Fourth Spatial Dimension 101

A direct link to the above video is at http://www.youtube.com/watch?v=uDaKzQNlMFw

The above video makes it very clear in its description at youtube that its author believes this has nothing to do with our concept of 4D as spacetime. Nonetheless, it shows multiple visual examples that apply to the "long undulating snake" concept I've talked about with my project from the outset. Am I a 3D shadow of my 4D self? And is that 4D self projected from a 5D hologram that includes many other possible versions of myself? That's the conclusion that seems to align with multiple theories of cosmology, while leaving room for more metaphysical discussions as well.

It's interesting to see how many comments there are on youtube from people suggesting that this video shows a way to understand how ghosts can appear and disappear, or pass through walls, or come from another time and place, another position with the 4D continuum. I suspect that such suggestions do not sit well with the creator of this video, but I of course have discussed similar possibilities from time to time.

But for me, I have to keep returning to this important point. I agree with this video! The fourth dimension is not time. Time is a direction, not a dimension. Saying that "time" is the fourth dimension would be like saying "forward" is the third dimension: both are directions, and both could be thought of as directions in any spatial dimension. "Forward" has its backward, "time" has its anti-time, and when you pair the two opposing directions you are thinking about a full spatial dimension using arbitrary labels.

Is the third dimension made from length, width, and depth? Sure, those labels work together. So do pitch, yaw, and roll. So could east/west, north/south, up/down: as long as you come up with three ways of thinking that are at right angles to each other, you're on the right track. But because these dimensions enfold one another, it's not really relevant to say that "forward" is only a direction in the third dimension: depending upon your frame of reference you could apply "forward/backward" to any spatial dimension, including the fourth. That goes for any spatial manipulation terms you can think of, which is why "branching" and "folding" have their usefulness in these discussions but they're only part of many ways of thinking about all this.

So. Some people think discussions of fourth-dimensional spatial objects like hypercubes have nothing to do with discussions of the fourth dimension as spacetime. In Playing Games in Extra Dimensions, we looked at a lovely iPhone/iPod app called Hipercubo. This game was created by Brazil's Roger Sodré, of Studio Avante. While Roger tells me he is a long-time fan of Imagining the Tenth Dimension, he is also another person who thinks spatial 4D is a separate concept from spacetime 4D. Here's one way of blending these two ideas together.

Try to imagine a 4D hypercube as viewed from the fifth dimension. The shape will be static and unchanging, the hypercube is always a hypercube. Now imagine the shape representing a human being from birth to death as viewed from the fifth dimension. That "long undulating snake" imagery we've used really is a gross oversimplification - the complex web of atoms and molecules, water and energy, choices taken and not taken, and all the potential "worldlines" representing a single person is a vastly more complex shape than a simple hypercube. In both cases, that extra dimensional pattern casts a shadow into the third dimension which moves in specific ways: but a rotating hypercube casts a much more predictable and essentially unchanging shadow than the 3D shadow cast by a living and breathing human being!

Let's close this entry by looking at the following video, which is my second most popular on youtube (after the three versions I've posted of my original Imagining the Tenth Dimension animation). It discusses the confusions surrounding 4D as four spatial dimensions that have nothing to do with time. It is built around the M-Theory claim that there are 11 dimensions, ten of which are spatial and one of which is "time": it's called "Aren't There Really 11 Dimensions?".



Enjoy the journey,

Rob Bryanton

Next: The Forest