(Click here for the complete Imagining the Tenth Dimension FAQ list)
5a. I've watched the animation many times but I still don't understand the logic. Can you help?
5b is below.
Some people get this set of ideas intuitively, some people watch the animation many times before the puzzle starts to fit together for them. Of course, those who believe that time cannot be thought of as a full dimension might tell you the reason you're having trouble understanding the animation is because it makes no sense past the fourth dimension. For those who can get over that mental hurdle, there are still those who have been left with questions. Since this project began, I have posted responses to this question using a large variety of approaches as text responses at YouTube, and in numerous discussions at the tenth dimension forum.
Here are some blog entries that work through the construction of the dimensions using different approaches:
What's Around the Corner?
You Are the Point
Why Do We Need More Than 3 Dimensions?
How to Make a Universe
You Can't Get There From Here
Infinity and the Boltzmann Brains
Hypercubes and Plato's Cave
Flatlanders on a Line
Matthew Buquoi started a thread at the tenth dimension forum (special thanks to Matthew and to Val Clifford for their valuable contributions to this discussion) called "Debunking the Tenth Dimension Video" which provided some good opportunities for discussion of where some of the common confusions lie.
A user comment at YouTube asked for clarification on the jump from the 5th to the 6th dimension, this is what I replied:
Think of the fifth dimension as our probability space. Our fourth dimensional line is being chosen from probabilistic branches that exist within the fifth dimension: our 4D timeline is like the stalk of a dandelion, and the 5D branches are like a dandelion gone to seed, branching out in different directions from the end of that stalk.
But there are many possible expressions of our universe that aren't available to us from our position in the fifth dimension because of what has come before: so no amount of choice, chance or circumstance will make those available branches include the version of our universe where it's 2008 and Kurt Cobain is still alive. To get to that version of the universe, then, requires us to move through the sixth dimension where every possible expression of our universe's "spacetime tree" exists simultaneously, including the branches that we will never be able to witness, and the ones that we will choose to never witness.
5b. Doesn't the animation misrepresent what a Flatlander would see?
In a word: yes. This idea is explained in the book but not in the animation. To watch a video and read a blog about this this, click here for "What Would a Flatlander Really See?".
Draw a picture of a flatlander on a flat piece of paper. Now pick the paper up and hold it horizontally at eye level, so that all you can see is the leading edge of the paper. Now you are in the flatlander's plane, and you can start to imagine what it would be like to have a flatlander's perspective: all the flatlander can perceive is lines within his plane. As with our own 3D world, whatever's closest conceals what's further away, so if you look very carefully at our drawing of our "one-eyed-Jack" flatlander in the animation, you would have to conclude that all this poor fellow can see is the inside of his own face!
Likewise, what we are seeing in the animation is a "top-down" perspective of the flatlander's world, as seen from our 3D perspective. In the animation, portraying what a flatlander would really see seemed like too big a logical leap to ask of people just starting to be introduced to these ideas, but this criticism does come up regularly so in retrospect I probably should have included this idea in the animation. Oh well!
Imagining a flatlander with two eyes allows us to think of a form of binocular vision where the flatlander's brain would be able to assemble the slightly different image of lines coming to one eye and the other, and tell which lines were closer, which ones were curving away, etc.: but this is no different from we humans, who are taking the mostly 2D information coming in to each eye and assembling that into a 3D representation in our minds. I say "mostly" 2D because we are also able to move our heads around, which even with one eye covered does give us some additional information about what is close and what is far away - so this would be the case for a "one-eyed-Jack" flatlander as well. If the flatlander moves his head around he is able to gather additional information about the lines he is perceiving, but to our 3D minds this information would most likely still be very confusing: because all the flatlander would see is a jumble of lines all in the same plane.
Here are links to a few of the forum entries where this is discussed:
Other related blog entries:
Are Pictures More Important in Science?
The Long Undulating Snake
What Would a Linelander Really See?
A link to this video can be found at http://www.youtube.com/watch?v=JkxieS-6WuA
A link to this video can be found at http://www.youtube.com/watch?v=ySBaYMESb8o