## Sunday, March 2, 2008

### Hypercubes and Plato's Cave +

Edit: We've explored the visual ideas in this entry from a number of perspectives since it was published, here are some more recent entries:
Playing Games in Extra Dimensions
O is for Omniverse G to J
What's Around the Corner?
When's a Knot Not a Knot?
The Holographic Universe
Slices of Reality
Why Do We Need More Than 3 Dimensions?
Time in 3 Dimensions

One of the most common questions about this way of visualizing dimensions is whether the four dimensions of spacetime really are four spatial dimensions, or just three spatial plus one of time. I argue that for us "time" really is in the fourth spatial dimension which we, as creatures built from chemical reactions obeying the laws of entropy, are experiencing in a unique way. This relates closely to a phrase that is being uttered by many physicists nowadays: "time is an illusion". Saying that time is an illusion doesn't mean that we don't experience time from moment to moment, but rather it means that what we are experiencing as time is only a tiny window into a much greater underlying fabric, which ultimately encompasses the multiverse of all possible universes and quantum indeterminacy.

Hypercubes
The above youtube video shows what is commonly known as a four-dimensional cube: a hypercube, or tesseract. Before you click on the "play" button, we are not really "seeing" the hypercube, because a 4D object needs to be rotated for us to appreciate its higher dimensionality. In other words, without adding a time element to our appreciation of the shape shown in this animation, a significant part of what makes this a unique shape remains unseen.

In the above animation, we are looking on our computer screen at a flat 2D representation of a 3D shadow of a 4D object. Confused? If you go to the bottom of this blog entry there is another youtube movie, again showing a rotating hypercube. In this one, if you move your eyes so close to the monitor that your left eye sees the left half of the image and your other eye sees the right, your brain (with a bit of practice) can then merge those two halves into a stereoscopic visualization, from which you can get a hint of what we're really talking about here: "shadows" of a 4D shape being seen from the 3rd dimension.

Plato's Cave
Are you familiar with the allegory of Plato's Cave? It tells of some hypothetical people who spend their lives trapped in a cave, unable to see out into the real world, and all that they can surmise about reality is based upon the shadows cast upon the cave's walls as objects or people pass by the entrance to the cave. Trying to visualize higher dimensions is a similar exercise: our 3D reality is created by higher dimensional patterns, and what we witness from moment to moment, from day to day, from big bang to entropy and beyond those two extremes, is really just shadows of those higher-dimensional shapes and patterns. Ultimately, all of those shapes and patterns exist as potential within the underlying fabric of quantum indeterminacy.

Spimes
When Bruce Sterling talks about "spimes", he is talking about data that can be attached to a 3D object along a 4D timeline that gives us a 4D shape - RFID tags attached to items from a store's inventory give the store a "spime" representing each object's history, its locations in time and space from manufacture to sale. When I talk about the "long undulating snake" representing a particular person's body from conception to death, that's really just another spime. And at any particular moment in time, the person I see in front of me or the pair of pants I see at Wal-Mart can be thought of as really just a 3D shadow being cast from the 4D spime representing that person or object.

This is why it makes so much sense to think of time as really being in the fourth spatial dimension. Physicists use phrases like "time reversal symmetry" and "closed timelike curves" to reveal more about the fourth dimension as just another spatial dimension that could be manipulated and navigated within. It's also important to realize that our experience of time, the fourth dimension, as being continuous is an illusion. Our fourth-dimensional line is actually being constructed one planck length at a time, and any attempt to look at the universe in finer intervals than that kicks us back out to that underlying fabric of quantum indeterminacy in its unobserved state, which I refer to as the tenth dimension.

Because we are made out of 3D atoms and molecules, each higher spatial dimension is increasingly difficult for us to visualize. Like the hypercube, we can look at other visualization tools that help us to imagine those higher dimensional shapes, and the Calabi-Yau manifold is a good example of that. Garrett Lisi's E8 rotation may well be another, as it contends that all of the forces and particles within our universe are derived from an 8 dimensional matrix. And of course, my 11-minute animation contends that my way of visualizing reality could be a way for us to imagine how our 3D physical reality is derived from vibrating superstrings in the ten dimensions: but as I have always tried to make clear, my unique way of imagining the dimensions is not the proof for superstrings, it just has many interesting tie-ins.

String theorists say that for us the fifth dimension and above are curled up down at the planck length. This is why my animation talks about the 2D creature on the mobius strip, twisting and turning in the dimensions above but from his experience he is just traveling in a straight line. We 3D creatures feel like we're traveling down a straight line of time in the fourth dimension, but that line is being constructed one planck length after another from probabilistic outcomes available to us as a result of chance and choice in the fifth dimension. Let me say that again: we are really twisting and turning in the fifth dimension, but we think we're traveling on a straight line in the fourth dimension. This can be related to Everett's Many Worlds Interpretation of quantum mechanics, which says we are merely observing one state out of many possible states, all of which are contained within the quantum wavefunction: the many other versions of the universe where you and I made other choices continue to exist as potential within the multiverse. I'm proposing that those other outcomes are just different fifth-dimensional twists and turns.

"Time is an Illusion"
Now that a team of scientists at Oxford under the direction of physicist David Deutsch have published a proof equating the probabilistic outcomes at the quantum level with the parallel universes resulting from choice and chance out at the macro level (saying that both are equivalent and part of the same continuum from the quantum to the macro), what I'm portraying has more theoretical evidence to support it. The important insight that I'm adding here is that by realizing that the wavicles (simultaneous waves/particles) are in the fifth dimension, we tie in Kaluza's revelation about gravity and light in the fifth dimension, and we can see how those other parallel universes are just as real as our own but inaccessible/decoherent to the wave function for our own universe in its currently perceived state.

Many Worlds and many theories
What I'm portraying here is a way of visualizing the higher dimensions that ties together many different schools of thought: quantum mechanics and Everett's Many Worlds Interpretation are at the core, but there are many other possible tie-ins. String theorists say our universe is created by the interaction of a 3D brane and a 7D brane, my way of visualizing says that our 3D-universe-and-all-of-its-possible-timelines is locked in at the seventh dimension. Is our universe as we witness it just shadows of higher-dimensional holograms, a concept proposed by physicist Juan Maldacena as an extension to string theory? Whether our perceived reality is the shadows of superstrings, or a hologram, or an E8 rotation, or many other possible explanations, remains to be proved.

When physicists say that time is an illusion, they are saying that time as we experience it is just a shadow of what's really happening: just like the image of a hypercube being projected on a flat computer screen, we are looking at shadows cast by higher dimensional shapes as we go from instant to instant in our 3D universe.

Enjoy the journey,

Rob

Apocalypso Facto said...

Wow, this is amazingly mind-bending. I've thought about the "long undulating snake / spime" before, I just didn't know how to conceptualize it or even call it - so thanks a lot for this insight! This is a great job you're doing here.

Anonymous said...

Thanks, this was a very interesting read. The 3-D hypercube video was the best I've ever seen and I appreciate your posting it.

Andre de Wijze said...

As an interesting suggestion i would like to replace your hypercube with the following sphere: http://www.youtube.com/watch?v=x7d13SgqUXg&NR=1
Allowing 3D man to walk on the inside and the outside of the shape. And also increase chance of events.