Can you trust an elegant conjecture? 

Fun fact about Eigenvalues and Eigenvectors: They were invented by a Dutch mathematician, who decided to name them "eigenwaarden (Eigenvalues)" en "eigenvectoren (Eigenvectors)". Literally translated they mean "[The matrix'] own values" and "[The matrix'] own vectors". However, when they were shown to some English mathematicians, something went wrong in translation, and the English thought that they were invented by some German mathematician called Eigen, which is why the terms are capitalized.

I think Matt is the only person who can say "you get square roots of 17 everywhere" and get a laugh. I did laugh out loud.

"Eigen See Clearly Now" cracked me up! Haha, I really love this channel; keep it up, Matt!

I was wondering why you looked at the binary version rather than the classic base-10, so I looked it up. Turns out the ratio of successive terms in the base-10 sequence converges to λ = 1.303577... where λ is an algebraic number with a minimal polynomial of degree 71; i.e. λ is a root of a polynomial of degree 71 and no smaller polynomial, a fact which was proven by Conway.

I think conjectures are like politicians, they have to look good but not so good that you start to wonder if they spend more time on their appearance than their actual political work :)

The real question: is Eigen See Clearly Now heading to Spotify?

I've spend over a decade looking at eigenvalues/vectors on an almost daily basis (for exactly the reason Matt gives at 10:10), to the point that I'd completely forgotten it was something most people have never heard of. First, I felt smug. Then, I felt nostalgia for simpler times. Now, I just feel bitterness and jealously towards people who haven't had the Pauli matrices and Cayley-Hamilton Theorem burnt so deep in their brains that they've literally come up in their dreams.

That first sequence is one of those "so simple it's annoying" puzzles! Great video Matt as always.

Eigen see clearly now... that's the kind of quality content I subscribed for

i am extremely proud of the fact that it took me less than a minute to figure out the sequence at the start of the video.

I'm at a place in my math learning where I was just able to anticipate the next step being eigenvectors, but nothing about how to apply them, so I did appreciate the crash course on them. I'm sure I'll need to learn them six or eleven more times before they really stick

I'm a materials science student, so I've had to deal with Eigenvalues and Eigenvectors a lot. Needless to say, thanks for the segment explaining them! Because I've completely forgotten what they are and how they work-

Feeling a bit proud figuring out the first sequence in ~60 seconds when Matt mentioned it taking him all day. The thing that got my attention was the three consecutive 1's just above the only given '3'. That was enough to give away the trick!

I learnt about eigenvalues/vectors in a 2nd year maths unit as part of my eng degree. Sadly, I have never used them again since. That unit was taught poorly, most of us could barely understand what the lecturer was saying. Your explanation was much better, and an interesting application.

I was so fking happy when you showed the flowchart and I immediately thought of Markow-chains. In highschool, we learned this rather extensively and I was so glad I was able to recognize the application of something I learned just before you revealed it. Idk, it makes me so happy. Edit: loled when you delivered that genius punchline.

Thank you for explaining the use of Eigenvectors and Eigenvalues. My entire maths course in uni never actually explained why we might actually want to find them!

Thank you for the simplest and clearest explanation of eigenvectors/eigenvalues I've ever seen!

6:38 perhaps the greatest moment of this channel so far

Over the course of a couple of minutes you made me understand eigenvalues and eiganvectors better than an entire unit on the topic in Linear Algebra class back in college.

Recognised that sequence instantly. I learned it around a decade ago when I first played Knights of the Old Republic. It was one of the many puzzles they had in that game and I guess it stuck with me since I still remember it to this day.

Would love to see you do a video on the chess cheating controversy regarding Hans Niemann. The probabilities regarding this controversy are highlighted in Hikaru’s reaction video to the one Yosha posted. It might take a while to compile the data you would want, but it seems like something you would be interested in.

Thanks Matt for the opportunity to look at you while you say things looking towards us, helps a lot!

Oh wo that was awesome Matt!! Thank you so much I love your song i listen it at bandcamp:)

When I saw eigenvectors and eigenvalues flash up on screen it felt good remembering what those were from the little bit of linear algebra I did during college. I had a great professor. I kinda wish I had been going deeper into mathematics itself and not eventually shifted gears to computer science. He told us if we took his grad courses he would go into depth about the proof that got him his doctorate. Maybe I'll go back one day before he retires. I'm sure I could look it up but it hits differently when the person who discovered something explains it to you.

Any chance that Eigan See Clearly Now is gonna be released anywhere? 👀 I absolutely love it!

This is proof of the theorem that mathematicians are bored.

It's interesting to look at the binary look-and-say sequences with other starting points. The sequence starting with 0 → 10 → 1110 → ... looks a bit different (all end with 0, of course). You'll still get the same block graph, just without 1 and 11 [which are irrelevant anyways], so we'll expect to get the same ratio of ones and zeroes in the limit. But not every starting point gives such a sequence, for example when starting with 111, we just stay at 111, so the limit would be 0 (or ∞, depending on the point of view). Are there other sequences which don't grow forever?

"eigen see clearly now" omg i'm dying lmao

saw that sequence many years ago, it has been one of my favorites ever since

I stared at the puzzle at the start of the video for like 10 seconds before cracking it, and that euphoric high that came with the realization that I solved a puzzle in seconds, that an expert spent an entire day on cracking, is something I don't think is conceptually describable.

I learned maths in German and for a moment I was like "Wait, they call it Eigenvektor, too?". Maths really is a universal language. :D

As soon as I saw the graph I knew I'd be "blessed" to see matrices pop up. I remember having to deal with a similar problem when I was prototyping a game and ran into a similar problem relating to random walks which turned to markov chains, which turned to eigenvalue shenanigans. Cool math, but not exactly transparent to the people playing the game or immediately intuitive.

Wait when I first saw the title I thought it said "Can you trust an _elephant_ conjecture?" what what would an elephant conjecture even be

Great video! Small correction: the result at 9:20 contains a sign error. The eigenvalue is indeed -1, but the eigenvector should therefore be [1 -1]

For me, the most hilarious thing of all Matt's videos is to see how he primarily amuses himself with those Daddy maths jokes :D It totally cracks me every time :D

Great video. And a nice refresher of Eigenvector and Eigenvalue. Thought about how to do this about a week ago

I do remember seeing these kind of questions in maths books, and I learned to hate the very sight of them. Because they would appear, a bunch of stings of random numbers. And with no hint of any solution it just says "find the next number in the sequence". And in the answers it would be just a string of equally random seeming numbers. No hint of how one should arrive at that particular one. What the criteria for success was or anything. The result was that those who decrypted these hieroglyphic things felt smart and everyone else, me included, felt stupid. And encountering enough of similar tasks with no guidance, and no pedagogical help to be found. I just lumped them together as "one of those". I never got the tools to crack them, I was just left there, abandoned. Just writing a random number because a fail at least made it go away. This, and the fact that the maths books in general I encountered were seemingly written backwards. Making me do tasks before teaching me how to do them. Making me wonder if I was having a stroke, if I was having early onset dementia, then I turn the page and it explained the mechanics to solve the past few pages tasks. Sorry about the rant, I just had flashbacks to how exclusionary maths can be at times. I think it's part of why I liked computer classes, they at least knew how to teach. And in general, I knew what a success state was. I like finding out about math stuff nowadays. 15-20 years after those schoolbooks. I just wonder how many mathematical minds were lost, because of horribly written books.

It's interesting how much this video resonates with Sabine Hossenfelder's "Lost in Math", which is very much worth reading on the subject of elegance as a goal in math and physics.

For those of you playing educational RU-vidr bingo, Matt mentioned the names of Crash Course and the English translation of Kurzgesagt (In a Nutshell), as well as 3Blue1Brown. Well done Mr. Parker, well done, even if the first two were simply expressions you used and not intentional, which, let’s be honest, they likely were.

always impressed with your video quality!

Thank you Simon, from Cracking the Cryptic, I got the sequence immediately.

We really need a full version of "Eigen see clearly now"!

Can you do a video on Hans Niemann allegedly cheating in the chess Sinqued cup? I would love a statistical breakdown the same way you did with Dreams mc world record

Very interesting video! A small note: your audio is quite quiet, I had to max my speakers to reach a "normal" volume. Maybe 2x as loud would be perfect? Appreciate you!

Really great! The song is awesome! 😍

I love it when you give a number sequence and people think there's some sort of advanced algebraic or geometric relationship then its just... nope... Numbers.

This game doesn't really work in spanish, since the word for the number 1 is different than the word for "1 of something" ("uno" and "un"). So if you say "un uno" (kind of like "a 1") it's different that saying "uno uno" ("one one").

The Look and Say sequence will be added to my party tricks collection along with tying my shoes the mathematical way. Cheers

That's so crazy. I was reading about quantum entanglement the other day and stumbled upon eigenvalues/ -vectors as they relate to the wave function collapse. "Everything is, like, connected, man."

“Square roots of 17, everywhere.” *stares into camera* Math is hilarious if it’s well presented.

I literally just finished studying eigen vectors and values like, a week ago (although it wasn’t called like that in my course)! What a coincidence! I wonder if Maple uses the same algorithm for finding these values as we used, one of the task was to write a program that finds them. There is a way to find two pairs of answers, to be specific, to derive one pair from another, which is really neat!

I want egian see clearly now full song. That be my bop of the year

Thanks for reminding me about eigenvalues and eigenvectors. Haven't had to think about those maths since college, which was extremely novel to see appear in one of your videos.

I can't wait to have this as my ringtone

"We're not gonna do that using a network, we're gonna do that using a..." SPREADSHEET! "... matrix!" OK I was close, right?

I thought the motto of the channel was "Give it a go"

Matt: "A good reminder, just because it looks like something is the answer in mathematics, we don't know for certain until we do the maths" I shall Burn this into mind, it is one of the many things I struggle with, I'm constantly trying to eye-ball things. Amazing video.

You made it to 1 million subscribers. Congratulations Matt :)

I finally got one of these questions right!! I didn't even have to pause

I always felt we never learnt enough about the life and time of Dr. Eigen!

Neat description of Eigenvectors and Eigenvalues

I'd like to add a +1 request for the Hans Niemann chess cheating! Your Dream video made it really easy to understand. thanks!

thank you for the subtitles

So glad eigen finally see clearly now. Also, let it be known I did learn about eigenvalues in my Linear Algebra course!

I'm surprised. I figured it out in just a few minutes. Really helped having them displayed in a column like that.

I got this in like 5 seconds. Usually spend days with these in my head. Trying to workout if I haven’t already watched this video and then forgotten

I love that the look & say sequence feels like a pun that works in every(?) language

At 9:30 woudn't the eigenvalue be 1 instead of -1? Edit: Nevermind, the result vector should be [1, -1] instead of [-1, 1] the eigenvalue of -1 is ofc correct. Edit2: As Demigoddess pointed out there is in fact no error. Matt just skipped the step of factoring out -1 here.

I did a lot of engineering courses, saw eigenvalues and eigenvectors until I could claim I know them by heart. I thought that that segment wouldn't teach me anything new, but it did. I finally made the mental connection on why we actually use them for solving systems of differential equations! Thank you, Matt!

I saw this puzzle ages ago with the note that if you start the sequence with 22 it never changes. Be interested to see any other odd variations

I think it's amazing that someone was able to completely solve this problem, but we then have problems like the Collatz conjecture or the Lychrel number problem that can't be solved.

There was an 'Eigenmode' song at one of the Fermilab Physics Slams. I recall that it won over other entries.

That was crazy fun!

Matt, love your channel been watching for years! Got a show idea for you. The Will Wheaton dice curse.

Got it in five seconds! Thanks for that!

OMG! I remember doing all kinds of calculations on the decimal version of this "look & say" sequence with a friend of mine years ago. Someone had shown the question on the back of a napkin and we were intrigued. To be clear: this was in no way a mathematical question at that point - just a "try to figure out the next number while you're drunk and I'll get you a beer" thing. Once we got home we started exploring in excel of all things! (I know you love your spreadsheets Matt) And even tried some Visual Basic. But this was back in .... 2000 more or less, so, that went nowhere fast. This sequence gets big very quickly. But we tried to find some patterns. In acceleration in growth , then sequentially differentiating to see if we could find some constant in the depths. Then counting the occurrences of digits. Tried to find reoccurring patterns. I can't remember precisely, it was a long time ago, we were drunk, stoned and 20 years younger. But I'm so glad I saw this video. Thanks so much! But could you perhaps elaborate on the decimal version ? That must be worth its own video (?)

Well, I can say that I definitely wasn't expecting to have flashbacks to my linear algebra course today.

it's interesting for me, as an electrical engineer, to see that the first step looks very similar to how we build a transition table for a finite sequence acceptor state machine. I wonder if there is any correlation to the bit positions representing flip-flops needed to store the state machine's physical implementation and the logical transition between blocks. that could be a neat thing to look at. you'd need fewer flip flops than the number of digits in the sequences, but maybe some clever mixing of one-hot encoding or something. I don't know. could be interesting!

Apparently I'm here pretty early. Looking forward to watching this!

the best look and say sequence is 22,22,22,22,22,22,22...

ive seen that first sequence before and its ace, great pattern i would never have spotted without some hints

thanks for the bitty introduction to eigen values and vectors. i had heard the terms floating around for a couple years now. nice to hear a simplified explanation :)

Really nice video!

I can remember back to the 70s in school trying so hard to understand what Eigenvectors and Eigenvalues were, and totally not getting it other than some vague feeling that I ought to be able to. But today I got a bit closer to that with the bonus of a totally ear-worm song I'm going to be trying not to hum all day..... :D

That matrix *is* the graph. Lots of graph algorithms have very pleasant formulations in terms of operations on their adjacency matrices, at least when you can fit the adjacency matrix in memory...

@0:19 It's a read number. starting at 1. 1; one 1; two 1's; one 2, one 1; one 1, one 2, two 1's; three 1's, two 2's, one 1. Next: one 3, one 1, two 2's, two 2's. I'll continue watching in case there's an alternate sequence, but this one fits so far. The word one looks so weird right now. @1:00 didn't know there was a name for it. I've seen enough to make the comment.

I recognised that puzzle as I worked it out and won money in a pub quiz because of it 😁

I got my monthly dopamine allowance by hearing you say the intro problem took all day when I solved it in ~15 seconds

Look and say we're seeing saying13112221. When you take this sequence out to Infinity you still only ever see the integers 1 2 and 3 no other integers appear in the sequence. Also if you create a sequence that counts the amount of digits in each of the numbers of the look and say sequence and then create a ratio of two consecutive numbers in this new sequence as it approaches Infinity it equals a constant that is the unique positive real root of a polynomial of degree 71. The constant is called Conway's constant and it is approximately 1.303577...

Hey, I did eigenvectors and eigenvalues in economics! We did it for one module, for one exam, and I've completely forgetten everything about them ever since.

I realized where you were going about 15 seconds before you said eigenvectors, and I was so proud, I'm not a mathematician

The little jingle was quite good

I am so happy i took a linear algebra class so that I could relearn with Matt how to do matrix multiplication.

Matt Punner's Parks-- I mean Matt Parker's puns are always so out of nowhere but so good. Eigen See Clearly Now....

I have a math degree focussing in large part on linear algebra and I now understand Eigenvalues better than when I graduated.

Those were some great Matths and some even greater puns.

waw I LOVe that when you said if you didnt crack this youre gonna hate this, and JUST mere seconds later I understood and hated myself as predicted LOL ! Purely based on the way the numbers added in the sequence my quick guess was 132221 , but I couldnt explain why and im now very impressed that I was actually quite close without understanding what it was at all ! I just tried to look at why and where new numbers were added in the sequence but i didnt understand the logic until after lol

I can’t believe I got the sequence and it only took about a minute! That was so unexpected even when I knew what the pattern was

I felt like I was having a stroke during this explanation. I'm too old to have learned matrices in school, so this whole video felt like a definition of terms using only the terms defined within the definition. "The animal a dog is an animal that is a dog, and excludes animals that are not dogs. Even animals that are similar to dogs, but not dogs, are animals that are not dogs. Only dogs are dogs. Here is a proof."

got the sequence right away