Amazing Graphs - Numberphile

Full Amazing Graphs trilogy: bit.ly/Amazing_Graphs
Featuring Neil Sloane of OEIS fame. Even more unexpected graphs in our next video.
More links & stuff in full description below ↓↓↓
More Neil Sloane videos: bit.ly/Sloane_Numberphile
Neil is the master and keeper of the On-line Encyclopedia of Integer Sequences: oeis.org
Sequences in this video included:
oeis.org/A133058
oeis.org/A265326
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from Math For America - www.mathforamerica.org/
NUMBERPHILE
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Videos by Brady Haran
Animation and editing by Pete McPartlan
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[@numberphile]

Watch the full Amazing Graphs Trilogy (plus an extra bit): kzbin.info/aero/PLt5AfwLFPxWLkoPqhxvuA8183hh1rBnG

[@lejka23456]

nice

[@ChristopherRucinski]

For the 1st graph, what happens with the slope=1 line just before x=100 and just after x=200? Why do they partially repeat the line?

[@lejka23456]

@@ChristopherRucinski it is a mystery sherlock holmes is on the case

[@Marci124]

The link is broken for me.

[@indiapopularchannel7451]

Lottery guessing you tell me

[@MrBluesboy15]

Brady: That's amazing, who found that!? Neil: I did Brady: Alright

[@janlhab2329]

It says on the OEIS page that a guy named Max Barrentine is the author of this parallelogram sequence.. !. Why does Sloane claim he found it in this video then ?.

[@dabluse3497]

@@janlhab2329 he asked for who graphed it

[@yuvalne]

+

[@Triantalex]

??.

[@RealClassixX]

This man did the impossible. He remembered a character from Avatar.

[@pedroscoponi4905]

It's easy to remember the banshees, though. They're probably the best thing that came out of that movie...

[@RealClassixX]

@@pedroscoponi4905 The what?

[@ma7cus89]

He didn't even remember the character right, he said Scully not Sully, it remains impossible to remember those characters

[@Sylocat]

@@ma7cus89 How did you remember the actual name then? 🤔

[@jblen]

@@Sylocat a magical thing called Google probably

[@christophecarpentier9797]

The tooth term... ...🦷 Solid comedy

[@mattgsm]

Solid tooth

[@Tondadrd]

Using iOS? All I can see is a square, no emonticon...

[@isaaccisa]

@Death is our worst Enemy 2th -> twoth -> tooth (a mispronunciation of 2nd)

[@mbrusyda9437]

@Death is our worst Enemy a spare second.. you're doing this on purpose, aren't you

[@christophecarpentier9797]

@@Tondadrd works on a browser, not on the android youtube app

[@PjotrV1971]

I love that "Fly straight dammit!" sequence.. out of complete chaos, suddenly order emerges.. amazing indeed!

[@OlafDoschke]

Yes, that's not the only instance of deterministic chaos, also see Feigenbaum constant.

[@jacksparrow440]

have a look at langton's ant, you'll like it

[@paaaaaaaaq]

Turn it into chaos again and it is perfect.

[@danielroder830]

I wouldn't say complete chaos, there seems to be order in it, but not so obvious in the graphic representation. At the beginning of the chaotic part you can see parts of the lines that will later emerge. And it looks a bit wavelike there too. In a higher dimensional representation we would maybe see even more order, just a complete guess though.

[@filipsperl]

Is there a way to calculate where the first even term = 1?

[@Xbob42]

In today's episode of Numberphile, Number Grandpa reads us his graph-based Avatar slash fiction.

[@F20SW]

@@spikekiller4303 graf, graaf, grarf are the three pronunciations I've heard. I'm from the south west of England so I use the middle one, which is not dissimilar to the American way but the A is more dragged out.

[@xenontesla122]

@@spikekiller4303 11:48

[@penand_paper6661]

@@F20SW I pronounce it /græf/, using IPA notation when writing that

[@aquawoelfly]

Number grandpa is klien bottle guy.

[@mickeyrube6623]

Spike Killer Grav

[@BluishGreenPro]

Can we grant Neil immortality please? It seems like the man would love nothing less than to meticulously find beautiful graphs for eternity and share them with the world.

[@alexpotts6520]

Neil already has immortality, in a sense. The OEIS will be around long after he is gone.

[@KINGKROSBYSKINGDOM]

What is OIES ?

[@JBergmansson]

@@KINGKROSBYSKINGDOM The Online Encyclopedia of Integer Sequences

[@hexagonist23]

@@alexpotts6520 He's 83, he will probably die in the next 10-15 years.

[@Triantalex]

false.

[@undergroundmonorail]

it's incredible that this guy remembered anything from avatar

[@satyampandey2222]

Its an incredible movie so no shocker

[@KatzRool]

@@satyampandey2222 not a single person I know remembers anything about it, and the vast majority including me have never seen it

[@TheAlps36]

He did call the main character "Scully" though

[@wasdwasdedsf]

@@satyampandey2222 qua

[@eliavrad2845]

His job is about long sequences of numbers- he must have an amazing memory

[@Jkirek_]

"Who found that?" "I did" That's fair

[@andymcl92]

I think the more important question is "Why did someone work out that sequence in the first place?"

[@umbragon2814]

@@andymcl92 because mathematicians are insane

[@anarcho.pacifist]

insanely curious

[@calebvr3526]

Dc T

[@Triantalex]

??.

[@avi12]

0:25 "The tooth term" - it's brilliant

[@Adam-cn5ib]

i don't get it

[@DrShwazz]

He said 2th (tooth) instead of 2nd (second) lol

[@Czeckie]

i really liked "oneth"

[@LemoUtan]

A Scotsman would note that he bridged the 4th term

[@orsonzedd]

Tshirt when

[@M_Oz_]

I love watching these videos, because the people in them love what they are doing.

[@Luminous.A.Glory_VitaNostra]

M Oz SAME

[@mysticalpie4695]

Yeah and it's like a journey to be the ultimate genius

[@JeroenBouwens]

That's so cool! I was playing around with this, and found another interesting one based on the "fly straight, dammit" graph. If you change the rule for the case there is no GCD to "a(n)=a(n-1)+2*n+2", you get an almost regular graph that keeps rising to over 4 million, up until n=2090. At this point, it so happens GCD is equal to n, and the next value suddenly drops back to 2089, only to start rising again. I thought that was interesting anyway :).

[@GRbz026]

7:53 "So next graph, we look at the primes" * sneaky Amazon Prime box on the background *

[@VivaanTheCraft3r]

Oh yeah cool

[@thejelambar82]

Everybody: great movie Grandpa: fly straight dammit sequence

[@AXEUROLder]

Great movie? You mean Avatar?

[@General12th]

@@AXEUROLder Judging by this comment section, apparently Avatar was a mediocre movie that deserves to be left in the dustbin of bad culture history. Watch something else instead. I think they're wrong. But my opinion doesn't matter.

[@Jiggerjaw]

If James Cameron doesn't use this for marketing for the Avatar sequels, he doesn't know what's good for him.

[@SlightSmile]

They didn't 😥

[@johnpossum556]

I love how all the OS books form his computer standing desk.

[@rudiwinkelstein2483]

I guess there was no stackoverflow when he first learned about computers

[@hexagonist23]

@@rudiwinkelstein2483 They should print all of stackoverflow into a bunch of books

[@N.I.R.A.T.I.A.S.]

That 'Fly straight, dammit!' graph is incredible.

[@seanspartan2023]

He called the step graph very pedestrian and I chuckled 😂

[@charadremur333]

I get it now.

[@PhilBoswell]

If you look at the graph at 7:24 and follow those lines back, you can see them trying to form a bit before 100 and a bit after 200. This is like the classic chaos generator, jumping all over the place and then suddenly sobering up…except this one never falls off the wagon ;-)

[@elevown]

Only on zero and slope 1 tho for some reason not slope 2. wonder why?

[@ianmoore5502]

Are you speaking of the bifurcation diagram or is there another chaos generator i shouls know about?

[@mrpokemon1186]

Phil Boswell it went to rehab

[@catchara1496]

elevown because in order for it to form slope two consistently enough to be visible slope one has to be an order of magnitude more constant that doesn’t happen until then

[@moeboe6293]

I'm not quite sure what I've imagined Mr. Sloane of Integer Sequence fame to be like, but I probably didn't think he would be talking about the Avatar movie wearing a Barcelona shirt.

[@Rosie6857]

Given recent financial developments he'd be advised to stop calling it a Barcelona shirt and say what it really is, a Crystal Palace shirt.

[@christiangrantz6906]

This guy: "Parabolas... Boring! Boring!" Archimedes: "ExsCUSE me?!"

[@zyaicob]

Matt Parker is livid

[@MaksymCzech]

I remember how amazed I was at the graph of Dirichlet function, which is 1 for rational argument and 0 for irrational argument. The graph looks like 2 straight lines y=0 and y=1, but in reality those "lines" are full of "holes" and the function is discontinuous at every point of real line.

[@HasekuraIsuna]

11:21 savage He does not frick around with less interesting sequences

[@kjpg7413]

I'm just happy to see sequences that aren't base-10 specific!

[@renemunkthalund3581]

@@kjpg7413 Surely most sequences aren't…? (base-10 specific, we just choose to write them out in base-10).

[@Reliquancy]

@@kjpg7413 the prime one was base 2 specific though

[@kjpg7413]

@@Reliquancy you are correct.

[@redpepper74]

K JPG base-10 specific sequences by themselves are pretty disappointing, but implementing them into different bases and comparing the sequences can be pretty interesting.

[@mitchellclark4377]

I now have a Python function called 'dammit' because I wanted to try this for myself...

[@ayushrathore9190]

Can you please send me the code, I am waiting for it

[@lonestarr1490]

@@ayushrathore9190 Just implement the if-condition as given in the video and let it plot the result. That's far from hard, pal.

[@duncanbates5361]

@PIYUSH YADAVPython is a popular programming language.

[@frabol02]

I've seen Neil Sloane plotting sequences with a Barcellona shirt My life is complete

[@calebsousa2754]

*Barcelona bud

[@2fbDJLL]

1:56 *I wish I could have seen his facial expression when he said, “Fly Straight, Dammit!”* That was the best sequence name ever!

[@scottclowe]

The parallelograms are made by plotting X against (X minus the value made when X's digits are reversed in some base). Primes have nothing to do with it, and the result will still hold if you use a different base to base 2.

[@anothermoth]

The one thing limiting it to primes does is exclude even numbers after 2. If you graph with all numbers, you find the odd numbers form parallelograms as shown, and the even numbers form another set of equal sized parallelograms above the odd ones, filling in the space to the y=x line.

[@MrDannyDetail]

I was thinking the same thing, and looking for a comment like this. If it had've been a special property of primes then it would have in effect been a fairly simple primality test, which seemed unlikely to me.

[@cynoclast]

Does it work in a number base that isn't divisible by 2? I bet it doesn't.

[@FourthDerivative]

For the second sequence, is it important that the entries be prime? Or would you get the same pattern by doing the reverse-and-subtract operation on all the positive integers?

[@JayBringer111]

Been watching Numberphile since I was little and I absolutely love it. The fact that you've already got nearly 50,000 views within the first couple hours of posting is just marvelous. Keep up the good work Brady!!!!!! ILY

[@leonnuske2484]

Neil Sloane has to be my favourite. So chilled and passionate.

[@ker0356]

I never thought that I would be so interested in number sequences

[@msclrhd]

The Brady/Numberphile sequence: 11, 255, 16, 8128, 6174, 69!, 220, 284, 15, 153, 31, etc.

[@jacobbaartz7710]

This guy is the David Attenborough of mathematics. Something about how he explains graphs is so... Soothing.

[@lucbourhis3142]

The OEIS is amazingly useful. It helped me to find a formula for several sequences I could not find one for!

[@Ny0s]

This was great. How people come up with such sequences is beyond me, I admire that a lot.

[@Ruddigore]

There is nothing LESS about this video.. It's well worth a LOOK 👍.

[@E3rK57]

This was incredibly entertaining to watch. Love these "magical" graphs or plots! I will never forget about the "Everything Formula"! Can't wait to see the next vid!

[@ceruchi2084]

I love Neil. His appreciation of mathematics is so heartwarming.

[@xystem4701]

I love Neil! And I’ve been a big fan of the OEIS for a long time, what a great site.

[@gigs1890]

Your graphical work has gotten to be really impressive :O

[@InigoSJ]

This guy is the best. Every time a new of his videos comes up makes my day

[@mana24]

Moar graphs, brady! I can't wait! Thanks for the awesome vids

[@georgemachappy]

I would love few things more than to have an audiobook narrated by Neil Sloane.

[@jonathanwalther]

10:25 Who found it?! Prof cool as anyone could be: I did. Thänks for the gräphs. Love seeing these vids!

[@aaronthomaswebster]

This sequence looks a lot better with just all odd integers. Instead of just looking at primes.

[@JESSEverything]

I really like this guy's enthusiasm and passion for his work.

[@pixelatedmushroom]

Both of these were excellent, thank you for making the video!

[@grainfrizz]

Remember that movie, that second top grossing film of all time?

[@iliketurtles4463]

Pepperidge farms remembers... Harambe

[@KingofJ95]

It should be noted that, adjusting for inflation, Avatar is still number 1.

[@grainfrizz]

With inflation, it's gonna be Gone With The Wind

[@PeterJavi]

There were blue people in it. That's all I remember

[@xevira]

@@PeterJavi the Smurfs?

[@monoastro]

He knows a character's name from Avatar Get this man to Jacksfilms

[@Jiggerjaw]

Pretty sure it's Sully, not Scully - clearly more of an X-Files fan than an Avatar fan.

[@NocturnalCoder]

that thought crossed my mind too, lol

[@Jiggerjaw]

Oh, he got it right later in the video. REDEMPTION

[@MegaPhester]

Twitter for Online Encyclopedia of Integer Sequences

[@meghanto]

Never thought I'd see a big forehead clan member

[@WaffleAbuser]

I love the videos with Neil! They're really interesting!

[@noncanadian]

i love neil's speaking voice. would love to hear him narrate audiobooks

[@impossiblemission4ce]

1:36 "Remember that movie, called Avatar?" No, it's been scientifically proven that no-one remembers that movie, except for it being that movie with the blue people.

[@llamallama1509]

The Smurfs?

[@bearsfan519]

Ehh if you can remember Pocahontas you've got it covered.

[@francescosirotti8178]

@@bearsfan519 Pocahontas with cannons, to be precise

[@falconerd343]

Can't even find a clip of the scene he referenced. Definitely disappeared into the ether.

[@connorhamilton5707]

It is Fern Gully, but big and science fiction instead of small and fantasy.

[@raafmaat]

Ive never liked math.... hated it in school, never used it for my jobs either... but only recently (im 32 now) im starting to get into it because of vids like this! wish i would have been into it as a kid, i feel like i have missed out so much greatness! :(

[@aryanpatel2924]

raafmaat - I don't blame you. Even as a student who loves math in schools, I can't deny that a lot of school math is pretty tame compared to what is out there. I wish they would bring some attention to these crazy quirks that just blow our minds when we see them

[@jacksonpercy8044]

I used to enjoy maths, but when I started learning lots of more complex stuff without learning its applications, I lost interest. That said, I still love watching numberphile videos as much as I used to.

[@thePrinceOfPurpose]

I love these videos. Such amazing information in such a short period of time.

[@kunalchakraborty3037]

The prime inversion graph is as beautiful as it looks. Made my first c program to find the x and y values of graph upto any number of terms. Thanks for sharing.

[@ricardo.mazeto]

Brad, please make a video about the most interesting IOES sequences!

[@patrickstonecrusher]

"Look at this graaaaph" 😐👉📈 😐 😐

[@charadremur333]

Precisely

[@bxb77777]

Whenever I look at it make me laugh

[@sebastiansimon7557]

Comments you can hear.

[@chessandmathguy]

This was truly amazing! Please post more videos like that! Also, loved the tooth joke lol 🦷

[@tantzer6113]

This reminds me of Stephen Wolfram’s idea that within a generally irreducible trajectory in the way the universe moves through time (according to specific rules) there are going to be pockets of reducibility, where it becomes possible to formulate physical laws and make predictions.

[@guyarbel2387]

"Who found that ?" "I did" Lol

[@TECHN01200]

These OEIS videos make me want to find my own sets/sequences

[@FerousFolly]

Neil's love and passion for numbers is so contagious

[@CharmEng89]

the art is really sweet and those graphs are truly amazing!

[@xblizzqrd]

The fly straight dammit sequence really fascinated me, I started plugging in different values for d(0) and d(1) and I found that at some point it will always find it's balance and "fly straight" , anyone know why?

[@Eillcon]

Looks like a weird blue Gandhi. Nice video as always!

[@randomdude9135]

Mahatma Gandhi ji- the father of our nation(India). 😊

This makes me nurdgasm!! More graphs, please!

[@THELizardSlave]

I love Neil Sloane on Numberphile. Glad we're seeing a lot of him!

[@wompastompa3692]

_Fly Straight Dammit!_ Best sequence name.

[@Skrzynia]

4:20 Fly straight dammit sequence is XD. around horizontally number 420 there are 3 smiles made from dots perpendicularly around 420 900 and 1300. Insane coincidence. Im high

[@jmcusack]

:)

[@mrpokemon1186]

You on the 420?

[@michaelcherry8952]

This man derives great joy from graphing number sequences and he spreads his joy when he talks about them. It is infectious. There's a life lesson here...

[@japeking1]

I've just laughed out loud when the parallelograms came up......wondrous stuff. Thanks so much.

[@numberphile]

2th T-Shirt from this video: teespring.com/2th-t-shirt-numberphile

[@austynhughes134]

Just another great Numberphile video to kick off my Thursday!

[@MoosesValley]

Love Dr Sloane's soothing voice, the graphs, the formulas, the animations, and Dr Sloane's poetic descriptions "... says to the demon 'fly straight dammit' and from that point on ... the banshee is tumbling, the music calms down and they fly smoothly". Majestic !

[@brendawilliams8062]

You’re brilliant. Very gifted. Thankyou.

[@roverknight2502]

If my maths teacher would do lessons in asmr I'd actually listen

[@SpencerTwiddy]

Cool. I recommend listening anyway though👍🏼

[@aquawoelfly]

Id quit school

[@maxnullifidian]

Those parallelograms at 10:20 - what's their ratio to the previous/next one in the progression?

[@sebastianzaczek]

According to what he says after showing the parallelograms the Ratio should be 1:2 (1:4 for the Areas)

[@marcasmacdonncha4872]

Neil Sloane is my favourite of your guests simply because he seems to extract so much joy from his work; and as a result so do I! It only breaks my heart that he's referred to as British-American when I'd love to claim him as an Irish -man!

[@flygandeskote1702]

Excellent video, can't wait for part 2

[@christopherboon1677]

I love Neil Sloane, He's such a mathematical baller

[@peteman1000]

7:55 that moment when he says "we look at the primes" and there's an amazon prime logo right by his head.

[@RandomDucc-sj8pd]

0:27 i love how they took his mispelling and actually implemented it in the graph

[@utsavman47]

I like how it looks so intimidating at first but then it makes sense in the end and I feel like a smartass afterwards.

[@snejpu2508]

LOOK AT THIS GRAAAAAAAPH!!!

[@pandaraigner]

Damnit wasn't expecting this

[@DorFuchs]

Amazing!

[@arsmelancholiae]

Maths periodic videos! I love this channel.

[@delecti]

I love this guy, he's such a nerd and love talking about this stuff.

[@JCResDoc94]

☼ 4:43 id put money on this being better than the 5 Avatar sequels currently in the works.

[@jwhaseh2187]

Love these videos with Neil Sloane

[@thomaslarochelle3706]

This man has such enthusiasm, just look at him go, it’s beautiful!

[@TibiHell]

The tower of books topped by a laptop made me more uncomfortable than it should have

[@Wecoc1]

+1 for the Barça shirt +100 for not being the NEW Barça shirt

[@XavierFabregat]

Exactament, molt ben dit

[@Jack-en3pr]

Away kit is 😍

[@jazzsoul69]

Thank you so much for sharing this with everybody, Once again Geometry behind maths patterns reveals the higher beauty and poetry in all possible human domains

[@MrCheeze]

That sequence actually does a decent job of explaining why there's any doubt about things like the goldbach conjecture, even when I'll the values we've calculated so far have seemed to point to it.

[@royalninja2823]

Finally we have someone who actually remembers Avatar and can actually quote it!

[@numberphile]

More Neil Sloane videos: bit.ly/Sloane_Numberphile

[@bowlchamps37]

Wow, the is a tooth video.

[@Xnoob545]

Why does it redirect me to online youtube not the app (im on a phone obviously

[@loganstrong5426]

@@Xnoob545 it's because it's a shortened link, not a direct KZbin link. If it's a direct to KZbin link, that's when the phone knows to redirect to the app.

[@teabagfc]

Yes, please make more!

[@koenth2359]

@Sannesthesia yup, he's the OEIS guy.

[@samueldeandrade8535]

10:10 oh my Euler, this graph is simply AMAZING ...

[@dmsanct]

"parabola, you did it in high school. boring, boring boring" - this is one of my favourite numberphile quotes

[@drewdurant3835]

Your thumbnail for this video is very creepy :-)

[@AngryArmadillo]

I suspect that the binary prime reversal sequence has nothing to do with the primes themselves, and that a similar pattern would emerge when applying the rule to any random (sufficiently dense) sequence.

[@patrickhector]

Graph it and find out! I'd love to see if it's true, and I'm pretty sure a lot of others would too :D

[@scottclowe]

Yes, it seems pretty clear to me that this is not due to the primes, nor to using base 2 (you'd get the same effect with any base, just larger parallelograms for larger bases).

[@remad8771]

I came to the comments looking for this. Although, I do think the numbers would have to be odd, otherwise the reverse binary number will be shorter. My guess is that each sequence 2^n*(2*k+1) for some fixed n. would produce its own pattern of parallelograms. Could be wrong, I will need to plot it first.

[@pit__]

It works as long as all your numbers are odd. If you include even numbers you still get paralellograms, but their upper edges will be aligned to give one straight line

[@danielsteel5251]

Your 'suspicion' is suspiciously familiar to the #1 unresolved Erdős Conjecture. It's a bit like 'suspecting' that all the nontrivial zeroes of some zeta function lie on some line. (Hmm. What an intuition you have.) 😉

[@aidangarvey7049]

This guy's voice is so nice to listen to, hearing him recount what happens in Avatar was captivating. And the graphs in this video blew my mind.

[@mdsaif05]

Brilliant video. We should give it a best video of the year award.