Amazing Graphs - Numberphile

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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
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Videos by Brady Haran
Animation and editing by Pete McPartlan
Patreon: / numberphile
Numberphile T-Shirts: teespring.com/stores/numberphile
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9

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7 авг 2019

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Комментарии : 1,2 тыс.

@numberphile 4 года назад

Watch the full Amazing Graphs Trilogy (plus an extra bit): ru-vid.com/group/PLt5AfwLFPxWLkoPqhxvuA8183hh1rBnG

@lejka23456 4 года назад

nice

@ChristopherRucinski 4 года назад

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 4 года назад

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

@Marci124 4 года назад

The link is broken for me.

@indiapopularchannel7451 4 года назад

Lottery guessing you tell me

@MrBluesboy15 4 года назад

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

@janlhab2329 3 года назад

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 2 года назад

@@janlhab2329 he asked for who graphed it

@yuvalne Год назад

@Triantalex 7 месяцев назад

??.

@christophecarpentier9797 4 года назад

The tooth term... ...🦷 Solid comedy

@mattgsm 4 года назад

Solid tooth

@Tondadrd 4 года назад

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

@isaaccisa 4 года назад

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

@mbrusyda9437 4 года назад

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

@christophecarpentier9797 4 года назад

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

@PjotrV1971 4 года назад

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

@OlafDoschke 4 года назад

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

@jacksparrow440 4 года назад

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

@paaaaaaaaq 4 года назад

Turn it into chaos again and it is perfect.

@danielroder830 4 года назад

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 4 года назад

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

@Xbob42 4 года назад

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

@F20SW 4 года назад

@@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 4 года назад

@@spikekiller4303 11:48

@penand_paper6661 4 года назад

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

@aquawoelfly 4 года назад

Number grandpa is klien bottle guy.

@mickeyrube6623 4 года назад

Spike Killer Grav

@BluishGreenPro 4 года назад

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 4 года назад

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

@KINGKROSBYSKINGDOM 4 года назад

What is OIES ?

@JBergmansson 4 года назад

@@KINGKROSBYSKINGDOM The Online Encyclopedia of Integer Sequences

@hexagonist23 Год назад

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

@Triantalex 7 месяцев назад

false.

@Jkirek_ 4 года назад

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

@andymcl92 4 года назад

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

@umbragon2814 4 года назад

@@andymcl92 because mathematicians are insane

@anarcho.pacifist 4 года назад

insanely curious

@calebvr3526 3 года назад

Dc T

@Triantalex 7 месяцев назад

??.

@RealClassixX 4 года назад

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

@pedroscoponi4905 4 года назад

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

@RealClassixX 4 года назад

@@pedroscoponi4905 The what?

@ma7cus89 4 года назад

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

@Sylocat 4 года назад

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

@jblen 4 года назад

@@Sylocat a magical thing called Google probably

@M_Oz_ 4 года назад

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

@Luminous.A.Glory_VitaNostra 4 года назад

M Oz SAME

@mysticalpie4695 4 года назад

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

@avi12 4 года назад

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

@Adam-cn5ib 4 года назад

i don't get it

@DrShwazz 4 года назад

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

@Czeckie 4 года назад

i really liked "oneth"

@LemoUtan 4 года назад

A Scotsman would note that he bridged the 4th term

@orsonzedd 4 года назад

Tshirt when

@undergroundmonorail 4 года назад

it's incredible that this guy remembered anything from avatar

@satyampandey2222 4 года назад

Its an incredible movie so no shocker

@KatzRool 4 года назад

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

@TheAlps36 4 года назад

He did call the main character "Scully" though

@wasdwasdedsf 4 года назад

@@satyampandey2222 qua

@eliavrad2845 4 года назад

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

@johnpossum556 4 года назад

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

@rudiwinkelstein2483 4 года назад

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

@hexagonist23 Год назад

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

@JeroenBouwens 4 года назад

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 4 года назад

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

@VivaanTheCraft3r 3 года назад

Oh yeah cool

@Jiggerjaw 4 года назад

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

@SlightSmile 10 месяцев назад

They didn't 😥

@thejelambar82 4 года назад

Everybody: great movie Grandpa: fly straight dammit sequence

@AXEUROLder 4 года назад

Great movie? You mean Avatar?

@General12th 3 года назад

@@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.

@seanspartan2023 4 года назад

He called the step graph very pedestrian and I chuckled 😂

@charadremur333 4 года назад

I get it now.

@N.I.R.A.T.I.A.S. 4 года назад

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

@PhilBoswell 4 года назад

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 4 года назад

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

@ianmoore5502 4 года назад

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

@mrpokemon1186 4 года назад

Phil Boswell it went to rehab

@catchara1496 4 года назад

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 4 года назад

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 2 года назад

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.

@MaksymCzech 4 года назад

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 4 года назад

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

@kjpg7413 4 года назад

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

@renemunkthalund3581 4 года назад

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

@Reliquancy 4 года назад

@@kjpg7413 the prime one was base 2 specific though

@kjpg7413 4 года назад

@@Reliquancy you are correct.

@redpepper74 3 года назад

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.

@frabol02 4 года назад

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

@calebsousa2754 4 года назад

*Barcelona bud

@mitchellclark4377 4 года назад

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

@ayushrathore9190 4 года назад

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

@lonestarr1490 4 года назад

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

@duncanbates5361 4 года назад

@PIYUSH YADAVPython is a popular programming language.

@christiangrantz6906 4 года назад

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

@zyaicob 3 года назад

Matt Parker is livid

@2fbDJLL 4 года назад

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 4 года назад

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 4 года назад

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 4 года назад

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 3 года назад

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

@leonnuske2484 4 года назад

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

@ker0356 2 года назад

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

@msclrhd 4 года назад

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

@JayBringer111 4 года назад

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

@lucbourhis3142 4 года назад

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

@jhonnyrock Год назад

0:46 Parabola: And I took that personally...

@jacobbaartz7710 4 года назад

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

@georgemachappy 4 года назад

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

@Ny0s 2 года назад

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

@DorFuchs 4 года назад

Amazing!

@mana24 4 года назад

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

@Ruddigore 4 года назад

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

@gigs1890 4 года назад

Your graphical work has gotten to be really impressive :O

@jonathanwalther 4 года назад

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

@aaronthomaswebster 4 года назад

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

@FourthDerivative 4 года назад

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?

@monoastro 4 года назад

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

@Jiggerjaw 4 года назад

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

@NocturnalCoder 4 года назад

that thought crossed my mind too, lol

@Jiggerjaw 4 года назад

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

@MegaPhester 4 года назад

Twitter for Online Encyclopedia of Integer Sequences

@meghanto 4 года назад

Never thought I'd see a big forehead clan member

@ceruchi2084 4 года назад

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

@xystem4701 4 года назад

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

@noncanadian 4 года назад

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

@ricardo.mazeto 4 года назад

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

@grainfrizz 4 года назад

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

@iliketurtles4463 4 года назад

Pepperidge farms remembers... Harambe

@KingofJ95 4 года назад

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

@grainfrizz 4 года назад

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

@PeterJavi 4 года назад

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

@xevira 4 года назад

@@PeterJavi the Smurfs?

@FerousFolly 4 года назад

Neil's love and passion for numbers is so contagious

@utsavman47 4 года назад

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

@raafmaat 4 года назад

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 4 года назад

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 4 года назад

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.

@Eillcon 4 года назад

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

@randomdude9135 4 года назад

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

@E3rK57 4 года назад

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!

@InigoSJ 4 года назад

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

@TECHN01200 4 года назад

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

@impossiblemission4ce 4 года назад

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 4 года назад

The Smurfs?

@bearsfan519 4 года назад

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

@francescosirotti8178 4 года назад

@@bearsfan519 Pocahontas with cannons, to be precise

@falconerd343 4 года назад

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

@connorhamilton5707 4 года назад

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

@pixelatedmushroom 4 года назад

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

@JESSEverything 4 года назад

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

@guyarbel2387 4 года назад

"Who found that ?" "I did" Lol

@patrickstonecrusher 4 года назад

"Look at this graaaaph" 😐👉📈 😐 😐

@charadremur333 4 года назад

Precisely

@bxb77777 4 года назад

Whenever I look at it make me laugh

@sebastiansimon7557 3 года назад

Comments you can hear.

@WaffleAbuser 4 года назад

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

@THELizardSlave 4 года назад

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

@wompastompa3692 4 года назад

_Fly Straight Dammit!_ Best sequence name.

@roverknight2502 4 года назад

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

@SpencerTwiddy 4 года назад

Cool. I recommend listening anyway though👍🏼

@aquawoelfly 4 года назад

Id quit school

@japeking1 4 года назад

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

@michaelcherry8952 4 года назад

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...

@numberphile 4 года назад

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

@snejpu2508 4 года назад

LOOK AT THIS GRAAAAAAAPH!!!

@pandaraigner 4 года назад

Damnit wasn't expecting this

4 года назад

This makes me nurdgasm!! More graphs, please!

@CharmEng89 4 года назад

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

@xblizzqrd 3 года назад

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?

@austynhughes134 4 года назад

Just another great Numberphile video to kick off my Thursday!

@BVasquezp 4 года назад

This is kind of stuff i would to see in an art gallery

@chessandmathguy 4 года назад

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

@christopherboon1677 4 года назад

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

@peteman1000 4 года назад

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

@flygandeskote1702 4 года назад

Excellent video, can't wait for part 2

@thoaily8352 4 года назад

It's incredible how a set of seemingly random numbers can generate such a thing like that

@Skrzynia 4 года назад

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 4 года назад

@mrpokemon1186 4 года назад

You on the 420?

@TibiHell 4 года назад

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

@thePrinceOfPurpose 4 года назад

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

@delecti 4 года назад

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

@JCResDoc94 4 года назад

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

@drewdurant3835 4 года назад

Your thumbnail for this video is very creepy :-)

@jwhaseh2187 2 года назад

Love these videos with Neil Sloane

@mdsaif05 4 года назад

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

@royalninja2823 4 года назад

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

@maxnullifidian 4 года назад

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

@sebastianzaczek 4 года назад

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

@kunalchakraborty3037 4 года назад

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.

@brendawilliams8062 3 года назад

You’re brilliant. Very gifted. Thankyou.

@themathhatter5290 4 года назад

10:50 Brady, come on.

@Wecoc1 4 года назад

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

@XavierFabregat 4 года назад

Exactament, molt ben dit

@Jack-en3pr 4 года назад

Away kit is 😍

@arsmelancholiae 3 года назад

Maths periodic videos! I love this channel.

@epicepidemic7131 4 года назад

I'm jealous of his corner desk with the fun striped wallpaper....

@FunWithBits 10 месяцев назад

also has a striped shirt

@numberphile 4 года назад

More Neil Sloane videos: bit.ly/Sloane_Numberphile

@bowlchamps37 4 года назад

Wow, the is a tooth video.

@Xnoob545 4 года назад

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

@loganstrong5426 4 года назад

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

@teabagfc 4 года назад

Yes, please make more!

@koenth2359 4 года назад

@Sannesthesia yup, he's the OEIS guy.

@Intellllect 4 года назад

Ladies and gentlemen, at this time we ask that you all please rise and direct your attention to Numberphile anthem. Amazing Grpahs! how sweet the sound...

@tantzer6113 3 года назад

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.

@FedericoTrentonGame 4 года назад

The most amazing thing is how someone actually remembered a scene from the highest grossing film that nobody remembers anymore

@grieferjones2237 4 года назад

1:35 I really don’t want to reme-oh, you mean the one with the blue people. Carry on.

@AngryArmadillo 4 года назад

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 4 года назад

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 4 года назад

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 4 года назад

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__ 4 года назад

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 4 года назад

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.) 😉