How many points can be found in the surface of the Earth?

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The other day I was wondering if as the universe is infinite and you can say that every single point in it is the centre of the universe, or that there is no centre for the same matter. Since you are not able to set up a centre in earth's surface. Is then earth's surface infinite?

When you talk about straights in an x and y axis, you notice that they are endless, and therefore, they have infinite points. You cannot set up a centre in that line because it is infinite.

Actually my question is also applicable to a sphere such as a regular tennis ball.
What do you think?
 
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  • #2
CWatters
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The other day I was wondering if as the universe is infinite and you can say that every single point in it is the centre of the universe, or that there is no centre for the same matter.
Our best guess is that there is no centre to the universe.

Since you are not able to set up a centre in earth's surface. Is then earth's surface infinite?
I haven't a clue how those two ideas might relate to each other. Why should the universe not having a centre imply that the surface of the earth is infinite?
 
  • #3
mathman
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You seem to be mixing two different uses of infinite. There are an infinite number of points on the earths surface,etc. However the earth is of finite size.
 
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Dale
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The other day I was wondering if as the universe is infinite and you can say that every single point in it is the centre of the universe, or that there is no centre for the same matter. Since you are not able to set up a centre in earth's surface. Is then earth's surface infinite
The correct term is unbounded. A sphere is a 2D manifold which is finite but unbounded.

At this point we believe that the universe is unbounded, but we don't know if the universe is finite or infinite. If it is finite then the analogy with a sphere would be pretty strong.
 
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  • #5
Good ole' Zeno's paradox. It's fun to think about, but beyond human comprehension.

Some infinities are just smaller than others. Points & lines are small infinities contained within planes, which are larger infinities. Planes compose three dimensional shapes which are the largest infinity that we can perceive. There may be higher or lower dimensions with larger infinities or smaller ones, but we as 3D beings could never truly understand them. (Probably)
 
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phinds
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Good ole' Zeno's paradox. It's fun to think about, but beyond human comprehension.
That's ridiculous. Zeno's Paradox is thoroughly understood.
Some infinities are just smaller than others. Points & lines are small infinities contained within planes, which are larger infinities. Planes compose three dimensional shapes which are the largest infinity that we can perceive. There may be higher or lower dimensions with larger infinities or smaller ones, but we as 3D beings could never truly understand them. (Probably)
Only slightly less ridiculous. You are correct that there are different levels of infinity (although you examples are poor) but mathematically, they are understood. Were do you get this concept that infinities cannot be understood?
 
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  • #7
That's ridiculous. Zeno's Paradox is thoroughly understood.
Only slightly less ridiculous. You are correct that there are different levels of infinity (although you examples are poor) but mathematically, they are understood. Were do you get this concept that infinities cannot be understood?
I should've worded this a bit more carefully... When I said beyond human comprehension, I meant it in a more literal sense. We literally are unable to comprehend the size of an infinity, or one infinity fitting inside another. I understand that we can describe lines, planes, and infinities mathematically.
 
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phinds
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I should've worded this a bit more carefully... When I said beyond human comprehension, I meant it in a more literal sense. We literally are unable to comprehend the size of an infinity, or one infinity fitting inside another. I understand that we can describe lines, planes, and infinities mathematically.
I do agree that that statement is MUCH better worded, but I disagree with it completely. It is, I believe, perfectly well understandable (and understood) by mathematicians how levels of infinities exist. I can only conclude that you have read little mathematics. As you read more, you'll see what I mean.
 
  • #9
We're arguing over semantics here. I believe I answered the question just fine in an easy to understand way. Sure, you've probably read more math than I have, but that doesn't mean you can visualize 1 infinity baseballs. We're both right, share your cake with me.
 
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phinds
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We're arguing over semantics here. I believe I answered the question just fine in an easy to understand way. Sure, you've probably read more math than I have, but that doesn't mean you can visualize 1 infinity baseballs. We're both right, share your cake with me.
Well, there are two parts to your statement and I agree w/ the first part. I cannot speak for others but I'm with you in my inability to "visualize" or otherwise understand what infinity could be physically. The second part of your statement is that it cannot be understood how levels of infinity exist. I disagree w/ you there and that is where I think you'll change your mind if you read more math.
 
  • #11
Dale
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We literally are unable to comprehend the size of an infinity, or one infinity fitting inside another. I understand that we can describe lines, planes, and infinities mathematically.
Math is a product of and a tool for our understanding. To say that we cannot understand something but that we can describe it mathematically is, in my opinion, a self contradiction.
 
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  • #12
Well, there are two parts to your statement and I agree w/ the first part. I cannot speak for others but I'm with you in my inability to "visualize" or otherwise understand what infinity could be physically. The second part of your statement is that it cannot be understood how levels of infinity exist. I disagree w/ you there and that is where I think you'll change your mind if you read more math.
For the other levels of infinity, I was referring to the physical existence of objects that are infinitely larger or smaller than what we can see. The fourth dimension (time) may give objects a shape that we can't actually see... And there may be higher dimensions still. Some versions of string theory consider many dimensions of space. Not just three.

And I believe the crux of the OP's topic was the problem of the Earth having infinite surface area.
 
  • #13
Math is a product of and a tool for our understanding. To say that we cannot understand something but that we can describe it mathematically is, in my opinion, a self contradiction.
I don't think so. I know that one infinity can fit inside of another in math. The problem is that this also appears to be true in the physical world, not just in math... And I do not understand it. That is why I take it that this problem "Zenos Paradox" is beyond understanding. The concept of infinity makes perfect sense when just referring to mathematics, but when applied to a physical object like Earth's surface it defies explanation... Or at least I haven't heard one that I can understand.
 
  • #14
phinds
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I don't think so. I know that one infinity can fit inside of another in math. The problem is that this also appears to be true in the physical world, not just in math... And I do not understand it. That is why I take it that this problem "Zenos Paradox" is beyond understanding. The concept of infinity makes perfect sense when just referring to mathematics, but when applied to a physical object like Earth's surface it defies explanation... Or at least I haven't heard one that I can understand.
It sounds to me like you've never read a good explanation of Zeno's Paradox and don't really quite understand it. It is a MISUSE of an infinity that leads to the actually non-existent "paradox".
 
  • #15
Dale
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And I do not understand it.
Then state only that YOU do not understand it. Do not generalize your own conceptual challenge to everyone.
 
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In mathematics you don't understand things. You just get used to them. -John Von Neumann
 
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