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If string theory requires extra spatial dimensions, it also needs to say where they are and needs to explain why we haven’t seen them. And there are a number of possible explanations, perhaps the most developed one is an explanation I’ve been thinking about now for something like, 25 years or so, and it goes like this, dimensions actually come in two varieties, they can be big and easy to see or small and much more difficult to detect, so an example is image a garden hose, imagine you take a garden hose, you stretch it out really long, so you got this long horizontal line in front of you. Now from far away, that garden hose is going to look one dimensional. You’ll only be able to see its length because from far away, you won’t have the visual acuity to see there is a second dimension, a circular dimension that curls around the garden hose. Now of course in this example, it’s easy to ultimately detect the circular part, you got closer enough, you use a pair of binoculars or whatever, and you can recognise that the hose has two dimensions, even though you could only see one from far away. Maybe that idea applies not just to an object in the universe, but to space itself. Maybe space has three big dimensions, left, right, back, front, and up, down, which are the analog of the horizontal extent of garden hose, but just like the garden holes, which has a curled circular part, maybe our universe has curled-up dimensions all around us, curled up to such a fantastically small size that we can’t see them, we can’t see them with the naked eye, and perhaps we can’t see them even with today’s most powerful equipment.
