Rod Serling may have been more accurate than he knew when he stated in the Twilight Zone opening, There is a fifth dimension, beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. Perhaps it's time to take a closer look at dimension itself.
The desire to examine the nature of dimension is hardly new. Back in 1884, Edwin Abbott wrote a novel called Flatland, a short adventure in 22 chapters and less than 80 pages. It's now in the public domain, and is downloadable for free from sources such as Google Books and Project Gutenberg.
Flatland is a strange tale of beings in a two-dimensional beings, and the curious events that cause them to question whether a third dimension exists. In this world, to even suggest that there are 3 dimensions is tantamount to heresy!
Recently, there have been a couple of versions released. Below is a short 34-minute version featuring the voices of Martin Sheen, Kristen Bell, and Michael York, among others:
You have to love the 2-dimensional touches, such as refrigerators, briefcases, pitchers, and squaricles (the 2-dimensional version of cubicles). The references to Area 33H are a subtle joke, as 33 in hexadecimal is equivalent to 51 in decimal, so it's an Area 51 joke.
There's also another version that came out in 2007 (click for playlist), interestingly the same year as the one above. This one has a 95-minute run.
The main point of the original book, and both movies, is how hard it is to imagine dimensions outside of our own. Notice that perceptions are constantly being turned upside down. Arthur meets the king of Pointland, and the king of Lineland, and has trouble getting them to understand a 2nd dimension. Spherius has the same problems getting Arthur to understand the 3rd dimension. The final twist in the movie drives this point all too well.
To help you understand Flatland's conclusion, here's a wonderful segment from Carl Sagan's Cosmos explaining a tesseract, with help from the Flatland analogy:
Charles Hinton would extend on Abbott's work in 1907, releasing An Episode on Flatland: Or How a Plain Folk Discovered the Third Dimension. In this version, the Flatlanders lived on a large circle, as opposed to Abbott's infinite plane. The book itself is longer and more involved, and also involves political satire.
When Martin Gardner covered these works in his Scientific American column, which was later reprinted in his books The Last Recreations (Available on Amazon) and The Colossal Book of Mathematics (Also available on Amazon), it set the stage for a renewed interest in the topic.
A. K. Dewdney had written a monograph in 1979 called Two-Dimensional Science and Technology, which was reviewed in Gardner's column. With the response he received from that review, he was inspired to write the book Planiverse, which was released in 1984 (Preview the book here, and buy the full version is available on Amazon).
Planiverse begins in our world, with students in a classroom using a computer to try and work out how a 2-dimensional world would function. During this process, they wind up making contact with 2-dimensional beings, and begin learning about such a world in unexpected ways. I believe the modern twist of using a computer for communication with a 2D world makes this version of a 2D world easier to understand for most readers.
Many of the above resources refer to the difficulty of envisioning a 4th dimension. It's even joked about in the Flatland edition of XKCD. The video game mentioned in the comic, Miegakure, is currently under development. It will be interesting to see if it truly can help make the 4th dimension easier to understand.
If you still think the 4th dimension is hard to picture, what about 10 dimensions? Below is a handy guide to help you to imagine all 10 dimensions. It's not long, but you still may want to go through it in small portions, to help you better understand each stage:
To further explore the ideas here, check out the multi-media version (Flash required) and the text version at the author's website. He also maintains a 10-Dimension video blog on his YouTube channel.
I hope you've enjoyed this mind-stretching post. Please share any thoughts you have in the comments!