Amazing Graphs III - Numberphile

Featuring Neil Sloane from the OEIS. Full "Amazing Graphs Trilogy" and extras at: • Amazing Graphs on Numb...
More links & stuff in full description below ↓↓↓
Neil Sloane is founder of the OEIS: oeis.org
More videos with Neil: bit.ly/Sloane_N...
Amazing Graphs
Part 1: • Amazing Graphs - Numbe...
Part 2: • Amazing Graphs II (inc...
Part 3: • Amazing Graphs III - N...
Extra Bit: • A Not So Amazing Graph...
Sequences featured in this video include...
Stern's: oeis.org/A002487
Hofstadter's: oeis.org/A005185
And Remy's: oeis.org/A279125
Thanks Patrons: Arjun Chakroborty, Ben Delo, Jeff Straathof, Jeremy Buchanan, Andy, Yana Chernobilsky, Christian Cooper, Ken Baron, Bill Shillito, Nat Tyce, Ben, Bernd Sing, Dr Jubal John, Tom Buckingham, Giuseppe Bonaccorso, Adam Gold, Andrei M Burke, Adam Savage, Matthew Schuster, Matheson Bayley, James Bissonette, Robert Donato, john buchan, Steve Crutchfield, Jon Padden, Valentin-Eugen Dobrota, Eric Mumford, Charles Southerland, Arnas, Ian George Walker, Jerome Froelich, Tracy Parry, George Greene, Igor Sokolov, Alfred Wallace, Jussi Suontausta, Bodhisattva Debnath.
Back us on Patreon: / numberphile
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumb...
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoun...
And support from Math For America - www.mathforame...
NUMBERPHILE
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Videos by Brady Haran
Editing and animation by Pete McPartlan
Numberphile T-Shirts: teespring.com/...
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanb...
Sign up for (occasional) emails: eepurl.com/YdjL9

[@numberphile]

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

[@esotericVideos]

It says "Invalid parameters" when I click that link

[@devlinmcguire7543]

@@esotericVideos Same with me. I think there's something wrong with the link.

[@shawnrobertdoyle5242]

@Numberphile The link is broken. It says "Invalid Parameters" and shows an error page

[@888legends]

this man is the best. love the sequences

[@OlafDoschke]

Let me guess, you forget to change the status to public. Then you have no problem yourself.

[@majkgmajkg2613]

I wouldn't mind if it will become a new regular series.

[@masrock9203]

MajkG MajkG PLEASE THIS!!!

[@U014B]

Neil would have to add it to the OEIS.

[@elkandevening]

Pun? Love.

[@ShinySwalot]

Petition for a "Graph of the Week"

[@cheyenne1309]

YES!!

[@Philip_J]

All in for it!

[@ys1940]

Where do I sign

[@masrock9203]

SIGNED

[@benharris3100]

Yes

[@redtaileddolphin1875]

Literally said “ohhhh” out loud at that last one, that was certainly my favorite

[@minnarew]

fractal patterns are (almost) always pretty

[@Triantalex]

??

[@redtaileddolphin1875]

@@Triantalex what’s wrong

[@nymalous3428]

I like how the final graph, which was described as the Alps, was actually used in the animation following it. The quiet enthusiasm of Neil Sloane is very enjoyable.

[@mihailmilev9909]

That was my favorite too

[@MrMineHeads.]

Inject this directly into my veins.

[@ObjectsInMotion]

Inhale the graphs, exhale the graphs

[@zixuan1630]

:)

[@Triantalex]

??

[@thetophatgentleman4634]

Keep ‘em coming because these graphs are funny. Excellent work by the way.

[@sohambasak6382]

This Graph series is turning out to be one of the best series on Numberphile.

[@pcfilho425]

I have a dream. I submit an interesting sequence to the OEIS. Neil comments this sequence of mine in a Numberphile video. That's it.

[@numberphile]

That’s a grand slam.

[@bwatspro]

Make Sequencephile, starring Neil Sloane please, or keep them coming here. Either way, thank you amazing appreciated.

[@ringkunmori]

We need a graphophile channel dedicated to uploading cool graph every week

[@danielmarkkula3004]

This guy is amazing, the graph stuff is like mathematical ASMR.

[@oscaro.172]

I love these. It feels like productive ASMR.

[@OlliWilkman]

"Adam Savage" in the Patreon supporters. Wonder if it's the best known one.

[@philipabelanet5476]

Indeed it is.

[@roderickwhitehead]

I never met the dude.

[@ionlycommentwhenitsnecessa5906]

Creator of Minecraft Markus Persson Notch is a 3blue1brown supporter

[@wasdwasdedsf]

@@philipabelanet5476 do you know?

[@philipabelanet5476]

@@wasdwasdedsf He's mentioned being a fan of math & science channels.

[@Hjerpower]

Please keep this series up!

[@Bronco541]

Thos mans excitement for numbers is so infectious. He could talk about toilets and make it fascinating.

[@FanTazTiCxD]

4:49 the way he whispers *"Graaaph"* ... With such a calming and peaceful voice. I imagine myself finding inner peace in a beautiful natural environment somewhere in Nepal at a valley on a small island in a lake, with only the sounds of birds and the silent water... And as I am about to fall asleep, this old man comes by and whispers "Graph" into my ear as I fall deeply asleep

[@ToranDoesGaming1]

😅😅😅

[@Mroziwanman]

I cannot explain why but I have loved this series - thanks!

[@matteovecellio5733]

Honor to the amazing Neil Sloane, to Douglas Richard Hofstadter for his contribution to mankind represented by "Gödel, Escher, Bach: An Eternal Golden Braid," and to Brady Haran for letting me know such pure geniuses! From my heart thank you all for making my life even more beautiful and enjoyable! Brady go ahead!

[@whatisthis2809]

7:53 Do the flags which have numbers, are they actually in order of the sequence they just talked about? Nice easter egg, Numberphile ;D

[@colinstu]

2:32 "well... I guess..." said all bashful... I love it.

[@cyborg98]

The Alps graph has a bit of Sierpinski triangle kinda look to it

[@jaguarfacedman1365]

Yeah. A bit spooky.

[@UnIikelyhero]

I love this series so much, keep it up!

[@dotjoseph]

I see what you did there lol

[@RunstarHomer]

These three videos have been some of the best on Numberphile. I'd absolutely love to see more

[@bryanmills5517]

Neil Sloane's OEIS graphs and strange sequences are my favorite videos.

[@SSXSuperMan]

The one is amazing. I love how a number sequence can translate into nature so well.

[@Rotem_S]

7:52 is a Sierpinsky triangle thingy (like most binary recursive series seems like)

[@KatzRool]

YEAH MORE GRAPHS Brady: So this is the third and final episode of NOOOOOOOO

[@geckoman1011]

Neil might be my favorite of them all. He gets so excited and I like that

[@DaceCase]

You cannot possibly understand how happy I am to have this video I was so sad when I watched the second and this wasn't out yet

[@michaelrosenberg6528]

We need more than just a trilogy.

[@numberphile]

We’ll see what we can do.

[@zachdurocher1166]

This might be my favorite playlist on KZbin

[@maxhaibara8828]

I can't believe equations are better at drawing than me

[@jackwilliams7193]

to be fair, a lot of shapes and their combinations are just equations or series thereof

[@henk11ful]

These videos inspired me to recreate all these awesome graphs with Python. So much fun!

[@numberphile]

Great to hear.

[@mattbox87]

I love the way his desk is (dis?)organised In particular that the books are labelled on the pages rather than the spine and that there is a Mac sitting precariously on a stack of books where one is labelled "UNIX"

[@hassanhaider2380]

PLEASE don't end this series!!!

[@jwhaseh2187]

These Neil Sloane videos are the best

[@coffeedude]

I would watch these graph videos forever

[@pipershields4051]

this is my favourite channel to watch at 3am

[@crowd3r862]

I was looking for more content about graphs and sequences by this guy. His voice is so pleasant to listen to. More please!

[@SendyTheEndless]

That Hofstadter and his level-crossing feedback loops!

[@FrankHarwald]

Here's a thing: Hofstadter's series is non-primitive recursive but functional computable.

[@DanJohnson]

I could watch these all day!

[@maris_molotov]

Please don't stop making this series I love it so much

[@duffy666]

Neil Sloane is such an inspiration.

[@vycanon7057]

"ill put down a 0, no-ones is going to object to that" The subtle sarcasm is strong with this one.

[@alansmithee419]

4:24 I'd like to rename this list to "counting badly" (or slowly)

[@stevewhisnant]

This episode is pure delight! I love the graphs, espeically the "alps" at the end. We need more of the amazing and interesting sequences to fill our heads with morning smiles and wonder.

[@skyrider8890]

I need more of this! Just shows you how beautiful math is.

[@WillToWinvlog]

Yeah!!!! This series gets me HYPE!!!

[@otakuribo]

"third and final of the trilogy" 😭

[@ceruchi2084]

Wow, I love so many Numberphile presenters, but Neil Sloane has really rocketed toward the top among my favorites. He has an artist's soul.

[@gabrielximenes3652]

This man is now 80 years old. Incredible.

[@HonkeyKongLive]

YES!! My favorite video series on KZbin continues!

[@matheMEDician]

Love the editing And the way he says graph

[@micolmusic]

Fascinating. Dunno why but it feels like we're exploring the fabric of the universe or something by analysing how these sequence behave.

[@numberphile]

Cool!

[@randomguy263]

Whoa, that last graph was amzing.

[@drawapretzel6003]

the unknown sequence almost definitely will go on to infinity, because every term is smaller than n, for lack of a better phrase. theyre all assembled from >n, and all the number >n are by definition smaller than n, and they themselves are assembled from smaller numbers. Like he said, you dont get to N, or even close, theyre all close to half n. No set of numbers you add together can be greater than their own sum. If you add all the integers you might accomplish a supertask and reach some type of infinity, but you can always just add one to it, so no matter how many terms you add together, they dont ever become larger than infinity. the ratio to how far back you go for the two things you add remains the same, it is bounded by upper limits, because as it shows, you eventually reach a point where you dont go any further back, or forwards, before ballooning out again. Its form is dictated by its ratio, and its ratio is bounded, its irrational, but it is the sum of rational numbers. It cant EVER become larger than itself. No sum is larger than itself. As the numbers become larger, you add smaller and smaller numbers together, you might go further back, but then it becomes a smaller number to add together, and those small numbers guarantee that the NEXT term will be smaller than n, so, the sums might get bigger to a certain point, but then you go so far back, you find the small numbers again, and only add small numbers together. There is a reason it looks cyclic, because you can only grow the number of hops back you go so far, because eventually that means you add together SMALL numbers, and then dont go very far back. In fact, i think i can prove it. every term is n+1 greater along than the last one. But the smallest increment you can add is 1, so you cant ever add an increment greater than 1 to the step n. If you go back so far that you reach the first or second term, you just add 1. but then the NEXT term, is n+1, meaning even if you go n terms back, you find 1 again. It MIGHT get stuck in a loop of only adding 1 to itself forever, but it wont ever get into undefined, because it cant grow larger than 1 step at a time.

[@Onychoprion27]

My favorite graph is simply plotting how many iterations a number x goes through the Collatz Conjecture to reach 1

[@DavidThackerMusic]

Love this little series

[@unknown6656]

The last one is obviously a (squished) sierpinski triangle. Fun fact: you can calculate a binary sierpinski triangle by evaluating the following expression: "x ^ (x

[@Chrisheywoodbrown]

I absolutely love these videos. More please!!!!

[@trashmaster24]

We need more of these videos

[@chonchjohnch]

I genuinely enjoyed the last two videos so much that I got excited seeing this notification

[@CrixOMix]

MORE! These are amazing.

[@davidbuzatto]

I really, really, really like to listen Mr. Neil Sloane! More pleaaaase!

[@feliciabarker9210]

If you'd shown me that Q sequence and asked me who I thought came up with it, I think Douglas would have been my first answer without even thinking. It's very him.

[@moreaufamily437]

This sequence of videos on the graphs has been really amazing!

[@nathanderhake839]

I love these sequence videos

[@bangedagorilla]

MORE AMAZING GRAPHS PLEASE

[@CiuccioeCorraz]

So sad the series ended! Really liked the concept and really liked the mathematitian. It's so cool that there are so many sequences showing fractal behavoir when n is large enough!

[@Ymitzna]

Please make more! I love Neil Sloan and the videos are so interesting

[@Drachenbauer]

Funny, how he used the last graph as the mountain-background for a chilly winter-scene.

[@perappelgren948]

More Neil, please. He’s always interesting and he’s a very nice person!

[@MoosesValley]

The Alps on a snowy day ... beautiful !

[@runefjord8446]

This is professor Farnsworth from futurama come alive in a slightly less crazy form

[@TheSmegPod]

there's something a little bit scary about finding some random sequence rule that gives you some variation on a sierpinski triangle

[@MrxstGrssmnstMttckstPhlNelThot]

I actually audibly gasped I was so excited to see this!

[@ganster1239]

We should make a monthly contest, where we send our own sequences/graphs to Brady and Neil and they have to decide, which is the best!

[@Taffy-hb8rd]

I love these. This can’t be the final one.

[@Qba116]

The cathedral graph looks a lot like Sagrada Familia in Barcelona

[@LaGuerre19]

Prof Sloane's graphs make my day.

[@yvesnyfelerph.d.8297]

He is NOT a professor, certainly not anymore

[@leo17921]

@@yvesnyfelerph.d.8297 ye lol he's 80 years old

[@shugaroony]

@@leo17921 And doesn't look a day over 60.

[@RandalSlisz]

We need sooo many more of these! Great stuff. Wonderful. Amazing.

[@solahifuefos9301]

neils voice is so soothing

[@HunterJE]

If I had to nominate a favorite amazing graph it'd be OEIS-A004185, it's a super easy one to figure by hand, it feels a little "mathematically naughty" since it applies an operation you normally wouldn't expect to do to the digits of a number, and it results in a visually interesting structure when viewed as a scatter plot...

[@Ivan_1791]

More of this please.

[@ScottTilYouDrop]

Thank you for these amazing joyful videos!

[@CustomClass5]

More please. These are the best parts of math imo

[@Yoshiyosh]

The greatest trilogy in film history

[@EmilMacko]

This series could replace every future upload on Numberphile and I wouldn't even be that mad

[@perappelgren948]

So interesting! And Neil Sloane makes my day every time he’s Numberphile. So - could we have some more, please?

[@davidmilne8876]

Loves little series

[@tyhayter5022]

0:01 Stern's Sequence 1:56 Hofstadter's Q Sequence 5:40 The Chaotic Cousin 6:08 Remy Sigrist

[@wmpowell8]

The graph of Rémy Sigrist’s sequence looks like repeating Seirpinski triangles with a line on top

[@SephrasParadox]

These videos are phenomenal, please do more of these!

[@IndieSamurai101]

Public demand: 10 episodes of the Amazing Graphs series

[@legendgames128]

A variant on Rémy Segrist's rule is that no digits in binary that are the same are allowed to overlap. So that means n = 4 would mean that a(n) = 2

[@JakGruen]

0:00 I actually live in Göttingen Germany and was thrilled to hear that :D

[@imjonkatz]

Favorite videos of recent times! Thanks :D

[@PerMortensen]

I could watch this for hours.

[@diegofcm6201]

7:44 lots of sierpinsky triangles there