Off, dud, over, under, upon, hot, ono, oof, hi, lo, etc.

October 15, 2021 5:09 PM

HACKENBUSH: a window to a new world of math (SLYT) An absorbing video book review of Winning Ways for Your Mathematical Plays (1982) by Berlekamp, Conway, and Guy.

(Made with manim, the 3blue1brown animation library. Original piano backing music by the narrator/animator.)

posted by tss (12 comments total)

Sweet intro to mainm!
posted by clew at 5:34 PM on October 15, 2021 [1 favorite]

Thanks for posting this! [Shouldn't that be manim?]
posted by klausman at 9:51 PM on October 15, 2021

if __name__=="manim":
posted by clew at 10:55 PM on October 15, 2021 [1 favorite]

Back in grad school I signed up for Berlekamp's class on combinatorial game theory, but dropped it after a week, or so. Both the man and the subject struck me rather mad, though in a charming sort of way. This video almost made me regret that decision.
posted by epimorph at 11:05 PM on October 15, 2021 [2 favorites]

Got to see Conway give a talk once. One of the.. no THE most entertaining math lecture ever.
posted by sammyo at 4:41 AM on October 16, 2021 [2 favorites]

Mod note: I have manimized the post, carry on.
posted by cortex (staff) at 8:17 AM on October 16, 2021 [1 favorite]

Two related questions: does anyone know if the surcomplex numbers have a game application (a+bi with a, b surreal)? Does anyone know if 3 or more player games have surreal number systems (or solitaire games for that matter)?
posted by TreeRooster at 8:31 AM on October 16, 2021

I wonder if this is an answer to 3blu1brown's earlier this year call out to mathematicians (even amateur) to just go ahead and make that video. Mainly because the final bit where the narrator spills that this is probably the only video on their channel that isn't piano.

Either way, 'twas a love of labor and took a great deal of time and a deep dive into a favorite maths book. I Await episode two.
posted by zengargoyle at 9:31 PM on October 16, 2021

zengargoyle, the video creator Owen Maitzen explains in the pinned comment:

Although this video was submitted to the first Summer of Math Exposition contest, it was not originally created for that purpose. It began as a short Twitter thread on June 8th, where I pompously declared that, although I had never made a video with anything except Screenflick and iMovie, I would someday make "the definitive mathtube video on Hackenbush". Following that, I started the first draft of the script on July 10th, finished it on the 13th, and began making the animations on the 14th. It just so happened that the contest was announced a couple days later, and it gave me the perfect deadline to strive for.

From July 10th to August 22nd, I spent a good portion of my waking hours every day working on this video. Making the animations was about half of that time, totaling over 100 hours. The rest was writing the script, recording the voiceover, adjusting timings, producing the soundtrack, and applying layers of general polish. It was a massive chore, and the only reason I'd ever do something like it again is if there were another topic that excited me just as much and that didn't already have a dedicated video on it. Which seems unlikely, but who knows :)

So, it's a bummer that they will likely not be making another video of this type any time soon, but really we should just appreciate this video all the more for it.

Also, in case there are any CGT experts around: Towards the end of the video (starting around 44:10) they start throwing on the screen some numbers with an ampersand in the notation, like 0&off = {|1&off}, tis = 1&0, etc., but they never explain it. Does anyone here know what & means?
posted by a car full of lions at 5:19 AM on October 17, 2021

Not the most helpful explanation, but straight from the book (Vol 2, Ch 11, p 336):

In general there's a way of analyzing a loopy game γ in terms of two rather less loopy ones, s and t, and we write:

γ = s&t, s = γ(on), t = γ(off)

I've never been able to get all the way through Vol 1. I agree with the video that it's a lovely math book (... well, set of four math books), but something about the density of the material and the lightness of the presentation just puts me to sleep, and I've woken up with Vol 1 on my chest quite a few times.
posted by reventlov at 9:35 AM on October 17, 2021 [3 favorites]

I guess I'm not going to understand that unless I find out either (a) how to decompose a loopy game γ into two games s and t, or (b) what the notations γ(on) and γ(off) mean. If you're able to explain, that would be amazing; if not, thanks for trying! I guess I should just get my hands on a copy of Winning Ways.
posted by a car full of lions at 5:40 PM on October 17, 2021

I've never been able to get all the way through Vol 1

I tried once and barely made a scratch. I love this stuff and I love Conway, but I have such a hard time not getting overwhelmed by symbolic representation even when I find the ideas themselves explicable when I can navigate through. I really appreciate the video's step-wise, branching exploration of some of the elements of this stuff but even that did me in before the end.
posted by cortex at 11:08 AM on October 20, 2021