Carl Sagan on Flatland and Multiple Dimensions

Let's ignore for a second Einstein's fourth dimension of time. Is it possible to imagine a fourth dimension of space, separate from left-right, front-back and up-down? What would it look like? What direction could we point to?

To answer such a question, we could do what 1800's English writer Edwin Abbott did, both as a thought experiment on multiple dimensions, as well as a criticism of social hierarchy in Victorian England, in his famous novella Flatland (which you can also read for free here): start imagining what it would be like to add a single dimension to a world with fewer dimensions than our own, then take that sort of logic and apply it to our own world and see what kind of results you might be able to deduce.

Carl Sagan shows us how to do this, and then shows us what a representation of a tesseract (a fourth-dimensional 'cube' like the one shown above) would look like.

Were you struck by the fact that a single apple looked like at least four separate objects at the same time? I'll post a video soon showing a possible solution to the problem of the endurance of a self over time through a similar process. Stay tuned.