Everyone knows what a three dimensional object is, also it is very easy to recognize a two dimensional object. What is almost impossible to imagine is the 4th dimension and what a 4D object would look like. I just finished reading Surfing Through Hyperspace by Clifford A. Pickover and the book examines the wonders and the ideas of the 4th dimension. It is quite an interesting read to say the least, soon I will have a review up for it, but for this post I would like to talk about the ideas discussed in the book itself. This will probably be a two part post as there is a lot to discuss.
As I mentioned above the lower dimensions are very easy to visualize and comprehend. Our world is composed of 1D, 2D, and 3D objects throughout. What is interesting is that most scientist agree that there are many many more dimensions. I may be wrong but I think String Theory only works if there are 10, or 11 for M-Theory, dimensions in our universe. So most scientist agree that these extra dimensions exist, but the fact remains that if they do exist where are they and why can’t we see them?
Well from what I have read I think most of the higher extra dimensions are very very small. So with our technology, as it stands, cannot observe them in any way. From what I have understood while reading this book and the way it is explained I think the 4th dimension in theory could be accessible. Albeit we would have to advance our technology to the extreme, but still all signs point to the possibility and the probability of it happening.
What is the 4th dimension? I know it is the subject of tons of science fiction to say the least. But what exactly is the 4th dimension? At its basic level it is another degree of separation. It is easiest to give examples of lower dimensions to help visualize the upper ones. For a 2 dimensional being, they would live on a plane and could only move forward and back on the plane. Imagine a piece of paper and little dots or circles living on the paper. Each being on this paper would only be comprised of a length and a width. They cannot lift themselves off the paper nor can they see that there is another 3rd dimension. But you being a being (that’s a mouth full) of the 3rd dimension can observe their whole world and watch their movements in there entirety. You could also do things that seem magical to them. Like view inside of one of their structures, which would basically be a square or 4 walls. You could also view inside the beings themselves. They would think they have some privacy but you could see them from the 3rd dimension and if you wanted you could enter their house without opening the door. You could be the best criminal of a two dimensional world. You would be able to lift valuables out of a two dimensional locked safe with ease, just by lifting them into the third dimension, or as we would say “up.” The third dimension is depth, your magical powers as they would appear to the beings on the paper would simply be your ability to lift things off the two dimensional paper, up, into the third dimension. Seems simple enough right?
The thing that always scrambled my brain was that a two dimensional being would not be able to see the third dimension as we can. So it would appear that the jewels in the safe are disappearing from the safe then reappearing in your bag with the dollar sign on it. So for us 3 dimensional beings, it is hard to imagine the 4th dimension without being able to see it. We would appear almost as gods to the beings of the paper world, being able to do many extraordinary things just by lifting them into the 3rd dimension.
With that being said now imagine a 4th dimensional being and what they could do. They would appear as gods to us as well, being able to again lift valuables out of a locked safe, they could pick things out of our body without cutting us open, among other things. It is wonderful to think about and although it sounds more like science fiction than science fact.
In the book Pickover has tons of diagrams and visual charts to help the reader visualize the 4th dimension, or hyperspace as it is known among the academics. To help visualize the 4th dimension Pickover has pictures of hypercubes and hyperspheres, basically put hyper in front of any shape and it means that it is its 4th dimensional counterpart. A hyper cube or tesseract as it is also called is very cool to look at. Check out this link to help you visualize what it looks like http://en.wikipedia.org/wiki/Hypercube .
One last thing that I found interesting was that how a being of a lower dimension would view a being of the higher dimension. For a 2D being on the paper if we were to venture into their world they would only see a small cross section of us. Basically a thin 2D cross section of your body would be all they would see. Like if you got in the water and the surface was where the 2D beings lived all they would see is what is at the water level. Remember they cannot see anything that is not on the plane they live on, anything below of above the plane would be invisible to them as it is in the 3rd dimension, or up or down. Now for us 3D beings seeing a 4D being would be similar. All we would see are floating 3D blobs of whatever they are made of. We would not be able to see them in their entirety much like a 2D being would not be able to see us in our entirety. Later we will get into the aspects of our brains and how they can play an impact in all this.
There is way too much to talk about with this subject. Even after reading this book, and doing a little more research on the topic I still cannot wrap my brain around what the 4th dimension is. I mean conceptually I understand but it is hard to really imagine how it looks compared to three dimensional world.