Warning: Choking danger – may contain small pieces of Physics.
I think most people have difficulty visualising any world with more than three dimensions. I’ve always struggled to think about 1-D.
A football has three dimensions. You can kick it somewhere else, a short time later. A flat piece of paper has two dimensions and a straight line has one, I was told. “Later”, “flat” and “straight” are clearly references to particular ‘higher’ dimensions. Draw a straight line on a flat piece of paper and roll it up then throw it and I have a line in four dimensional space-time. ‘Lower’ dimensions refer to, perhaps are defined by, constraints in ‘higher’ dimensions. As we are not yet capable of switching off time, I’m not convinced the human mind has the necessary hardware to experience one dimension.
I’ve always known intuitively that 1-D was very difficult to isolate. A line is the path an imaginary point might take over time if it was banned from the second and third dimensions, or indeed if we just ignored any movement through those two dimensions. If the line on the piece of paper had instead been an optic fibre on a roll, the light passing down it could still be considered to be in our conventional understanding of one dimension (plus time.) The only way it is possible to observe 1-D would be as a point at a moment in time, though it would have to be an infinitely small light source. We can imagine a set of such points at exactly the same moment in time. Such a line could never be observed by a human. I’d normally blame Heisenberg but I think the ‘infinitely small in all but 1 dimension’ thing has given him a lucky break this time.
I returned to this subject after reading James Gleick’s description in his book ‘The Information’ of Richard Dawkins’ thoughts in ‘The Selfish Gene’ that although we are all familiar with the 3-D double-helix structure of DNA, the information it contains is effectively a bit-stream, like the light in our fibre. If we watch a single firefly, flashing against a jet black night, we are observing the output of the one-upon-a-time dimension. That may be as close as we can get.
1-D is hard for the same reason as 5-D; we have never seen it. We now have the technical capability to construct virtual worlds in more than 3(+Time) Dimensions but we humans don’t have the sensory input equipment necessary to observe them all at once. We may need to take our brains to another dimension, as predicted by ‘The Prodigy’, and Max Romeo before them.
It is left as an exercise for the reader to estimate the size of a bit.