1. We don't experience fourth dimensional space in everyday life.
It's tough to picture a fourth dimension because we don't live in a fourth dimensional world (as far as we know). Our brains and senses are hardwired from birth to perceive three dimensions. From preschool, we are schooled in a three-dimensional world. We start with lines, which form shapes, which form solids. This is a natural progression, but it leads to a set-in-stone understanding of our world as three-dimensional.
Everyday, we experience 'up and down', 'left and right', 'forward and backwards'. We don't even consider a fourth dimension because it's not necessary for our everyday lives (unless we're mathematicians or theoretical physicists). |
2. It's difficult to explain dimensions verbally.
As we know from reading Flatland, we know that explaining new dimensions verbally is difficult. The sphere failed to explain three dimensions to the clearly intelligent narrator, but failed; likewise, the narrator was unable to convince anyone - his grandson, his brother, or the Council - of the existence of three dimensions. In trying to describe mathematics concepts, sometimes visuals are easier to understand than spoken or written explanations.
3. It's also hard to visualize extra dimensions.
![Picture](/uploads/3/8/9/3/38931597/2622041_orig.gif)
Even visuals don't help sometimes. In some cases, it makes it harder.
On the left, an image of a tesseract (a fourth dimensional shape) undergoing simple rotation about the fourth dimension is shown. Images like this can actually make picturing a fourth dimension even more complicated.
Mrs. Fitch: Alright, let's learn! Does everyone understand the fourth dimension?
Student: Yeah, I think so!
Mrs. Fitch: Great. Now look at this picture!
Student: ... Now I don't understand! I thought I did, but now I'm even more confused!
Mrs. Fitch: Oh no! That is unfortunate!
On the left, an image of a tesseract (a fourth dimensional shape) undergoing simple rotation about the fourth dimension is shown. Images like this can actually make picturing a fourth dimension even more complicated.
Mrs. Fitch: Alright, let's learn! Does everyone understand the fourth dimension?
Student: Yeah, I think so!
Mrs. Fitch: Great. Now look at this picture!
Student: ... Now I don't understand! I thought I did, but now I'm even more confused!
Mrs. Fitch: Oh no! That is unfortunate!