A direct link to the above video can be found at http://www.youtube.com/watch?v=MV47Mcmo25I
This line has length only – no width or depth. Right at this instant, we could define a point at the tip of my nose, and another at the tip of your nose, and visualize a line that passes through those two points. Even though that line most likely passes through the earth's crust to get from my position on the planet to yours, that means little to the one-dimensional line we have just drawn.
And as you and I go about our day, that line will move around, continuing to pass through those two points we've defined. Billions of light years away, if we were to follow that line, it would be passing through one galaxy after another as you and I change our positions relative to each other back here on Earth (and the Earth itself turns on its axis and orbits around the sun and the galaxies move through space), but ultimately at any one instant we are still just talking about a simple one-dimensional line.
So, no matter what dimensions we're thinking about, there will always be a point that we can define that represents a dimension in a certain state, and a second point representing a dimension in a different state, and there can be a one-dimensional line that passes through those two points. But what that line passes through to get from one point to the other, and what that line extends to as it passes beyond each of those points, can be a mind-boggling realm of information and different forms of reality.
That's the simple power of the line. Traveling from one point to another is a way of thinking about "time" for any dimension, since time is a way of describing change from state to state. While we, as creatures made out of 3D atoms and molecules, perceive the line that gets us from one state to another as being in the fourth dimension, that concept works equally well for any dimension, which is why with this project we say that "time" for an imaginary two-dimensional creature would be one of the two possible directions in the third dimension, and so on.
In Imagining the Zeroth Dimension, we talked about how our universe or any other arises from a breaking of symmetry, and how the original animation that started this project visualizes the dimensions by starting with a point of indeterminate size and moving through the first, second and so on with repeating logical steps. This process also works from the other end: we can start with the tenth dimension as a point of indeterminate size, then imagine the descending steps from the ninth, eighth, and seventh dimension to represent an increasingly finely detailed "paring away" of the possibilities represented in the tenth dimension as a timeless Set Of All Possible States, or an ultimate ensemble of all possible information patterns conceived as a single unchanging entity. Thinking, then, of the "point" that represents our universe locked in at the seventh dimension, and thinking of a point in any other dimension, allows us to think about all the one-dimensional lines that could exist within or be connected to our universe, and how all those lines still represent only a tiny subset of the potential contained within the tenth dimension.
Finally, in Imagining the Second Dimension, we talk about how this one-dimensional line we're portraying has caused some people to say "that's impossible, something with no width or depth can't exist". If you're one of those people, this will be a good next entry for you to read.
Till then, enjoy the journey!
Next: New video - Connecting Zero to Ten