So what application do anaglyphs have to our study of the fourth dimension anyway?
3D anaglyphic vision is just one way of creating a 3D representation using a two dimensional medium. But what about taking the system up another dimension. Is it possible to make 4D anaglyphs? And even if we make them, is it possible to view them?
We could feasibly attempt a three dimensional version of our two dimensional anaglyphic images. For example we could construct two cubes out of red and blue transparently colored straws and position them close to each other. However, because it is fourth dimensional, we may need to have three or four different structures instead of just two. Looking at these with red/green glasses would be interesting, but what we see would fall far short of anything in the fourth dimension.
The problem lies in the fact that we lack any ability to see the fourth dimension. We are 3D beings to the extent that our eyes are engineered to view in the world in 3D. We simply wouldn't see a 4D object even if it was in front of our faces. Yet, even if we could see a four dimensional object, this isn't enough &endash; for we would also have to know it. To truly perceive objects not only do we need to receive the right information (see it) but we also must be able to process that information (know it). Because we can do neither of these in 4D, the idea of 4D anaglyphs will not work.
So anaglyphs, as we had hoped, will unfortunately not be a gateway to the fourth dimension. However, the use of 3D anaglyphs can still be useful to us in other ways. For example, we can use anaglyphic imaging to view our 4D representations as 3d objects. A perfect example of this is the anaglyphic version of the hypercube animation.
To be sure, anaglyphic images do not create 3D models. They simply help us understand our 2D representations better. In other words, the 3D anaglyphic images are subject to the same restriction that 2D images are. For example, you cannot walk around an anaglyphic model. What the anaglyph is really doing is taking the 3D illusion that the pictures already gives us and makes it more real. The following are examples of how anaglyphs can enhance our view of the 2D images found in the book.
Representation of the 4D Klein Bottle
Banded Torus
Banded Torus in Rotation
The orginial images were taken from the website of Thomas Banchoff