A group of mathematicians and graphic designers have created a series of videos helping to visualise 4-dimensional space. Head to the ‘Dimensions’ website to access/download/purchase the video tutorials:
Mathematicians, freed in their imaginations from physical constraints, can conjure up descriptions of objects in many more dimensions than that. Points in a plane can be described with pairs of numbers, and points in space can be described with triples. Why not quadruples, or quintuples, or more?
There is the minor difficulty that our nervous systems are only equipped to conjure images in three dimensions. But that doesn’t stop Étienne Ghys of the École Normale Supérieure in Lyon, France, from visualizing the four-dimensional dynamical systems he studies: “I live in dimension four,” he says.
The narration is a bit dry and slow, and the constant rotating geometrics tended to confuse me more than anything (when he says “It’s easy, isn’t it”, I’m tending to reply “Er, no…”) But great stuff for bending your brain a little and thinking outside your normal perceptions – see how you go with it. (And I’d love to hear how ‘trippers’ out there relate to the 3D manifestations of 4D objects…something very “self-transforming” about them).
For old school multi-dimensional thinking, you can always check out Edwin Abbott’s brilliant Flatland. And Michio Kaku’s Hyperspace (Amazon US and UK) has a nice little summary of how extra-dimensional thinking fascinated early 20th century society – he quotes Linda Dalrymple Henderson as saying “[T]he fourth dimension had become almost a household word by 1910…Ranging from an ideal Platonic or Kantian reality – or even Heaven – the answer to all of the problems puzzling contemporary science, the fourth dimension could be all things to all people.”
