The Difference

[Starvingpercussionist]

This probably belongs in the Philosophy section, but heck, nobody reads that anyways. So here goes:

"What's the difference between a sphere with an infinitely large radius and a sphere with an infinitely small radius?"


Thanks to Alan for the inspiration for this. One of his posts said that the universe was a sphere with an infinite radius.


DISCUSS!!!...
please.

[interception]

I'm sorry, to me that makes no logical sense at all. The words "large" and "small" has no meaning when you are dealing with infinity.

The term radius is a measurement with a start and a end point. An infinite line cannot have either of those things.

While we are on the subject, how can something that is infinite have a shape? A shape defines boundaries, a sphere is a shape. Infinity however, is shapeless and without bounds by definition.

[Starvingpercussionist]

I'm sorry, to me that makes no logical sense at all.

It's not supposed to, heh. Infinity is a paradox, that's what I'm trying to point out. 

You see, in an infinitely large sphere, there is a center point but no end in any direction, so therefore the center point could be anywhere (or everywhere all at once, it makes no difference). In an infinitely small sphere the center point is the entirety of the sphere. When dealing with infinity there is no such thing as large or small, except in the case that you define infinity as being "out there" in some direction. Truthfully though, to try and define infinity is nonsense because it is impossible to contain, so any words or meanings attached to it cannot possibly be what it really is.

[astral traveler]

"What's the difference between a sphere with an infinitely large radius and a sphere with an infinitely small radius?"

this reminds me of the polarity of the macroverse and the microverse.  i believe that the metaverse is infinitely eternal and etenally infinite.

1. infinite macroverse: the idea that the macroverse is infinitely large, extending forever and ever, without beginning or end points.  there are no outer walls of the metaverse (although the metaverse is composed of an infinite number of universes).  the metaverse has no beginning or ending.

2. infinite microverse: the idea that a microverse is infinitely small, extending forever and ever.  in other words, the smallest molecules are composed of infinitely smaller particles that go on forever and ever.  there is no smallest particle that isn't composed of even smaller particles.

[interception]

Problem with infinity is, like you point out, our language fails us.

An "infinitely small point":
Oh you mean infinitely divisible "downwards", like a fractal? That I can sort of see logically.
Otherwise it makes no sense. A infinitely "small" "sphere" will be.... what... nothingness?

An "infinitely large sphere":
Again, for me logically speaking, an infinite volume cannot have a shape at all. It can not be defined as a sphere, because as soon as you do that, it would not be an infinite volume any more.
It will also not have one center point. I agree that in an infinite volume any arbitrary point can be the "centre" (as meaningless as this statement seems on the surface).

[interception]

Oh crap, I have contradicted myself. 

[Starvingpercussionist]

Problem with infinity is, like you point out, our language fails us.

An "infinitely small point":
Oh you mean infinitely divisible "downwards", like a fractal? That I can sort of see logically.
Otherwise it makes no sense. A infinitely "small" "sphere" will be.... what... nothingness?

An "infinitely large sphere":
Again, for me logically speaking, an infinite volume cannot have a shape at all. It can not be defined as a sphere, because as soon as you do that, it would not be an infinite volume any more.
It will also not have one center point. I agree that in an infinite volume any arbitrary point can be the "centre" (as meaningless as this statement seems on the surface).

If not one center point in an infinitely "large" sphere, then how many can there be? An infinity of them, or is it since a center point as geometrically defined is impossible, is it impossible for anywhere to be the center? And if one were to create the center, would one be creating an infinite sphere, since the center of a sphere with zero radius (infinitely small) is the entirety of the sphere?

These questions might be unanswerable, but trust me, there is a point. Only a false sense of knowledge can get confused in the first place. 

PS - I know infinity doesn't have a shape, I just say "sphere" for lack of a better word to give the concept meaning. 

[interception]

If not one center point in an infinitely "large" sphere, then how many can there be? An infinity of them, or is it since a center point as geometrically defined is impossible, is it impossible for anywhere to be the center?

Logically, it makes more sense that nowhere can be the center, because a center is also linked to a defined space. Infinity cannot be defined, there is nothing to be a center of.

These questions might be unanswerable, but trust me, there is a point. Only a false sense of knowledge can get confused in the first place. 

What is the point though?   

[Starvingpercussionist]

What is the point though?   

What's the point of a paradox? If there's no answer in the mind, then where can the answer exist? It must be in reality. Thus the point of a paradox is to attempt to bring you to reality by forcing you to search there for its answer.

If there is no difference between the largest thing and the smallest thing, then from where comes any difference at all? And if everything is intrinically connected, then how? If you want to find the answer to these questions, you need only look within yourself. After all, what's a point of view that sees nothing but itself? 

[galaxy_storm]

"What's the difference between a sphere with an infinitely large radius and a sphere with an infinitely small radius?"

Well, the difference is that a sphere with an infinitely large radius has an infinitely large volume, and a sphere with an infinitely small radius has no volume at all

Anything else you would like to know?

[Starvingpercussionist]

Well, the difference is that a sphere with an infinitely large radius has an infinitely large volume, and a sphere with an infinitely small radius has no volume at all

Anything else you would like to know?

Still though, how would you be able to know that that is really the difference unless you're able to compare them and find out? 

[galaxy_storm]

They both do not exist in our universe, you can't compare things which do not exist

[Starvingpercussionist]

Oh crap, what the heck happened? Why did it modify your post instead of posting mine? 

EDIT: I must've hit the modify button, lol. Damn, I thought I hit "quote". I didn't know the modify button actually worked on other people! Sorry, I'll repost here and fix your post.

They both do not exist in our universe, you can't compare things which do not exist

Well now, how do you know there isn't really an infinite space between any two things? Geometrically speaking, the line between any two points always contains an infinite amount of points.

Just because you can't define infinity doesn't mean it can't exist - it only means it can't exist in the mind. However, it is impossible to compare anything to infinity because of its all-encompassing nature. While on the one hand you could say that you can't compare things that don't exist, you could also say that you can't compare things which are one and the same.

An infinitely small sphere is the same as an infinitely large one if neither can really be defined, and that's the paradox I'm trying to show.

[AmbientSound]

The difference lies in how you perceive and relate to the sphere. It's all in your mind. And mine.

[Starvingpercussionist]

The difference lies in how you perceive and relate to the sphere. It's all in your mind. And mine.

How does one relate to the invisible? And if the differences between infinity only exist in the mind, then what does sameness really mean? 

[AmbientSound]

Invisible? Or undetectable?

Sameness is:

The removal of all the mind's filtering systems and perceiving everything simultaneously. Perhaps even the removal of the mind itself, assuming that it is not a necessary tool for us to gain the understanding of sameness.

Or

Being unable to perceive any difference pertaining to what is being compared/observed (a false sense of sameness).

[Starvingpercussionist]

Good answer. 

Invisible or undetectable? I'd say the best choice of words would probably be "utterly indescribable".

I am led to believe that the mind is unnecessary to gain an understanding of sameness (or "oneness") because of the fact that the mind cannot describe what it is. I believe that "sameness" is ultimately "The Truth" and that "The Truth" is always self-evident - this means that seeing Truth is to have a simultaneous understanding of it. The only reason I would believe this is because I have seen oneness, and in fact see it all the time but yet I cannot possibly recall its appearance. Upon the appearance of oneness though, there is always this simultaneous understanding that goes with it - the answer to a paradox if you will.