Dimensions

What would it be like to enter a world of different dimensionality? While not the main point of the story, this subject is explored in the classic novel Flatland, perhaps with shades of Plato’s Allegory of the Cave in The Republic. I’m sure there have been many attempts since Flatland to explore this experience, but I haven’t read any of them. Perhaps this is why I was enjoyably tickled by imagining entering different dimensions through the eyes of novelist Cixin Liu in Death’s End, the conclusion to his trilogy that began with The Three-Body Problem.

Dimensionality isn’t the key storyline of Death’s End, which mainly explores further consequences of the Dark Forest answer to Fermi’s Paradox on a galactic scale. But there are parts that explore what it is like for a three-dimensional being to enter four-dimensional space. It is difficult to imagine the experience but Liu does a nice job, in my opinion, by richly describing the visuals as best he can. He also follows the well-worn path of making analogies to what a two-dimensional being would experience going into three-dimensional space.

We humans are so dependent on our eyes as a sense organ, and our lives are caught up interacting with objects of roughly similar size to us. It can be challenging to imagine something much larger in size. In our day-to-day experience, we treat the Earth as (mostly) flat. It is also challenging to imagine something much smaller in size. As a chemist, I’m used to imagining the structures of molecules, predicated by a theoretical model, and using analogies to familiar objects such as balls, sticks and springs. I even picture atoms in unique colors: hydrogens are white, oxygens are red, nitrogens are blue, because I have been socialized into the chemistry community to think that way.

A two-dimensional denizen in Flatland approaching a circle would have to go around it. The three-dimensional analogy: If I was walking and came up to a large pillar, I would have to go around it. The pillar looks like a solid wall, as far I can tell. To the two-D ant, the circle would look act as a similar barrier. However, if the two-D ant could access the third dimension as it approached the boundary, it could keep going straight ahead ‘through’ the circle by being infinitesimally above or below it. At least that’s what it would like to an observer ant. The observer ant sees the other ant disappearing into the barrier and emerging on the other side. Seems ghostly! 

If a three-dimensional bubble appeared in Flatland where the circle was located, the ant that enters the bubble and experiences 3D can now move above or below the plane and look out at its surroundings. It would then be able to see the front, rear, outline and the internal structure of the other ant simultaneously. In fact, it would be able to see all of Flatland. Now it might not be used to seeing all that additional data in one go, not to mention other objects in the third dimension. And perhaps if it rotates, it can now see a cloud hanging above Flatland in a different plane. The data coming in would be overwhelming. Rotating a little bit more would reveal even more that was previously unseen!

By analogy, if you entered a four-dimensional bubble, all of your previous 3D world would be laid out simultaneously. These objects would look ‘flat’ to you, and if you encountered a ‘solid’ looking object, it could be four-dimensional or possibly higher. I suspect it is possible to simulate this through virtual reality although it would likely make one nauseous to see a different landscape so-to-speak every time you tilt your head slightly. Not to mention, you should be able to see all your internal organs simultaneously if you were to look at any part of your own body.

In The Matrix movies, the experienced operator simply gets used to looking at streams of code that describe what is going on in the Matrix. If you’re encountering it for the first time, it just looks like a rain of gobbledygook symbols. That’s one way to process an incoming data stream. We are, in fact already getting used to overlaying additional data streams on top of the 3D world we experience. Witness the phenomenon that is Pokemon Go, making use of augmented reality. Layers upon layers of augmented reality can be geotagged to a particular spot. Like radio, you tune into your desired station. Except, your device can probably overlay more multiple data streams simultaneously. That would be trippy. (I recommend Vernor Vinge's Rainbow's End.)

What’s even more trippy – we’ve only briefly discussed expanding spatial dimensions – could one encounter an additional time dimension? I’m not sure how my brain would deal with that. But the language of mathematics can describe behavior in multiple dimensions, and I’m guessing as you familiarize yourself with the language, you’re becoming like an operator looking at Matrix code. I suppose I could go learn more math. Or maybe I’ll just enjoy reading and watching science-fiction.