Look-and-Say Numbers (feat John Conway) - Numberphile

The legendary John H. Conway on properties he discovered within the so-called Look-and-Say Sequence. Conway Playlist: bit.ly/ConwayNumberphile
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[@IoEstasCedonta]

"I hope I'm getting it right..." I hope I get a constant named after me, only so that I can personally get it wrong.

[@sriruparoy4946]

That's rude :/

[@sporebryan2000]

@@sriruparoy4946 it was a witty remark. Not rude

[@WoWhistorian]

@@sriruparoy4946 It's not rude, lol. I mean this man accomplished so much in his life that he actually forgot (or didn't even really forget, just mixed up some digits) in a constant named after him. I mean if most people had a constant named after them they'd remember it for the rest of their life because it'd likely be the highlight of their career, but it was essentially just one achievement in a lifetime full of them for Conway.

[@pooponunicycle]

'None of the boys wore long party dresses, or if they did they weren't distinguishable from girls'. Best quote ever.

[@coloneldookie7222]

"Anyway, one of them came up to me..." Wait...is he talking about one of the girls in the long party dresses, one of the boys not in a party dress, or a boy in a party dress? The world may never know!

[@greeeb.]

Colonel Dookie it had to have been a boy, Conway says "he said.." before beginning the sequence explanation!

[@NoriMori1992]

+nrh756 But the boy wasn't wearing a long party dress.

[@SHUBHAMGI]

how did you know :)

[@JorgetePanete]

SABER - FICTIONAL CHARACTER you forgot the intertogation mark

[@daniele_93]

"I couldn't get it", then proceeds to find an irrational root of a 71 degree polynomial and the 92 seeds of the sequence. Just when you thought you got him. RIP John Conway

[@Stormgebieder]

John Conway passed away on 11 april 2020... A great mind has left us. :'(

[@rogermouton2273]

that's sad

[@myriadsfeynman9096]

Noooo seriously? I think I had put this video in the Watch Later playlist when he was still alive then...

[@ganondorfchampin]

He died on a Doomsday.

[@mchlbk]

A victim of corona virus.

[@angel-ig]

@@ganondorfchampin Wow, it's true! Sadly, most people won't understand. R.I.P., by the way

[@NoriMori1992]

That's so cute that instead of just skipping class they threw a party! 0:45 - "Some of the girls wore nice long party dresses. None of the boys wore long party dresses - or if they did they were indistinguishable from girls." The deadpan delivery nails it. XD

[@XenophonSoulis]

Rest in peace. One of the most brilliant minds of our time...

[@Xnoob545]

Rip

[@shubhamg9495]

Immense respect.

[@liyi-hua2111]

rip

[@Triantalex]

false.

[@Goryllo]

I actually "discovered" this series myself in middle school, and noticed that 22 was the only number that didn't generate a string...

[@livedandletdie]

22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22... Oh and 2|3, 12|13, 1112|1113, 3112|3113, 132112|132113, 1113122112|1113122113, 311311222112|311311222113, 13211321322112|13211321322113, is interesting because the first half is just 1 less than the second half always.

[@itchykami]

He missed an opportunity; 22 should have been Helium; since it's a 'noble sequence'

[@rodrigoappendino]

@@livedandletdie Can you prove it?

[@rodrigoappendino]

@@itchykami But helium has 2 protons, so it's like it can decay into an hydrogen, but hydrogen can't decay.

[@Itwasalwaysme_Noone]

But did you really find this yourself? Because I knew about this kind of sequence myself, but did we knew it from Conway, even if we didn't know who he was when we were kids, this kind of knowledge was spreading around even before the internet. Maybe we saw it from someone else. So I wonder, did we knew about the sequence independently of, or because of Conway?

[@TopShelfization]

1 1 was a race horse, 2 2 was 1 2, 1 1 1 1 race, 2 2 1 1 2.

[@randomdude9135]

I don't get it

[@randomdude9135]

@Deus Vult Fun thing is I was binge watching Vsauce. So Vsauce actually makes you smart 😂

[@alansmithee419]

I love this. I vaguely remember it from a while ago. I was very young then.

[@skydragon3857]

@@randomdude9135 its a quote of sorts

[@Gioeufshi]

Knew about this sequence before it got viral. like a boss.

[@dark808bb8]

+Gio Eufshi this video came with a very strong dejavu feeling. i think a lot of people may have played with numbers like this before. :)

[@ClementinesmWTF]

Rest in peace Mr Conway. This was my favorite math “party” stumper as far back as the 8th grade and has always been a fun thing to look at and study (or even just to write down). Your work will live on in (in)famy for history as some of the most interesting problems-turned-games for even the those who least enjoy math. You’ve left an impression that is everlasting and we won’t soon forget.

[@afourthfool]

Reminds me of the "only number that describes itself": 10233221, with the hundreds thousands' place being independent. Read audibly, it says: " One Zero, Two threes, Three twos, Two ones.", describing itself. Sourced from some book somewhere.

[@smiley_1000]

What about 22?

[@phanindrasarma7973]

Could it be Finding Moonshine? I'm not really sure but that's where I read about John Conway for the first time

[@davinchristino]

@@smiley_1000 Actually, 22, 4444, 666666, 88888888 should all work.

[@karmapolice9477]

@@davinchristino No. Because 4444 gives "44" and then "24" and then "1214" and so on. 666666 gives "66" and 88888888 gives "88". It's only 22 that continues forever : 22, 22, 22, 22...

[@OrionFyre]

I remember being given this problem as an extra credit problem in my geometry class. Of the ~25 students, two of us got it right (this was back in HTML1.1 days). That evening I got home and began playing with it. It consumed me for a whole month. Even writing my first REAL bit of code on a machine my uncle gave me to print out on screen the sequence and navigate it forwards and backwards and to store sequences and highlight them in other numbers. This stupid little puzzle my teacher gave me 5points of credit for solidified in earnest my fascination with computers and programming that has endured to this day. Ahhh the nostalgia, THANKS BRADY!

[@ijabbott63]

R.I.P. John Horton Conway, born 26 December 1937, died of COVID-19 on 11 April 2020 (aged 82).

[@Sylocat]

When I saw that some of the numbers contained 3113, for a moment I thought the 1's were Knuth up-arrows.

[@alejrandom6592]

Lol

[@keniangervo8417]

Wow, nice nicee! The real question is how the heck did they find out the Conway constant is the root of that 71-degree polynomial?! The polynomial doesn't seem to have any structure in it really. The plus and minus signs alternate chaotically as well as the quantities of X's. I would really like to know more about this.

[@ignorantFid]

Each term in the sequence depends on the last one. So it's a kind of recurrence relation, like the Fibbonacci sequence. If you write the recurrence as a 92-by-92 matrix, the polynomial should show up in the matrix's characteristic polynomial.

[@aleksapetrovic7088]

Wolframalpha

[@ganondorfchampin]

@@ignorantFid With more detail, as each element has a certain number of digits, to get the number of digits in the sequence you only need to know the number of times each element appears in the sequence, not the position. This allows the relevant information for the proof to be captured with a 92 dimensional vector, even though the order information is missing. This also defines a metric on the vector space (form of L1 norm) to get the length of the sequence. Each element generates a specific number of specific other elements regardless of where it is positioned, so the transformation from the vector summarizing one sequence to the next is linear and thus can be represented by a matrix. I'm guessing the determinant must give the average impact on the L1 norm after the transformation is applied, which is where the characteristic polynomial and Conway's constant show up.

[@Ovenman940]

Did the student get credited in the paper?

[@alejrandom6592]

For what?

[@quantumgaming9180]

For giving Conway the sequece​@@alejrandom6592

[@manon-gfx]

the PNG file format uses this technique to compress images. Let's say you have an image with a bunch of red pixels, and then a bunch of blue pixels. You can store the images as *amount**color*, so you would go for example 20Red, 40blue, etc. It uses some more tricks for stuff like gradients, but in essence it's the same technique.

[@tabularasa0606]

Run Length Encoding.

[@RealCadde]

And that is why PNG is smaller (and crisper) for screenshots of an application but JPG is smaller (and not so noticeably compressed) for photos and such.

[@StigHelmer]

Actually it doesn't. PNG uses deflate compression in combination with prediction. Basically, it replaces patterns it has seen before with pointers to those patterns. There's a computerphile video on the compression technique used.

[@doccleveland]

Brady you should spend a week with this man!

[@doccleveland]

...and Dr. Holly K.

[@daedra40]

doccleveland you doctors!

[@Sylocat]

The roman numeral "IIII" at the end made me think of counting in Unary (base one). If you count in Unary, all the numbers in this sequence are in exact sequential order.

[@OGPatriot03]

"none of the boys wore long party dresses, or if they did they were indistinguishable form girls" - So funny.

[@larrytroxler7017]

The legendary John Conway on KZbin! What great times!

[@AntonAdelson]

This is a good version of the "petals around the rose" problem. Since I was already acquainted with that one, solving this one took me one second.

[@itsalongday]

It's my favorite sequence of numbers and I spend many times in school after tests when I was bored and I had much fun with it.

[@bw0n6]

Thank you for this fun and fascinating video. If I may make a suggestion, I think a Numberphile series on Surreal Numbers with Professor Conway would be an excellent topic.

[@kay486]

COnway videos are the best! i really RELLY hope we will see more in the future!

[@Soldier842]

This was really interesting! These kind of video's make me increasingly interested in the mystery of numbers.

[@mitalisharma440]

the fact that this recursion has a characteristic in another chaotic seeming recursive matrix(life or so , in conway's terms) is beautiful. and , such interlinks with no relations whatsoever, "catch my fancy". colouring such numbers, also brings them to life, bringing out patterns, with "no relation whatsoever".

[@beardymonger]

I don't care if Professor Conway reads the phone book, more please. Many more please :-)

[@unvergebeneid]

I would tend to agree but if I recall correctly, Conway at one point in a past episode didn't try to be polite about the fact that the interview bored him to death so I wouldn't count on it.

[@CrimsonDrake90]

Penny Lane Yeah, that was heartbreaking.

[@user93237]

Penny Lane After watching it once more I think it was meant in an ironic way. He says he’s doing interesting things and clarifies that he means doing mathematics and not what he’s literally doing at the moment (giving an interview). I guess that guy simply has a very odd and dry sense of humour.

[@Martykun36]

that's gonna be a bit difficult now

[@RedRad1990]

Yeah, guys like Matt Parker are great educators and attract new "followers"... but there's this strange magnetism in those "old professors" like Conway

[@zoranhacker]

I've tried this but a bit differently, instead of counting all the same consecutive digits I counted all the same digits in the whole number, and discovered that it eventually starts alternating between 2 numbers for a seed of 1: 1 11 21 1211 3112 (here is the difference, I count all the 1s in the whole number at once, not only the first one) 132112 311322 232122 421311 14123113 41141223 24312213 32142321 23322114 32232114 23322114

[@franzluggin398]

I was intrigued by this and implemented a generator for this sequence in python. It seems every single-digit input produces one of two cycles: 1,2,3,4: They all produce this exact same pattern after a few iterations: 32232114 23322114, also, all four reach 23322114 first. 5-9 and 0: They all produce constant sequences after a few iterations, and all limits look the same except for the last digit (the input digit): 332231141X, with X being the input digit (5-9 or 0). I tried a few other random integers

[@zoranhacker]

Franz Luggin that's awesome

[@Xabylon]

This is known as a "pea pattern"

[@junjo9581]

I'm seriously loving this..

[@matambale]

I heard this puzzle long ago on a radio show called "Car Talk" - would have been 1987 or later, though, when the show went national.

[@thekkl]

I like videos like this, they give me a rare glimpse into just how smart some people are.

[@topstitchgirl]

I had fun typing this out over several rows. And if you align the text, you also see a nice curve (or curves it's centre align) appear.

[@sinecurve9999]

This is fantastic! Thanks for sharing!

[@cesardalealbo]

Rest in peace, legend!

[@adlerdrahms8966]

I'm so glad I'm alive at the same time this man is.

[@Kowzorz]

I love this Conway stuff

[@TopTheComment]

Yay, I love this sequence!

[@BelialsRevenge]

Wow, i missed this one. Great episode!

[@StefandeJong1]

1 MILLION SUBCRIBERS! Congratz, guys!

[@zibiwisniewski340]

Absolutely amazing!

[@anishsurepeddi5422]

Congrats On 1 Million Subs!

[@NotLegato]

it's not to a million yet! give it an hour or so haha

[@fasfan]

I fully admit I don't understand a lot of the videos on this page.... I can see the concept and believe the speaker. But I enjoy them all none the less. I was excited when this one started because I was on board and was keeping up right up until he started putting chemistry in it. Then I was only partially on board. lol.

[@SendyTheEndless]

I managed to work out the sequence before Conway revealed the secret, but to be honest, I think the title "Look-and-Say Numbers" somewhat made it easier to deduce, than it would have been for Conway in the original setting, not having a snazzy video title to clue him in :)

[@TaliesinMyrddin]

A teacher put this on the board when I was in high school. Took me about a minute to get up and add the next line, and no one else in the class seemed to get it.

[@tilulu73]

So, how does it feel to rediscover this sequence 2 years after ? ^^

[@rolandgerard6064]

@delwoodbarker, the precise words to explain the logic, chapeau...

[@TakeWalker]

Fascinating!

[@MartKencuda]

I'm happy he got to talk about something other than the Game of Life.

[@firstiesify]

Very cool. I'm gonna try this on my friends.

[@VictorChavesVVBC]

Really awesome results for such a simple math game-like problem.

[@skele56]

When I first saw the sequence in the form of a problem I was around 11, and I though I was the only one who though deeply about it. Of course the only real conclusion my 11-year-old self reached was that there could never be a 4.

[@thomasthetankengine2653]

skele56 Same

[@MoneyChanger02]

Came on 1/11/21 (to us Americans) to pay respects. RIP Professor Conway

[@AManOfMusic]

Rest in peace John Conway.

[@ToineHulshof]

Grats on 1 million subs!!!

[@immakitty88]

this channel consists of the nerdiest of nerds... I love it

[@LEATHERrebelJUSTICE]

There's two mathematicians named John Conway born in the 30s. Stop it universe, just stop it.

[@stumbling]

There would have to be a prime number of John Conways, wouldn't there!

[@giacomopamio1191]

Sorry, but isn't 2 a prime number?

[@maxadam2447]

Though this Conway is older, the two were birthed independently.

[@K-o-R]

The sequence of John Conway just split in the 30s, and both halves continued correctly.

[@MrCubFan415]

K.o.R Underrated reply :)

[@TheWhitePianoKeyProductions]

wow, I didn't know this one, but when he showed the 4th one, I knew it already :D this is a cool sequence

[@MogaTange]

I’m guessing it’d be impossible to have a 4 in the sequence because that would require say “1111” which would require you to count the same number twice back to back when you could just say “21”.

[@WhatsACreel]

Brilliant video as always! If you've got John Conway handy for any upcoming filming sessions, would you mind asking him to explain that Blue Eyed Islander riddle? Would you film a Numberphile on the topic with the man himself? As far as I know Mr. Conway provided the first solution (certainly one of the most accepted solutions), he used a concept of common knowledge. I've read solutions, they go: “if you know a person knows, you know he's got blue eyes”, and then I can't understand anything. It's rather logic-based, as opposed to arithmetic. It's an excellent riddle and the solution is genius. If Mr. Conway and yourself have time to film such a session, it would be a historic moment in the riddle's history, and something I think the world would cherish forever. Either way, thanks for all your work Brady and Mr. Conway!

[@arithmeticum]

advent of code brought me here

[@9ThePatch]

My dad showed this to me when i was in junior high. I filled a note book. There is also a growing pattern in the front of the number as well as the back. In the front it's every other. In the back it's every third. This pattern grows from the inside out. Try coloring the pattern green as you go down you will see what i mean.

[@TristanBomber]

Numberphile, you do a lot of videos on imaginary and complex numbers, but have you thought about doing on e about quaternions (a + bi + cj + dk)and their properties and uses?

[@LukeSnyderMusic]

I wish the name of this sequence wasn't in the video title; I've never run across it before, and it ruined the puzzle :(

[@jaydanl3830]

so close to 1,000,000 cant wait for their number vid on 1 million :D

[@SumNutOnU2b]

RIP professor Conway. A truly great man.

[@gedgar]

This was already my favorite pattern but now my fave mathematician over analyzed it and nade it better

[@Deathrael]

SURPRISE!!

[@thdremily]

Seeing a relationship between different number bases would be cool too! like with hex, e.g. 4dd8 has 142d18, that could make the polynomial constant representation enourmous!!!

[@lichdomftw]

He has a wonderful sense of humor.

[@bluebears6627]

RIP. A legend

[@warmCabin]

This is identical to an old and simple as dirt data compression algorithm called Run-Length Encoding. You can see that certain sequences get shorter, like 4442222 -> 3442. But random data tends to get longer, which is why these sequences always grow in length.

[@voveve]

We played this in 6th-7th grade a lot, starting with different numbers... Never thought there was hard math behind! XD

[@sr.junior4670]

Rest In Peace

[@rogermouton2273]

I think of John Conway as a mathematical mystic. What a mind.

[@t850]

...spark of curiosity ignied the flame of ingenuity. It's interesting to see how mathematicians mind thinks over a number "problem" by relating it to a known physics phenomena...:)

[@benjaminjosephmyers]

WOW they just hit 100,000,000 subscribers!!!

[@Xonatron]

6:55 - I went to Acadia University in Nova Scotia. Too bad I was able to be at this lecture. RIP Conway.

[@123must]

A genius ! Thanks

[@cliffthecrafter]

This sequence appeared in a video game called "Please Don't Touch Anything".

[@RezaAP]

Wow... this was very interesting... Thx

[@lucasrabelo10]

This man is really a genius!

[@vgstep]

RIP John Conway, what a ledgend

[@oliwiermoskalewicz1988]

RIP 😭

[@athulu]

Rest in peace, John Conway.

[@absupinhere]

I really wasn’t expecting this 😂

[@ABitOfTheUniverse]

I like John. This may seem rude, but I'd like to see more old mathematicians on here. They're like wise, yet befuddled, wizards. There is something about minds like that that I would like to find a connection too. Beyond the adorableness of it. Maybe it's their personality, still intact, their lack of common characteristics of communication, shining through coupled with the deterioration of their bodies, in this case, the vocal cords and the face. However, I imagine there is something more going on upstairs, inside. Maybe they've spent their lives investing in the neocortex, and I recall that being the first thing to go as the brain deteriorates. While it's the newest part of the brain for mammals like us, and the one that makes us so richly complex, it doesn't seem to stay intact as long as the older, more basic parts. My apologies if that sounds morbid or disrespectful, but I like brains. All brains are interesting but it's the outliers that are particularly fascinating.

[@antiantiderivative]

Liking brains doesn't make you disrespectful, it makes you a zombie.

[@hab1939]

.

[@Triantalex]

cringe..

[@RENCIOL]

I really need to start playing with the ideas in my head like prof.conway lol :)

[@TomMalufe]

It's very funny to me that someone could do a whole lecture (and have it attended by highly educated people) on the interesting mathematical properties of a riddle.

[@biswarupmukherjee8068]

He was a legend , Rest in peace sir

[@sabinus9441]

I guessed it before disclosure; but I think the way he intoned it gave it away...

[@DJejbarros]

You'll be missed, sir...

[@jacks.4390]

Ah this is nice. I saw this problem a while ago and I didn't get it either; I feel better.

[@StevenRoemerman]

If you put a gun to my head and demanded that I explain how to recreate this sequence. I think I'd end up with a new hole in my head. I don't understand how you get the third sequence.

[@WalterKingstone]

Brady can you make a video with John Conway talking about his 'chained arrow notation'? It's like a much bigger version of Knuth's Arrow Notation.

[@richardx4264]

John Conway-Rest In Peace

[@mrKreuzfeld]

If I remember correctly, in early roman numerals, they wrote IIII instead of IV. This would probably lead to something different :)

[@TeShiky]

I didn't figure it out when someone told me about it. In fact I figured it out by my self!

[@illdie314]

I feel proud of myself, i figured it out on my own :D

[@unvergebeneid]

Is there any meaning associated with the other (complex) roots of the Conway polynomial?

[@Wotsdid]

Nice, I've never seen this sequence before. Also: Will you maybe make a video with John Conway about FRACTRAN? Would be awesome :)