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Why Humans Will Never Understand
I have always more or less been on a quest to understand the Universe. I decided to start with understanding the more fundamental aspects of the Universe and then build on that understanding to understand more complicated things. But the question came up as to what was the most fundamental thing in the Universe. Elementary Particle Physics seemed to be a good place to start. What could be more fundamental than Electrons, Protons, and Neutrons? Well you quickly find out that Elementary Particles are just made out of Energy. So Energy seemed to be the thing to start with. Eventually I learned that Energy can arise out of Space itself. So what does this mean about our concept of Space? It would seem that Energy might be made out of Space. So then the regression back to find the most fundamental thing ended up with trying to understand Space, which of course is Nothing. How do you study Nothing?
Eventually I realized that Space was not really Nothing it was Something. Since Space is Something it could exist or not exist. The common notion that Space is an ever existent background Thing that extends out infinitely in three directions could be wrong. There could be different kinds of Spaces besides our 3D Space. There could be a 4D Space. There could be no Space. The possibility of no Space is almost impossible to grasp by the 3D human brain.
I thought that if I could show that 4D Space is a workable reality for a Universe , then I would be able to convince myself that Space is a Thing just as Energy and Matter are Things. The concept of Nothing then becomes a concept of Absolute Nothing where there is no Matter, Energy, or Space.
To understand 4D Space I thought I should try to experience what it would be like to be a 4D Conscious being living in and moving around in a 4D World. See Exploring the 4th Dimension Using Animations. I generated many Animations to help me do this. I think the Animations were helpful but I still feel that I am unable to exactly experience a 4D World in the same way an actual 4D being would. The key thing that we must do is understand how a 4D being can see a 3D Cube as a Flat object. Anything else you think you know is irrelevant until you understand that.
Let us look at a 2Der trying to understand the Flatness of a solid Square. To him a Square is only viewed on edge. He sees the Width and Depth of it but, the inside points are always unseeable as they are blocked by all inside points in front of them. A Square is a nice solid object. He knows theoretically that from a 3D point of view he would be able to see all the inside points of his Square at the same time. He also knows theoretically that his Square will look Flat. But he does not have the 3D view advantage that we do. He is unable to travel around into the 3rd dimension and see the Square from all those viewpoints you would get by doing that. Instead, he must only theoretically rise out of 2D Space into 3D Space and only theoretically look down on the Square. He can then move across the Square and make a collection of views. He can then lay them out around him in his 2D Space and try to make sense out of it all. If he moves across the Square in a symmetric way he will have a collection of Lines. All he can do is see one Line at a time because that is how his Visual system works. The act of theoretically obtaining these views tells him nothing about where that extra direction into 3D Space is. All he has is the collection of Lines but still has no clue how to put them together so that he can see all the points at the same time. It will still boggle his mind as to how the Square could ever be viewed as Flat. To the 2Der something Flat is a Line like object. To him something Flat would for example have measurable Width but no Depth. In his mind by saying the Square is Flat would make him try to put all the Line views of his Square onto a single Line which is a physical impossibility in his 2D Space. He will never really be able to view 2D Flatness as it is.
The situation is analogous for us 3Ders trying to see how a Cube could ever be viewed as Flat. Theoretically we know we can go into 4D Space and look down on the Flat Cube that is back in our 3D Space. By analogy we will be looking at different views as we look down and move across the Flat surface of our cube. Each view will be a slice of the Cube. When we are done, we will have a collection of Squares that are cross sections of the Cube. By doing this we have no insight as to where we went to get the collection of Squares. We have a collection of Squares and still have no knowledge of how to connect them together in a Flat way. Take 2 adjacent Squares. The mental task is to arrange them so that they are in the same plane but yet corresponding points in the two Squares are able to touch. This is impossible for us to imagine, but this is what is possible when you have a 4th dimension.
I must insist that the problem with understanding 4D is a limitation of our Brains. We do what we can but cannot really get there. At least not the "there" that I want to be at. Again, a Tesseract is just a simple empty box. All the discussion, argumentation, and mind-bending Projections and Slice analysis shows us that something is basically missing in our ability to comprehend it. A Tesseract would be a completely simple, intuitive, and obvious thing for even the dumbest 4Der to comprehend. I cannot help it I have to say it again: It is just a Box! A 4Der would see it as being made from Flat 3D Objects which in our Space are Cubes. If you were to ask a 4Der to describe how the sides of a Tesseract look, he would say that they are Flat Objects that have 3 dimensions. He would have to strain to see the Cubeness of the side. He would recognize that two sides of the Tesseract would connect at Line like objects (to him), but these Line like objects would be two dimensional. The Line like objects correspond to the faces of the Cubes that we would see by Projection or Slicing. He does not see faces of Cubes he sees Line like Objects that are two dimensional. The sides of the Tesseract can pivot on these Line like Objects as if they were hinges. This means that rotations in 4D take place on 2D Objects not 1D Objects like in 3D Space.
Even though I was not able to experience 4D in the way I had hoped I believe that the Animations have shown me that a 4D World is possible and therefore that our 3D Space is only one type of Space. Also, if there can be 3D Space or 4D Space then there can be No Space.
The one thing I learned from the Animations is that the reason I don't understand 4D Space is because I am too embedded in this 3D Universe. I can think about 4D Space in theory and use all the different techniques for visualizing it but my 3D brain will never let me fully understand it. I do not think anyone can. We would need a 4D Brain to do this.
To be able to see in our 3D World we have a Visual Cortex that is roughly a flat (but folded) 2D patch of a little more than 1 billion Neurons. If it were a square patch it would be about 32000 Neurons on each side. A 2D being would only need a line of these Neurons or 32000 of them. The whole 2D Brain Neuron count would be scaled down by a factor of 32000. A 2D Brain would be 32000 times less intelligent than a 3D Brain. A 4D Visual Cortex by analogy would have to be a cube of Neurons with 32000 Neurons on all sides. It would be a 3D Cube so the 4D being would view it as flat. A 4D being's Visual Cortex would have 32000 times more Neurons than a 3D being's Visual Cortex. The 4D Brain Neuron count would be scaled up by a factor of 32000 and a 4D being will probably be 32000 times more intelligent than we are.
So the conclusion we have to come to is that we, and I mean all of us 3D beings, can never know what it would be like to actually be a 4D being. We are just not smart enough. You might think you understand 4D using one of the techniques but you never really get there. You need to be able to see our 3D Space as being Flat. I think this is an important realization for Philosophy and the study of the limits of our ability to understand things.
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