Can you trust an elegant conjecture?
325,479
Published 2022-09-13
Nathaniel Johnston's post on The Binary “Look-and-Say” Sequence:
www.njohnston.ca/2010/11/the-binary-look-and-say-s…
Huge thanks to my mate Jonny Berliner for recording Eigen See Clearly Now because I thought it would be funny. Check out his website and channel for more science music fun.
www.jonnyberliner.com/
/ @jonnyberliner7212
More on the general Look and Say Sequence:
mathworld.wolfram.com/LookandSaySequence.html
I told you 3blue1brown had a good visual explanation for eigen-stuff.
• Eigenvectors and eigenvalues | Chapte...
Thanks to Ben Sparks for helping out with the graphics as well.
youtube.com/c/SparksMaths
Cheers to my Patreons for helping enable these videos. That whiteboard wasn't free you know! Keep me in whiteboard pens here: www.patreon.com/standupmaths
CORRECTIONS
At 11:17 I accidentally have Nathaniel Johnston's name as "Daniel Johnston". No idea how that happened. But I'm very sorry.
- Let me know if you spot any other mistakes!
Filming and editing by Alex Genn-Bash
Eigen See Clearly Now music by Jonny Berliner channeling Jimmy Cliff
Eigen See Clearly Now lyrics by Matt Parker and Johnny Nash
Non-Eigen music by Howard Carter
Maths graphics by Ben Sparks
Design by Simon Wright and Adam Robinson
All Comments (21)
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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.
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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.
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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 :)
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"Eigen See Clearly Now" cracked me up! Haha, I really love this channel; keep it up, Matt!
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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.
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That first sequence is one of those "so simple it's annoying" puzzles! Great video Matt as always.
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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.
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The real question: is Eigen See Clearly Now heading to Spotify?
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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.
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Eigen see clearly now... that's the kind of quality content I subscribed for
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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
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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-
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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!
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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.
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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!
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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.
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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
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This is proof of the theorem that mathematicians are bored.
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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.
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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.
