I like how you bring up the "mathematical time-coordinate" as our idea of the "4th dimension." If I can focus on the idea that the "4th dimension" is essentially "time", physics applications (e.g. something as simple as graphing position, velocity, or acceleration of an object in motion against...
It's hard to convince people that they should hear and/or learn about the 4th dimension, string theory, and all of the like without giving them real world examples as to why these are all important.
I've been trying to find a way to incorporate the 4th dimension in particular into a short...