As inhabitants of our three dimensional world, we struggle to imagine what the 4th dimension is and what it looks like. Carl Sagan provides an excellent explanation.

Video Summary

Carl Sagan uses flatland to describe dimensionality issues and the concept of a 4th dimension. Flatland creatures know of left and right but have never heard of up or down. One day, a 3D creature from above comes down to flatland but can only be seen as its points of contact. It sends the flatland creature above flatland where he enters a new 3rd dimension known as Up. The square returns and cannot explain the Up dimension he was in to the other flatland creatures, because he cannot show the 3rd dimension. Carl Sagan explains that is the same limitation we face when we try to envision the 4th dimension. If we take a three dimensional cube and project it through a 4th dimension (at right angles to the three dimensions) we get a four dimensional hypercube called a tesseract. Unfortunately, we cannot see a tesseract, because we are trapped in the 3rd dimension.