Exploring the Fourth Dimension: An Analogy to Flatland and Beyond

[JerryMac]

I was thinking about the analogy of an observer living in a two dimensional world. So as it goes, this observer would see a 3d sphere as a 2d circle. As the 3d sphere moves through the dimension the observer cannot see, the circle would seem to appear on his plane from nowhere, grow to the diameter of the sphere, and then shrink back to nothingness.

Now we use this same concept using an observer in 3 dimensions, observing a 4 dimensional object moving through. Shouldn’t the observer see a 3 dimensional object appear out of nowhere, grow, and then disappear?

If there were a fourth dimension wouldn’t we see this all the time? Maybe it's the case where things in four dimensional space never cross the 4th dimension coordinate we are locked into?

Sorry if this is a stupid question. I’m a layman who keeps himself up all night pondering these things.

 

[silmaril89]

If there were a 4th dimension like that, it wouldn't necessarily be unreasonable to expect objects to appear and disappear in front of our eyes due to them moving along that fourth dimension that we cannot see.

The only scientific based idea of extra dimensions that I've come across are those dealing with string theory. The first thing is that it claims we are living in a 3 dimensional brane world, and that most of the particles in our world are stuck to that 3 dimensional brane not allowing these particles to move in any strange ways. That's the first reason why you wouldn't see things materializing out of nothing. There are a few particles that would be able to become 'unstuck' from the 3 dimensional brane. These are particles that are treated as closed loop strings. As far as I know the only one they speculate to be like that is the graviton. So, with matter particles, they will basically just stick to the 3 dimensions we are used to.

Now, the other part about string theory, is that these extra dimensions would be so incredibly tiny that we could not possible see or move through them.

Anyway, it seems doubtful that there is a 4th dimension that would be similar to the analogy of the 3rd dimension to flat land that you described. If there was, I think there would be a lot of evidence to support it by now.

Hopefully that all makes sense and answers your question.

 

[edgepflow]

I think you have the right idea and are asking the right questions. Of course, maybe there is no 4th spatial dimension or maybe it is too small to observe.

 

[JerryMac]

Thanks for the responses!

I've read Elegant Universe but it seems to only touch the surface, for a deeper understanding I guess I have to start getting into the math of it. :)

Can anyone recommend any other books that delve into this subject?

 

[silmaril89]

I couldn't really recommend a specific book on string theory. You can find a few textbooks on string theory from Amazon, but it's be difficult to say what was the best one (take a look at the reviews). A book that I would highly recommend though, is The Road to Reality by Roger Penrose. It covers so many different topics in physics and will certainly cover some interesting things about geometries and dimensions of space. The first 300 or so pages are devoted to math.

 

[Siriusly]

If there were a 4th dimension like that, it wouldn't necessarily be unreasonable to expect objects to appear and disappear in front of our eyes due to them moving along that fourth dimension that we cannot see.

The only scientific based idea of extra dimensions that I've come across are those dealing with string theory. The first thing is that it claims we are living in a 3 dimensional brane world, and that most of the particles in our world are stuck to that 3 dimensional brane not allowing these particles to move in any strange ways. That's the first reason why you wouldn't see things materializing out of nothing. There are a few particles that would be able to become 'unstuck' from the 3 dimensional brane. These are particles that are treated as closed loop strings. As far as I know the only one they speculate to be like that is the graviton. So, with matter particles, they will basically just stick to the 3 dimensions we are used to.

Now, the other part about string theory, is that these extra dimensions would be so incredibly tiny that we could not possible see or move through them.

Anyway, it seems doubtful that there is a 4th dimension that would be similar to the analogy of the 3rd dimension to flat land that you described. If there was, I think there would be a lot of evidence to support it by now.

Hopefully that all makes sense and answers your question.

why do you think of objects as being strictly one, two or even three dimensional, and why do you assume that these dimensions/ directions would be separated from ours? we are not three dimensional, we simply experience a small portion of our total selves. the same could be said for our infinite theoretical two dimensional selves (cross sections of our 3d selves expriencing only 2d, time being the above dimensional movement.)

 

[silmaril89]

why do you think of objects as being strictly one, two or even three dimensional, and why do you assume that these dimensions/ directions would be separated from ours? we are not three dimensional, we simply experience a small portion of our total selves. the same could be said for our infinite theoretical two dimensional selves (cross sections of our 3d selves expriencing only 2d, time being the above dimensional movement.)

Could you provide a source to back up your claims?

 

[Siriusly]

1. the fact that there are no "other dimensional objects appearing.
2. info from .

the only way i understand that all these "dimensions" co-exist in the universe as we see it.

 

[silmaril89]

What "other" dimensional objects are you talking about? This doesn't give any explanation for what you were trying to get at with your first post. I've seen the video you posted. Please be very clear and very specific at what you have against my first answer and what you are trying to show.

 

[ecneicS]

Consider time as a fourth dimension. The same way that a 2 dimensional observer's observations are affected by the 3 dimensional system you described (the sphere), the same way our 3 dimensional observations are affected by time.

Before I go further though, you have to understand that in 2 dimensions, the sphere appears, grows, and then disappears is entirely because of the properties of the sphere. If we observed a rectangle, the process would look quite different (and more awesome if it was off-axis, in my opinion). So when looking for a fourth dimension, we should not expect everything to appear, grow, and then disappear.

So consider that time is a fourth dimension. Then even though we only see in 3 dimensions, what we see should depend on the fourth dimension (time). Look at your hand, and then move it. It has clearly has changed positions (either that or everything around it did). This change is analogous to the spherical scenario you described.

This is why some people consider that we live in 3+1 dimensions.

 

[Dale]

If there were a fourth dimension wouldn’t we see this all the time?

Yes, we do see this all the time. Except that most particles are shaped differently in 4D than hyperspheres.

 

[silmaril89]

Nobody will deny that time can be considered 4th dimension. The explanation ecneicS gave is not why people consider that we live in 3+1 dimensions. The reason people consider that is due to special relativity. The lorentz transformation equations for space include time. Also the following expression is invariant x^2 + y^2 + z^2 + c^2 t^2. From that time on space and time were intertwined into what is now known as spacetime.

The question originally proposed by the OP was about extra SPATIAL dimensions. Everyone knows we can use time as another dimension, no one is questioning that. What we are interested in, is determining if there are extra SPATIAL dimensions. Forget about time in this discussion.

 

[Dale]

The question originally proposed by the OP was about extra SPATIAL dimensions.

It didn't seem that way to me:

Shouldn’t the observer see a 3 dimensional object appear out of nowhere, grow, and then disappear?

 

[silmaril89]

Right, JerryMac discusses the idea of a 3 dimensional object that is moving through the fourth spatial dimension. And if this was happening then when the object got to the location in the 4th dimension that we are at it would appear out of nowhere, then disappear. This is very similar to a 3 dimensional sphere moving through flatland as described in the original post. When that 3 dimensional sphere gets to the location in the 3rd dimension that flat land is in, it will appear and disappear. We are only discussing spatial dimensions here.

 

[Dale]

Right, JerryMac discusses the idea of a 3 dimensional object that is moving through the fourth spatial dimension. ... We are only discussing spatial dimensions here.

I disagree. "appear", "grow", "then", and "disappear" all seem like time words rather than space words. Let's let the OP clarify.

 

[silmaril89]

Well, time is passing as well. So 4+1 dimensions. But yes, it isn't completely clear, hopefully the OP will respond.

 

[avemt1]

Well, time is passing as well. So 4+1 dimensions. But yes, it isn't completely clear, hopefully the OP will respond.

I think the OP had read Isacc Asimov's Book : Flatland, and is looking for repetition in the general populace for those ideas as to whether he accepts these ideas as holding weight.

If he reads this: Flatland was a fictional book based off of 1940s ideas of physics. Now obviously we have walked a longer road and now have more understanding of the universe. (but possibly more questions, although more refined than vague.) For the context of that book yes, under the understood constraints as pertaining to spatial dimensions only, and time dimension is separate and persistent throughout the different dimensions, that is the effect you would see. The sphere will appear, then seem to grow in size, then reach a maximum size and then decrease to nothingness.