Lights Out is a puzzle that sits in a very interesting place mathematically: while many puzzles can be solved with the help of math, Lights Out is solved exactly and completely by math (linear algebra in particular). Linear algebra doesn’t just make it easier to solve: it finds an exact solution, and does it so cleanly that it seems like Lights Out was made for mathematical reasons (even though it wasn’t, unlike some other puzzles).
So if you’re ever stuck in a video game that has this puzzle (which seems to be just about all of them), just give the following video a quick watch and then whip out your favourite linear algebra software to solve a too-large-to-want-to-solve-by-hand linear system:
The Manim Python script for creating the animations in this video is attached below since, given how absurdly long it took to put together, it would be a shame if no one else made use of it for anything. So please, make use of it – make more videos about Lights Out!
I’ve been meaning to make a series of videos on Conway’s Game of Life for a few years now, and I finally decided that rather than rehashing topics that are already covered in the textbook, I’ll make videos explaining particularly notable new discoveries as they’re made. Unfortunately, the news that Life is omniperiodic is somewhat well-worn at this point, so I started this week with a video about the newly-discovered true period 15 and 16 glider guns (which are both the first guns of their respective periods ever found, and which were found less than 5 hours apart!):
The video does delve into some “rehashed” stuff, like what a B-heptomino is, and how guns work in general, but that’s unavoidable if I want the video to be understandable to more than 100 or so people in the world. Hopefully a few news videos like this might actually convince enough people that Life is interesting enough so as to bump that “100” number up in the near future!
After a 3-year hiatus, I’m back making math videos, not least of all thanks to my new fancy-schmancy basement studio:
This time I’m trying this crazy technique called “editing”, rather than just recording myself and dumping raw video footage online (which, believe it or not, is what I did for my previous videos – those were all recorded “live”). My first new video is now up, which investigates the problem of how to place 3 non-overlapping circles in a triangle so as to cover as much area as possible (a problem that is often incorrectly thought to have the Malfatti circles as its solution):
I used Manim for the triangle and circle animations and Capcut to edit everything together. I’m going to aim for one video per week or so, and hopefully will be able to put together a decent Applied Calculus playlist this summer.
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