Forget about time
For a while now the idea of other dimensions existing around us has intrigued me. Extra dimensions are often a key component of various permutations of string theory however the number of dimensions that need to be stacked on top of each other often makes visualising them nearly impossible (Bosonic String Theory requires up to 26!). It’s easier then to focus on something closer to us. How about trying to picture something just one dimension above those that we’re familiar with? I’m not talking about time, I’m talking about another geometric dimension of top of the 3 you’re familiar with. It’s still remarkably hard to picture, but some analogies to our plain old familiar world can be made to help you get to grips with it.
Bad movies with murdering cubes
The reason it’s so hard to imagine a 4th dimensional object is because we couldn’t ever really truly perceive one (using our eyes at least). So, let’s consider what it’s like for a lower dimensional being to perceive something in a higher dimension. If we think of hypothetical ant that is walking along a sheet of paper, we can imagine that he has no perception of up and down, only of forwards, backwards, left and right. What would this ant see if a 3 dimensional object like sphere passed through the paper? It would be a 2 dimensional dot as the sphere first touches the paper. The dot gets bigger expanding in to a larger and larger circle until it gets halfway through at which point the reverse happens until it passes back out of view. So then, for us a fourth dimensional cube passing through our 3D world would look remarkably strange. We would see a 3 dimensional cross section of the 4 dimensional cube (called a tesseract or hypercube) pass through our world. As it does so, it would appear to us to be twisting and turning in completely bizarre and impossible looking ways when in reality it’s simply moving through the 4th dimensional plane, there’s a relatively bad movie called Hypercube which sort of visualises that in a slightly more murdery way.
Step down to step up
Interestingly, another method we can use to better imagine the 4th dimension is by thinking about its shadow. The shadow of something tends to be a representation of the original object but cast down by one dimension. If you think about a cube lit by a torch you can imagine the shadow looking like a pencil drawing of a 3D cube, it would be recognisable to us despite having been stepped down by 1 dimension in to a flat 2D shadow.
So then, applying this to the 4th dimension, the shadow of a 4D tesseract would be 3D! This is of course pretty hard to get your head around. I think the reason why it’s hard to imagine what a tesseract would look like when Googling an image is because you’re stepping it down by 2 whole dimensions, from 4D to our 3D world and then displayed on a 2D screen, try to get your head around this rotating tesseract to see what I mean.
If only there was a new piece of technology that would better let you explore this, wait…
VR to explore 4D?
I don’t imagine this will be worrying Valve in terms of knocking their games off the VR top spots but an interesting experience would be some kind of 4D version of a recent game I played on the Vive called Quanero. In this game, you’re tasked with solving the cause of an explosions and shoot out at a bar. You can move around the scene looking at the incident from different angles, slowly rewinding or fast forwarding time till you understand the chain of events that occurred. Trying to get your head around the motion of a 4D object moving through our 3D world could be done in a similar way. One handset controlling the motion through the 4 axis and the other controlling position and time. It would still be very hard to understand but since you’re only stepping the tesseract down by 1 dimension it should be at least slightly easier
The original virtual reality
Here’s an interesting thought, all the time we’re conscious we’re limited by our own senses but when we’re dreaming, these physical limitations aren’t there. It stands to reason then that someone with an IQ off the charts or an ability visualise like Nikola Tesla, might be able to see in 4D in their dreams if they trained their mind to do so. A character from the film Waking Life talks about using his lucid dreams as a way to imagine what 360 degree vision would be like, surely this is just a progression of that? What other limitations could you overcome? Impossible hues of colour or maybe an Escherian staircase? Your imagination would be your only limitation.