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.
@vigilantcosmicpenguin8721
2 жыл бұрын
It's like, oh, tell me about it! I hate those square roots of 17.
@eroraf8637
2 жыл бұрын
What’s so scary about sqrt(17)? I can estimate that in my head as 4.12-ish. It’s the square roots of really small numbers that I’m scared of!
@whatzause
2 жыл бұрын
 I think if anything makes it “scary“ it's just that Who would expect a prime number, out of the blue like 17, to appear in an analysis of a recreational, vocally spawned series, and appear under a sqrt radical yet? And if you want something scarier see the cool KZitem videos on finding the sqrt of i, and the one deriving (i ^ i) which turns out to be a REAL number! (I double-checked the latter, [ i ^ i ], with my TI-89, and it confirmed it.)
@mentalaren8841
2 жыл бұрын
Me, a HCSSiM alum: I see this as an absolute win!
@mihailmilev9909
2 жыл бұрын
SAME!
@jeroennouwens9972
2 жыл бұрын
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.
@NorbiPeti
Жыл бұрын
I was wondering why they are named this way, since in Hungarian they are just called 'own vectors'.
@PC_Simo
Жыл бұрын
@@NorbiPeti In Finnish, they’re called: _”Ominaisarvot”_ and: _”Ominaisvektorit”_ (literally: ”Characteristic Values” and: ”Characteristic Vectors”), and we also have something called: _”Ominaisavaruus”_ (”Characteristic Space”; a collection of all the Eigenvectors with the same Eigenvalue). 🇫🇮🇭🇺
@wiseSYW
Жыл бұрын
Leonard Eigen, very famous German mathematician!
@NoLongerBreathedIn
Жыл бұрын
Although not in en-US. In the States, it's always lowercase except at the beginning of a sentence.
@PC_Simo
Жыл бұрын
@Flavianus So, pretty much directly translatable. 🤔
@MrNiceGuyMEGA08
2 жыл бұрын
"Eigen See Clearly Now" cracked me up! Haha, I really love this channel; keep it up, Matt!
@ShinySwalot
2 жыл бұрын
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 :)
@Gapiedaan
2 жыл бұрын
nice conjecture you got there
@finno3882
2 жыл бұрын
They’re also similar in that if they look like Boris Johnson then you know you’ve done something VERY wrong
@jamesrayner9980
2 жыл бұрын
Who said that?
@MyOneFiftiethOfADollar
2 жыл бұрын
By your reasoning the Goldbach conjecture is like a politician.
@vigilantcosmicpenguin8721
2 жыл бұрын
@@Gapiedaan It's very elegant. Almost a little _too_ elegant, don't you think?
@randomz5890
2 жыл бұрын
That first sequence is one of those "so simple it's annoying" puzzles! Great video Matt as always.
@Tim3.14
2 жыл бұрын
Yeah, and if you know a lot of different kinds of mathematical sequences, it probably just means you'll waste more time checking if any of them work, before it dawns on you to just say the numbers out loud.
@sebastianjost
2 жыл бұрын
the mathematician's answer to those "puzzles" is always the same: There is no unique solution. There are infinitely many sequences starting with those numbers. Some are finite, some are infinite. A simple one is always: "They are the zeros of some polynomial, which I can work out if you want me to."
@SilverLining1
2 жыл бұрын
@@sebastianjost True, but we're not in a vacuum. When someone gives you a sequence and asks for the pattern, the conventional assumption is that the pattern is clever and unique. A pattern that can be generated for any given sequence is neither unique nor clever
@Nossairito
2 жыл бұрын
I always get a slightly bitter taste whenever I think about it because I remember getting it wrong, and it feels like having met an old friend or a celebrity, making a terrible impression on them, and having them leave with that image of you, it always feels a little sad how I'll never get another first time trying to guess what it is haha
@reepicheepsfriend
2 жыл бұрын
It took me about 20 seconds to get it, does that make me smart or stupid?
@erwark
2 жыл бұрын
The real question: is Eigen See Clearly Now heading to Spotify?
@veryboringname.
2 жыл бұрын
I wonder if he had to revenue-split the video because of the tune.
@Jhopsssss
2 жыл бұрын
Eigen see clearly now... that's the kind of quality content I subscribed for
@collin4555
2 жыл бұрын
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
@whatzause
2 жыл бұрын
Six or eleven? Maybe 6.16611...😊
@collin4555
2 жыл бұрын
@@whatzause since you're remarking on it, I suppose it's what feels like a comfy numerical rendering of "more than one or two handfuls of times", 5n + 1, because a hand has five fingers and all But dissecting it takes a little bit of the whimsy out of it, possibly
@whatzause
2 жыл бұрын
@@collin4555 Right. My comment was satirical of course. BTW, I had seen this series decades ago, but am surprised at its being discovered to have mathematical meaning. As ever, Matt’s presentations are super!
@RugnirSvenstarr
Жыл бұрын
For what it's worth, this is an area that in my experience pretty much every professor re-teaches at the beginning of every course involving it. It's complicated and difficult to get a good intuition for, so yeah you will have to learn and forget it a bunch of times before it sticks and that's ok 😁 (Ofc each time the reminder builds on top of new knowledge from each part before but people myself included regularly lose the basics of eigenvectors each time we apply it in new and amazing ways, I must have watched the mentioned excellent threeblue1brown video at least 10 times in the last 5 or so years )
@Jiffy_Park
2 жыл бұрын
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.
@CptGallant
2 жыл бұрын
I finally used eigenvalues and eigenvectors in my engineering masters degree, and in two completely different situations. The solution to problems in structural dynamics is effectively an eigenvalue problem. And they also come up when you consider stresses and strains on a 3D element. So just within structural engineering there are at least two ways eigenvalues/vectors are useful. No doubt there are countless applications in other fields.
@grutarg2938
2 жыл бұрын
I had the same experience! For some reason the class on matrices was taught over the summer when most of the school was closed. So all math majors were required to stay on alone and try to learn this stuff in the heat from a professor who was too old to still be teaching. He would make minor arithmetic mistakes in every matrix, and if we attempted to point it out, it would take 5 minutes for him to find what digit we were referring to and correct it. After a while, we wouldn't tell him, but just note it quietly between ourselves. Although I learned enough to pass, I never understood it.
@johnchessant3012
2 жыл бұрын
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.
@kingp1n817
2 жыл бұрын
I didn't understand anything but that sounds cool!
@iveharzing
2 жыл бұрын
So a polynomial with as the highest term _a*x^71_ ?
@jodikirsh
2 жыл бұрын
@@iveharzing Yes.
@EebstertheGreat
2 жыл бұрын
@@iveharzing Yeah, λ is the unique positive real root of the polynomial x⁷¹ − x⁶⁹ − 2x⁶⁸ + . . . + 3x − 6. The full polynomial is printed here: en.wikipedia.org/wiki/Look-and-say_sequence#Conway's_constant_as_a_polynomial_root.
@eliasmochan
2 жыл бұрын
And the same politinomial works for base 89 ;) (Or any base bigger than 3, since the look and say sequence will never have 4 consecutive equal digits in bases that have a symbol for 3).
@giansieger8687
2 жыл бұрын
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.
@jmalmsten
10 ай бұрын
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.
@Dalenthas
2 жыл бұрын
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.
@danielyuan9862
2 жыл бұрын
My high school LinAlg class didn't even cover eigenvalues and eigenvectors. We did other stuff that was questionable in terms of whether it should belong in that class.
@ButzPunk
2 жыл бұрын
Thank you for the simplest and clearest explanation of eigenvectors/eigenvalues I've ever seen!
@bean0873
2 жыл бұрын
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.
@falquicao8331
2 жыл бұрын
It would be a great example on how not to use probabilities
@BryanLu0
Жыл бұрын
@@falquicao8331 It's because of the definition of top engine move. You can select a certain set of engines to stack the eval
@baileyayyy5085
Жыл бұрын
no
@notgonnabetelling1469
2 жыл бұрын
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.
@nicholaskane9456
7 ай бұрын
You should become an engineer
@heighRick
Жыл бұрын
Thanks Matt for the opportunity to look at you while you say things looking towards us, helps a lot!
@mossworksmedia
2 жыл бұрын
Any chance that Eigan See Clearly Now is gonna be released anywhere? 👀 I absolutely love it!
@petraw9792
2 жыл бұрын
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
@veni1
2 жыл бұрын
außer dass wir in deutsch die gottverdammten kommata verwenden statt einfach nen punkt
@JosephDavies
2 жыл бұрын
A lot of math terms are German, even in English. :)
@timseguine2
2 жыл бұрын
The English word for Ansatz is amusingly also ansatz
@at7388
Жыл бұрын
@@timseguine2 Ich dachte, die englischsprachige Mathematikergesellschaft hat "Ansatz" bereits anglisiert, so wie es Matt mit "Eigen" (I can) bereits gemacht hat.
@timseguine2
Жыл бұрын
@@at7388 "onsotz"
@SkyBlue-cv8qb
2 жыл бұрын
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.
@danielyuan9862
2 жыл бұрын
Number theory relationships also matter.
@thecakeredux
2 жыл бұрын
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."
@adaetz1042
2 жыл бұрын
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]
@SebastianHasler
2 жыл бұрын
There's not a unique eigenvector corresponding to an eigenvalue. You can scale an eigenvector by a constant and it's still an eigenvector for the same eigenvalue. In fact, you can take any vector from the eigenvalue's eigenspace.
@The1RandomFool
8 ай бұрын
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.
@RichardHolmesSyr
2 жыл бұрын
"We're not gonna do that using a network, we're gonna do that using a..." SPREADSHEET! "... matrix!" OK I was close, right?
@YOM2_UB
2 жыл бұрын
A spreadsheet is basically a matrix of cells
@RichardHolmesSyr
2 жыл бұрын
@@YOM2_UB They both have rows and columns, anyway
@aok76_
2 жыл бұрын
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!
@Cloiss_
2 жыл бұрын
:O
@aok76_
2 жыл бұрын
@@Cloiss_ :O
@TheyCallMeNewb
2 жыл бұрын
There was an 'Eigenmode' song at one of the Fermilab Physics Slams. I recall that it won over other entries.
@AuroCords
2 жыл бұрын
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").
@omp199
2 жыл бұрын
1:13 "But now we've got two ones, so the next one is 2 1s." Except it isn't. It's "2 1", not "2 1s". So you've got a similar discrepancy in English.
@AuroCords
2 жыл бұрын
@@omp199 yeah, but I guess the algorithm is still coherent beyond language: every time you start a new row of numbers state two inputs : 1st how many 2nd of which number, then keep going..
@omp199
2 жыл бұрын
@@AuroCords Yes. That's right.
@DanTheStripe
Жыл бұрын
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.
@dyanpanda7829
2 жыл бұрын
I realized where you were going about 15 seconds before you said eigenvectors, and I was so proud, I'm not a mathematician
@minkuspower
2 жыл бұрын
"eigen see clearly now" omg i'm dying lmao
@popcorny007
2 жыл бұрын
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!
@tsjost
2 жыл бұрын
Yes, it's very quiet, making the music and sound effects become extremely loud. Voice should be normalised to -6 dB.
@mrturtle6614
2 жыл бұрын
You made it to 1 million subscribers. Congratulations Matt :)
@annleach7908
2 жыл бұрын
The Look and Say sequence will be added to my party tricks collection along with tying my shoes the mathematical way. Cheers
@howuplaydisgame5171
2 жыл бұрын
I'm unaware of the mathematical way of tying my shoes. Can you teach me?
@sstrick500
2 жыл бұрын
The ultimate nerds and geeks party trick! I'd be at that party.
@Starwort
2 жыл бұрын
I'd like to know about the shoes thing too please
@annleach7908
2 жыл бұрын
@@Starwort see the link above
@Starwort
2 жыл бұрын
@@annleach7908 there's no link, you got shadowbanned
@ChickenGeorgeClooney
2 жыл бұрын
Matt Punner's Parks-- I mean Matt Parker's puns are always so out of nowhere but so good. Eigen See Clearly Now....
@morre6748
2 жыл бұрын
I love that the look & say sequence feels like a pun that works in every(?) language
@stealthemoon8899
2 жыл бұрын
I got my monthly dopamine allowance by hearing you say the intro problem took all day when I solved it in ~15 seconds
@flobiish
2 жыл бұрын
@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.
@corbinlegrand
2 жыл бұрын
So glad eigen finally see clearly now. Also, let it be known I did learn about eigenvalues in my Linear Algebra course!
@dylanwilliams269
2 жыл бұрын
I can't wait to have this as my ringtone
@jasonremy1627
2 жыл бұрын
I thought the motto of the channel was "Give it a go"
@Bethos1247-Arne
2 жыл бұрын
FINALLY. After ALL THE YEARS, I understood Eigenvektoren and Eigenwerte.
@Zwijger
2 жыл бұрын
I felt kinda good solving it in 3 minutes of paused time when Matt said it took him a day. It's the little things.
@electricpengu1n59
2 жыл бұрын
That Jane Street advert is such a bizarre calling.. I currently have time and the interest in internships and I might apply once the sense of shock wears off
@NthMetalValorium
2 жыл бұрын
damn that's a brilliant way to use an ad break
@Marronii
2 жыл бұрын
Because I found your channel through your Dream Cheating video, I'd love to see a video about the current chess cheating drama and the maths behind it.
@GodwynDi
2 жыл бұрын
I'm surprised. I figured it out in just a few minutes. Really helped having them displayed in a column like that.
@zperk13
2 жыл бұрын
"I spent all day but I cracked it"... it took me 20 seconds...
@thorzweegers7616
2 жыл бұрын
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 (?)
@bryanburgess3950
2 жыл бұрын
the best look and say sequence is 22,22,22,22,22,22,22...
@НикитаЛукашов-л1ч
2 жыл бұрын
Really great! The song is awesome! 😍
@martindooley4439
2 жыл бұрын
Brought back memories of matrix manipulation and eigan isms at Uni in the late 80s modelling real time systems. Laplace transforms Nichols plots and the like.
@kevinmartin7760
2 жыл бұрын
The examples I've seen discussing this sequence (in base 10) never seemed to get to the point where there are 10 of any digit to demonstrate that the counts are broken into their digits. This doesn't really follow the "look & say" rule though, more like "look and say like a 1960's computer". To be truly "look and say" you have to use numbers, not digits. When you have 10 of an item to count, you say "ten" not "one zero". The easiest way to look at this is to put spaces between the numbers, so the sequence becomes: 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 3 1 2 2 1 1 1 3 1 1 2 2 2 1 etc. and you eventually get 10 of a number (perhaps a 1) so the string would be ... 10 1 ... and the next would be ... 1 10 (n) 1 ... On this basis you get a sequence of sequences of numbers, which do not depend on the base of the numbers. This is also ignoring the fact that one pluralizes nouns. Perhaps the sequence should be: 1 1 1 2 1s 1 2 1 1s 1 1 1 2 1 1 1 1s 3 1s 1 2 3 1s 1 1s 1 3 1 1s 1 1 1 2 1 3 1 1s 1 1 1 1s 1 1 1 3 1 1 1 1s 3 1s 1 2 1 1 1 3 1 1 1 1s 3 1s 1 1s 3 1s 1 3 3 1s 1 1s 1 3 1 1s 1 1 1 2 3 1s 1 3 3 1s 1 1s 1 3 1 1s 1 1 1 1s 1 3 1 1s 1 1 2 3s 1 1s 1 1 1 1s 1 1 1 3 1 1 1 1s 3 1s 1 2 1 3 1 1s 1 1 2 3s 1 1s 1 1 1 1s 1 1 1 3 1 1 1 1s 3 1 1 1s and so on. At first I thought you never would get more that 1 of anything except '1', but on the before-last line there were two pairs of the number 3 so the next line had "2 3s" in two places. But then, do you have to continue pluralizing the numbers, "one", "ones", "oneses" etc?
@SquintyGears
2 жыл бұрын
God I'm such a nerd for enjoying that song so much
@Tim3.14
2 жыл бұрын
It's delightful, isn't it? 😊
@logandihel
2 жыл бұрын
I faceplanted so hard when you revealed the answer to that sequence
@stephaneclerc667
2 жыл бұрын
OK that joke was more than I expected, you won
@jonathangratus233
2 жыл бұрын
I always felt we never learnt enough about the life and time of Dr. Eigen!
@mrphlip
2 жыл бұрын
10:53 - why yes, subtitles, I agree, 3b1b's theme song does smell quite good
@Kraus-
Жыл бұрын
Bruh you killed me with that "Eigen see clearly" bit. Lmao this is why they call you stand up maths.
@Henrix1998
2 жыл бұрын
For a good moment I thought the ratio was 1.46 and I was shocked you were comparing them so equally
@flamshiz
2 жыл бұрын
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!
@_Ampersand_
2 жыл бұрын
The mention of eigen value sent my tiny engineer brain into a hissing panic.
@thatwerdogeek1107
2 жыл бұрын
This video immediately brought back my Data Structures and Algorithms PTSD
@BerndTheBrick
2 жыл бұрын
Fun fact: 'Eigen...' ist simply german for 'self' and not a name. So it should be 'self vector', but the translator some hundred years ago didn't noticed and though it was a name such everything else. So it came to Eigen vector, Eigen values and so on.
@Anonymous-df8it
2 жыл бұрын
Same with -ology, but that's from Greek!
@berni1602
2 жыл бұрын
Matt, hello. Let me tell you a phenomenon that recently happened where I live and that I think you would be great at explaining it. Two days ago, on September 19, there was an earthquake in Mexico with a magnitude of 7.6. That's normal since we're surrounded by tectonic plates. But something intriguing is that there was an earthquake on September 19, 2017, in Mexico with a magnitude of 7.1. Well, it's now been two high-magnitude earthquakes on the same date in the same place, which is not that improbable. However, there was an earthquake on September 19, 1985, in Mexico with a magnitude of 8.1. To nobody's surprise, many people have come to the conclusion that the date is cursed because the probability of having 3 high-magnitude earthquakes on the same days in different years is not even close to 1%. Yesterday, I was reading that some mathematicians have made an approach to the birthday paradox, taking into account the high-magnitude earthquakes that occur in Mexico and using them as values for combinations, therefore concluding that it's quite probable that this happens. I'd love to see a video where you tackle this topic. Even more, there have been other two earthquakes, on September 9, 2017, with a magnitude of 8.2; and on the same date (September 9) in 2021, with a magnitude of 7.1. Are probabilities against us, or people simply can't approach statistics?
@arielioffe1810
2 жыл бұрын
10:36: a parade of square roots of seventeen promptly parades accross the screen.
@IanSlothieRolfe
2 жыл бұрын
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
@Platanov
2 жыл бұрын
3b1b really does need to up his theme song game.
@rubixtheslime
2 жыл бұрын
"Just plug it into Maple" For anyone too cheap for Maple, or if you just prefer FOSS anyways, I cannot recommend SymPy enough. Symbolic manipulation, number theory, so many more things I've never even touched before, all fully interfacable in python. Definitely has a slight learning curve to it, but it's 100% worth it.
@yoyamon6811
2 жыл бұрын
about the first problem, my excuse is that in spanish (my main language), instead of saying "one one" to describe two number ones, we say "un uno", which means "a one". Saying "uno uno" to describe two number ones does not work in spanish. :p Fun problem anyways.
@jacefairis1289
2 жыл бұрын
5 seconds into the video, and its already Real John Conway Hours
@coryman125
2 жыл бұрын
This intro is one of those very rare times I've gotten one of those puzzles before even being told to pause :) I think it was because I saw "111" directly over a "3" and connected those
@tyotypic
2 жыл бұрын
Got it in five seconds! Thanks for that!
@shadeblackwolf1508
2 жыл бұрын
I like the look and say sequence but i've seen it in a few flavors. You have the look and say in order sequence. There is also a tally version where 1211 goes to 1231 to 131221. This series eventually ends on a number that tallies to itself: 14233221
@mpalin11
2 жыл бұрын
Ahh, a new Matt Parker video. The best moment of the day.
@Schenkel101
2 жыл бұрын
In school, I loved maths but hated matrices. This video tells me that hasn't changed.
@gustavoexel5569
2 жыл бұрын
One thing I found interesting about the first sequence, is that its exponential is perfectly exponential, the number of digits of the N-th element of the sequence (in base 10) is 2.6689 * exp(0.265052 * N)
@danielyuan9862
2 жыл бұрын
Wdym perfectly exponential? The number of digits must be an integer, so I don't get what you mean by "perfectly exponential."
@gustavoexel5569
2 жыл бұрын
@@danielyuan9862 Ok perfectly wasn't the best word to describe, it has some deviation, up to the 10th term the errors are like 2, 3, which isn't much, but since the terms are small is about 15%. After the 20th term the errors are well below 0.1%, so yeah, it isn't perfect, but the behavior is definitely exponential, which isn't obvious at all.
@singerofsongs468
2 жыл бұрын
Spoilers for the intro! I have paused the video before any explanation was given, so this is just my best guess. - - - - - each term in the sequence is a string representation of the term before it. 312211 aka “three 1s, two 2s, one 1” describes the previous string “111221,” which describes “1211” - “one 1, one 2, two 1s.” Thus, the next term in the sequence, following 312211, is “13112221”
@apteropith
2 жыл бұрын
i was not expecting that song, had to step away immediately; "the rain is an equivalent scalar" was just too powerful a line for my fragile mind
@melody3741
Жыл бұрын
The second one looks more thought out to me. If it has that many parts, SURELY they all serve a purpose.
@WhiteSpatula
2 жыл бұрын
Square roots of seventeen everywhere! LOL! I’m putting that one in my back pocket. Gotta have brilliance like that at the ready!
@dancinswords
2 жыл бұрын
I appreciate how he doesn't realize what he's gonna end up saying the first time, but then on the repeat he says "determinant" normally
@rokevh7800
2 жыл бұрын
Lack of pausing time? Like we don’t have a pause button 😂😂
@emilyscloset2648
2 жыл бұрын
10:52 I actually think is a beautiful explanation, cause as much as the 3Blue1Brown point out it is invariant. It is beautiful to see it as it would have been discovered and I think more intuitive
@NathanielMath
2 жыл бұрын
"Thanks to Nathaniel Johnston for doing the maths in the first place." You're welcome!
@ccktravis4128
2 жыл бұрын
Me at the start: ooh this is interesting Me 5 minutes in: *saves to watch later*
@yuzuyellow9374
2 жыл бұрын
I like the puzzle. Self Describing sequence :D
@metashdw
2 жыл бұрын
I must have seen this before because I instantly figured it out
@BruceDuncan
2 жыл бұрын
6:30 "... most people have never heard of" *cries in physicist*
@TheFireHawkDelta
Жыл бұрын
Surprisingly I cracked the pattern in under a minute! Guessing that it's a gimmick rather than the output of a continuous function meant it didn't take long for me to figure out the pattern. The next values are 13112221, 1113213211, and 31131211131221.
@andrestricker4118
2 жыл бұрын
6:01: Plot twist: If you extend the matrix to 10000x10000, turn 0 to black and 1 to white and zoom out, a picture of Matt appears. I am not saying that this would be the perfect Parker Square
@UglyRooks
2 жыл бұрын
A (totally unimportant) correction for the 2:22 mark ("are there more ones, are there more sevens?"). It is very easy to prove that there can be no digit greater than 3 (therefore no 7s). [I hope I am not repeating anyone else's comment, I did a quick scroll and did not see any such remark.]
@WRSomsky
2 жыл бұрын
Eigen See Clearly Now --- *GROAN* -- Wish I'd thought of that. 😁
@ZedaZ80
2 жыл бұрын
:0 this was such a nice refresher on eigenvectors and eigenvalues, haven't looked at them in 9 or 10 years
@redsgxd
Жыл бұрын
11:26 That 1.465571.. value is actually the solution to "x = 1 + 1/x²"
@KaliTakumi
2 жыл бұрын
Honestly I just added the digits and thought it was a cryptic way of writing the Fibonacci sequence. In hindsight, that was kind of silly
@theJade
2 жыл бұрын
Some spreadsheets have been floating around about the recent Chess drama with Hans and cheating allegations. Have you seen the spreadsheet (I know you love spreadsheets) and can you break it down for us?
@sisig2419
Жыл бұрын
At one point i thought it could be 5/3. Then some weird cubic root of a number involving sqrt(93) came in and destroyed any dream of an easy life.
@ThecMaster
Жыл бұрын
& weeks ago. I had never heard of eigenvalues and eigenvectors.. But now. I even know how to use them. Jusat took a course in Linear Algebra
@jakubharwacki
2 жыл бұрын
I am glad that there are people on earth who understands all this eigen-stuff so i don't need to :)
@peterhawes9680
2 жыл бұрын
I would pause the video to solve a puzzle but KZitem sticks a massive banner on the bottom third of the screen. How can we complain about this? Also, I don't understand exactly how blocks or chunks can solve the problem when successive 1's from different blocks will contribute to the same 'count' of 1's at the next stage. Otherwise, the method is well explained.
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