analogy. And that's all it is... AFAIK, there are no itty-bitty 2-dimensional life forms inhabiting the surface of our balloon.

And keep away from my universe with that pin!
[img]/phpBB/images/smiles/icon_biggrin.gif[/img]

28. Ahh.., see what you are saying, DonnieB, and it demonstrates the limitations of analogies. That one does simplify the concept, of how all galaxies would appear to be receding, no matter which 'dot' you occupied. {fidgets with his mom's old shinny hat-pin} The reality is of course, much more complex. Our 'bubble' is expanding, bubbles don't have to be perfectly globular, rarely are in fact. And the "dots" of galaxies, would be destributed within its volume, not just on its surface.
Other than "open," not really certain of our universe's geometry. (Anyone?) The one consistent feature, on a cosmic as well as sub-atomic scale, the universe is about 99%(?) nothing.

29. NubiWan,

You are still mixing analogies. While it is true that the "dots" are distributed throughout the interior of the "bubble", the bubble is a portion of a three dimensional "surface" curved through higher dimensions.

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Um, Wiley?

Have you had some time to go over my wild claims? Can I get a Wiley seal of approval? [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

I checked with aperson with vastly superior mathematical knowledge than me and he feels it's okay.

How do you stand?

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