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I'll just be the first to admit that I am indeed too dumb to grasp this concept. I've stared at it for a long time, but I do not get it.

by jsonmez 13y ago

joshdick 13y ago
I had a math professor who put it this way: Just think of a general n-dimensional Euclidian space, and then set n=4.
- cobrausn 13y ago
  My first CompSci professor told me that he had trouble at MIT grasping some of his early math where they were using n-dimensions, and when he asked his professor what the 'n-ball' was, he drew a circle on the board and said 'that, when n is equal to two'. Fun times.
- finnh 13y ago
  Counting sheep is easy: just count the legs and divide by four.
_Adam 13y ago
You're probably trying to think about it in spatial terms. But it's impossible to understand a 4D object with 3D spatial reasoning. I would say ALL humans are too "dumb" to grasp this concept. Of course the math is fairly simple, but there's a difference between understanding the math and truly understanding what a world with 4 spatial dimensions would be like.
- 3rd3 13y ago
  One can, though, get an intuitive spatial understanding for the projection of a higher dimensional object into 3D space.
bladedtoys 13y ago
It's tricky because there is just no way to show 4D phenomenon without a lot of sacrifice. I ended up using a combination of "perspective" for size and differing transparency and a fair amount of movement. All of these are artificial of course. The explanation on the page takes another approach: all black and white line drawings and a lot of brevity. But it's really a hell of a lot of fun tying to figure out how to present impossible to visualize phenomenon. And you are not remotely too dumb: if my story didn't come through it's my fault.
- codeflo 13y ago
  Displaying a 3D image in a 2D space also requires sacrifices. Obviously to a lesser extent, because you only lose one dimension, but the principles are the same. Reconstructing a 3D scene from photographs is an insanely tricky problem, and it only looks simple to us because our brains have specialized circuits for that task.
  - kybernetikos 13y ago
    Makes me wonder what this game would be like on the occulus rift.
moron4hire 13y ago
I think of it this way: if you try to draw a 3D cube on a 2D screen, what you really have is a 2D image. If oriented correctly, and nobody told you anything about that cube, you might mistake it for a 2D hexagon. If instead that cube were rotating, you would see the change in the shape of the hexagon and realize that the image is supposed to be a cube. But the reality is, it's still a 2D image. It's just a representation, and context and animation help you get back to the notion that it's a 3D image. Now, think for a minute about how the screen works. There are rows and rows of pixels. Each of those rows is actually a 1-dimensional image, a slice of the whole. If you were to only see one row of pixels at a time, you'd not be able to figure out what the image is. Maybe if you knew certain parameters about the image, that it was of very low fidelity, simplistic shapes, you'd be able to analyze one row after another and figure it out. You'd have extreme difficulty just looking at a 1-dimensional image, or a serious of such, and figuring out it would be of a 3-dimensional object. To really see the image, you again need it animated. The rows are scanned out very quickly, and your brain blurs it all together. So, when you're dropping from N to N-1 dimensions, you lose something, something that you can sort of get back if you add some motion in. When you drop from N to N-2 or more, you lose so much that you have a really hard time figuring it out. Now we can finally come back to the tesseract. It's a 4D object. We're trying to display it on a 2D display. It's not going to work out too well. You've really got to stare at it, think about what is going on, understand that you're dealing only with a very low fidelity, simplistic shape. Analyze it, rotation after rotation, and you might be able to figure it out. Or, in other words, it would be a lot easier if you had a real 3D display.
- T-hawk 13y ago
  So, when you're dropping from N to N-1 dimensions, you lose something, something that you can sort of get back if you add some motion in. Adding the motion restores the subtracted dimension as time. That's why that works.
- gliese1337 13y ago
  A 3D display doesn't help much; being able to take advantage of stereo effects helps a little, since you can see it from multiple slightly different angles at a time (one per eye). But your retina is still 2D- you can't perceive 3D objects directly through the visual system, just 2D projections of them. A native 4D creature would presumably have a 3D retina that can directly perceive 3D projections of 4D objects and infer 4D structure from them like we infer 3D structure from 2D projections. Maybe a tactile display could improve things somewhat (though you'd still be lacking access to 3D-internal structure), but as long as you're going through the human visual system, it takes some significant effort to reconstruct the 3D projections and then go the extra step to inferring 4D structure, no matter how good your display technology is.
arg01 13y ago
I struggle with picturing 4D rotating objects, I find it easier to deal with slicing the object up and picturing that. To clarify if you think of a single picture from an MRI it's a slice of a 3D object and you can move up and down the object to see each slice. If you move through all the slices you can get an idea of the 3D shape. With the 4th dimension it's similar except each of the slices is a 3D shape. So a 4D “sphere” sliced up this way would look like a 3d sphere that gradually got bigger until halfway through the 4D “sphere” then gets smaller again. You can also somewhat consider it a 3D object that changes shape with time but since time is a dimension you can go back and forward along it. That's how I picture 4D objects which is admittedly not as well as some people do.

I'll just be the first to admit that I am indeed too dumb to grasp this concept. I've stared at it for a long time, but I do not get it.

by jsonmez 13y ago

I'll just be the first to admit that I am indeed too dumb to grasp this concept. I've stared at it for a long time, but I do not get it.

joshdick 13y ago

I had a math professor who put it this way: Just think of a general n-dimensional Euclidian space, and then set n=4.

cobrausn 13y ago
My first CompSci professor told me that he had trouble at MIT grasping some of his early math where they were using n-dimensions, and when he asked his professor what the 'n-ball' was, he drew a circle on the board and said 'that, when n is equal to two'. Fun times.
finnh 13y ago
Counting sheep is easy: just count the legs and divide by four.

_Adam 13y ago

You're probably trying to think about it in spatial terms. But it's impossible to understand a 4D object with 3D spatial reasoning. I would say ALL humans are too "dumb" to grasp this concept. Of course the math is fairly simple, but there's a difference between understanding the math and truly understanding what a world with 4 spatial dimensions would be like.

3rd3 13y ago
One can, though, get an intuitive spatial understanding for the projection of a higher dimensional object into 3D space.

bladedtoys 13y ago

It's tricky because there is just no way to show 4D phenomenon without a lot of sacrifice. I ended up using a combination of "perspective" for size and differing transparency and a fair amount of movement. All of these are artificial of course. The explanation on the page takes another approach: all black and white line drawings and a lot of brevity. But it's really a hell of a lot of fun tying to figure out how to present impossible to visualize phenomenon. And you are not remotely too dumb: if my story didn't come through it's my fault.

codeflo 13y ago
Displaying a 3D image in a 2D space also requires sacrifices. Obviously to a lesser extent, because you only lose one dimension, but the principles are the same. Reconstructing a 3D scene from photographs is an insanely tricky problem, and it only looks simple to us because our brains have specialized circuits for that task.
- kybernetikos 13y ago
  Makes me wonder what this game would be like on the occulus rift.

moron4hire 13y ago

I think of it this way: if you try to draw a 3D cube on a 2D screen, what you really have is a 2D image. If oriented correctly, and nobody told you anything about that cube, you might mistake it for a 2D hexagon. If instead that cube were rotating, you would see the change in the shape of the hexagon and realize that the image is supposed to be a cube. But the reality is, it's still a 2D image. It's just a representation, and context and animation help you get back to the notion that it's a 3D image. Now, think for a minute about how the screen works. There are rows and rows of pixels. Each of those rows is actually a 1-dimensional image, a slice of the whole. If you were to only see one row of pixels at a time, you'd not be able to figure out what the image is. Maybe if you knew certain parameters about the image, that it was of very low fidelity, simplistic shapes, you'd be able to analyze one row after another and figure it out. You'd have extreme difficulty just looking at a 1-dimensional image, or a serious of such, and figuring out it would be of a 3-dimensional object. To really see the image, you again need it animated. The rows are scanned out very quickly, and your brain blurs it all together. So, when you're dropping from N to N-1 dimensions, you lose something, something that you can sort of get back if you add some motion in. When you drop from N to N-2 or more, you lose so much that you have a really hard time figuring it out. Now we can finally come back to the tesseract. It's a 4D object. We're trying to display it on a 2D display. It's not going to work out too well. You've really got to stare at it, think about what is going on, understand that you're dealing only with a very low fidelity, simplistic shape. Analyze it, rotation after rotation, and you might be able to figure it out. Or, in other words, it would be a lot easier if you had a real 3D display.

T-hawk 13y ago
So, when you're dropping from N to N-1 dimensions, you lose something, something that you can sort of get back if you add some motion in. Adding the motion restores the subtracted dimension as time. That's why that works.
gliese1337 13y ago
A 3D display doesn't help much; being able to take advantage of stereo effects helps a little, since you can see it from multiple slightly different angles at a time (one per eye). But your retina is still 2D- you can't perceive 3D objects directly through the visual system, just 2D projections of them. A native 4D creature would presumably have a 3D retina that can directly perceive 3D projections of 4D objects and infer 4D structure from them like we infer 3D structure from 2D projections. Maybe a tactile display could improve things somewhat (though you'd still be lacking access to 3D-internal structure), but as long as you're going through the human visual system, it takes some significant effort to reconstruct the 3D projections and then go the extra step to inferring 4D structure, no matter how good your display technology is.

arg01 13y ago

I struggle with picturing 4D rotating objects, I find it easier to deal with slicing the object up and picturing that. To clarify if you think of a single picture from an MRI it's a slice of a 3D object and you can move up and down the object to see each slice. If you move through all the slices you can get an idea of the 3D shape. With the 4th dimension it's similar except each of the slices is a 3D shape. So a 4D “sphere” sliced up this way would look like a 3d sphere that gradually got bigger until halfway through the 4D “sphere” then gets smaller again. You can also somewhat consider it a 3D object that changes shape with time but since time is a dimension you can go back and forward along it. That's how I picture 4D objects which is admittedly not as well as some people do.