Hello! I'm a musician, coder, activist, and aspiring teacher from Halifax, Nova Scotia. This channel is for non-music content; my music channel is at youtube.omaitzen.com.
I've always been praised for being good at math, but I don't think I've ever actually liked it. For some reason, I've always found it unpleasent to temper with numbers and solve "normal" equations. In a strange way I've been thinking of numbers as too limiting, as if it was made too complicated by unnecessary conventions where they didn't have to be. The thoughts of how 0/0 is undefined or that there are no number that gives a negative when multiplied by itself made me angry. When I first heard of complex numbers, it was in a form of a certain "i" treated like a number, not like a parameter like "x". Initially letters in calculations made me feel worse, I thought of this as more limitations in my mathematics playground, but when I heard that concept explained, I was fascinated. By the age of 12, in 5th grade, barely after they taught us exponents, I was regularly finding myself spending hours upon hours trying to understand the promise of these mysterios complex numbers - like a genie, they offered to grant me the ability to obtain negatives in squares, if I could bear the burden of accepting more limitations that such prepositions would mean. Yet I haven't had my hunger satiated. Not even in quaternions and octonions and more obscure hypercomplex systems - I was happy to trash a+b=b+a like a fever dream - offered me respite. I was by no means a math genius, it often took me hours to grasp the school math. Tempering with functions was exciting, but all the laws of trigonometry, logarithms and integral calculus didn't hit me, they were just expanding deeper into limitations, not taking a look aside like I wanted, like trying to tame infinity and indefinition by treating them as numbers, or inquiring in p-adics or defining numbers using set theory. When I tried sharing my findings and failings with others, I've found no one who understood. Eventually I abandoned this idea of lifting notions and looking for absolutely unbound mathematics - I figured the world is not perfect. Geometry was similarly challenging, but I think it was because it required practise which I didn't want to put in. I've found great interest in physics of all subjects. It brought me strange calm, its calculations had a sense of purpose, were grounded in understanding reality, they at least didn't itch me like algebra, which almost screamed how it is abstract, yet it didn't ever make a push further into its abstractions. I'm now a physics university freshman. Matrices seem great, but I can't seem to find anything but new trigonometry in it, more formulas and properties, pushing for depth, not breadth. This video rekindled my thoughts in that direction. It was the first time in a very long time I've heard someone speak aloud what I was thinking about for years. Conway's works somehow missed me completely, despite all of my searches. His number system is for sure the closest I've been to what I want of mathematics. oof+oof=off? That's mesmerizing! I truly recommend anyone and everyone watch this video and look at this book.
i have an objection to the infinite part where you equate 3*(2/3)=2, the 2/3 there is actually less than or more than 2/3 ALWAYS, because infinity is not an actual number, it lacks specificity, but you must choose a specific number, therefore the value is never actually 2/3, even if the pool of what you can choose from is infinite. infinity as an actual number is known as a floating abstraction for this very reason.
yeah. It's a joke based on the "A button challenge" in mario 64 where you try to complete the game with minimal A presses. In that challenge they started talking about a half A press, hence why he plays that song when talking about a half branch.
I can only add to what everyone has said. This is, to me, truly one of the greatest videos on this platform. This way of conveying mathematics is simply so extremely beautiful to me. I would also add that (apart from the mathematical content, which was simply wonderful) now I also understood Conway's statement of regretting inventing the Game of Life, for it was only this he was being associated with. All this deep, much more beautiful mathematical structure can only come out of the mind of a true genius and artist. Your fascinating video really connected what I had considered to be unrelated ideas. While I do not believe in the supernatural, I still believe that this legacy will prevail and that some idea of post-death impact is relevant to your person. It makes me very sad, both emotionally as a human and academically as a math learner and teacher, that you have not lived to see the true fruits of what you have achieved. Even more so than before, I now know that I will dedicate my life to mathematical (and CS) theory and teaching the alike to everyone.
This is a difficult video to understand, even for people with more math experience. If you took away some interesting ideas from the video then that's enough.
Since you're an art major, hopefully you can appreciate that the comment above is like responding to someone who doesn't "get" an art piece by saying "art doesn't matter and this is just some pretentious BS anyways."
@@zmaj12321 The difference is I'm a hypocrite, because I do like art, even though it's even more useless than math. I'm just a miserable asshole who hates people that are smarter than me.
@@zmaj12321Besides, math is supposed to be like "objective" like, it a thing that you can actually measure, not getting means you're a moron, not getting art just means that you don't get it, as it speaks to like whatever the fuck. Basically not getting art is normal, not getting math is for people who breath with their mouth
you can't represent all games with hackenbush. I don't think tiny can be represented. you CAN represent oof (tiny = {0|oof}) using the fragile branches. in the video a representation of all {n,-m} with natural n,m is shown. for oof={0,off}, just use n=0 and m=on=-off.
14:44 despite this, i still think * is infinity. you could represent the number line as two lines that are like opposite sides of a circle, * being at the corresponding point as 0, and the rest of the corresponding numbers to the left and right. things on the left of the * line are still negative, and on right are positive. [Ok nevermind, after the *2 and *3 and...stuff, i think this infinity anology wont work]
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.
What is the practical use of dividing infinity into infinity into infinity into infinity. I suggest we stick to some level of discrete, for utilities sake.
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.
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.
Im laying here, giggling like a little child because after he said „on plus on“ i thougt it sounded similar to en passent which he acknowledged with a „holy hell“ which is so nieche internet reference im so happy for this being such a little detail
So now I know why he hated the fact that people associated him too much with Conway's game of life! Wow, there was so much other fundamentally interesting stuff he did!
This is the first time a RU-vid video encouraged me to buy a book. Its not one I could get used for 99¢, iits still quite a popular. I'm surprised the surreal physics channel didn't get me here, but you did.
What a beautifully made and fascinating video! I mean, wow, there's a lot to digest here, but you knocked it out of the park. Well done. (Every new thing I learn about John Conway makes me appreciate him even more; may he rest in peace.)
