Flatland - Exploring Other Dimensions

Plato's myth of the cave is an allegory that tries to make the point that there may be more to reality than meets the eye, that our experience is simply of a very limited and lowly aspect of reality. Given the knowledge and technology of the time, Plato's use of puppets and shadows in his ancient writing is brilliant in conveying the difference between the real and the apparent, but in the 1800's, Edwin Abbott took this idea much further, and in a way more rigorously and convincingly, as he was able to tell it through a creative exploration of mathematical space:

Compare the experience of a creature from three-dimensional space against one from a two-dimensional world. Easy, and completely reasonable to understand why the two-dimensional figure was skeptical of "more" dimensions, even if it was wrong, right? Well, apply the same reasoning to the difference between four-dimensional space and the three-dimensional space we're all used to. Wouldn't the reasoning you applied in the first case also apply to this one? And just like that time we were introduced to these ideas by the irreplaceable Carl Sagan, when he tried to show us the projection of a tesseract, here's a fun little animation to inspire your imagination and help you explore the beauty of mathematical space that can be understood by the mind even if it cannot be always perceived by the senses :)

Now, are there 'really' more dimensions than the three spatial ones we're used to or is this just a fancy mathematical abstraction? That's a topic for another discussion :p