How is time a dimension? And how do we visualize it?

About the author

Alan Parry, PhD Associate Professor of Mathematics Utah Valley University

Quick Summary

I'm looking to create a video targeted at the general audience that discusses how time is a dimension like any other, how we can use spatial dimensions to visualize it, and (maybe) how some popular movies like Interstellar have tried to depict this and where they failed.

Target medium

The target medium is a video.

More details

For the video outline, I was thinking something like the following.

Intro - include some cool discussion about how time is mysterious and hard to conceptualize and how it was novel around the turn of the century to think of time as just any other dimension, but that that understanding contributed to our current view of the universe.
Mathematical explanation of what a dimension is (loosely, the number of coordinates required to uniquely specify a location) and some examples of 0D, 1D, 2D, and 3D images. Include some counterintuitive ones, like how a sphere (the surface; if you include the interior, it's a ball) is actually 2D, not 3D, since it only requires two coordinates to indicate a location (e.g. latitude and longitude).
4D is super hard to visualize because we only think in three dimensions since those are the spatial ones we have experience with.
The universe is a 4D spacetime with three spatial dimension and one temporal dimension. But in most ways the temporal dimension behaves just like the others. We can measure our location in it, we (involuntarily) move along it. But is it really like a spatial dimension?
Enter Animation: 2D animation, like a cartoon, can be thought of as 3D space-time, with two spatial dimensions and one temporal dimension. But since it's 3D, we can visualize it spatially. Here it would be awesome to show a short animated cartoon of some character, like Donald Duck (or something that won't get Disney to sue us), and then to translate that into a 3D object, by using its 2D images as a foliation. That is, we stack the 2D images on top of each other (sort of like a glued together flipbook) to create a 3D solid of the character that is as long as the cartoon was timewise (we could translate seconds into some arbitrary length measure). In fact a movie is essentially the same thing, but you navigate back and forth through time with the fast forward and rewind buttons on the remote.
Worldlines: Generalize the 2D animation as a 3D object to a 4D version and you have what physicists call in relativity a worldline. A worldline is the path of an object (like a point mass) through the 4D spacetime. Usually, we can think of our own worldline as the path our body would take which is really gluing together the worldlines of all the particles we are made up of. Alternatively, we can think of it as gluing together every instant of our 3D bodies (including its location) into a 4D solid that is as long as our lifetime.
Interstellar gets this a little wrong at the end of the movie because while Matthew McConaughey can move through time like a spatial dimension, it depicts different moments of time as windows in which McConaughey can look and see a movie. Rather it should have been a glued together stack of essentially 3D still frames that he could move back and forth through. If the aliens wanted to make it possible to understand for humans, they would have suppressed a spatial dimension and made a stack of 2D images through time. (Anyway, we don't have to include this if my collaborator was less interested).

All the above is up for discussion and change to anyone interested. But I have no experience in animation and limited, but growing experience in video production. I have a newer YouTube channel Philomath Party that's trying to grow. One of my more recent videos that shows one of my more valiant efforts, but also shows why I need some help on the production side since I don't have a lot of time for that is this one on PEMDAS is a Lie (Or why it should really be PEMA).

Contact details

The best way to contact me is via email at alanreidparry "at" gmail "dot" com

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