Infinite Regress | Why is everyone telling me I am wrong?

[iDimension]

I love having discussions with my friends about cosmology, physics and just the universe is general but can someone explain to me why ALL my friends tell me this way of thinking is just plain wrong.

We were talking about whether or not we think the universe is infinite or not and I told them that if the universe is everything that exists, then by its own definition it must be infinite, otherwise it clearly isn't everything that exists.

Secondly I said to them that if the universe isn't everything then the universe must be inside of something else which in turn is infinite, and likewise if that isn't infinite then that something must be inside of something etc.

So even if that is true that must mean that a is inside b, b is inside c, c is inside d ... to infinity so whichever way you look at you always arrive at infinite.

They told me that infinite regression like this is a paradox and basically it stems from the inability to ask or even think about different possibilities, we simply don't have the mental capacity to think of other possibilities.

They said that if everything needs to be inside something else then nothing can exist as there can never be the first "thing" but I told them that this is ok with infinity because just as +infinity doesn't have a finish point, -infinity doesn't have a starting point so it just means that it has been happening forever.

To be honest none of us really have a clue what we are talking about but as friends sometimes they frustrate me when they say I am wrong lol so I come here for some advice.

It just seems that no matter how many layers you peel back, no matter what when if or how the final answer just seems to be infinite.

 

[Bandersnatch]

The universe can be everything there is, and be finite. It could be curved like the hypersurface of a 4-dimensional hypersphere, or one of many other closed shapes, of finite size.

The usual analogy is the one dimension-lower case of the universe being the 2-dimensional surface of a 3-dimensional sphere. The surface is finite(you can calculate the area easily). It is all there is. It's got no boundaries.

Note that the existence of the higher dimension to embed the surface(or our universe) in is not required for the curvature to be present. All you need to have is certain rules about parallel lines and angles in a triangle being satisfied.

 

[nick1o2]

They told me that infinite regression like this is a paradox and basically it stems from the inability to ask or even think about different possibilities, we simply don't have the mental capacity to think of other possibilities.

I remember an analogy which said that you can't teach a dog physics, it can't comprehend physics. Likewise we might not be able to comprehend physics to an extent.

 

[iDimension]

The universe can be everything there is, and be finite. It could be curved like the hypersurface of a 4-dimensional hypersphere, or one of many other closed shapes, of finite size.

The usual analogy is the one dimension-lower case of the universe being the 2-dimensional surface of a 3-dimensional sphere. The surface is finite(you can calculate the area easily). It is all there is. It's got no boundaries.

Note that the existence of the higher dimension to embed the surface(or our universe) in is not required for the curvature to be present. All you need to have is certain rules about parallel lines and angles in a triangle being satisfied.

So it's possible to travel in any given direction at the speed of light for eternity and I will never come back to where I started and I will never "escape" the universe?

Because with the Earth analogy I can see me eventually coming back to where I started not to mention being able to travel outwards and eventually leave Earth which means it isn't 3dimensionally unbounded.

Are you saying that no matter where we are located in space we are always on the 2 dimensional plane and we can never enter the 3 dimensional plane?

 

[Bandersnatch]

So it's possible to travel in any given direction at the speed of light for eternity and I will never come back to where I started and I will never "escape" the universe?

Because with the Earth analogy I can see me eventually coming back to where I started not to mention being able to travel outwards and eventually leave Earth which means it isn't 3dimensionally unbounded.

Are you saying that no matter where we are located in space we are always on the 2 dimensional plane and we can never enter the 3 dimensional plane?

If the universe is a closed hypersphere, then just as on Earth, you could conceivably travel in one direction for so long so as to come back to where you started. That is, if not for the expansion of space.

You can never "escape" the universe, whether it's finite or not.

And yes, in the Earth-surface analogy, no entering higher dimension. In that analogy, there are two-dimensional beings, to whom the third dimension is as abstract as the fourth spatial dimension is to us. Furthermore, the 3rd dimension might or might not exist. That is, it is not required.

 

[DiracPool]

Secondly I said to them that if the universe isn't everything then the universe must be inside of something else which in turn is infinite, and likewise if that isn't infinite then that something must be inside of something etc.

So even if that is true that must mean that a is inside b, b is inside c, c is inside d ... to infinity so whichever way you look at you always arrive at infinite.

I think the issue here is your assertion that "something must be inside something else." One of the first misconceptions big bang cosmologists try to dispel to their listeners is that, after the big bang, space expanded into something. The standard big bang view (save multiverse theories) is that the expanding space is all there was or is, and to talk about it expanding into something else is a confounding way to look at the expansion.

Once you start talking about" a" expanding into "b," and b expanding into c, etc., your friends are right, you can't avoid an infinite regress. The assumption when you do this is that you must implicitly give this b, c, d, etc. "space" some sort of physical properties, or else it makes no sense to talk of their existence. What are those physical properties? See where this is going?

 

[iDimension]

I think the issue here is your assertion that "something must be inside something else." One of the first misconceptions big bang cosmologists try to dispel to their listeners is that, after the big bang, space expanded into something. The standard big bang view (save multiverse theories) is that the expanding space is all there was or is, and to talk about it expanding into something else is a confounding way to look at the expansion.

Once you start talking about" a" expanding into "b," and b expanding into c, etc., your friends are right, you can't avoid an infinite regress. The assumption when you do this is that you must implicitly give this b, c, d, etc. "space" some sort of physical properties, or else it makes no sense to talk of their existence. What are those physical properties? See where this is going?

Yes and I know that our universe doesn't expand into something, unless our universe is finite? Even if we live in a bubble universe that must mean these bubble universe are contained in something, even if that something has 0 properties. Basically just an empty void volume.

But my main argument was that if the universe is everything then it has to be infinite and if the universe isn't everything then it must be finite.

 

[Chronos]

Infinities give rise to paradoxes, which is why scientists attempt to remove mathematical infinities from calculation that express the laws of nature [e.g., renormalization]. In, for example, an infinite universe everything that can possibly happen has happened somewhere at sometime in the universe. That would imply the universe is not infinite because we have not observed all possible events in the universe [like black dwarfs], and we have compelling reasons to believe the universe has a finite age. That raises the question how can an infinite universe have a finite age? This question has haunted philosophers and physicists alike for millennia. We are forced to admit the obvious - that the OBSERVABLE universe is temporally and spatially finite. There may be distant recesses beyond our observational grasp [where all this unobserved stuff resides] that will forever be inaccessible. We do not know and probably never will. Every test ever imagined, many of which are quite ingenious, has failed to answer this fundamental question.

 

[cosmik debris]

Yes and I know that our universe doesn't expand into something, unless our universe is finite? Even if we live in a bubble universe that must mean these bubble universe are contained in something, even if that something has 0 properties. Basically just an empty void volume.

But my main argument was that if the universe is everything then it has to be infinite and if the universe isn't everything then it must be finite.

The problem is an empty void volume has properties. The point has been made by a previous poster, a universe can be closed and not imbedded in anything.

 

[eforster]

Traveling at the speed of light

So it's possible to travel in any given direction at the speed of light for eternity and I will never come back to where I started and I will never "escape" the universe?

Because with the Earth analogy I can see me eventually coming back to where I started not to mention being able to travel outwards and eventually leave Earth which means it isn't 3dimensionally unbounded.

Are you saying that no matter where we are located in space we are always on the 2 dimensional plane and we can never enter the 3 dimensional plane?

According to the Lorentz Transformation formula, space and time disappear when you travel at the speed of light. To an outside observer you'd be perceived as a photon, while your own observation would be that you are not going anywhere, because "where" doesn't exist.

 

[PeterDonis]

According to the Lorentz Transformation formula, space and time disappear when you travel at the speed of light.

No, this is not correct. The Lorentz transformation is mathematically undefined for $v = c$. That means it doesn't correspond to anything physical: if you're traveling slower than light, you can't change your state of motion to travel at the speed of light.

 

[MFPunch]

@iDiminsion
You are in fact wrong and so are your friends. Your argument is actually pretty good, though. Your assumptions are certainly plausible and your reasoning is sound. But here's the problem:

Secondly I said to them that if the universe isn't everything then the universe must be inside of something else which in turn is infinite, and likewise if that isn't infinite then that something must be inside of something etc.

So even if that is true that must mean that a is inside b, b is inside c, c is inside d ... to infinity so whichever way you look at you always arrive at infinite.

The key concept here is the 'boundedness' of the universe. All bounded spaces have an edge and all finite spaces are bounded. So if the universe is finite then it has an edge, which means there has to be something beyond it and then that leads to all that infinite regression stuff up there. Now for the interesting part:

They told me that infinite regression like this is a paradox and basically it stems from the inability to ask or even think about different possibilities, we simply don't have the mental capacity to think of other possibilities.

Slap the next person that gives you that "beyond our comprehension/mental capacity" crap and erase that phrase from your mind forever. There's no reason that the universe has to be limited to just 3 dimensions like we are. It could be 4 dimensional space where there can exist finite spaces that are not bounded. If it's not bounded then it doesn't have any edges and without edges there's no "beyond" for anything else to be.

 

[Ich]

The key concept here is the 'boundedness' of the universe. All bounded spaces have an edge and all finite spaces are bounded. So if the universe is finite then it has an edge, which means there has to be something beyond it and then that leads to all that infinite regression stuff up there.

That's simply not true. "Bounded" is not the same as "having a boundary". Bandersnatch gave counter examples.
If there is no boundary, it is not necessary to introduce an "outside world", so iDimension's line of reasoning is invalid.

 

[PeterDonis]

It could be 4 dimensional space where there can exist finite spaces that are not bounded.

That's not limited to 4 dimensional spaces. A circle is a 1-dimensional space that is finite but not bounded. A 2-sphere (like the surface of the Earth, or at least of an idealized Earth)is a 2-dimensional space that is finite but not bounded. And so on.

 

[MFPunch]

That's simply not true. "Bounded" is not the same as "having a boundary". Bandersnatch gave counter examples.

I meant to say "in 4 dimensional space there can exist finite spaces that have no boundary." Wish I could go back and fix that.

 

[MFPunch]

That's not limited to 4 dimensional spaces. A circle is a 1-dimensional space that is finite but not bounded. A 2-sphere (like the surface of the Earth, or at least of an idealized Earth)is a 2-dimensional space that is finite but not bounded. And so on.

Are you saying that the universe could be 2 dimensional?

 

[PeterDonis]

Are you saying that the universe could be 2 dimensional?

No. But you seemed to be saying that, in order for it to be even possible to have a finite space that is not bounded, you have to have a 4-dimensional space (i.e., 4 spatial dimensions, not just 3). That's not correct. You can have a 3-dimensional space that is finite but not bounded (as well as the 1- and 2-dimensional ones that I gave examples of).

 

[MFPunch]

No. But you seemed to be saying that, in order for it to be even possible to have a finite space that is not bounded, you have to have a 4-dimensional space (i.e., 4 spatial dimensions, not just 3). That's not correct. You can have a 3-dimensional space that is finite but not bounded (as well as the 1- and 2-dimensional ones that I gave examples of).

I didn't mean to say a finite space that isn't bounded I meant to say a finite space without boundaries. And how is a circle not bounded? All finite spaces are bounded.

Honestly I was way too tired at the time and that post is really poorly written so I don't blame anyone for being confused. I read it the next morning and even I had a hard time following what I was trying to say.

 

[Drakkith]

I didn't mean to say a finite space that isn't bounded I meant to say a finite space without boundaries. And how is a circle not bounded? All finite spaces are bounded.

Not true. The surface of a finite sized sphere is unbounded. You can continue to move around the surface of the sphere forever without ever reaching a boundary. Note that we are talking only about the surface of the sphere, nothing else.

 

[iDimension]

Not true. The surface of a finite sized sphere is unbounded. You can continue to move around the surface of the sphere forever without ever reaching a boundary. Note that we are talking only about the surface of the sphere, nothing else.

Sorry if I am repeating myself but I hope you can explain it a little better. If the universe is finite then it has a shape and like all shapes, they have boundaries in the 3rd dimension. So it would seem that if I travel in the 3rd dimension long enough, I will escape the "surface" and after some time, I can look down and see the object which means that I must be in some other space or volume.

I don't think we have anyway to tell which direction in space is the 3rd dimension, in fact I don't think it makes any sense to ask that question as the universe is hollow so any direction is the 3rd dimension so eventually, moving at the speed of light or even 1million times the speed of light, it would theoretically be possible to leave this universe and again after some time, look down and see the universe.

I believe that to understand cosmology correctly one must train their mind to think abstractly and it takes time to understand this stuff but I am having real difficulties.

I can just imagine travel at 20billion times the speed of light (impossible I know but to make a point) and then just crashing into an untraversable wall that stops us going further, but even then that wall must have some thickness which itself should extend to infinity?

Either that or physics will troll us once again by just teleporting you back to where you started from once you cross a certain boundary. Why is this stuff so hard to understand :(

 

[Bandersnatch]

Not true. The surface of a finite sized sphere is unbounded. You can continue to move around the surface of the sphere forever without ever reaching a boundary. Note that we are talking only about the surface of the sphere, nothing else.

I think there's a confusion on terminology here. From what I understand, bounded is not the same as boundary-less. Bounded means that all points in the set lie a set distance from each other. I.e., it's equivalent to the universe being "finite". Having a boundary means there are points lying outside the set in the same space, equivalent to an "edge".
A 1D circle or a 2D sphere would then be bounded but without a boundary. A 1D line and 2D surface would be unbounded and without boundary. A 1D line segment and 2D disc would be bounded and with a boundary.

I'd like somebody else confirm that, as I see PeterDonis made the same mistake(if it's a mistake), and I don't have enough confidence in my maths to make a definitive statement.
It certainly is in line with what wikipedia has to say on the subject, for whatever that's worth.

@iDimension: you're still thinking of the shape of the universe as being a something in 3D. The shape is 4-dimensional. You can not leave the 3D universe to travel in the fourth spatial dimension. I dare you!

Imagine that old arcade game Asteroids. The way it's made, you can travel in the cardinal directions off the screen, to emerge from the oposite side.
From the point of view of the ship in the game, there are no edges. You can travel infinitely long and never leave the screen.
You certainly can not leave the screen in the z(perpendicular to the screen) direction. You never have to worry about shooting yourself in the eye, or being hit by a stray asteroid. The 3rd dimension is meaningless from the point of view of the contents of the game.

This is equivalent to the space represented in there being toroidal in shape. If you had a torus in 3D, then tracing a finger along its 2D surface would net you the same effect of wrapping around to get back where you started.

Similarly, the universe has got a shape, in the sense that its geometry resembles that of a something 4-dimensional that we can describe. Seeing the shape or hitting the edge makes as much sense for us as it makes for that little ship in Asteroids.

 

[Dale]

If the universe is finite then it has a shape and like all shapes, they have boundaries in the 3rd dimension. So it would seem that if I travel in the 3rd dimension long enough, I will escape the "surface" and after some time, I can look down and see the object which means that I must be in some other space or volume.

This is simply not true.

Take a shape and pick any point in that shape and make a little neighborhood of points around that point. If you can smoothly map those points to points in $\mathbb{R}$, then the shape is 1D (like a line). If you can smoothly map those points to points in $\mathbb{R}^2$ then the shape is 2D (like a triangle). Etc. So the surface of a sphere is a 2D shape. It may or may not be embedded in a 3D space, but the shape itself is 2D.

A shape has a boundary if there are some points in the shape where if you make the little neighborhood you find that there are no neighboring points in some direction. For example, in a triangle a point in the middle has a neighborhood that goes in all directions, but on a corner the neighborhood only goes in certain directions, so a corner is on the boundary of a triangle.

Now, consider the surface of a sphere. Again, it is a 2D shape, but every point in the shape has a complete neighborhood. There is no boundary. So a sphere is a 2D shape which has a finite surface area, but no boundary. In contrast, a triangle is a 2D shape which has a finite surface area, and a boundary. There are also shapes, like a plane, which have an infinite are and no boundary, and shapes like a half-plane which have an infinite area and a boundary. So the finite or infinite size of a shape does not in any way imply whether or not it has a boundary.

The universe is a 4D shape, and our best current theory is that it has no boundary, but we don't know if it is finite or not (AFAIK). Either possibility is logically compatible with there being no boundary.

 

[iDimension]

This is simply not true.

Take a shape and pick any point in that shape and make a little neighborhood of points around that point. If you can smoothly map those points to points in $\mathbb{R}$, then the shape is 1D (like a line). If you can smoothly map those points to points in $\mathbb{R}^2$ then the shape is 2D (like a triangle). Etc. So the surface of a sphere is a 2D shape. It may or may not be embedded in a 3D space, but the shape itself is 2D.

A shape has a boundary if there are some points in the shape where if you make the little neighborhood you find that there are no neighboring points in some direction. For example, in a triangle a point in the middle has a neighborhood that goes in all directions, but on a corner the neighborhood only goes in certain directions, so a corner is on the boundary of a triangle.

Now, consider the surface of a sphere. Again, it is a 2D shape, but every point in the shape has a complete neighborhood. There is no boundary. So a sphere is a 2D shape which has a finite surface area, but no boundary. In contrast, a triangle is a 2D shape which has a finite surface area, and a boundary. There are also shapes, like a plane, which have an infinite are and no boundary, and shapes like a half-plane which have an infinite area and a boundary. So the finite or infinite size of a shape does not in any way imply whether or not it has a boundary.

The universe is a 4D shape, and our best current theory is that it has no boundary, but we don't know if it is finite or not (AFAIK). Either possibility is logically compatible with there being no boundary.

So in your personal opinion do you think (everything) is finite or infinite? Forget about our universe or any other universes which may or may not exist, beyond any other space-times etc.

Do you think the answer is more likely to be finite or infinite or do you think they carry equal probability of being true?

For me it just seems that if out universe isn't infinite then there will be something which is infinite or if that isn't true, there will be an infinite amount of finite things. It just seems so much more logical that everything is infinite and unbounded in any and all dimensions.

 

[MFPunch]

@Drakkith, @PeterDonis
I think both of you guys are still confusing bounded with having a boundary. I used the wrong term in my original post. I wasn't confused and I didn't misunderstand anything. I just literally typed the wrong word over and over for whatever stupid reason.

No. But you seemed to be saying that, in order for it to be even possible to have a finite space that is not bounded, you have to have a 4-dimensional space (i.e., 4 spatial dimensions, not just 3). That's not correct. You can have a 3-dimensional space that is finite but not bounded (as well as the 1- and 2-dimensional ones that I gave examples of).

I'm assuming when you say "not bounded" you mean "without a boundary" in which case my response to iDimension's latest post below will also apply to yours.

Why is this stuff so hard to understand :(

You're actually a lot closer to understanding it then you think you are. In fact you already know the solution you just don't realize it yet. It's right here:

Sorry if I am repeating myself but I hope you can explain it a little better. If the universe is finite then it has a shape and like all shapes, they have boundaries in the 3rd dimension.

I can see why you're so confused. Because you're right. All 3-dimensional objects with a finite volume do have boundaries. So if our universe is finite then it has a boundary and there has to be something else beyond it. But there's no reason that the next universe has to be 3-dimensional like ours is. It could have 4 dimensions. There are 4 dimensional objects that have a finite volume but do not have any boundaries.
It could even have more than 4 and then there's even more crazy shapes and all kinds of nonsense. The point is your argument is only valid for our universe because we don't know the geometry of the next one.

Do you think the answer is more likely to be finite or infinite or do you think they carry equal probability of being true?

For me it just seems that if out universe isn't infinite then there will be something which is infinite or if that isn't true, there will be an infinite amount of finite things. It just seems so much more logical that everything is infinite and unbounded in any and all dimensions.

Probability is something else and is meaningless in this context. Neither one is more likely than the other. A finite universe fits a little neater into our current understanding of how the universe works but the simple fact is we don't know.

 

[Bandersnatch]

All 3-dimensional objects with a finite volume do have boundaries.

I think now it's your turn to make a mistake. The surface of a 4D hypersphere(i.e., 3D volume) is finite and without boundaries. It's still a 3D object. Same as a surface of a 3D sphere is still a 2D object.

 

[PeterDonis]

I'm assuming when you say "not bounded" you mean "without a boundary"

Correct.

All 3-dimensional objects with a finite volume do have boundaries.

No, they don't. A 3-sphere, for example, is a 3-dimensional object with a finite volume that has no boundary. You really need to review some basic topology.

 

[iDimension]

Correct.



No, they don't. A 3-sphere, for example, is a 3-dimensional object with a finite volume that has no boundary. You really need to review some basic topology.

No boundry in the 1st and 2nd dimension but it does have a boundary in the 3rd dimension?

 

[PeterDonis]

No boundry in the 1st and 2nd dimension but it does have a boundary in the 3rd dimension?

No. No boundary means no boundary, period.

For example, suppose our universe were, spatially, a 3-sphere. (And suppose, for purposes of this thought experiment, that the universe is not expanding, so the size of the 3-sphere is constant.) Then we could, in principle, send out spaceships to explore the entire 3-sphere, and measure its finite 3-volume, and none of those spaceships would ever encounter a boundary.

[Edit: Just to clarify, it is, in principle, possible that our actual universe *could* be, spatially, a 3-sphere, as I described it above (except that our actual universe is expanding, so the finite volume of the spatial 3-sphere would be increasing with time). According to our best current measurements, it is unlikely that our actual universe is like this, but there is nothing theoretically or logically that makes it impossible.]

 

[Dale]

For me it just seems that if out universe isn't infinite then there will be something which is infinite or if that isn't true, there will be an infinite amount of finite things. It just seems so much more logical that everything is infinite and unbounded in any and all dimensions.

But "it just seems" is a pretty poor argument.

I have no idea if the universe is finite or infinite, bounded or unbounded, but the question certainly cannot be answered by the argument you used. The argument you are using is geometrical and geometry permits all the combinations.

 

[Drakkith]

I can just imagine travel at 20billion times the speed of light (impossible I know but to make a point) and then just crashing into an untraversable wall that stops us going further, but even then that wall must have some thickness which itself should extend to infinity?

That's extremely unlikely. The most plausible explanations are that you will either never run into any wall and continue on forever, or you will eventually come all the way around the universe and end up back where you started.

 

[berkeman]

Thread closed for Moderation...

 

[Dale]

The thread is reopened with a reminder to keep the conversation courteous.

 

[iDimension]

That's extremely unlikely. The most plausible explanations are that you will either never run into any wall and continue on forever, or you will eventually come all the way around the universe and end up back where you started.

But how is this possible sinse we are not on the surface of the universe, we are in the universe. If you are inside a finite object and travel in a direction, you can't come back to where you started right?

Or do you mean that the Earths 2D shape lives on a 3D object and our 3D reality lives on a 4D object? Btw the 4th dimension is time or?

 

[Bandersnatch]

Or do you mean that the Earths 2D shape lives on a 3D object and our 3D reality lives on a 4D object? Btw the 4th dimension is time or?

This is it, more or less. It's what we've all been saying all this time. Only with the caveat that the fourth dimension needen't actually exist as anything physical.
Everywhere in this thread where dimensions were mentioned, they were meant to be purely spatial.

 

[Dale]

If you are inside a finite object and travel in a direction, you can't come back to where you started right?

You have already been given several examples where you can, such as a ring, a sphere, and their higher-dimensional versions. A ring is a finite 1D object, and if you travel in either direction far enough you do in fact come back to where you started. Do you not understand that?