Monday, February 12, 2007

More dimensions, vicar?

The concept of extra dimensions has fascinated me for ages – what would the world be like if we were able to move or see in more than the three spatial dimensions that we appear to be confined to?

The easiest way I’ve found to imagine extra-dimensions, is actually to think of less. Think of a universe where things can only move in two or even one dimension, how would life forms interact and live if they were restricted to a single plane, like stick-men on a piece of paper.

Now, when we think of our child-hood scribbles created on a scrap of paper, we tend to believe they can look out of that world and into ours, but what if they are so completely confined to that page that they have no concept of anything outside it – they live in page-world. All they can see is a line of perceptual experience, as if you were looking at the page edge on. Now consider drawing a line on this page-world, a 2-d being would see it as an impenetrable barrier it would have to move round, by going left or right, there would no concept of going over it – that would be madness.

Once you have this concept you can start expanding it. To create a house or prison for these flat-world beings to live in, you just need to draw a square or any polygon, no need for a roof. Now think about the anatomy of the beings themselves – when we draw them we imagine their skin to cover their entire image as projected into our 3-d world, but all they would need is a single, complete line to encase their internal organs and protect them from the harshness of the external 2-d environment. This is an interesting point as it leads to our first significant limitation for our 2-d life forms. They couldn’t have a complete digestive tract. If they had a mouth and separate anus connected by a tube, that tube would effectively split the creature in two. Only amoebae and cnidarians, (where its gastrovascular cavity functions as both mouth and anus) could exist. The interesting thing is that these beings think the line that makes up their outer skin, is complete and hides and protects their delicate innards from harm and scrutiny, but for us looking from the 3rd dimension they are as obvious and vulnerable as fish in a glass bowl.

Once these differences are appreciated you can start to have fun with them. From their perspective they think they’re pretty safe, living inside their various polygon houses they’ve built for themselves to shut out the dangers and prying eyes of the other two dimensional beings, but from our perspective in the 3rd dimension there is nowhere to hide. We can see both inside and outside their little dwelling, even inside and outside their body at any one instant, which would be baffling for these 2-d life-forms to comprehend, with no concept of an extra dimension. It would be like having the power of a God to these flat-worlders – you could reach into their lives and “magic” a feast on their dinner table, or if feeling malevolent, pluck out one of their internal organs and watch their confused brain and shocked 2-d facial expression as they expired.

Now you can do this again, if you shrink down to one dimension, the 2-d world would look mockingly on these 1-d creatures as they inched up and down their string like world unable to pass by other life forms with their perception reduced to a single point. That’s not very interesting though, I think you know where I’m going with this – what about our 3-d world, imagine applying the concepts we’ve seen in the 2-d world here. Being able to: see inside and outside your body at the same instant; see what is round the next corner or in the bowels of the earth without ever peeking or digging; diagnose and cure illness or cancer without any expensive equipment. Sounds very much like what we understand to be mysticism or shamanism doesn’t it?

Maybe, all we need to do to cure the sickness enveloping this world is to lever ourselves off this piece of 3-d paper and let our multi-dimensional brains acclimatise to the out-of-this-world viewpoint and see what stupid little cube-worlders we are.

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