NOTES & DISCLAIMERS: This video uses some slightly different terminology than is established in Winning Ways. This is a conscious decision made in service of a smoother educational experience, with the understanding that adjusting to the book's terminology will be easy after absorbing the video. These terminological changes are as follows: 1. Winning Ways mostly uses "game" to mean "position in a game". However, it does frequently use "position" instead, and also sometimes uses "game" in the more common sense (what else would you call Hackenbush, generally, if not a game?) Solidifying the distinction between these two terms, and referring to positions exclusively as "positions", seemed like a good choice for this video. 2. Winning Ways calls the two players in a combinatorial game "Left" and "Right", rather than "Blue" and "Red", respectively. The book introduces the vertical bar notation pretty early on, so it makes sense to name the players based on whose options are on which side of the bar. It's also a lot more necessary when dealing with games that don't involve blue and red things. However, since this video is focused on Hackenbush, using "Blue" and "Red" saves time and a lot of mental overhead. 3. Winning Ways refers to Hackenbush positions as being comprised of "edges", rather than "branches", and refers to "erasing" them rather than "chopping" them down. My decision to use the latter terminology here was just a stylistic choice, motivated by the fact that in an animated environment, we're no longer limited to pencil-and-paper modes of thinking. 4. Winning Ways uses "number" only to mean "surreal number". Things like ﹡ and ↑ are not called "numbers", but either "games" or "game values". It seems like existing on a number line, being directly comparable to numbers, and having defined behaviour for interacting with numbers via addition, subtraction, multiplication, etc. is not enough to be considered a number. Nevertheless, I think using the word "number" for these things is a lot less confusing, and helps a lot more to drive home the point of the video. The very few times that I need to refer to surreal numbers specifically, for example in defining what a switch is, it's only a small sacrifice to add the word "surreal". ﹡ and ↑ aren't numbers in the "traditional" sense, but neither is √ω. Tradition is what we make it. 5. Winning Ways prescribes the pronunciation "slash" for the vertical bar, rather than "bar". It only mentions this once, as the book, being written with text, never needs to actually pronounce the symbol. Saying "slash" every time a vertical bar appears on screen would have been too jarring for me, and it would have taken a few more words to introduce that pronunciation, so I went with what seemed more natural. 6. Winning Ways does not use "epsilon" to refer to the reciprocal of ω. However, this is a somewhat established usage of "epsilon" - the Wikipedia article on surreal numbers uses it, for example - and I talk about tiny numbers enough that it's useful not to have to say "one over omega" all the time. In addition, the introduction of dotted lines representing "fragile" branches is nonstandard. Unfortunately, switches are not possible in standard Hackenbush, so to get around this, Winning Ways introduces a separate game called "Childish Hackenbush", with the rule that you're not allowed to leave any branches floating in the air. I thought it was simpler and more elegant to add to the existing game, rather than changing it. This is also one reason why I chose not to make the ground a dotted line, like it is in the book. Smoothness of animation and the ability to transform the ground into a number line were other reasons. Finally, the book uses shorthand like 1﹡ for 1 + ﹡, and 1↑ for 1 + ↑. They explain this as being analogous to how we write 1½ for 1 + ½. This notation is convenient given the ubiquity of such values in the book, but I didn't feel the need to introduce it for this video. 1 + ﹡ is, thankfully, still a valid, and much more immediately intuitive, way to write 1﹡. BACKSTORY: 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 :)
I'm no medium but I'm quite sure this video is fiercely appreciated by Berlekamp, Conway and Guy. Not just for the mathematical content but also for its jovial and beautiful presentation. I get the desire to put into other people's minds the awe for something that has been awing you. Given that I'm still thinking about this hours after watching the video, I'd say you've succeeded there.
"defined behaviors for interacting with numbers via addition, subtraction, multiplication, etc"...wait, what's up-star times up-star? doesn't the notion applicable to surreal numbers not work here?
@@Doodle1283 you could say that yeah, it is all original stuff. i'd maybe call it semi-rehearsed improvisation - i recorded it about thirty seconds at a time, planning ahead a bit for each section so that the music syncs up reasonably well with the content
Owen I hope you lived a life you enjoyed and if you were alive I would have hoped from the bottom of my heart that you create a life for yourself that you love. I saw this video 24 hours ago and ever since I have had the urge to quit my corporate job and work in academia. I have not been able to shake this feeling as I had anticipated. You have at the very least changed one solitary life; mine.
when I first started watching I assumed you had pulled that last line out of your head to be funny. it was funny! but by the time I reached the end, Oof
I scrolled down to the comments after we got to "up", saw this comment and went "haha - exactly!" I was not prepared for "draw the thermograph of oof" to be literally relevant The mathematical hubris I have just fallen victim to is pain
@@382Misnothere He unfortunately made the decision to leave and take his brilliant mind with him. He will forever be missed by his close ones and also thousands of random math enthusiasts on the internet. Rest in peace Owen.
Came back to this mathematical masterpiece for a second viewing only to discover that Owen has passed away. While I didn’t know him, this news is still a punch to the gut. I love maths and this video is so inspiring, shedding light on some greatly underrated work in the field. I don’t know what Owen was going through, but it makes me think back to my own struggles with mental health and suicidal ideation, some of which continues to this day. I’m glad Owen was able to leave a positive impact on so many people, including with this video. I like to think that Owen was able to inspire and create future mathematicians with this video, as he has definitely inspired me to keep going further. I hope his family is doing okay and handling the loss well. Owen, you are an inspiration to many, through your music and this beautiful video, it truly is one of my favorites.
@@SimonClarkstone I found out by looking through the comments here and on his other music channel. I believe his mom, Rohan Maitzen, also confirmed that he had died on December 30th. I didn’t find out about this until my second viewing of this video.
Oh dear. I was just going to suggest that this is resubmitted for #SoME2. I was hoping that Owen might have released another "book review" which I had missed, because this video is just so good. Definitely inspirational and I hope that it influences countless future mathematicians and ponderers. As far as I'm concerned, Owen joins these greats with this contribution to the world and will be missed.
We have a tradition in my family of watching documentaries together, i watched this twice and was so enamour i convinced my family to see it with me, thank you for a great memory and a new wish Owen, and rest well knowing you showed at least 200 thousand people the beauty of math and little games to overthink.
How does this keep showing up. Just a few days ago i watched another education youtuber in a video about electron spin, and they did it the same joke. I can't believe there's so many people that all know the same video. Then again, given that they're all math and science people and it was a very technical video, i'm not too surprised
Rest in piece, Owen. I never knew you, but this video put real delight into my life for whatever that's worth. Your appreciation for beauty and whimsy in equal measure was a bright light to me, and you helped me understand the love I hold deeply for math. Thank you, and godspeed
@@rohanmaitzen9033 His memory is going to live on. I'm a professor in Nebraska, United States. I'm implementing his views on math from this video in a course that I teach to hundreds of teachers, some of whom will undoubtedly teach their students. I hope he's doing some amazing math on the other side.
man, coming back to this for a fourth watch or something, i did not know owen had passed away. thank you from the bottom of my heart for this little gem i adore and all the other things i never knew you for. rest in peace.
Amazing video! The perfect mixture of approachability and depth. I know they're a lot of effort to make, but I'll definitely be watching if you make more :)
This video brought back some happy memories! When I was in Grade 9, 1978-79, I was in a math club lead by Richard Guy. (It was for participants in a city-wide math contest, which I had won.) Attendance dwindled to just him and myself, and then he began to introduce me to what he was working on with John H. Conway: they were writing Winning Ways. So I learned about Hackenbush and other games, the { | } notation, defining integers as games, * and ↑ and so on. He also mentioned the "Bűvös kocka" of Ernő Rubik. I bought a copy of the 2-volume first edition of Winning Ways when it was published. Prof. Guy also taught a calculus course I was in, in 1982.
that sounds amazing. grade 9 was when i first learned this stuff as well, it really is a surprisingly accessible topic that is perfect for a math club i'm jealous that you got to spend so much time with guy - he seems like a great guy. also a prolific chess composer apparently!
@@colinpitrat8639 Also be aware that there are cheaper versions that... print the book in BLACK AND WHITE... don’t fall for them, they’re basically scams due to incompetence of the publishers
Oh my god I can't believe I didn't pick up on that in my two previous viewings of this video! That's just amazing. So sad to come back for a third viewing just to see that Owen is no longer with us. This comment helped cheer me up. What a brilliant guy he seemed to have been. RIP Owen Maitzen
Whimsy is detrimental to the fundamental seriousness of mathematics, and also quite unimportant in a very, very large chunk of contexts. I'd know, I'm a mathematician. It's nice you care, but people would only really *respect* him for his work in group theory.
@@eshansingh1 For recognition? For academic achievement? I mean, I'm not a PhD, I'm an autodidact, but I still value academia quite a lot. But that's besides the point. People do mathematics both for recognition from others and to advance human knowledge ultimately. Sure, you can take creative liberties when developing mathematical theory (like Conway, Berlekamp, and Guy did with combinatorial GT, which is arguably the worst branch of mathematics ever created), but that won't really matter all that much. Thanks for coming to my TED talk.
pure delight at the reveal that "over" stunningly is less all the positive surreals, as crazy as they are, but then manages to be *greater* than the already introduced up series... what a wonderful video, with wonderful pacing and storytelling. thank you for making it.
The “Down the Rabbit Hole” section reminds me of the descent into insanity at the end of Tantacrul’s video where he reviews Sibelius. Or his review about Dorico.
completely and utterly speechless. This is the most well thought out, elegant, genuinely informative math video, (if not video in general,) that I've ever watched. It feels as if this video encapsulates my passion for mathematics in its purest, maximally concentrated form. Mathematics, in essence, is about playing games with the universe itself. I am awestruck with the profundity of it all, not to sound melodramatic by any means. I say this with the most heartfelt and genuine thanks that I can give, thank you for making this video. Rest in peace.
It’s such a sad shock to hear of Owen’s death. Owen, you and I never knew each other, but you touched me, in your own small way. I just so happened to come across this video, and was blown away by the math, yes, which is amazing, but also the MUSIC! I’m also a composer myself, and after finding your music channel I listened for quite a while to your improvisations, which I found totally enrapturing and inspiring. You seem like you were similar to me in a lot of ways, and definitely the kind of person I would’ve liked to have known. A lot of people miss you. Rest In Peace.
Brilliant reference at 6:23 -- not only are you referring to the "0.5 A-presses" joke, but the notes playing at this part of the video ACTUALLY play the Title Select Theme from Mario 64. Bravo, holy cow.
Quality standards for maths content just got surreal. From sound to animation, the presentation is as polished and sharp as one would expect from but the best maths TH-camrs out there; the flow of topics and pace of explanations are just right; the subject itself is immensely enthralling and your exposition more than makes it justice. This essay leaves any mathematician in an excited position for more, I will probably rewatch this ω times until someone (hopefully you) explores the colon principle in a follow-up.
When I got to 44:00 and heard "You can dive headfirst into the world of on, off, dud, over, under, ..., upon, hot, ono, ...", I couldn't help but think... "oh *no* indeed" -- But yeah, this is incredible! I feel like every 5 minutes I've only been playing in the kiddie pool of numbers compared to the universe coming up.
This is sincerely one of the greatest video essays on this platform and it's a crying shame that it doesn't have more views, and an even bigger tragedy with what happened with Owen.
You already know this, but this is beautiful. Thank you so much. This video makes me want to be better at pursuing the things that fascinate me and presenting them to the world. And to be a better pianist. Even if you never produce anything like this again, this will remain one of my favourite channels.
Thank you glimbo, I hope you continue pursuing the things that fascinate you. I was inspired by this video as well and I hope many others continue to be inspired too.
I think Grant needs to have some kind of "Honorable Mention" list for things that were inspired by his SoME1 challenge, but did not get included for whatever reason including missing the deadline, but was made known (if not actually released or draft-released) in time for his wrap-up and postings about it.
This is a really good video!! It's filling the Vihart-shaped hole in my heart -- perhaps not stylistically, but in the sense of exploration and mathematical play. I've always been somewhat confused by the surreal numbers, but in their original context of game theory they seem not just useful, but completely natural -- of course they're defined in terms of what they're less than and greater than, because in games that's often all you can tell. It gives a lot of motivation to their definition, which in turn really helps me understand their behavior. Also, the music is really great!! It reminds me a lot of Untitled Goose Game, not just stylistically, but in how it seamlessly ebbs and flows to perfectly match the video. Really good job with that, it's so good
This video is amazing. The wonder, the confusion, the discovery, the humor, it's all perfect. Your passion for maths is contagious, hopefully thousands of people will see this.
i took a combinatorial games course last year where we explored our way through the surreals and this is an absolutely incredible video, captures a lot of the coolest stuff in the basics of combinatorial game theory. genuinely one of the best math videos ive seen in a long while
Thank you for this video! When I was in highschool we were tasked to write a short (10 to 15 pages) "paper" to prepare us for university. I chose surrreal numbers as my topic and spent almost a year with Conways work through On Numbers and Games and lectures of him I found here on youtube. I wasn't in a good state of mind at the time and didn't put in as much effort as I wanted. But still during this time I gained a deep respect for Conway and he became somewhat of a mentor figure for me and someone I dreamed of meeting in person one day, knowing full well it was quite unrealistic. So when I heard he died from covid last year it felt like a personal loss, as I lost this little dream of meeting him one day. All of this just to say thank you, once again, for this video, as it is a wonderful homage on the work of these men and some of the most beautiful mathematics I ever encountered.
This video finally explained to me what Conway was saying in one of his lectures when he said that using his surreal notation you can create numbers that are neither positive nor negative but also not a zero.
This video is incredibly well-executed from start to finish. And for a first(?) video essay, too! Really stupendous work. If you do choose to make more of these, I'm sure you'll excel. And if you don't, well, you can at least rest assured you've made an all-time classic. P.S. If you haven't seen them, I suspect anyone who enjoyed this video would enjoy "30 Weird Chess Algorithms" and "There Are 48 Regular Polyhedra." Same vibe, same vein of hyper-niche but obscenely funny math lectures. Edit: Just learned of Owen's passing. It is a tragedy on many levels. Take care of yourself, whoever you are that's reading this.
This is exactly the intersection of math, philosophy, art, game theory, and dumb pannenkoek references that I needed. Even if you never make another video, know that this one was absolutely enough. More is welcome though ;^)
"hours of chill piano improv to relax slash study to" lol the deadpan humor never stops and-hold on, that was all original music?! You pulled a sneaky on us; this video was actually about adding songs to my study playlist with Vihart's Pi Day improv! I like how it's a similar vibe, calmly philosophizing about math memes... Speaking of, 2:03 isn't the Loss meme, but now we can rigorously define it :P
This might be my favourite math video ever. I've watched it 3 times now and I've just decided to order the book. I'm extremely thankful to you for doing this, you legend. I don't know you personally but I really hope you're having a good day when you read this❤
The more i watch the layers of greatness this video builds and finally in the end it turns out its just an unpaid advertisement for some obscure book, that better believe that I am putting it on my wishlist. Wow, really enjoyed!
@@jan_Eten that's a really good one too. I watched this vid when i was in a rough spot and it really brought me back to those old vihart videos. It really makes math feel like this world of endless possibility.
Man I gotta make a comment on this video I first heard about combinatorial game theory on Discord, with a message that mentioned the confusing terminology introduced by the original mathematicians that's kinda just stuck Then today (which, for the record, is 2023-12-22, or 2023 December 22nd in a more readable format that I totally didn't just make up), I was watching TH-cam, and somehow I ended up in the niche of long math-y video essays, and so eventually I ended up here. I watched the entire thing, and I found it funny, informative, and just plain wild at times - particularly the comment about the "wordbuilder's almanac", which I took note of and found very funny indeed because of my interest in conlanging (which may or may not be diminishing in favour of Scrabble nowadays? I honestly couldn't say.). Anyway, after watching it, I read the comments and discovered of Owen's passing. This struck me in a way that would be impossible to replicate - in that the thrills that I experienced watching the video were turned somber. But my point is that this was an amazing video - I loved it, and I'm absolutely certain that many others have done and will do as well. If you're the sort of person that reads comments before watching videos, and you're reading this, then please watch this video. I beg you. It is possible that you will be delighted and horrified in many different ways that I'm not exactly sure how to put into words (because I'm no good with words, so please be forgiving), but I promise that you *will* enjoy it. :) Thanks for watching my Ted talk ig - now go watch this video! ;)
I first watched this video shortly after it released and I remember having loved it tremendously. As I was re-watching it today, like you, I found out about his tragic passing. The day of you watched and posted this comment happened to be my birthday. The video is truly a masterpiece and I'm happy we agree on that. Peace ✌
three years later, it's still a masterpiece without peer. this will always be your legacy, owen: introducing hundreds of thousands to a unique and distilled form of joy and wonder. RIP
Thank you for the legacy left with this presentation masterpiece, RIP. I'm a mathematician at heart and would have never learned about the work behind Winning Ways if not for this video. I will surely buy the book now and can only hope one day I can pass along the curiosity to my family. Glad to see views racking up recognition, crazy that Owen is gone just 4 months after this release.
This was incredible all the way through, from the animations, to the explanations, to the background music that somehow always fit the topic. Awesome!!
This… is probably my favorite video I’ve seen on TH-cam. I’ve been trying for a couple months to find someone who wanted to play around with surreal numbers with me. You just showed me how much deeper this world goes, with an absolutely beautiful piece of work. Thank you for making this. I loved your music as well, I will go check out your other channel now. Thank you thank you 🙏 ✨❤️
This is super inspiring to see a TH-camr make a very high quality math video of their chosen topic without being an established mathtuber. Great work and I want to do the same.
What an incredible video. I'm just lost for words. Every math teacher should make sure their students see this video. How could you not fall in love with numbers after seeing this.
This might just be my favourite maths communication video ever. Playful, presents a topic that's lesser-known in popular maths, and easy to understand. Great work, I'll definitely be reading Winning Ways soon.
Maybe it's just because It's 2am and I've had a long day, but finding out Owen is dead filled me with so much sadness and anger that I broke down crying. I just finished watching this whole video straight for the third time, I was in adoration of your work, thinking that it may well be my favourite video on the Internet and now I find out you killed yourself? This is so unfair, my friend. You were even in Earth Strike like me. I can't even express how devastated I am. Rest in Peace you beautiful soul.
This is now my favourite math video I have ever watched. I even remember looking up surreal numbers before and not really understanding them, so it was a pleasant surprise to find out midway through this video that this is what the video was about all along!
This video was simply mind-blowing, and by far my favorite video from the Summer of Math Exposition contest! Not to dis any of the other entries, but I can't fathom how this wasn't selected as the overall winner. Congrats on a stupefying feat of math exposition - you captured precisely what it is that makes mathematics so wonderfully strange and beautiful. I am forwarding it to everyone I know!
words cannot describe the feeling you gave me with this video , Owen. I am a silly little year one CompSci student and Ive never been this excited to learn something. Thank you for this beautiful piece of art that is this video. I want to get this book as a christmas present.
I got it as a Christmas present last year because of this video! I love it so much… best gift I’ve ever gotten, and I’m excited you’ll get that thrill too come this December. It’s definitely not the type of read you do on public transport… it takes serious concentration and note taking, and it definitely requires effort for you to learn the material, but that put in effort makes it super rewarding. I’m glad that even in his wake, Owen can share his beautiful outlook on math and inspire others like you and I to pursue the whimsical in the academic. Rest In Peace, Owen 💛
Once again this video popped up in my recommended. While I didn't watch it through this time around, like the last two times, I just had to come here and ventilate the vast feeling of sadness that swept over me. Rest in peace Owen.
Hands down the best math video I've seen in a long time, it'd be a shame for this to be the only video you make in this field given your clear talent for scriptwriting, animations, and overall enjoyability. That being said, if this is the last math video you make, thanks for making it such a good one; I definitely plan to return for at least a couple rewatches later down the line. Awesome stuff!
I keep coming back to this video, I just love it so much. It's incredibly effective at helping the viewer understand whats going on and it preserves the playful tone of the original books. Fantastic work!
Thank you so much! I never got into hackenbush back in the day but the cluster around zero is incredibly fascinating like spinor rotation over an infinitesimal
Ohmygoodness someone recommended this video to me and I'm so happy I watched it. I haven't laughed so much about math in so long, whilst also learning so much. This is so awesome and I would love it if you made more videos like this. I am immediately subscribing and I'll recommend this video to anyone I think would like it. Thank you so much.
One of the best videos ever uploaded to this platform, regarding math or anything. It almost feels like numbers such as star or up are representing values extending into a dimension that doesn't exist on the number line (like the y axis, the thermograph). Kind of a quirk of the fact that you only have positives and negatives to express something that has more than 2 "directions." Makes me wonder what math would be like if there were more than just positives and negatives, like super-positives and negatives way out past omega, or neutrals within zero.
I absolutely adore this video! I love how it gets crazier and crazier till a point where I gave up trying to keep up and just enjoyed wherever it was going! You have a great knack for organizing content and I hope you continue to make videos!
I love this video!! Such interesting concepts, love it. Never knew previously of this application of abstract algebra to game theory, and it really embodies the playfulness that makes mathematics fun!
Excellent video. When I started watching I thought it reminds me of surreal numbers, and then Boom! This is the video you want to keep for retirement and then to watch again and again.
Hi Owen: Thank you so much for making this video. I started reading Winning Ways myself after watching your video, and I'm absolutely fascinated with everything about it. Thank you so much for introducing me to CGT and surreal numbers.
Holy moly, that's a way to make a video about that subject. At first, I didn't know at all what I'm into, it just presents to you as a video about a fun little game, and usually a bit of mathematics on the side. And here - that curve was fascinating. How you kept us engaged, stimulated our curiosity to learn more and more. Your introduction into that point of * (star) was amazing. You first forget about everything else and talk about the game. Then, introduce the rest in a logical way, very easy to understand. Again, holy moly, that is incredible. You understood everything about didactics, and the art of teaching to the network of nerves inside our cells, by providing and attaching to something relatable first, so that the network can easily grow from there, more than most professors I've ever met. The current way of introducing dry mathematical structures first, is the wrong way to teach. Brains don't work that way very well. Isolated forms of knowledge are very hard to keep within the network. Each and every relatable connection increases the chance more and more, that the knowledge is easier to learn, and remain within the network. That's why every person in an educational position should know: Always start relatable and build up a framework first, that facts can later be connected and attached to. Isolated knowledge doesn't work well for learning.
NOTES & DISCLAIMERS:
This video uses some slightly different terminology than is established in Winning Ways. This is a conscious decision made in service of a smoother educational experience, with the understanding that adjusting to the book's terminology will be easy after absorbing the video. These terminological changes are as follows:
1. Winning Ways mostly uses "game" to mean "position in a game". However, it does frequently use "position" instead, and also sometimes uses "game" in the more common sense (what else would you call Hackenbush, generally, if not a game?) Solidifying the distinction between these two terms, and referring to positions exclusively as "positions", seemed like a good choice for this video.
2. Winning Ways calls the two players in a combinatorial game "Left" and "Right", rather than "Blue" and "Red", respectively. The book introduces the vertical bar notation pretty early on, so it makes sense to name the players based on whose options are on which side of the bar. It's also a lot more necessary when dealing with games that don't involve blue and red things. However, since this video is focused on Hackenbush, using "Blue" and "Red" saves time and a lot of mental overhead.
3. Winning Ways refers to Hackenbush positions as being comprised of "edges", rather than "branches", and refers to "erasing" them rather than "chopping" them down. My decision to use the latter terminology here was just a stylistic choice, motivated by the fact that in an animated environment, we're no longer limited to pencil-and-paper modes of thinking.
4. Winning Ways uses "number" only to mean "surreal number". Things like ﹡ and ↑ are not called "numbers", but either "games" or "game values". It seems like existing on a number line, being directly comparable to numbers, and having defined behaviour for interacting with numbers via addition, subtraction, multiplication, etc. is not enough to be considered a number. Nevertheless, I think using the word "number" for these things is a lot less confusing, and helps a lot more to drive home the point of the video. The very few times that I need to refer to surreal numbers specifically, for example in defining what a switch is, it's only a small sacrifice to add the word "surreal". ﹡ and ↑ aren't numbers in the "traditional" sense, but neither is √ω. Tradition is what we make it.
5. Winning Ways prescribes the pronunciation "slash" for the vertical bar, rather than "bar". It only mentions this once, as the book, being written with text, never needs to actually pronounce the symbol. Saying "slash" every time a vertical bar appears on screen would have been too jarring for me, and it would have taken a few more words to introduce that pronunciation, so I went with what seemed more natural.
6. Winning Ways does not use "epsilon" to refer to the reciprocal of ω. However, this is a somewhat established usage of "epsilon" - the Wikipedia article on surreal numbers uses it, for example - and I talk about tiny numbers enough that it's useful not to have to say "one over omega" all the time.
In addition, the introduction of dotted lines representing "fragile" branches is nonstandard. Unfortunately, switches are not possible in standard Hackenbush, so to get around this, Winning Ways introduces a separate game called "Childish Hackenbush", with the rule that you're not allowed to leave any branches floating in the air. I thought it was simpler and more elegant to add to the existing game, rather than changing it. This is also one reason why I chose not to make the ground a dotted line, like it is in the book. Smoothness of animation and the ability to transform the ground into a number line were other reasons.
Finally, the book uses shorthand like 1﹡ for 1 + ﹡, and 1↑ for 1 + ↑. They explain this as being analogous to how we write 1½ for 1 + ½. This notation is convenient given the ubiquity of such values in the book, but I didn't feel the need to introduce it for this video. 1 + ﹡ is, thankfully, still a valid, and much more immediately intuitive, way to write 1﹡.
BACKSTORY:
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 :)
I'm no medium but I'm quite sure this video is fiercely appreciated by Berlekamp, Conway and Guy. Not just for the mathematical content but also for its jovial and beautiful presentation.
I get the desire to put into other people's minds the awe for something that has been awing you. Given that I'm still thinking about this hours after watching the video, I'd say you've succeeded there.
try:"∗"
"defined behaviors for interacting with numbers via addition, subtraction, multiplication, etc"...wait, what's up-star times up-star? doesn't the notion applicable to surreal numbers not work here?
I'm so curious about how you produced the soundtrack that plays for such a long time? Did you compose all of it?
@@Doodle1283 you could say that yeah, it is all original stuff. i'd maybe call it semi-rehearsed improvisation - i recorded it about thirty seconds at a time, planning ahead a bit for each section so that the music syncs up reasonably well with the content
Owen I hope you lived a life you enjoyed and if you were alive I would have hoped from the bottom of my heart that you create a life for yourself that you love.
I saw this video 24 hours ago and ever since I have had the urge to quit my corporate job and work in academia. I have not been able to shake this feeling as I had anticipated. You have at the very least changed one solitary life; mine.
Did he die?
@@FishStickerYes, very tragically.
The learning curve of this video:
- Water is wet
- 1+1=2
- Compute the meaning of life
- Draw the thermograph of Oof
when I first started watching I assumed you had pulled that last line out of your head to be funny. it was funny! but by the time I reached the end, Oof
@@laurenpinschannels yep, me too
I scrolled down to the comments after we got to "up", saw this comment and went "haha - exactly!"
I was not prepared for "draw the thermograph of oof" to be literally relevant
The mathematical hubris I have just fallen victim to is pain
The meaning 9f life is this video
@@akkronym48 Tell me more about pain, does blue or red win? Neither?
rewatching this masterpiece after the new patricia taxxon video. rest in peace owen, you gave us one of the best videos on this whole damned platform
It was crazy hearing her talk about this, then going to the video and remembering I've seen the whole thing
what happen to own
@@382Misnothere He committed suicide 4 months after this video was released, you can an obituary by googling his name.
@@382Misnothere He unfortunately made the decision to leave and take his brilliant mind with him. He will forever be missed by his close ones and also thousands of random math enthusiasts on the internet. Rest in peace Owen.
@@Dalrocwait leave TH-cam or leave the earth?
Came back to this mathematical masterpiece for a second viewing only to discover that Owen has passed away. While I didn’t know him, this news is still a punch to the gut. I love maths and this video is so inspiring, shedding light on some greatly underrated work in the field. I don’t know what Owen was going through, but it makes me think back to my own struggles with mental health and suicidal ideation, some of which continues to this day. I’m glad Owen was able to leave a positive impact on so many people, including with this video. I like to think that Owen was able to inspire and create future mathematicians with this video, as he has definitely inspired me to keep going further. I hope his family is doing okay and handling the loss well. Owen, you are an inspiration to many, through your music and this beautiful video, it truly is one of my favorites.
Oh goodness. How did you find out he had died?
@@SimonClarkstone I found out by looking through the comments here and on his other music channel. I believe his mom, Rohan Maitzen, also confirmed that he had died on December 30th. I didn’t find out about this until my second viewing of this video.
@@AReformedCatholick what did he die of ? , I hope he can rest in peace and sorrows to all his family.
Oh dear. I was just going to suggest that this is resubmitted for #SoME2. I was hoping that Owen might have released another "book review" which I had missed, because this video is just so good. Definitely inspirational and I hope that it influences countless future mathematicians and ponderers. As far as I'm concerned, Owen joins these greats with this contribution to the world and will be missed.
at least his life didn't go to waste
We have a tradition in my family of watching documentaries together, i watched this twice and was so enamour i convinced my family to see it with me, thank you for a great memory and a new wish Owen, and rest well knowing you showed at least 200 thousand people the beauty of math and little games to overthink.
"A branch is a branch, you can't say it's a half" got a solid laugh out of me, wonderful
The background music with it is what got me
I didn't hear the music on my first watch, that was great
As soon as I recognized the piano piece I had to check if Bismuth was credited. Nope, does it himself, too. Awesome!
How does this keep showing up. Just a few days ago i watched another education youtuber in a video about electron spin, and they did it the same joke. I can't believe there's so many people that all know the same video. Then again, given that they're all math and science people and it was a very technical video, i'm not too surprised
I’m beginning to think the math, conlang, and pannenkoek communities are really just the same community
Ok people are finally seeing this, excellent. One of the truly essential videos on this site imo.
I just came from your video and I’m going to watch this now. 12 tone and this sort of thing
Thank you for your art
Thanks for raising awareness of this, Patricia
ive been putting this one off for a while and your video caused me to finally watch it, thx so much
I remember watch this video when it came out. Coming back to it is quite the trip
Rest in peace, Owen Maitzen. ♥
Rest in piece, Owen. I never knew you, but this video put real delight into my life for whatever that's worth. Your appreciation for beauty and whimsy in equal measure was a bright light to me, and you helped me understand the love I hold deeply for math. Thank you, and godspeed
@Scuffed Physics I am Owen's mother and I am very sorry to say that he died on December 30.
@@rohanmaitzen9033 His memory is going to live on. I'm a professor in Nebraska, United States. I'm implementing his views on math from this video in a course that I teach to hundreds of teachers, some of whom will undoubtedly teach their students. I hope he's doing some amazing math on the other side.
@@rohanmaitzen9033 I am so sorry for your loss! Rest in peace, he was an inspiration to many, and I wish the best for your family!
Rest in peace Owen. This was a truly brilliant work, and we're all sad to have lost you.
man, coming back to this for a fourth watch or something, i did not know owen had passed away. thank you from the bottom of my heart for this little gem i adore and all the other things i never knew you for. rest in peace.
Amazing video! The perfect mixture of approachability and depth. I know they're a lot of effort to make, but I'll definitely be watching if you make more :)
agree
What are u doing here I love your work also
I'm frequently surprised to see your comments on low-view-count videos. Have you considered publishing a list of channels you recommend?
This verified comment is going to blow up.
@@raconvid6521 And yet it wasn't to be
This video brought back some happy memories!
When I was in Grade 9, 1978-79, I was in a math club lead by Richard Guy. (It was for participants in a city-wide math contest, which I had won.) Attendance dwindled to just him and myself, and then he began to introduce me to what he was working on with John H. Conway: they were writing Winning Ways. So I learned about Hackenbush and other games, the { | } notation, defining integers as games, * and ↑ and so on. He also mentioned the "Bűvös kocka" of Ernő Rubik. I bought a copy of the 2-volume first edition of Winning Ways when it was published.
Prof. Guy also taught a calculus course I was in, in 1982.
that sounds amazing. grade 9 was when i first learned this stuff as well, it really is a surprisingly accessible topic that is perfect for a math club
i'm jealous that you got to spend so much time with guy - he seems like a great guy. also a prolific chess composer apparently!
@@owenmaitzen339 rip you. you had a great mind
@@owenmaitzen339rest in peace, fly high
YES.
THIS IS THE ESSENCE OF MATHEMATICS.
I WANT TO BUY THIS BOOK NOW.
Same here! Too bad it's so expensive 😕
@@colinpitrat8639 Won't sail the 7 seas?
@@colinpitrat8639 Also be aware that there are cheaper versions that... print the book in BLACK AND WHITE... don’t fall for them, they’re basically scams due to incompetence of the publishers
@@colinpitrat8639 openlibrary!
This video has really touched me, one of if not the best math video I've seen. Rest in peace Owen, you've left behind a true masterpiece.
I've watched this video three times and will almost certainly watch it several more. I only just noticed "on plus on - holy hell" this watch through.
I love the Mario 64 music slowly creep in when he mentions the “1/2 A press” of the red branch.
Oh my god I can't believe I didn't pick up on that in my two previous viewings of this video! That's just amazing.
So sad to come back for a third viewing just to see that Owen is no longer with us. This comment helped cheer me up. What a brilliant guy he seemed to have been.
RIP Owen Maitzen
John Conway had such a lovely sense of whimsy. This is the best math video I've ever seen. RIP Owen.
Whimsy is detrimental to the fundamental seriousness of mathematics, and also quite unimportant in a very, very large chunk of contexts. I'd know, I'm a mathematician. It's nice you care, but people would only really *respect* him for his work in group theory.
@@Gordy-io8sb nice bait
@@thezipcreator What about my comment is bait?
@@Gordy-io8sb why even do math, at the end of it all? if not for a little bit of whimsy?
@@eshansingh1 For recognition? For academic achievement? I mean, I'm not a PhD, I'm an autodidact, but I still value academia quite a lot. But that's besides the point. People do mathematics both for recognition from others and to advance human knowledge ultimately. Sure, you can take creative liberties when developing mathematical theory (like Conway, Berlekamp, and Guy did with combinatorial GT, which is arguably the worst branch of mathematics ever created), but that won't really matter all that much. Thanks for coming to my TED talk.
pure delight at the reveal that "over" stunningly is less all the positive surreals, as crazy as they are, but then manages to be *greater* than the already introduced up series... what a wonderful video, with wonderful pacing and storytelling. thank you for making it.
The “Down the Rabbit Hole” section reminds me of the descent into insanity at the end of Tantacrul’s video where he reviews Sibelius. Or his review about Dorico.
That's exactly what I started to think about too, especially with the distorted voice pitch moments.
Sibelius crashed
@@txikitofandango Add up and down
Sibelius Crashed
Find the Thermograph of oof
Sibelius Crashed
Cut away a branch
Sibelius Crashed
the comment section beneath this video is a perfect representation of my interests... have we been living the same life, lads?
Alternatively, Oliver Lugg's video on unhelpful category theory facts
completely and utterly speechless. This is the most well thought out, elegant, genuinely informative math video, (if not video in general,) that I've ever watched. It feels as if this video encapsulates my passion for mathematics in its purest, maximally concentrated form. Mathematics, in essence, is about playing games with the universe itself. I am awestruck with the profundity of it all, not to sound melodramatic by any means. I say this with the most heartfelt and genuine thanks that I can give, thank you for making this video. Rest in peace.
"Throw away Cantor and submit yourself to Conway" sounds like a calling of a religious cult, but those are usually less crazy than this
Ever heard about Pythagoras?
@@FlorianWendelborn He wouldnt let people sit on certain size stools
If you read Donald Knuths book on surreal numbers Conways rules are presented as a religious relic
Gadagadegada aaa oooo
It’s such a sad shock to hear of Owen’s death. Owen, you and I never knew each other, but you touched me, in your own small way. I just so happened to come across this video, and was blown away by the math, yes, which is amazing, but also the MUSIC! I’m also a composer myself, and after finding your music channel I listened for quite a while to your improvisations, which I found totally enrapturing and inspiring. You seem like you were similar to me in a lot of ways, and definitely the kind of person I would’ve liked to have known. A lot of people miss you. Rest In Peace.
how do you know he died?
Listening on spotify. Thanks for sharing I love piano and this is great!
Brilliant reference at 6:23 -- not only are you referring to the "0.5 A-presses" joke, but the notes playing at this part of the video ACTUALLY play the Title Select Theme from Mario 64.
Bravo, holy cow.
The video is full of little things like that if you look. That one was my favorite, but I also like "on plus on ... holy hell"
@@BrightyLighty_ yoo a fellow ii fan
@@jan_Eten mi jan pi toki pona kin!
@@BrightyLighty_ tenpo suno ni li epiku a!
Quality standards for maths content just got surreal. From sound to animation, the presentation is as polished and sharp as one would expect from but the best maths TH-camrs out there; the flow of topics and pace of explanations are just right; the subject itself is immensely enthralling and your exposition more than makes it justice. This essay leaves any mathematician in an excited position for more, I will probably rewatch this ω times until someone (hopefully you) explores the colon principle in a follow-up.
I love how a community spontaneously formed, filled with silly surreal math jokes-- great comment!
When I got to 44:00 and heard "You can dive headfirst into the world of on, off, dud, over, under, ..., upon, hot, ono, ...", I couldn't help but think... "oh *no* indeed"
--
But yeah, this is incredible! I feel like every 5 minutes I've only been playing in the kiddie pool of numbers compared to the universe coming up.
Wonderful, wonderful, wonderful video! I can't imagine a better introduction to all these concepts. Thank you very much, Owen, and rest in peace.
i have to admit that 53:54 actulally got me laughing at a maths video just because of how absurd and mind bending it had gotten at that point
I'm at 19:32 and I checked it out for a second and what??? Lmao
This is sincerely one of the greatest video essays on this platform and it's a crying shame that it doesn't have more views, and an even bigger tragedy with what happened with Owen.
You already know this, but this is beautiful. Thank you so much. This video makes me want to be better at pursuing the things that fascinate me and presenting them to the world. And to be a better pianist.
Even if you never produce anything like this again, this will remain one of my favourite channels.
Thank you glimbo, I hope you continue pursuing the things that fascinate you. I was inspired by this video as well and I hope many others continue to be inspired too.
I think Grant needs to have some kind of "Honorable Mention" list for things that were inspired by his SoME1 challenge, but did not get included for whatever reason including missing the deadline, but was made known (if not actually released or draft-released) in time for his wrap-up and postings about it.
And it did!
This is a really good video!! It's filling the Vihart-shaped hole in my heart -- perhaps not stylistically, but in the sense of exploration and mathematical play.
I've always been somewhat confused by the surreal numbers, but in their original context of game theory they seem not just useful, but completely natural -- of course they're defined in terms of what they're less than and greater than, because in games that's often all you can tell. It gives a lot of motivation to their definition, which in turn really helps me understand their behavior.
Also, the music is really great!! It reminds me a lot of Untitled Goose Game, not just stylistically, but in how it seamlessly ebbs and flows to perfectly match the video. Really good job with that, it's so good
Yes you are 100% correct!!!
I have nothing to add but this is a great comment and I wholeheartedly agree
Not to mention the Surreal numbers kinda' expose religiously devoted finitists as doofuses.
This video is amazing. The wonder, the confusion, the discovery, the humor, it's all perfect. Your passion for maths is contagious, hopefully thousands of people will see this.
i took a combinatorial games course last year where we explored our way through the surreals and this is an absolutely incredible video, captures a lot of the coolest stuff in the basics of combinatorial game theory. genuinely one of the best math videos ive seen in a long while
Thank you for this video!
When I was in highschool we were tasked to write a short (10 to 15 pages) "paper" to prepare us for university. I chose surrreal numbers as my topic and spent almost a year with Conways work through On Numbers and Games and lectures of him I found here on youtube. I wasn't in a good state of mind at the time and didn't put in as much effort as I wanted. But still during this time I gained a deep respect for Conway and he became somewhat of a mentor figure for me and someone I dreamed of meeting in person one day, knowing full well it was quite unrealistic. So when I heard he died from covid last year it felt like a personal loss, as I lost this little dream of meeting him one day. All of this just to say thank you, once again, for this video, as it is a wonderful homage on the work of these men and some of the most beautiful mathematics I ever encountered.
i love the pannenkoek reference with "a branch is a branch, you can't say it's only a half"
This video finally explained to me what Conway was saying in one of his lectures when he said that using his surreal notation you can create numbers that are neither positive nor negative but also not a zero.
This video is incredibly well-executed from start to finish. And for a first(?) video essay, too! Really stupendous work. If you do choose to make more of these, I'm sure you'll excel. And if you don't, well, you can at least rest assured you've made an all-time classic.
P.S. If you haven't seen them, I suspect anyone who enjoyed this video would enjoy "30 Weird Chess Algorithms" and "There Are 48 Regular Polyhedra." Same vibe, same vein of hyper-niche but obscenely funny math lectures.
Edit: Just learned of Owen's passing. It is a tragedy on many levels. Take care of yourself, whoever you are that's reading this.
This is exactly the intersection of math, philosophy, art, game theory, and dumb pannenkoek references that I needed. Even if you never make another video, know that this one was absolutely enough.
More is welcome though ;^)
@Scuffed Physics Which part? Did he make a new video?
@Scuffed Physics Shit...
"hours of chill piano improv to relax slash study to"
lol the deadpan humor never stops and-hold on, that was all original music?!
You pulled a sneaky on us; this video was actually about adding songs to my study playlist with Vihart's Pi Day improv! I like how it's a similar vibe, calmly philosophizing about math memes...
Speaking of, 2:03 isn't the Loss meme, but now we can rigorously define it :P
This might be my favourite math video ever. I've watched it 3 times now and I've just decided to order the book.
I'm extremely thankful to you for doing this, you legend. I don't know you personally but I really hope you're having a good day when you read this❤
he committed suicide last year
@@zero_wing_ Holy shit, you're right...
Man that's awful...
@@driesvanheeswijk1633 the dreamers leave the rest of us to suffer in this hell called life. It is very sad. Very very sad.
This video feels like it was handcrafted for me, and what it beautiful craft it is. Made me rethink math as a more joyful, artistic pursuit.
RIP Owen
The more i watch the layers of greatness this video builds and finally in the end it turns out its just an unpaid advertisement for some obscure book, that better believe that I am putting it on my wishlist.
Wow, really enjoyed!
Imma be honest. This might be my new favorite math video on TH-cam. I love how playful everything is.
yeah up ðere wiþ *there are 48 regular polyhedra*
@@jan_Eten that's a really good one too. I watched this vid when i was in a rough spot and it really brought me back to those old vihart videos. It really makes math feel like this world of endless possibility.
Definitely one of the best recreational math videos I’ve seen on this platform. Incredible stuff!
big chungus!
I suppose for computer mathers
Man I gotta make a comment on this video
I first heard about combinatorial game theory on Discord, with a message that mentioned the confusing terminology introduced by the original mathematicians that's kinda just stuck
Then today (which, for the record, is 2023-12-22, or 2023 December 22nd in a more readable format that I totally didn't just make up), I was watching TH-cam, and somehow I ended up in the niche of long math-y video essays, and so eventually I ended up here.
I watched the entire thing, and I found it funny, informative, and just plain wild at times - particularly the comment about the "wordbuilder's almanac", which I took note of and found very funny indeed because of my interest in conlanging (which may or may not be diminishing in favour of Scrabble nowadays? I honestly couldn't say.).
Anyway, after watching it, I read the comments and discovered of Owen's passing. This struck me in a way that would be impossible to replicate - in that the thrills that I experienced watching the video were turned somber. But my point is that this was an amazing video - I loved it, and I'm absolutely certain that many others have done and will do as well.
If you're the sort of person that reads comments before watching videos, and you're reading this, then please watch this video. I beg you. It is possible that you will be delighted and horrified in many different ways that I'm not exactly sure how to put into words (because I'm no good with words, so please be forgiving), but I promise that you *will* enjoy it. :)
Thanks for watching my Ted talk ig - now go watch this video! ;)
I first watched this video shortly after it released and I remember having loved it tremendously. As I was re-watching it today, like you, I found out about his tragic passing. The day of you watched and posted this comment happened to be my birthday. The video is truly a masterpiece and I'm happy we agree on that. Peace ✌
@@rafaelarevalo8047 The day I am reading this comment of yours happens to be mine too :)
three years later, it's still a masterpiece without peer. this will always be your legacy, owen: introducing hundreds of thousands to a unique and distilled form of joy and wonder. RIP
I am positively blown away by this video. Never have I felt so close to the brilliant mind of Conway...not even when he has explained it! Bravo^omega!
Bravo^ω
This is a very valuable video, thank you very much
By far the best SoME video IMO.
Thank you for the legacy left with this presentation masterpiece, RIP. I'm a mathematician at heart and would have never learned about the work behind Winning Ways if not for this video. I will surely buy the book now and can only hope one day I can pass along the curiosity to my family. Glad to see views racking up recognition, crazy that Owen is gone just 4 months after this release.
Absolutely stunning video! Definitely confused with any best TH-cam videos one could imagine
Good thing there's math students spreading the word :p
Amazing video! Thank you for sharing. RIP sir.
Possibly the best video on TH-cam
At 6:22 the piano starts playing super mario 64 music as you make the 1/2 a press joke, you are amazing
this is oh so insanely good, probably the best advanced math educational video ever produced. Please do more
Please, I beg you, Continue making videos like these from time to time, they are the most absolute delight
Thank you, Owen, for this video, which is not only about Hackenbush and combinatorial games and a book review but a love and passion for math.
The best vídeo ever made about it!!! And its your first vídeo! This is surreal.
This was incredible all the way through, from the animations, to the explanations, to the background music that somehow always fit the topic. Awesome!!
This completely blows my mind. And when they sneaked thermodynamics into it I almost fainted. I mean, what the actual...
My sincerest thank you! This is likely the most beautiful video I've ever seen.
This… is probably my favorite video I’ve seen on TH-cam. I’ve been trying for a couple months to find someone who wanted to play around with surreal numbers with me. You just showed me how much deeper this world goes, with an absolutely beautiful piece of work.
Thank you for making this. I loved your music as well, I will go check out your other channel now.
Thank you thank you 🙏 ✨❤️
This is super inspiring to see a TH-camr make a very high quality math video of their chosen topic without being an established mathtuber. Great work and I want to do the same.
What an incredible video. I'm just lost for words. Every math teacher should make sure their students see this video. How could you not fall in love with numbers after seeing this.
This video deserves the world.
This might just be my favourite maths communication video ever. Playful, presents a topic that's lesser-known in popular maths, and easy to understand. Great work, I'll definitely be reading Winning Ways soon.
Maybe it's just because It's 2am and I've had a long day, but finding out Owen is dead filled me with so much sadness and anger that I broke down crying. I just finished watching this whole video straight for the third time, I was in adoration of your work, thinking that it may well be my favourite video on the Internet and now I find out you killed yourself? This is so unfair, my friend.
You were even in Earth Strike like me. I can't even express how devastated I am.
Rest in Peace you beautiful soul.
💔
Bravo! One of the best math/algebra videos I've ever watched!
This is now my favourite math video I have ever watched. I even remember looking up surreal numbers before and not really understanding them, so it was a pleasant surprise to find out midway through this video that this is what the video was about all along!
Brilliant. I just wanted to check the first minutes quickly but couldn't stop watching it in one go. Amazing effort.
Same.
it's unbelievable that this is your first video, it's just so good, if you make more of them I'll certainly watch
You have literally launched me into a stratosphere of math. Thank you so very much!
This video was simply mind-blowing, and by far my favorite video from the Summer of Math Exposition contest! Not to dis any of the other entries, but I can't fathom how this wasn't selected as the overall winner. Congrats on a stupefying feat of math exposition - you captured precisely what it is that makes mathematics so wonderfully strange and beautiful. I am forwarding it to everyone I know!
Great vid. If this is your only math vid, you're certainly going out on a high note
words cannot describe the feeling you gave me with this video , Owen. I am a silly little year one CompSci student and Ive never been this excited to learn something. Thank you for this beautiful piece of art that is this video. I want to get this book as a christmas present.
I got it as a Christmas present last year because of this video! I love it so much… best gift I’ve ever gotten, and I’m excited you’ll get that thrill too come this December. It’s definitely not the type of read you do on public transport… it takes serious concentration and note taking, and it definitely requires effort for you to learn the material, but that put in effort makes it super rewarding. I’m glad that even in his wake, Owen can share his beautiful outlook on math and inspire others like you and I to pursue the whimsical in the academic. Rest In Peace, Owen 💛
Quicksand is the perfect font for this style, you really nailed your visual style 100%! This is pure art, mate. Congratulations!
I just saw his obituary. Rest in peace.
This is the video I'm going to share when I try to explain what mathematics really are.
Thanks for making this video, for surreal
This has to be one of my favorite educational TH-cam videos I have ever seen. Hats off to you!
The way you planned this whole video out ended up being genuinely poetic! Really really great job!
This video is a masterpiece in every way.
Once again this video popped up in my recommended. While I didn't watch it through this time around, like the last two times, I just had to come here and ventilate the vast feeling of sadness that swept over me.
Rest in peace Owen.
this is an amazing video and a fantastic intro to game theory, combinatorics AND surreal numbers, all in one! thank you so much!
Hands down the best math video I've seen in a long time, it'd be a shame for this to be the only video you make in this field given your clear talent for scriptwriting, animations, and overall enjoyability. That being said, if this is the last math video you make, thanks for making it such a good one; I definitely plan to return for at least a couple rewatches later down the line. Awesome stuff!
I keep coming back to this video, I just love it so much. It's incredibly effective at helping the viewer understand whats going on and it preserves the playful tone of the original books. Fantastic work!
Incredible video! This deserves at least 10^7 views.
You have created something truly beautiful, Owen.
This is one of the best math videos I have ever seen. Thank you
Thank you so much! I never got into hackenbush back in the day but the cluster around zero is incredibly fascinating like spinor rotation over an infinitesimal
Rest in peace, Owen! You made something wonderful; I can’t thank you enough. I never knew you, but I wish I could have.
how do you know he's dead?
@@tmplOS his obituary is publicly available
@@bnuuyliker thanks.
Ohmygoodness someone recommended this video to me and I'm so happy I watched it. I haven't laughed so much about math in so long, whilst also learning so much. This is so awesome and I would love it if you made more videos like this. I am immediately subscribing and I'll recommend this video to anyone I think would like it. Thank you so much.
One of the best videos ever uploaded to this platform, regarding math or anything. It almost feels like numbers such as star or up are representing values extending into a dimension that doesn't exist on the number line (like the y axis, the thermograph). Kind of a quirk of the fact that you only have positives and negatives to express something that has more than 2 "directions." Makes me wonder what math would be like if there were more than just positives and negatives, like super-positives and negatives way out past omega, or neutrals within zero.
I absolutely adore this video! I love how it gets crazier and crazier till a point where I gave up trying to keep up and just enjoyed wherever it was going! You have a great knack for organizing content and I hope you continue to make videos!
16:43 That transition from stars to dots is SICK holy shit
I love this video!! Such interesting concepts, love it. Never knew previously of this application of abstract algebra to game theory, and it really embodies the playfulness that makes mathematics fun!
Excellent video. When I started watching I thought it reminds me of surreal numbers, and then Boom! This is the video you want to keep for retirement and then to watch again and again.
Hi Owen:
Thank you so much for making this video. I started reading Winning Ways myself after watching your video, and I'm absolutely fascinated with everything about it. Thank you so much for introducing me to CGT and surreal numbers.
Owen's dead, man. He committed suicide in December.
Holy moly, that's a way to make a video about that subject. At first, I didn't know at all what I'm into, it just presents to you as a video about a fun little game, and usually a bit of mathematics on the side. And here - that curve was fascinating. How you kept us engaged, stimulated our curiosity to learn more and more. Your introduction into that point of * (star) was amazing.
You first forget about everything else and talk about the game. Then, introduce the rest in a logical way, very easy to understand. Again, holy moly, that is incredible. You understood everything about didactics, and the art of teaching to the network of nerves inside our cells, by providing and attaching to something relatable first, so that the network can easily grow from there, more than most professors I've ever met. The current way of introducing dry mathematical structures first, is the wrong way to teach. Brains don't work that way very well. Isolated forms of knowledge are very hard to keep within the network. Each and every relatable connection increases the chance more and more, that the knowledge is easier to learn, and remain within the network. That's why every person in an educational position should know: Always start relatable and build up a framework first, that facts can later be connected and attached to. Isolated knowledge doesn't work well for learning.