Planing Sequences (Le Rabot) - Numberphile

[@numberphile]

Mandelbrot papers offer: www.patreon.com/posts/52011294

[@christianherrmann]

Can someone tell me why in the binary numbers with shaving to empty sequence it's is becoming 0? Because in the setup the shaved outcome for single head/tail gets to a zero size run, an empty set. Making it 0 is not a zero run but a 1 run..

[@anon6514]

@@christianherrmann It seems legit if you expect a number on the right every time. Zero is natural choice for the value of a number with no digits. The only alternative is set the planing operation to be undefined on sequences with no repetition. Either are fine in my opinion. In the null case, the note on the piano would just be a pause.

[@johnjeffreys6440]

Do you guys take suggestions for video topics?

[@mayukhpurkayastha2649]

Please sir next content Bangladeshi child soborno isaac bari🇧🇩🇧🇩🇧🇩🇧🇩

[@RameshRamesh-ut9lj]

Hi

[@hzr6597]

'My study is very messy' 18 years to find a letter.

[@christosvoskresye]

I can relate.

[@AbhijayPaul]

Imagine being content with the fact that he never read your letter only for him to find it almost 2 decades later

[@christosvoskresye]

@@AbhijayPaul I would have blamed the post office.

[@jk23233]

Imagine the letter contains a proof of the Riemann hypothesis...

[@christosvoskresye]

@@jk23233 If you have a proof for that, you need to make it public, not send it in a private letter. The letter would constitute a terrible temptation to claim it for oneself.

[@mytube001]

I propose that the inverse rabot should be called "veneer". Applying a new layer instead of shaving one away.

[@aenetanthony]

I agree with this

[@PaulSmith-zs5je]

le vernis

[@JoeTaber]

Ding ding ding!

[@phiIippejean]

@@PaulSmith-zs5je vernis is more like varnish, a wood veneer translation is placage

[@Восьмияче́йник]

bof, je préfère vernis

[@joshuamiller5599]

“Does every number appear? Yeah, sure.” Best proof ever.

[@mads_in_zero]

The "sure, why not?" conjecture.

[@hilbert_curve3680]

I guess for every number in binary just duplicate each digit in place: 100110 -> 110000111100 101 -> 110011 1 -> 11 and so on. Applying le rabot to it reverses this transformation.

[@Tefans97]

@@hilbert_curve3680 wouldn't you just add one to each sequence rather than duplicating it? Apart from that, it makes sense

[@Fay-cd8ik]

He went on to explain why...the expanded sequence part. 😊

[@cosmicvoidtree]

It’s also fairly simple to reason about why you get infinitely many of every number.

[@clutchyfinger]

This man is clearly an immortal, 18 years is but a moments time for him.

[@peterfireflylund]

He doesn't look like an 81-year-old, does he?

[@Triantalex]

false.

[@Denema123]

That Conway piano and the logo. Excellent tribute.

[@achtsekundenfurz7876]

08:12 Conway & sons -- a reference to both Steinway & sons and John Conway, the inventor of the cellular automaton called "Game of Life." The logo is a glider, a shape in that automaton that recreates itself at a different location.

[@MegaPhester]

It's so cool that the riff established at the beginning of the sequence always comes back on the beat, since that part of the sequence only comes back at multiples of 16. Makes it feel like a composition. The fact that the melody happens to sound phrygian-ish is hilarious as it makes it sound like thrash metal.

[@benedictul]

Not gonna lie, it kinda reminds me of something on Megadeth's Rust in Peace - or maybe Slayer? Just alter the time signature a bit and you got a hit imo.

[@danielpalma7279]

at 100 bpm sounds metal af

[@recklessroges]

Who ever chose "Conway & Sons" for the piano name,,, thank you. (I'm not crying.)

[@MrDizzle715]

Can you explain please? Idk what that references.

[@renagonpoi5747]

@@MrDizzle715 Conway is the mathematician behind the game of life and the problem associated with it. He has made multiple appearances in Numberphile. Sadly he passed away last year due to CoVID.

[@ServentForAnubis]

I also like how it had the glider as the logo.

[@todorkolev7565]

@@renagonpoi5747 thanks for explaining. I am ridiculously bad at picking up references :D Even though I am a huge nerd for Game of Life!

[@AaronRotenberg]

@@todorkolev7565 Also, it's a pun on Steinway & Sons, a famous piano manufacturer.

[@KevinLarsson42]

7:10 DJ Neil Sloane - Le Rabot (Mod88 Remix)

[@imademedikasurya3917]

Hello

[@KevinLarsson42]

@@imademedikasurya3917 Hello to you :D

[@Rodhern]

If you want to go Mod88, and we all do, I would have chosen the middle of the keyboard as zero, maybe say 440Hz as the zeroth note.

[@KevinLarsson42]

@@Rodhern yeah I had the same thought when I listened to it

[@musik350]

more like opus clavicembalisticum - preludio corale - quasi pedali soli

[@impendio]

I actually like how dramatic the sequence sounds, I’m a huge sucker for experimental stuff and breaking data sets into music is a very interesting prospect to me.

[@idjles]

7:13 the piano‘s name and logo brought tears to my eyes.

[@PhngluiMglwnafh]

I love how delighted Neil Sloane gets over integer sequences. He didn't just create the OEIS, he is the OEIS

[@KurtSchwind]

Huge props for the game of life reference on the piano.

[@csababekesi-marton2393]

I always enjoy Mr. Sloane's lectures as nothing else. Cheerful, highly intelligent and interesting. His personality is ideal for being a professor.

[@wiseSYW]

it sounds pretty metal. even "binary rabot" sounds like a metal band name!

[@MaximeJean94]

Pretty sure that calling that expanding transformation "inverse Rabot" is incorrect. The rabot can delete runs, the expanding can not create new ones. Expanding 0 just gives you 00 which is 0, but there are plenty of ways to get to 0 with the rabot. Doing expanding then rabot gives you the starting number, but not the other way around, for instance expanding 1010 gives you 11001100 and rabot that you get 1010, but rabot 1010 gives you 0 and reexpanding that gives you 0.

[@miikavihersaari3104]

That's true. However, this same property applies to differentiation, yet it's considered the inverse operation to integration.

[@beesnation5008]

The term for that is a one-sided inverse.

[@lachlanstewart9314]

If I go too long without these episodes... I get sloanely :(

[@buzzzysin]

That certainly is an interesting bassline

[@jimoubenremouga9546]

That man is so chill that i want him to be my math teacher

[@Bronco541]

For some reason everyone of these sequence videos feels like he is revealing a surprising secret of the universe. Its very exciting

[@razieldolomite698]

The musical transposition was awesome. Never before have numbers sounded so menacing

[@ralfoide]

Mr. Sloane can magically transform a sequence of numbers into an amazing story. That was truly interesting. _Il n'y a rien à raboter dans cette histoire ;-) ... Merci Mr. Sloane !_

[@stkyriakoulisdr]

The real nugget in this video is that the piano reads "Conway and sons" instead of "Steinway and sons"

[@Desmaad]

R.I.P. Conway.

[@tsquaredtest1]

7:14 "Conway and Sons" LOL Very Clever. I would replace any Steinway with one of these

[@dhoyt902]

Only OEIS fans know the thrill of seeing "N.J.A. Sloane has published your changes to Axxxxxx" in one's email.

[@sghuisman]

Can relate!

[@Xonatron]

I made it in too!

[@bsharpmajorscale]

Yes! It makes me feel like a real part of the mathematical community! I had a sequence that I submitted because I was playing around with concatenating even numbers and counting the digits. Probably because I wanted to do some crazy stuff for Four 4s. It was really great.

[@Triantalex]

false.

[@Mr_Inconsequential]

Imagine that one guy waiting on reply to this letter he sent 18yeats ago

[@BluishGreenPro]

I wonder what are the best “tunes” the OEIS has to offer? Also, those Mandelbrot prints are really nice

[@avisternlieb449]

You can use the keyword "hear" in OEIS to see the ones they recommend listening to! Neil Sloane's favorite to listen to is Recaman's Sequence (A005132). There's also a Sloane Numberphile video on it!

[@numberphile]

We’ve made videos about others that sound good.

[@jazzabighits4473]

@@numberphile is there a playlist? :o

[@cxpKSip]

@@avisternlieb449 It wasn't Sloane, I don't think...

[@achtsekundenfurz7876]

There should be an OEIS sequence of all sequences sounding like music.

[@edskev7696]

The sequence is OEIS A318921

[@TRIC4pitator]

Final boss music

[@ButzPunk]

I think the inverse of the _rabot_ should be _bora,_ following the long French tradition of transposing a words' syllables to create new words (cf. «l'envers» → «verlan»).

[@davemarm]

You mean borat?

[@sanofy]

The verlan version of a word has the same meaning as the original word. bora would mean rabot.

[@danamulter]

I have no idea what he's talking about, but his enthusiasm is infectious.

[@kennethleitner1337]

to add on a thin layer (the opposite of planing off a thin layer) is to veneer: placage in French

[@mrsmartypants9136]

Or is it just planing with a poor quality tool? It has the opposite effect of planing: the wood becomes less smooth!

[@KevinLarsson42]

Those animations in this video are amazing!

[@astromus]

"Conway and Sons" - What a wonderful tribute!

[@johnchessant3012]

The (3/2)^k - 1/2 pattern is so expected and unexpected at the same time

[@venceremosallende422]

Gosh there could be a whole netflix series on the OEIS....

[@zidanez21]

Some viewers of Numberphile are younger than the time he took to finally see that letter

[@curtiswfranks]

This inspires me: It might take me eighteen years, but I will get back to it (whatever 'it' is) someday.

[@TG-ru8wl]

It started with the Mendelbrot set video and now I'm just addicted to Numberphile.

[@josephjohannes3240]

Me during the first half of the video: "I have no idea where this is going" Me at 7:15 : _oh_

[@glowingfish]

Same thing---I thought this was pointless until I got to the music.

[@archivist17]

I like listening to sequences. Beautiful idea.

[@SquirrelASMR]

I used to subconciously videos of this guy were filmed in a tent at the world math circus, but I just recently realized it was just because his wallpaper has stripes.

[@kateorman]

I couldn't sleep, so I listened to this in the middle of the night, and the music scared the living daylights out of me!

[@cidercreekranch]

Sticking with the woodworking theme, you could call the expansion operation the process of laminating a number onto the existing numbers.

[@kane2742]

Yeah, I was thinking it could be the French word for "veneer."

[@bazzad81]

@@kane2742 that would be ‘placage’

[@dro56789]

This binary planing sounds like a Doom song...

[@wagglebutt]

I was thinking Peter Gunn.

[@hamishlivo]

Metallica riff

[@macronencer]

Yes! My first reaction was that it sounded "a bit metal".

[@chrisa4284]

videos with Neil Sloane = instant watch + like

[@miokelphelts1]

Check out Keith Jarrett's solo piano Vienna Concert Part 1 ~25:00-31:00, July 13, 1991. Never made sense to me until I saw this video.

[@ericaferro9556]

Eerily similar.

[@Eulercrosser]

To get the sequence A027649, you must first make the sequences an integer sequence by multiplying by 2^(k-1), where k is the number of bits.

[@h.-.-]

Where can I find the 10hr clip of this piano track?

[@livedandletdie]

Nothing beats a Neil Sloane videos. If you didn't release anything but videos with Neil, there would not be any boring videos on this channel.

[@alvarogaliana3271]

ahhh, the sequence guy! i love these!

[@RandyKing314]

The Sloane videos never disappoint 👍👍👍

[@BryanLeeWilliams]

I love Neil's videos

[@landlord21]

Man I wish I had friends like this guy

[@edsanville]

We need a video "3 hours of Rabot's sequence music"

[@sparkmagea99]

"It has a great sound"; proceeds to talk over it so we can't hear it haha

[@expomath9348]

Always an amazing content ! Big up from France Numberphile 😘😘

[@jeeaspirant-abhi1394]

This channel best for mathematical specially.

[@andrewgalbreath2101]

Combining my two favorite hobbies: Math and woodworking!!

[@paulofernandes1375]

Play that on an electric guitar, it would sound metal af!

[@deckydoodle6792]

I love Neil Sloane!!

[@cajcsfsa]

Wow!! Impressive impressive and amazing dedication

[@christophecarpentier9797]

As a French viewer, hearing "_le rabot_" pronounced so solemnly feels both weird and majestic.

[@marklemoine1634]

That piano animation is astounding!

[@mkwilson1394]

Feels like E phrygian perhaps? The b2 is really prominent with all of the 1s. Nice pedal point!

[@Krebzonide]

You should do a video on how QR codes work with their masking and error correction stuff.

[@WhyDontYouBuildit]

Maths and my favourite tool in one video. Wow!

[@tonaxysam]

The song is very catchy :D "Le rabot" operations is very interesting indeed

[@InTheBeginningTheUniverseWas]

haven't watched the video yet, but since it's Neil you know it's going to be amazing

[@deeprecce9852]

I conjecture that papers and books in Mr Sloane's room contain more numbers than alphabets!!

[@Marguerite-Rouge]

I really like the sound of the sequence ! It reminds me Philip Glass music.

[@omikronweapon]

If you imagine Neil's mind to have a soundtrack like this, suddenly a lot falls into place :)

[@macronencer]

8:15 The name and logo on that piano are priceless!

[@MrJdsenior]

"2003 it arrived, I only just found it on the floor" LOL, with ya there, my friend :-) I've seen a composition, done by Peter Bence for a school (music college) project that was inspired by the Fibonacci sequence, but yours is the first I've seen that actually PLAYS the sequence, directly, from a simple one to one ratio of key positions to sequence. Clever, I'm going to pass this on to a few people and see what happens, will let you know with a link if anything does. :-)

[@martinfisker7438]

That piano animation must have taken ages

[@SO3rl]

I see Neil Sloane, I click, and I like.

[@user-vn7ce5ig1z]

7:17 - That music sounds like a chase-scene from an action-thriller. 🤔 I assume it's not copyrighted… 🤨 It sounds even better at 2× speed. 😉

[@vincentproud6589]

That music sounds so spooky, like a scary moment from a horror game or a chase scene.

[@Logicallymath]

A full 12-minute video YAY!!!!!!

[@marcelheymuth2113]

"Conway and Sons" on the Grand Piano is great! RIP John

[@cetyl2626]

Pretty cool. The music really feels like the binary structure

[@grahamumbo9059]

I was never taught this for A-level. No wonder I don't understand it so why do I find it so fascinating?

[@matanshtepel1230]

nice animations!

[@nijiru4448]

The music for the binary sounds like it would be awesome for a haunted house. :3

Here's something I quickly came up with: · Make a list of numbers and put 1 into it. · Repeatedly: Multiply any number in the list with any power of 2 and add any number from the list to it which is smaller than half of that power of 2, then put the result into the list. · Finally (whenever you don't want to continue with the step above anymore), only multiply each number in the list with any power of 2, without adding anything. With this method, you should be able to reach every number whose binary representation "flattened" turns into 0 and no other numbers, right? Example: Your list is {1,101,1001}, you pick 1001, multiply it by 10000 and add 101 (5

[@LeventK]

Teacher: The test isn't that confusing. The test:

[@qwvpv]

9:24 perhaps a "Veneer", is a woodier and more metaphorical opposite to planing, than "Expanding". Planing Veneering Le Rabot Le Vernis (disclaimer: I am not french, so there may be a better translation out there!)

[@RaineQi]

Watching the binary series getting planed I caught a pretty sequence unfolding, the number of shavings. The number of runs in each term for the binary sequence goes 1,1,2,1,2,3,2,1,2,3,4,3,2,3,2,1,2 Continued it goes (2),3,4,3,4,5,4,3,2,3,4,3,2,1,... On a graph it makes lovely peaks and valleys because the difference between consecutive terms is 1. I wonder of it remains 1 throughout the sequence...

[@RaineQi]

I think there's a pattern to the peaks and valleys too The first peak doesn't exist because its 1,1 so its 0 The next peak is 2, there is 1 term between the 1s The next peak is 3, there are 3 terms between the 1s before and after 3 The next peak is 4 which has 7 terms before it goes back to 1 The next peak is 5 which has 15 terms before it goes back to 1 again The new sequence is 0,1,3,7,15,... So the next term is defined as double the previous plus 1. Doesn't this have a name?

[@BryanWLepore]

[ hmmm... all these OEIS sequences are compelling subjects for musical exploration ] 7:08 “... and I would like to play this sequence for you.” Stunning... It sounds like 4/4 time ... I wonder how the time signature or meter is determined...

[@joedeshon]

OMG. 7:02 Neil channelling the spirit of John Williams, the composer of the Jaws theme! I need to use this in the chase sequence of my next horror film!

[@user-vn7ce5ig1z]

Except Williams didn't write the Jaws theme, the hack just ripped of Dvorak's _Allegro con fuoco._ ¬_¬

[@skyscraperfan]

How do you expand zero ones or zeroes?

[@jweezy101491]

I feel like the expanding operation and the planing operation are not inverses. When Neil said you can do one, then the other, and get back to where you started, I'm not sure that's correct. If I have 101, and I plane it, I get 0. If I then expand, I get 00 or 0, not 101. It is true if you expand first, then plane second. 101 -> 110011 -> 101. Because of this, I don't think Neils proof that this sequence hits all numbers is correct. If we take all the binary numbers and plane them, then expand the results, we do not get back the binary numbers we started with. Correct me if I am wrong, but it seems that proof requires a 2-way relationship between the expand and plane functions, not the the 1-way relationship we see.

[@sageinit]

Should try planing down the three main number sequences derivable from the plastic number - in balanced ternary.

[@c434rdd410]

so,this video is not for woodworking hand plane sequence?

[@L1N3R1D3R]

I'm pretty sure the inverse isn't surjective (onto), since the planing process can remove individual numbers and there isn't any way to tell how many runs there were. See how many 0's there were after planing; how do you invert that process to get back to each individual number? Sure, adding one to every string is bijective, but that's not the same process as the inverse of removing one from every string when the domain is every possible sequence of numbers, not just the ones with strings of more than 1 in length. You seemed to spend no time on this point when it's more complicated than that.

[@cosmicvoidtree]

The sequence number of the planed binaries is A318921.

[@trizgo_]

OMG EXCITEMENT I LOVE SLOANE VIDS

[@pedrofellipe8028]

Can we get a metal cover of this?

[@literallylegendary]

"Conway and Sons" with a Conway Life glider is an awesome reference to Conway's Game of Life

[@FinetalPies]

Full song on the second channel? I'm hoping so