time and dreamtime

That we have three dimensions of space and one dimension of time is interesting. We might have ended up with a universe with just two dimensions of space, and one of time. This would the world of Flatland, as descried by Edwin Abbot in a book from 1880. Creatures living in Flatland could only move in left-right or up-down directions, having no height. They’d be like ants traveling across  a flat sheet of paper.

Another option is that there is more than one time dimension: time and dreamtime. If time is one-dimensional, then, like an ant trapped on a line, you can only go forward. If time is two-dimensional, you could circle around in the time-dreamtime plane and visit anywhere in time you wanted, like an ant free to roam on a sheet of paper. Normal causality would not exist in such a world.

That certainly isn’t the world we know. But what if the second dimension of time was just too small for us to notice in everyday life? To picture this, think of a soda straw. It has a two-dimensional surface; you can make a straw by cutting a strip of paper and curling it into a tube. To locate a point on the straw, one needs two coordinates: the vertical position along the length of the straw and the angular position around its circumference. Creatures living on the surface of a soda straw would really be inhabitants of a two-dimensional Flatland, but if the circumference of the straw was small enough, it would look to them like Lineland. Curl up that straw tightly enough, and it looks like a line, even though it does have a second dimension – its circumference – which is just too small to measure.

This is what String Theorists mean when they talk about the Universe having seven or eleven dimensions, only some of them are curled up and too small for us to detect. Going back to the ant on the straw, think about what it would mean if the second dimension of the straw was an extra time dimension: dreamtime.

When I dream I imagine that the second dimension of time is unfurling, and I can travel around the straw in ways I can’t when waking. And when I dream and look back at my waking self, I can perform a kind of meta-analysis of my psyche that is often stunningly perspicacious.