Explain the 3-Sphere to me.

[Tiki Tom]

Right now I am reading “Reality is not what it seems” by the physicist Carlo Rovelli. Although physics is usually above my head, this book is written (mostly) in understandable layman’s terms. I especially like how he starts with the ancient Greeks and adds, layer by layer, how humanity reached its current understanding of the nature of things. Which brings me to my current problem. Now Rovelli is talking about how Einstein’s theory of General Relativity led him to the conclusion that the universe is a 3-sphere, i.e., that the universe is “both finite and without boundary”. I kind of, sort of get the concept that spacetime is curved and that, theoretically, if you head off into space in a straight line you will eventually come back to the same spot. However, to me, in my three dimensional mind-set, this implies that the universe is like a bubble with an outer boundary (and what is beyond that?). I can’t seem to grasp the “finite and without boundary” part of the idea. I’ve googled the question but have mostly come up with upper-level physics explanations and incomprehensible equations.

To try to further clarify my question, I’ll now quote from the book: “For thousands of years, men had asked themselves whether the universe was infinite, or had a limit. Both hypotheses entail thorny problems. An infinite universe does not seem to stand to reason: if it is infinite, for example, there must exist somewhere a reader just like you who is reading the very same book (infinity is truly vast, and there are not sufficient combinations of atoms to fill it with things always different each time). In fact, there must be not only one but an infinite series of readers identical to yourself… But if there is a limit to the universe, what is the boundary? What sense is there in a border with nothing on the other side?” …”But Einstein finds a third way: the universe can be finite and at the same time have no boundary. How?” Enter the 3-sphere.

I have not yet got to the part of the book where he starts talking about more exotic things: alternative universes, quantum gravity, places that are “outside of time”.

 

[KILO NOVEMBER]

Because we can experience no more than three spatial dimensions, we can't imagine what more than three spatial dimension might be like (well, not without mind-altering substances to screw up our brain chemistry). These extra dimensions are not spatial in any sense we can grasp. You might find Flatland , a book written in the late 19th century will provide some insights.

So, given that we can't conceive of more than three spatial dimensions, if you start to look at other properties of objects (beyond length, breadth, and height) as "dimensions", you can begin to appreciate the idea, if not experience it.

Take yourself, for example. You have three spatial dimensions (height and waist circumference), weight, a time dimension (your age), you have other properties (hair color, eye color, native language), well, just about anything combination of things that describe you can be "dimensions".

 

[GHT]

To try to further clarify my question, I’ll now quote from the book: “For thousands of years, men had asked themselves whether the universe was infinite, or had a limit. Both hypotheses entail thorny problems. An infinite universe does not seem to stand to reason: if it is infinite, for example, there must exist somewhere a reader just like you who is reading the very same book (infinity is truly vast, and there are not sufficient combinations of atoms to fill it with things always different each time). In fact, there must be not only one but an infinite series of readers identical to yourself… But if there is a limit to the universe, what is the boundary? What sense is there in a border with nothing on the other side?” …”But Einstein finds a third way: the universe can be finite and at the same time have no boundary. How?” Enter the 3-sphere.

You can go mad trying to comprehend the universe. We are told that it all started with a big bang. What caused the bang? Gases. But before the big bang there was nothing and science says that you can't make something out of nothing, hasn't stopped alchemists from trying though. So where did the gases come from?
Until recently, the universe was said to be finite, if so, what's beyond it? And why doesn't the universe fall into whatever void there is beyond it? The universe has to be infinite to avoid the previous scenario. I haven't come across the 3-sphere concept before but what amuses me about such explanations is that science poo-poos the idea that there is a Creator yet is ready to give convoluted scientific explanations. I guess that the fact that we are finite makes for understanding infinity somewhat difficult. Like I said, you can go mad trying to comprehend the universe.

 

[Inkstainedwretch]

Three spheres identifies a pawnshop.

 

[frustrated physicist]

Right now I am reading “Reality is not what it seems” by the physicist Carlo Rovelli. Although physics is usually above my head, this book is written (mostly) in understandable layman’s terms. I especially like how he starts with the ancient Greeks and adds, layer by layer, how humanity reached its current understanding of the nature of things. Which brings me to my current problem. Now Rovelli is talking about how Einstein’s theory of General Relativity led him to the conclusion that the universe is a 3-sphere, i.e., that the universe is “both finite and without boundary”. I kind of, sort of get the concept that spacetime is curved and that, theoretically, if you head off into space in a straight line you will eventually come back to the same spot. However, to me, in my three dimensional mind-set, this implies that the universe is like a bubble with an outer boundary (and what is beyond that?). I can’t seem to grasp the “finite and without boundary” part of the idea. I’ve googled the question but have mostly come up with upper-level physics explanations and incomprehensible equations.

To try to further clarify my question, I’ll now quote from the book: “For thousands of years, men had asked themselves whether the universe was infinite, or had a limit. Both hypotheses entail thorny problems. An infinite universe does not seem to stand to reason: if it is infinite, for example, there must exist somewhere a reader just like you who is reading the very same book (infinity is truly vast, and there are not sufficient combinations of atoms to fill it with things always different each time). In fact, there must be not only one but an infinite series of readers identical to yourself… But if there is a limit to the universe, what is the boundary? What sense is there in a border with nothing on the other side?” …”But Einstein finds a third way: the universe can be finite and at the same time have no boundary. How?” Enter the 3-sphere.

I have not yet got to the part of the book where he starts talking about more exotic things: alternative universes, quantum gravity, places that are “outside of time”.

 

[frustrated physicist]

I agree. The 3-sphere description is not helpful or well explained, although the book overall is quite good. (I'm about half way through). Also, the "extended present" diagram and description is actually misleading since it depicts the present as having a non-infinitesimal duration. The time/space depiction is usually presented in a much clearer fashion and tied directly to the speed of light. I know what Rovelli is trying to get across, but the diagrams and text just don't convey it in this instance.

 

[tonyb]

“Reality Is Not What It Seems” might be a fitting description for the curious person’s ongoing education.

We get more or less close to understanding, but we never quite get there. Keeps things interesting.

I may buy myself a copy. I’ve read next to nothing on this subject to date, so it may be a struggle.

 

[Tiki Tom]

Because we can experience no more than three spatial dimensions, we can't imagine what more than three spatial dimension might be like (well, not without mind-altering substances to screw up our brain chemistry). These extra dimensions are not spatial in any sense we can grasp.

So... For example, if I were a two-dimensional person crawling around on the surface of a three-dimensional globe (and I had no way to grasp that there was a third dimension), the surface that I was crawling on would seem to me to be infinite... yet I'd keep crawling back to the same spot.

Same deal, only we three-dimensional people are crawling around on a "globe" that has four or more dimensions?? Okay, I can almost grasp that... But then I still want to ask "what's beyond those extra dimensions?" (Which I guess only points out that I am still only capable of thinking in 3-dimensions.)

 

[Tiki Tom]

Whoa. I think I just had a brain fart.
So... Does that mean that, no matter how many extra dimensions you add, the universe will ALWAYS remain at every level "finite but without boundary?" Even to an infinity of levels? Elegant solution. I think. (?) Pass the bong.

 

[tonyb]

Whoa. I think I just had a brain fart.
So... Does that mean that, no matter how many extra dimensions you add, the universe will ALWAYS remain at every level "finite but without boundary?" Even to an infinity of levels? Elegant solution. I think. (?) Pass the bong.

I recommend listening to “Surf’s Up,” the solo recording, just Brian and his piano, made in his sandbox in ’67. It might help put you in the right frame of mind. Provided there are frames. Or not.

 

[HudsonHawk]

You can go mad trying to comprehend the universe. We are told that it all started with a big bang. What caused the bang? Gases. But before the big bang there was nothing and science says that you can't make something out of nothing, hasn't stopped alchemists from trying though. So where did the gases come from?
Until recently, the universe was said to be finite, if so, what's beyond it? And why doesn't the universe fall into whatever void there is beyond it? The universe has to be infinite to avoid the previous scenario.

This is a common misunderstanding of the big bang theory. It does not suggest there was "nothing", and does not attempt to explain what was there prior to the big bang. The big bang only explains why the universe *looks* the way it does to us. It's not as if the universe was created from some sort of explosion at a singular point.

 

[Peacoat]

Right now I am reading “Reality is not what it seems” by the physicist Carlo Rovelli. Although physics is usually above my head, this book is written (mostly) in understandable layman’s terms. I especially like how he starts with the ancient Greeks and adds, layer by layer, how humanity reached its current understanding of the nature of things. Which brings me to my current problem. Now Rovelli is talking about how Einstein’s theory of General Relativity led him to the conclusion that the universe is a 3-sphere, i.e., that the universe is “both finite and without boundary”. I kind of, sort of get the concept that spacetime is curved and that, theoretically, if you head off into space in a straight line you will eventually come back to the same spot. However, to me, in my three dimensional mind-set, this implies that the universe is like a bubble with an outer boundary (and what is beyond that?). I can’t seem to grasp the “finite and without boundary” part of the idea. I’ve googled the question but have mostly come up with upper-level physics explanations and incomprehensible equations.

To try to further clarify my question, I’ll now quote from the book: “For thousands of years, men had asked themselves whether the universe was infinite, or had a limit. Both hypotheses entail thorny problems. An infinite universe does not seem to stand to reason: if it is infinite, for example, there must exist somewhere a reader just like you who is reading the very same book (infinity is truly vast, and there are not sufficient combinations of atoms to fill it with things always different each time). In fact, there must be not only one but an infinite series of readers identical to yourself… But if there is a limit to the universe, what is the boundary? What sense is there in a border with nothing on the other side?” …”But Einstein finds a third way: the universe can be finite and at the same time have no boundary. How?” Enter the 3-sphere.

I have not yet got to the part of the book where he starts talking about more exotic things: alternative universes, quantum gravity, places that are “outside of time”.

Please stop; my head hurts. And I wanted this to be an easy day.

 

[The Jackal]

I will probably spend the rest of the day reading and contemplating this theory.

The best comparison I've read so far is to a ball. To someone very small/close to the surface of the ball, it only has 2 dimensions: forward/back and left/right. But when you pull the frame back, those 2 dimensions exist in a world that actually has 3, and the up/down that was not observable creates the actual 3d form.

It stands to reason that if we, small as we are, can observe 3 dimensions, then the "surface" of the universe would also lie within a larger existence that contains at least one additional dimension that we are unware of.

We are standing on the surface of the ball and can't tell that it is sitting in a larger space.

 

[Tiki Tom]

“The universe is finite yet without boundary” you say? “Flee in any direction and you will ultimately come back to the same spot?” Further, we are told that, for us three-dimensional beings, there is no “outside” of the box.
Additionally, it is impossible to flee into the past. Travel into the future, of course, normally leads to death. We are trapped in space and time.

I think I may have to agree with George Hotz. Namely:

“It’s easy to imagine [beings] that are so much smarter than you and they could build a cage you wouldn’t even recognize.”

George Hotz wants to break humanity out of the AI simulation that he thinks we are prisoners in.

https://www.theverge.com/2019/3/9/18258030/george-hotz-ai-simulation-jailbreaking-reality-sxsw-2019

If you’ve endured this thread this far, you may well be open to the idea that his vision of reality is at least worth considering.

 

[Harp]

Additionally, it is impossible to flee into the past. Travel into the future, of course, normally leads to death. We are trapped in space and time..

https://www.theverge.com/2019/3/9/18258030/george-hotz-ai-simulation-jailbreaking-reality-sxsw-2019

Manafort's 16-count Manhattan DA slam comes to mind. SL2/G indeed.

 

[Lean'n'mean]

We are trapped in space and time.

Don't be so defeatist. We are whizzing through space on this marble, at over 100,000 km/h & as for time, we are constantly advancing through time or rather we are perpetually entering the future.
That's hardly being trapped.
The universe is as yet, unfinished but even so I have a hunch that it is a lot less complex than man's primitive primate brain, blinded by it's own science, imagines it to be.

 

[Tiki Tom]

MIT scientist says it is more likely than not that we are living in a computer simulation.

https://www.digitaltrends.com/cool-...r-scientists-about-the-simulation-hypothesis/

 

[scottyrocks]

I will probably spend the rest of the day reading and contemplating this theory.

The best comparison I've read so far is to a ball. To someone very small/close to the surface of the ball, it only has 2 dimensions: forward/back and left/right. But when you pull the frame back, those 2 dimensions exist in a world that actually has 3, and the up/down that was not observable creates the actual 3d form.

It stands to reason that if we, small as we are, can observe 3 dimensions, then the "surface" of the universe would also lie within a larger existence that contains at least one additional dimension that we are unware of.

We are standing on the surface of the ball and can't tell that it is sitting in a larger space.

I don't know that this is a valid comparison. I don't think size has anything to do with it, especially when size is relative.

We are on a big ball, and we perceive three dimensions. A much smaller person (microscopic to us) on a basketball-sized sphere would perceive the same relative dimensions that we do, assuming they are at least humanoidish as we are.

 

[The Jackal]

A much smaller person (microscopic to us) on a basketball-sized sphere would perceive the same relative dimensions that we do, assuming they are at least humanoidish as we are.

And that's the rub. A microscopic organism traveling along the skin of an apple has no concept or frame of reference to understand that the apple is a large 3 dimensional object sitting on a desk, in a house, on a planet, in a galaxy, so on. The universe as that organism knows it, is just the skin of the apple and it's immediate surroundings.

In this theory, we are the microscopic organism. We understand the 3 dimensional space around us, but wouldn't be able to recognize if the universe as we know it is, for all intents and purposes, sitting on a big desk just like the apple.

The organism recognizes the apple, but doesn't understand that the apple is sitting in a room. We recognize the universe as we know it, we wouldn't understand that it's sitting in a room.

 

[scottyrocks]

And that's the rub. A microscopic organism traveling along the skin of an apple has no concept or frame of reference to understand that the apple is a large 3 dimensional object sitting on a desk, in a house, on a planet, in a galaxy, so on. The universe as that organism knows it, is just the skin of the apple and it's immediate surroundings.

In this theory, we are the microscopic organism. We understand the 3 dimensional space around us, but wouldn't be able to recognize if the universe as we know it is, for all intents and purposes, sitting on a big desk just like the apple.

The organism recognizes the apple, but doesn't understand that the apple is sitting in a room. We recognize the universe as we know it, we wouldn't understand that it's sitting in a room.

Okay, got it, but the micro-organism will never have the potential to understand anything as we sit here and contemplate the universe. And us sitting on the ball is no different than the the M.O sitting on a ball other than that we have the potential to discover what the 'desk' actually is. But we are both sitting on a ball in three dimensions. We are aware of it, and the M.O. isn't, but it's still three dimensions.

Now I think I'm lost. haha