We humans see everything in three dimensions. To us, everything can be described by length, width and height. We can also see two and one dimensional objects; shapes on paper and points. But what about dimensions higher than the third? Can you even begin to imagine what it would be like to see in 4D? I’m not talking about those lame 3D cinemas that blow air/ smoke into your face and rock you around, I’m talking about the abstract scientific fourth dimension: time. To get an idea of how difficult it can be, Edwin Abbot Abbot (A Square), the author of Flatland demonstrates how a 2-dimensional being has trouble understanding the third dimension, while we obviously take it for granted. A short, very enjoyable and insightful read. You can find a link to read it at the end of the post.
The World of Flatland
The main character in Flatland is called “A Square”. A four sided being and, you guessed it, a square! In the first part of the book, Square goes about explaining to us, the reader who lives in Space (the 3D world) how life works in Flatland. You might think “How hard can it be, everything is flat!”, Mr. Square begs to differ. Go down to the Flatland level and you don’t have the privilege of seeing everything from above. How do you recognize your relatives or people in general when they all look like lines? Imagine not being able to see height, then everything looks like lines, try looking at a paper sideways. I’ll leave the details of how life goes on in Flatland for you to read. The author also goes on to describe the intricate social structure and history of Flatland. Surprising that those exist for some shapes on a piece of paper right? 😛
A Visit From a Sphere
This is where the story “kicks off”. A Sphere comes in from Spaceland and takes Mr. Square by surprise. Mr. Square cannot even begin to imagine what the Sphere really looks like. Remember, Mr. Square cannot see height! But then the Sphere magically grants Mr.Square the ability to see in 3D, and they go on an exploratory journey throughout 3D, 2D, 1D and even 0D worlds and investigate how their inhabitants behave and perceive other dimensions. Mr. Square is then returned to Flatland, how the heck does he explain the third dimension to everyone there? Won’t he sound like a complete nutcase? I’ll leave that for you to decide, dear reader.
Imagine being able to “see” in 4D. That would be pretty weird/awesome. Although don’t expect to go around seeing everything in 4D after reading this book :P. You won’t have that insane moment of epiphany and clarity after reading the last sentence. However, I personally feel the book does get you MUCH closer to understanding the nature of the fourth and higher dimensions. The fictional background to the story just makes it much easier to digest, in contrast to reading math books or scientific papers on dimensionality. Very enlightening, you’ll definitely feel a bit smarter compared to not reading it. When you have some free time, find it here: http://www.geom.uiuc.edu/~banchoff/Flatland/
P.S. This was written in 1884, Einstein was 5 years old at this time, very far from making the fourth-dimension well recognized in the scientific community (space-time and relativity). Also, check out this comic once you’re done reading: http://xkcd.com/721/