As you probably know, the world we live in already has four dimensions - 0 is time, 1 is forwards-backwards, 2 is left-right, and 3 is up-down. (I'm going to ignore time from now on, since I'm talking specifically about spatial dimensions.)
However, there's been research done on additional dimensions, with string theory saying that there might be nine or more. Obviously we can't see any more dimensions, but people have come up with metaphors for explaining this. One of the most famous is the book "Flatland", narrated by a square living in a supposedly two-dimensional universe. People are polygons, the higher classes having more sides, and buildings are made of several line segments in a pattern.
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| A square from Flatland and his house, as seen from above by a three-dimensional observer. |
When a three-dimensional person comes to the narrator's house, he's able to use that additional dimension to move through walls by stepping over them, and can become "invisible" by just being above the world, or somehow seal a door shut by putting a nail through from top to bottom.
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| This is also how the teleportation works in "A Wrinkle In Time". |
A four-dimensional being would theoretically be able to do the same things in our world as we could in Flatland. However, there are other interesting ways that the fourth dimension could apply.
What if the fourth dimension did exist, but nobody could directly affect it or move through it? We might actually be four-dimensional, just like A. Square might actually be a cube in the third dimension, but unaware of it. But we might not be the same at each "cross-section"...
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| This was my original "explanation" for how it might work, using the two-dimensional metaphor. |
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| [Click the image if it isn't animating] |
If that were true for people, in the fourth dimension, then it would be possible (by some mysterious force...) to change shape, by shifting through the fourth dimension to a different three-dimensional "cross-section". This could also allow teleportation and invisibility of a sort, as explained before.
Ridiculously improbable, of course, but mathematically possible.
This is so cool! I remember being mindblown by the Flatland videos and 4-D theories in Algebra 2. I still can't bring myself to make up my own conclusions about the fourth dimension, but I really like the thought and work you've done here.
ReplyDeleteYour drawings are really great, and your "explanation" almost looks like a historical document, from Euclid or da Vinci (possibly due to your awesome script). Looking forward to reading more of your musings!
Very interesting first post, Daniel! The illustrations add dimension to the prose (no pun intended), and make the ideas you're discussing clearer. Like Gloria, I especially like the hand-drafted one. As you allude to in your introductory post, I think your challenge in this blog will be to incorporate enough narrative and personal context to your posts that readers who are not inherently captivated by complex and technical scientific ideas will be drawn in. In this post, I might have expanded a little in the first paragraph on the friend you were talking to and how the question of lycanthropy came to be one you were intrigued by, then perhaps you might've brought this context back toward the end of the post. I think the connection to a book that many of your readers will have read or at least heard about is a good strategy.
ReplyDeleteA promising first post!
I was originally a little intimidated by all of the diagrams in your blog. After reading your first entry though, I think they were perfect for representing the concepts you were trying to get across. Your discussion of the possibility of a fourth dimension was fascinating. I look forward to reading more interesting posts like this one.
ReplyDeleteWow, this is really neat! You manage to make a rather esoteric subject accessible to the average blog reader with your clear explanations and diagrams. Keep it up! This is a pretty neat theme.
ReplyDeleteI love Flatland! This brings back so many memories from Algebra II. The idea of different "cross sections" as an explanation for shape shifting is a really interesting concept. Usually all of those phony werewolf romance books offer no explanation other than... Well they don't really offer an explanation, just some wishy washy deity.
ReplyDeleteAnyways, despite this post being about math stuff, I still really liked it! Thanks for enlightening me on lycanthropy :)
--Julia Z.
Awesome entry! Next time, I request you prove the existence of dragons, since Mr. Buck isn't going to let me do it for my project.
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