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Wrong Turn on the Dragon - Numberphile
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- Опубліковано 15 сер 2024
- The legendary Don Knuth on the Dragon Curve and learning from his mistakes.
More links & stuff in full description below ↓↓↓
Reddit discussion: redd.it/2qt0f4
More Dragon Curve: bit.ly/DragonList
Don Knuth's book "Selected Papers on Fun and Games" has an excellent chapter going into this in more detail.
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Thanks to Erik Stens for helping out on this video.
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That's just the cutest thing ever! him and his wife creating this giant custom built dragon curve mosaic and even putting their signatures in… I guess the two of them are one happy geeky couple :)
There's no wrong turn. Don is just remembering incorrectly which end is the starting point.
His tiles are correct.
That's awesome, we should let him know
Yes, the middle turn is the only turn that is not symmetrical.
It seems that Don thought that he had made a mistake but it turns out the only mistake was believing that there was a mistake :D
I checked this using a screenshot from the video overlaid on a computer generated version. You're right, it's an exact match but just rotated 90°. I'm guessing he knew this and wanted to sneakily point out that flipping the 9th fold creates a rotation of the whole pattern. Mathematicians!
@@patrickbrown7438 This is consistent with every legend I've heard of Don Knuth.
It's always nice to see great men who also seem to be just as nice in person.
His wiki page reveals that he is a really interesting person - having applied himself to so many fascinating projects.
James Fernance It's also nice he's so open about this mistake.
Adrian Fisher He's probably not so nice if you break into his house and ask him a question about whether to use zero- or one-based indexing :)
Games14159 how would you know that?
His books were kinda intimidating; rappelling down through his skylight seemed like the best option.
Or that's what I'm assuming
Do you guys really understand what a freaking genius this man really is? My children and their grandchildren will read his books, and hopefully their great grandchildren will as well.
IT's Surreal
He wrote one of the seminal works in the field of computing namely The Art of Computer Programming. I studied it at university in the '80s and still remember quite a lot of it.
Enlightenment Aren't your children's grandchildren the same as your great-grandchildren?
Almost no one outside of computer science would read this guy's TAOCP.
Joshua, he didn't. At least he's not finished yet… ;-)
Fun Fact: YOU DID NOT ERR!
It is a valid dragon curve but 90 degrees turned. That's the same figure as if you'd do the last fold in the wrong direction.
He certainly errs less!
Holy moly... This is the same Donald Knuth of The Art of Computer Programming fame!
Spot on about erring, but less. And a great object lesson on the matter.
And of TeX fame of course. Yep, the one. I'm also fangirling out about Brady having visited him :)
Yes this is our legend! Holy cow the world would have looked different if it wasn't for this guy.
Brady is moving up the ranks ;) No smart person on this planet can hide from his camera!
Niosus "Holy cow the world would have looked different if it wasn't for this guy." I shudder just to think of it! We would have _horrendous_ full justification with huge and irregular blank spaces between words .... wait.
fleeb A living legend indeed! Although I'm embarrassed to say that I'm more familiar with TeX than with TAOCP... It's mind-boggling what some guys can do _while taking a break from the "serious" stuff_ (Knuth with TeX, Torvalds with Git etc.)
Penny Lane xD
I love the way the poem is mentioned and discussed at the start like a warm up, but then comes back to wrap the video up. Great work numberphile, lovely video.
I discovered this as a kid when I stole a whole roll of bus ticket paper and started messing around with it. When I realised it started to make a more complex pattern the more I folded it I then cheated and did the next few steps in MS Paint.I had no idea it was a mathematical thing that had a name until I got to university.
So basically his artwall and that writing on the wall say the same thing. Maybe it wasn't an error after all.
But if it was intentional, then it wasn't an error which means that the intentional meaning is lost and both artworks promptly vanish in a puff of logic. ↯
Aryan Arora You are starting to way overdiscuss this joke ;)
Party over
Wow beautiful ending
I can't believe this, my idol made a mistake. Don didn't make a wrong turn, so his conclusion about it is wrong! Take the image at 6:10, rotate the dragon 90 deg CW, and it will be exactly the red appearing curve. If Don had mistaken anything at all, it's swapping the begin and end of the curve.
+ZomB1986 wow... youre right
+ZomB1986 Ya, I noticed that; it would mean that the start and end would be switched, but the one on his wall doesn't say which is the start or end, so I don't really feel like that matters.
+Ella Jameson amusingly, a work is normally signed at the end, so he got it more "right" than he intended!
Wow! I didn't even notice.
You could say that it's their journey together and where the signatures are is not the starting point but where they are now...
Respect, this guy is the K in the KMP algorithm.
Hell Yeah!
So you just glance over TeX?
Also the K in the RSK correspondence.
KMP is a trivial algorithm to be honest, there are better things he has accomplished.
Umm, yeah... like the whole Art of Computer Programming series of books?
that was a very nice story, i like how in the end you realize both of those pieces of art work together, as apposed to in the begining you think one conveys our process for figuring things out and the other conveying the precision of mathematics.
That ending was brilliant! I love when I hear a story and the end hits me like a punch in the chest.
Hey Brady, you should ask Don Knuth about 0⁰! He wrote an article “Two notes on notation” explaining (among other things) why 0⁰ is defined as 1, rather than undefined like your “Problems with Zero” video claims.
Don Knuth is an absolute genius, I'm so happy you got a chance to speak with him. I can't wait to see more videos with him.
Thanks for everything Don Knuth. Wrote all my ten University semester assignments using TeX and LaTeX. Brilliant!!!
If the world was made a bigger deal of people like him, there probably wouldn't be wars. This man is so peaceful and calm and intelligent, that it's a shame that i've come to met him only through youtube.
Awesome to finally see this guy speak after putting dozens of hours into an essay on him. Keep up the great work Brady!
Great story! The mistake gives it a great character.
Wow, what a treasure. Beautiful gesture by the folks at Heath Ceramics as well.
There is no error!! If You rotate the whole "correct" structure by 90 degrees counterclockwise you'll end up with the "incorrect" structere. Then you just have to switch the startpoint with the endpoint
I love Don Knuth! Can't wait for more. You should all watch as many of his christmas lectures as possible. They are amazing!
How is this wrong? Yes he made 1 wrong turn but making this turn "correct" actually just flips the entire thing by 90 degrees. If you compare the 2 versions, the "wrong" one and the "right" one, and just rotate the right one counterclockwise by 90 degrees its identical to the wrong one.
Flyfunner it's*
The wrong turn is in the middle of the curve so only half of it is flipped.
@@bscutajar It's still a correct dragon curve. Use an editing software to rotate the curve and you'll see its a perfect match
Omigod Don Knuth. Omigodomigodomigod. I'm gonna go re-read "Concrete Mathematics" all over again.
What, did you expect "The Art of Computer Programming" joke? It's Numberphile!
Yes! Great to see all these legends appearing on the channel. Can't wait for the next videos :).
Wow I wasn't expecting this living legend here, what a nice surprise ! Can't wait to see what comes up next featuring this code divinity
Oh yeah, this is the video with the toothpaste streak!
I clapped at the end of this video... wonderful delivery, both narratively and visually!
I am fortunate to have been friends with Bill Harter and the late Jack Heighway for over 40 or 50 years. They share the same genius and the love of science and math as D. Knuth. I was happy to accompany Bill Harter to a lunch with Martin Gardner (equally charming, btw) at which this, and other fun effects and phenomena were discussed. Episodes in my lucky live.
ART OF PROGRAMMING!! OMG! THIS IS SO AWESOME THAT YOU HAVE HIM ON! THIS MAN IS TRULY LEGENDARY!
This is such a lesson in humility. If a genius like Don Knuth can make mistakes and admit to them then I have no right to hubris of any kind.
I had to check if this "Don" is Donald Knuth, that Donald Knuth. Boy he's a living legend, I have 2 books that he (co wrote) and that guy had huge impact on my education. A living legend.
YAY, so excited you're going to have Knuth in your videos now! So freaking excited!
The way those two pieces of art are linked is awesome. It's better having the error.
It comes often in human history that 'mistakes' often turn out prettier than the right thing.
Golly, I could sit down for a decade and pick his brain, never getting tired.
Gotta love the fact that my phone alerts me to random videos, it lets me be in the under 301+ club and be one of the first to comment! XD
Also my comment has the first like and first reply if by me!
Good day! Tell your friends!
You can configure these notifications, but not in the mobile app. You can on the main UA-cam site
+Jamie Den Adel I probably will after Christmas break is over I'm a seventh grader with only a few real friends that live a couple of miles away from me.
+Harm Prins Hmm, I didn't know that, I will definitely check that out, thanks!
Also I can't believe I'm top comment after an hour and 60 comments! This is one of the first times I've ever commented other than to reply to other comments so this is very cool!
I was taught AP Calculus AB by his son, John Knuth. Needless to say, he was a great teacher.
I'd like to comment on this. But I can't. There is nothing I could write that would feel right on a video featuring Don Knuth. You are so privileged to have met him. Regarding the dragon, if there was an error (which is not certain according to some comments), it would make this even more a work of art.
Knuth has an obsession with dragon curves too? I had no idea! I have a folder of them I drew in high school. Incredible.
Donald Knuth is A BIG GENIUS and A BIGGER HUMAN BEING!
Great Donald Knuth! Thank you for creating the powerful LaTeX. I have written my academic life with it!
Finally I understand the chapter heading pictures in Ian Malcolm's Jurassic Park...
Oops, I meant Michael Crichton, not Ian Malcom. Still, it's a pretty cool design
@@silvariuscoyote > Freudian slip! That pose (in the movie at least) is the most iconic thing perhaps from the entire decade of the 90s
Imagine if Bruce Lee came around for dinner and, as he walked through the door, Don said, "Enter the dragon!"
My most enthusiastic laudations to Brady and long time daunting inspiration Don!
Really brightened a dreary morning :) Wisdom reaches me with numberphile as much as knowledge.
The Legend: Don Knuth. He is one of the people that got me interested in doing software engineering. I owe a lot to him.
1. @1:15. Dragon curve to our left (think it's on their right) 2. Piet Hein is a well known Dutch hero and sailor
Genial! Can I replicate with or without mistake, maybe only three or four iterations at most!
Great ending!
True art is rarely found in absolute perfection but usually where happy accidents happen.
Geeze Brady. Thanks for having Don Knuth on!
Fun fact: Grook, or Gruk in danish, is a word invented by Piet Hein. The word is a contraction between the danish word for ugly (grim) and beautiful (smuk). Grim + Smuk = Gruk or Grook in english.
If you turned the new dragon counter-clockwise 90 degrees its the same as the original isnt? So maybe he didnt screw up the dragon but forgot where he started maybe
jacob fife it's*
@@JorgetePanete You really don't have anything else to say, do you? Also, you correct "it's", but not "don't" and isn't"? How inconsistent, you're useless even in your self-satisfiying cmments.
@@RealLifeKyurem Where I live we call that "mucho texto".
@@JorgetePanete From where I live, what you're doing is called "saying something because you want to feel smart".
that ending was perfect
This is going on the list of things I'm definitely going to make, but will never get around to
The curve on the wall is still the correct shape, just turned 90° so that the piece with their names is actually the end and the other one is the start, so it doesn't really seem like that big of a deal.
Oddly enough, it's an interesting take on Chaos Theory too (as all fractals are), as this one tiny change made the entire pattern different.
Brady, I love, how you ask mr. Knuth about his feeling about an error, while having toothpaste all over your face :)
I don't know why, but this almost made me cry.
Well, those wall decorations will stay ewually awesome as long as they stay together. That's a pretty great coincidense afterall.
The 'wrong' curve and the 'right' curve look the same to me, just rotated to the right. Correct me if I'm wrong, but I think they're the same. You'd just have to say the other end was your starting point.
They are the same. Either the graphic is wrong or they're literally Hitler when it comes to which angle the Dragon Curve must be seen.
Having the error makes it unique, and more human, definitely adds value :)
That's wonderful when someone admits a mistake.
That dude freakin' loves life.
I just painted a Hilbert curve on my wall with the inside and outside painted different colors so I had a 0 width line
When will we see a Dr. Grime video again?
I think Don Knuth has an extremely relaxing voice.
Knuth is a legend! Love this guy!
I want to make this in my own home. I also think it would be cool to have a tile representation of Conway's game of life as artwork. Maybe with a glider gun or some fairly recognizable configuration. Mathematically inspired artwork.
At the end of the video it shows Don playing his organ and adjusting a monitor. I'd love to see this extra footage but I can't find it! Does anyone know where I can watch it?
the real guy, the best guy,
don knuth, booyah
After he noticed his mistake I wonder if he sent himself $2.56
I was expecting a presentation on fractals, but this was way better!
What a great story. Don Knuth is a giant.
Very interesting. Piet Hein (Denmark) is my distant cousin, and we share Piet Hein (Netherlands) as a common relative. Just saying. His grooks are some of my favorite sayings too.
I thought he was going to say that the ceramics company suggested changing one of the curves and he said OK to make it fit on the wall :)
Fun fact: Don Knuth’s first published article was in MAD Magazine, a spoof item on the “Potrzebie system of weights and measures”.
Wow, just wow.
Heres a video topic for you: dragon curve numbers - each left or right turn is 1 or 0 and that binary number is converted to decimal.
Because of the title, I thought for a second this was about the maths of D&D!
Speaking of Piet Hein, you ought to do some videos about him and his work...
The brightest minds are artists at heart - Nehad Hirmiz
Narrowly avoided an off-by-one error at 2:15
Fascinating though, despite the error in the picture we still don't see any intersection within the system itself.
Yeah, I was wondering why the bulkier chunks were on the opposite side and not where they always are. I even thought that he had mistaken just the beginning.
Brady, the mathematicians you show are always interesting!
This is really similar to how I used to doodle in college. I had pages of these kinds of diagrams. If only I had Don's knack for science!
I love mathematics-based art. Congratulations on your beautiful, if mathematically-incorrect, work of art!
It´s actually correct ;). You just hjave to flip it by 90 degrees.
I think I have an idea for a future video! Mega!
First, the function: N in an M-agon: N[M]=N[M-1][M-1][M-1]... with M "[M-1]"'s. And now, let's see N in a Triangle: N[3] = N^N.
Now, Mega = 2[5]. 2[5] = 2[4][4]. 2[4] = 2[3][3]. 2[3] = 2^2 = 4. 4[3] = 4^4 = 256. But there's still 256[4]. 256[4]=256[3][3][3][3]...[3][3][3] with 256 "[3]"'s. 256[3] yields a huge number, but 256[3][3] is outright monstrous. Then, we have 254 "[3]"'s to go. You can tell Mega is incomprehensibly huge right now...
Wonderful story.
Don Knuth seems like a pretty awesome guy.
such a great ending
Aww damn Brady, I was hoping Santa was getting you a tripod.
but that is the middle - so the beginning of the folding - the first fold
so the "wright" dragon curve is only rotated 90deg from the "wrong one", otherwise they are the same!
if i'm wrong - show me how?
Maybe you could analyse the properties of the dragon curve if you make random turns. If it's 10% random how much does the curve hug itself? If it's 20% random and so on... Of course a 100% random curve will just go anywhere... unless you're infinitely lucky.
I have Piet Hein's gruks in 7 boks :) Many of Them are very beautifull :)
i got interested in these kind of stuffs thanks to Dan Brown.
The Father of Algorithmic Analysis himself?? Whoa!!