Thoughts on the scale of the universe?

[Dumac Dwarfking]

I'm purely hypothesising here, and would love input from one more knowledgeable than myself, but as far as I can see, the universe seems to be a finite one. By my reasoning, in a universe of infinite size movement would not be possible. I'll try to explain as best I can.

Zeno's paradox is as follows:

"Achilles and the tortoise are going to run a race. Achilles, being confident of victory, gives the tortoise a head start. Before Achilles can overtake the tortoise, he must first run to point A, where the tortoise started. But by then the tortoise has crawled to point B. Now Achilles must run to point B. But by then the tortoise has gone to point C, etc. Achilles is stuck in a situation in which he gets closer and closer to the tortoise, but never catches him."

Zeno is demonstrating the infinite dichotomy of a line segment. The paradox argues that movement is impossible. However we know that movement is possible, and while it may be mathematically to possible to dissect a line segment an infinite number of times, there couldn't possibly exist an infinite number of dissections on a line segment, being that it is of finite size (please correct me if I'm wrong).

Now, by my reasoning, in order for a universe to be infinitely large, it would also have to be infinitely small, as both of these traits are relative attributes. If the universe was infinitely small, the space between two finite objects would be subject to Zeno's paradox, and any movement made would be subject to this infinite dichotomy, making motion impossible.

Any thoughts?

[FallentoReason]

"Achilles and the tortoise are going to run a race. Achilles, being confident of victory, gives the tortoise a head start. Before Achilles can overtake the tortoise, he must first run to point A, where the tortoise started. But by then the tortoise has crawled to point B. Now Achilles must run to point B. But by then the tortoise has gone to point C, etc. Achilles is stuck in a situation in which he gets closer and closer to the tortoise, but never catches him."

I don't think that true. From memory I remember in highschool maths there was a vector question that had the same description mathematically as this. If you crunch some numbers, you'll find that Achilles catches up to the tortoise. It's common sense really, because the faster object will inevitably catch up to the slower object infront of it.

The thing is though, that this question words it in a tricky way. It's making you think about the situation at certain points in time, primarily, everytime Achilles gets to the point where the tortoise used to be after he last reached a similar point. Even through this reasoning though one can imagine that the distance between 'ghost tortoise' (Achilles' position that he reaches every time) and true tortoise is getting smaller everytime you pause and measure.

there couldn't possibly exist an infinite number of dissections on a line segment, being that it is of finite size (please correct me if I'm wrong).

You can keep slicing infinitely. Think of a line segment from 0 to 1. Chop that in half. Now we have 0 to 0.5. Chop that in half. Now we have 0 to 0.25.....now we have 0 to 0.000000000001. Chop that in half ad infinitum.

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In terms of the universe being infinitely large, I think the only requirement for that is that it can't be bounded, therefore by mathematical definition, infinite.

[Cato]

For fuck's sake. Are you seriously suggesting that an adult human being in the 21st century doesn't understand the significance of the Cosmic Mircrowave Background Radiation (clue: the universe isn't infinitely large)?

Natural facts are not dependent on human opinion.

[Waratah]

Could it be a finite universe with infinite universes.

I'm sure Dr who would know.

[Tino]

but as far as I can see, the universe seems to be a finite one.

The universe is generally considered to be infinite in size. Think of it this way - you get a starship and you cruise in it way out to the "edge" of the universe where you reach a "wall" of some kind, representing the "end" of the universe. How thick is that wall? What's on the other side of the wall? Since the Universe is by definition everything, the thickness of the wall and everything on the other side of it is still the universe. Whatever "end" you could find, it's still universe on the other side of the end.

there couldn't possibly exist an infinite number of dissections on a line segment, being that it is of finite size (please correct me if I'm wrong).

There's no reason that a line segment can't be infinitely divided, which is what resolves Zeno's paradox. Whatever you think is the smallest possible line segment, I can mathematically divide in half.

Now, by my reasoning, in order for a universe to be infinitely large, it would also have to be infinitely small, as both of these traits are relative attributes.

I'm not clear on what you mean by "infinitely small" but I assume it means that it can be divided into infinitely small segments. As mentioned above, that can be done.

[Dumac Dwarfking]

You can keep slicing infinitely. Think of a line segment from 0 to 1. Chop that in half. Now we have 0 to 0.5. Chop that in half. Now we have 0 to 0.25.....now we have 0 to 0.000000000001. Chop that in half ad infinitum.

I understand that mathematically you can keep slicing indefinitely, but in reality would it be plausible? Or would you reach a point where it could no longer be sliced as the pieces would be to small?

[FallentoReason]

You can keep slicing infinitely. Think of a line segment from 0 to 1. Chop that in half. Now we have 0 to 0.5. Chop that in half. Now we have 0 to 0.25.....now we have 0 to 0.000000000001. Chop that in half ad infinitum.

I understand that mathematically you can keep slicing indefinitely, but in reality would it be plausible? Or would you reach a point where it could no longer be sliced as the pieces would be to small?

Mathematically, you can. Think of the smallest particle known to us. It has a width. Now take that distance and slice it in half.

You can just keep zooming in on your new line segment and slicing in half forever. I can't really think of anything that wouldn't let you 'zoom in' and slice again. Such is the nature of distances.

[Dumac Dwarfking]

For fuck's sake. Are you seriously suggesting that an adult human being in the 21st century doesn't understand the significance of the Cosmic Mircrowave Background Radiation (clue: the universe isn't infinitely large)?

Natural facts are not dependent on human opinion.

I agree, my opinion has nothing to do with the facts.

I know a little about CMBR, but obviously not very much. What significance does that have in terms of the scale of the universe?

[FallentoReason]

Ah, I guess the only way you couldn't ever slice again is if your distance eventually becomes a point. With a distance, you have a space between points A and B to slice in, but with a point C there is no width left to slice in half.

When does a distance turn into a point? I'm not sure, or if ever!

[Dumac Dwarfking]

I understand that mathematically you can keep slicing indefinitely, but in reality would it be plausible? Or would you reach a point where it could no longer be sliced as the pieces would be to small?

Mathematically, you can. Think of the smallest particle known to us. It has a width. Now take that distance and slice it in half.

You can just keep zooming in on your new line segment and slicing in half forever. I can't really think of anything that wouldn't let you 'zoom in' and slice again. Such is the nature of distances.

I see what you're saying, it's just something I struggle to grasp (puny brain). As far as I'm aware, infinity as a concept is not something that has been observed or proven.