Thanks for having me on, this was a blast!

@Ryan_Thompson

4 жыл бұрын

A 2n-dimensional ball could have exploded right next to me and I wouldn't have noticed, I was so engrossed in the video. :-)

@3blue1brown

4 жыл бұрын

Also, let's all acknowledge the real delightful collaboration at play here, which is that between pi and e.

@arunasb7048

4 жыл бұрын

Omg! This is pure logic with pure smartness incorporated in it... This literally blew my mind... My pupils still remain dilated..

@JonathanMLM

4 жыл бұрын

when will you do the essence of probability and statistics?

@Lukoro1357

4 жыл бұрын

"And these blast points? Only imperial storm troopers are that precise. The probability is zero."

Consistency is only a virtue if you’re not a screw up. -Grant Sanderson, 2019

@vandebunted

4 жыл бұрын

Savage advice. Also true.

@arpitdas4263

4 жыл бұрын

True

@AlisterCountel

4 жыл бұрын

Arvasu Kulkarni I cant remember when I saw it, but there was a demotivational poster with that as the line, and someone who had split an arrow...at the very edge of the target.

@888legends

4 жыл бұрын

@@AlisterCountel yes! that takes me like 15 years back

@mohammedal-haddad2652

4 жыл бұрын

Is Grant Sanderson the happiest person on the planet?

Grant : Has unnecessarily expensive and fancy compass Also Grant: Uses random piece of cardboard as a "straight" edge

@beeble2003

3 жыл бұрын

Well, you do need a pretty decent compass to draw large circles. Though a piece of string would be more in keeping with the "straight" edge.

@Alan_Alien

10 ай бұрын

He used all the money to buy that fancy compass... Duh!

@charlesboys9674

9 ай бұрын

XD

@Triantalex

5 ай бұрын

??.

"Consistency is only a virtue if you're not a screw up." Grant Sanderson - 2019

@Czmlol

4 жыл бұрын

Surprisingly profound.

@bentrash7885

4 жыл бұрын

What does he mean by that tho

@DeepFriedOreoOffline

4 жыл бұрын

@@bentrash7885 In layman's terms: Doing things in a consistent way is only beneficial if you are consistently doing them well. There is a saying that goes something like "Consistency is key." I assume it is a play on that.

@R.T.and.J

4 жыл бұрын

screw up here, can confirm

@georgesamaras2922

3 жыл бұрын

Consistency is only a virtue if you're not a screw up. Well, it's possible but its probability is zero.

One benefit of inviting 3blue1brown is that he does the animations himself.

@numberphile

4 жыл бұрын

He’s a very good guest!!!

@vikraal6974

4 жыл бұрын

A guest of rigour

@Ensivion

4 жыл бұрын

@@numberphile this one felt like a collab more than an interview, I liked the video none the less. I hope this will give 3blue1brown even more exposure and maybe help out a few people who may not have the best of teachers, to learn calculus and linear algebra the right way.

@leif1075

4 жыл бұрын

@@numberphile Why does he say probability is zero for rational points? That's wrong. Please correct this.

@abhijeetkrishnan

4 жыл бұрын

There are an infinite number of rational points. The probability of choosing any single rational number therefore is 0.

my parents: "are you ever gonna get a girlfriend?" me: "it's possible, it's just probability zero."

@corngrohlio

4 жыл бұрын

But, as Grant said, "probability is zero, don't worry about it", LOL

@Rekko82

4 жыл бұрын

That makes me a loser.

@brianevans4

4 жыл бұрын

This is excellent. That could be a meme. It has potential on Reddit

@definesigint2823

4 жыл бұрын

So is that..."zero" potential?

@AmberSK15

4 жыл бұрын

Just say you're already in an unhealthy relationship with the number e.

Everybody gangster till the animated personified pi shows up.

@redpepper74

3 жыл бұрын

Alan Deutsch when you jump from 3D to 4D, it becomes gangster * π^2

Lightning never strikes the same place twice 3B1B: *Nay, but my darts shall!*

@Verrisin

4 жыл бұрын

it's possible, but the probability is zero.

@ViratKohli-jj3wj

3 жыл бұрын

It's possible, but it's probability is Zero

@achtsekundenfurz7876

3 жыл бұрын

He's quite the "dartist" at this game

@Sohlstyce

2 жыл бұрын

fun fact: lightning actually strikes multiple strikes during discharge

@rishabnavaneet

2 жыл бұрын

I messed up the like count :D

One day I’m gonna prove Grant wrong and find the real number line out in nature.

@bestnocture

4 жыл бұрын

Said like a true engineer, sir!

@tyzonemusic

4 жыл бұрын

I personally wouldn't expect the real number line to be so natural

@stanley2696

4 жыл бұрын

@@tyzonemusic Made my day. Thank you!

@L0j1k

4 жыл бұрын

Mathbro!!!

@ThePotaToh

4 жыл бұрын

You might only find the natural number line. And certain constants of nature. Sad to say but reality is often disappointing.

I felt so weird watching this video, because 3blue1brown is talking but, with his face

@geekjokes8458

4 жыл бұрын

that was me in his first Q&A... "did you hire an actor or something"

@ENCHANTMEN_

4 жыл бұрын

I thought he was a π

@GijsvanDam

4 жыл бұрын

How did you imagine him talking before?

@frechjo

4 жыл бұрын

One could say he switched form talking from a Pi to talking from a piehole..? I'll show myself out

@Intermernet

4 жыл бұрын

To paraphrase Bill Bailey: "Ain't you that guy from KZread? What are you doing talkin' round like normal?"

This is probably the best demonstration of a useful application of higher dimensional math that I've ever seen. Compressing a series of 2D coordinates into a single nD coordinate to get the probability of the whole set. Awesome!

@ninelaivz4334

Жыл бұрын

What is its practical use?

@SplendidKunoichi

Жыл бұрын

"2d coordinates that can be compressed (normed) into a single coordinate" is an all but complete operational definition for the field of complex numbers (the formal name for this would be the "canonical real structure" if im not mistaken). its no exaggeration to say every STEM field finds its own wildly different favorite use of complex numbers. but more than that, the entire subject of algebra, as you may or may not know, has a pretty large hole in it that isn't actually possible to close using anything other than these same 2d numbers. so in a way, they really are the very thing ensuring any and all reasoning you do using your school textbook math will be logically rigorous; that it has the consistency to carry useful meaning by default in whatever practical context you can give it.

I’ve had an unhealthy relationship with e since the late 80s.

@peteneville698

4 жыл бұрын

Was Bob Holness your dealer?

"I'm gonna try to make this a worse shot" *hits the middle* 3Blue1Brown Suffering from Success

@alansmithee419

4 жыл бұрын

Overburdened with brilliance.

@angelodc1652

4 жыл бұрын

Task failed sucessfully

@scathiebaby

4 жыл бұрын

A victim of his success.

@scathiebaby

4 жыл бұрын

Sounds like an error message in Windows.

@XarlesWolfgangSteel

4 жыл бұрын

He beat the 0% odd of hitting exactly the same spot as before

So, now the most calm and relaxing voice on youtube has also a face

@cyansea2370

4 жыл бұрын

and a handsome one

@user-jc2lz6jb2e

4 жыл бұрын

@@cyansea2370 back up. Somebody already put a ring on it

@j.albert2311

4 жыл бұрын

He's actually shown it a lot before this

@drag0nblight

4 жыл бұрын

Calming voice used well. Literally made me stay and listen to his lectures than other lecturers do.

@XenophonSoulis

4 жыл бұрын

There is Bob Ross on KZread and *he* has the calmest voice.

Using a compass on a glass table with no protection below it. That mad lad

@nikhilnagaria2672

2 жыл бұрын

:-)

@kurumi394

2 жыл бұрын

pretty sure most metals can't scratch glass unless it's something like hardened steel

19:53 you mean.. the Grant finale? 😏

@kirbylover_6

2 жыл бұрын

EYY

@nikhilnagaria2672

2 жыл бұрын

lol

Most people would see the subject of this video and say "why?" Numberphile and 3Blue1Brown see it and say "yₒ".

@kirglow4639

4 жыл бұрын

That's beautiful

@badhbhchadh

4 жыл бұрын

Exactly my thought when they said that

@L0j1k

4 жыл бұрын

Damn breh you fuccen killin it out here!

@johnchessant3012

4 жыл бұрын

I loved that quote when Ted Kennedy said it, and I love it even more here. :D

@jovi_al

4 жыл бұрын

This took me over 5 minutes to get and I'm glad I did

I feel like we enter Grant's brain every time his animation appears

@hai-mel6815

4 жыл бұрын

This is so trueee

@nbme-answers

4 жыл бұрын

We are!

@mueezadam8438

4 жыл бұрын

Josh Bone lol

I am not a mathematician, most of the stuff on numberphile goes over my head but it is just SO satisfying to watch. For example, I have no idea what e is, I didn't understand anything past explaining what the game is, but it is so damn satisfying to watch, it's like wizardry

I wasn’t sure whether I should make a pun about the vertical position of the very first dart thrown. Heck it, y-naught

@LunizIsGlacey

2 жыл бұрын

Hahaha! While some viewers may read the title and ask “Why?” Numberphile says “y naught!”

"I'm gonna try to make this a worse shot" *proceeds to shoot exactly the same spot Merida style

@621Tomcat

4 жыл бұрын

Well, shooting the exact spot is possible; but its probability is 0 :)

@RosarioLeonardi

4 жыл бұрын

That was the worst outcome possible.

@spiritusterra5688

4 жыл бұрын

You are the reference king.

@yto6095

4 жыл бұрын

imagine if darts were shot using a minibow

@wayanc1880

4 жыл бұрын

666 likes

"Infinity War was the biggest crossover in history" Brady Haran: Hold my Brown paper

@threepointonefour607

4 жыл бұрын

3 blue 1 brown paper

@gabrielkellar1935

4 жыл бұрын

And im over here thinking that its possible, but probability 0

@karolakkolo123

4 жыл бұрын

No that would be the mathvengers: eulergame on papa flammy's channel

@jackli5609

4 жыл бұрын

Gabriel Kellar i

@FlyingSavannahs

3 жыл бұрын

It's possible for me to know something about Infinity War, but because I don't the probability is 0.

This kind of content really does make me realize my enjoyment for mathematics. When I’m able to break the form of rigid, applied math and enjoy some almost philosophical branches of mathematics, it makes me want to pursue the subject despite my previously held distaste for the topic.

Grant:It's possible to hit an exact bullseye, it is just probability zero. *cue Mark Rober's auto-bullseye dart!*

“That’s not why mathematicians necessarily care about higher dimensions” That statement and concept just blew my mind slightly.

@romanski5811

4 жыл бұрын

Which minute mark does he say it?

@Fogmeister

4 жыл бұрын

Romanski right at the end. I’ll find it...

@Fogmeister

4 жыл бұрын

Romanski start from 26:20

@romanski5811

4 жыл бұрын

@@Fogmeister Thank you!!

@almightysapling

4 жыл бұрын

There are as many reasons to study math as there are mathematicians.

When to try to hit the dart so badly that it's actually a bullseye. What an amazing Parker Shot that was...

@wlan246

4 жыл бұрын

A "Parker Miss"

@GerSHAK

4 жыл бұрын

:D

The level of passion for mathematics Grant has is overwhelming. He inspires to quit everything, not just my job.. and just bury myself in my books.

I've read a number of Egan's books, and considering some of the bizarre things that goes on in them, I can totally believe he'd cook something like this up in his spare time. Furthermore, I'd just like to say that 3Blue1Brown continues to have the most pleasing math sounds around.

I used to think that this crossover ever happening was impossible But now I've realised it's just probability zero

@Why_It

4 жыл бұрын

But now that it's already happened, what's the probability of it happening again?

@Soken50

4 жыл бұрын

@@Why_It At least as much as grant hitting the same spot twice on a dartboard trying to do worse, that is to say 0, or in other words, definitely !

@2inthemorning

4 жыл бұрын

@@Why_It exactly as it was before

@AlabasterJazz

4 жыл бұрын

@@Soken50 Definitely! aka Definitely factorial. So it approaches 1

@Soken50

4 жыл бұрын

@@AlabasterJazz But I put a space to avoid confusion.

I have a suspicion Grant chose this specific puzzle to flex his exceptional dart-throwing skills

@labsupri6681

4 жыл бұрын

I use arch btw

Love this guy and love this channel. A few years ago, when I needed something a bit more mathy than Vsause, but my teenage brain couldn’t quite make it through a Numberfile video, here came Grant, explaining the beauty of math like no teacher or textbook I had had up to that point ever could. And probably ever since as well.

@albertandearthie7138

8 ай бұрын

Hey Vsauce, Michael here!

„Consistency is only a virtue when you‘re not a screw up“ 😂

I can't believe Grant has been handsome this whole time.

@ireallyhatemakingupnamesfo1758

4 жыл бұрын

Kyle Wright his smile gives me life

@jhuny

4 жыл бұрын

Too cute for animations lol

@trickytreyperfected1482

4 жыл бұрын

@@jhuny Animations cannot contain his adorability. He only decided on pi to represent him because he's a cutiepie

@jhuny

4 жыл бұрын

@@trickytreyperfected1482 his cuteness makes me positively irrational 🤪

@adamjnotthecongressmanschi7026

4 жыл бұрын

Right?!?

Two videos we now need: 1. A Healthy Relationship with E: What the factorial sum really means 2. Calculating the volume of spheres in higher dimensions

@poutineausyropderable7108

4 жыл бұрын

Essence of tailor series.

@AlexiLaiho227

4 жыл бұрын

check out grant's essence of taylor series video, and his e^πi video! they'll give you an intuitive understanding of e like none other

@trickytreyperfected1482

4 жыл бұрын

Calculating the volume of spheres in higher dimensions shouldn't be too hard, right?

@pleaseenteraname4824

4 жыл бұрын

Wolf Elkan For number 2, dr Peyam did a video on that

@pianoclassico718

4 жыл бұрын

@@trickytreyperfected1482 it's kinda the same idea as with triple integrals, except it gets higher, you're still integrating independent variables nonetheless the bounds do depend on those variables, unless you go to higher dimensional spherical coordinates system, which is much easier integration is but might be harder to derive and understand intuitively

Why is Grant's smile the only thing that keeps me going?

This is the best collaboration among the best 2 math channels. Looking forward for more of these!

When you spend too much on the editing software, so you get a cardboard ruler.

@felixmerz6229

4 жыл бұрын

I realize this was a joke, but I can't not state that 3b1b wrote it himself (python) and even published it.

@thetophatgentleman4634

4 жыл бұрын

Can’t not Double negative eh...

@felixmerz6229

4 жыл бұрын

@@thetophatgentleman4634 Well, yes. Deliberately, I wouldn't think anything else would have made a lot of sense.

@RobertSzasz

4 жыл бұрын

Straight edge 😋

@dlevi67

4 жыл бұрын

@@felixmerz6229 Surely you mean that nothing else would not have made a lot of sense?

"A healthy relationship with e?" Clearly, Grant has never been to a rave.

@paulinouillessautees

4 жыл бұрын

AHHAAHAHAHAHAHAH nice one

@attoblaze3395

4 жыл бұрын

dont get it

@sereysothe.a

4 жыл бұрын

AttoBlaze e = ecstasy

@TheTj4all

4 жыл бұрын

I was gonna like your comment but dont wanna ruin 666 likes

@JayadevHaddadi

4 жыл бұрын

best comment... ever

"im not that bad" *casually throws a near bullseye barely looking*

"Because why not" is the definition of why math is so fun. The rules are clear, the reasoning rock solid, but the freedom to play with the assumptions is unmatched. No physics to restrain you. No "right" way to approach a problem. Another fun one is "without loss of generality". I can't count how many times these words stopped me for quite a few minutes while I tried to understand why and make sure it really is... The revelation was usually fun. Not for obvious cases of course, but some authors can make the word "clearly" work VERY hard.

The way I rationalized the ratio of the volumes of a hypercube and n-ball is with the corners. You keep adding more and more corners that the ball can't reach.

@estranhokonsta

4 жыл бұрын

And the corners have more and more volume as the dimensions got higher. Just compare the corners in the Square/Circle to the ones int Cube/Sphere.

@XenophonSoulis

4 жыл бұрын

In 4D already you can put a whole hypersphere of half the radius on each of the corners.

@corngrohlio

4 жыл бұрын

nD-Hyper-Parker-Cube s much closer to nD-Sphere

@michalbreznicky7460

4 жыл бұрын

Also the corners get farther apart. A corner of an 100-D cube is sqrt(100)=10 units distant from the centre (assuming that all sides are 2 units long). One visualisation of this I like uses a projection into 2 dimensions. One can cut a 3D cube with an xy plane rotated 45 degrees around the x axis. This cut gets you a rectangle of dimensions 2 * 2.82. This plane also cuts out a circle of radius 1 from a sphere or radius 1. If you draw it, you'd notice unused space -- there's a margin of 0.41 units on each side, and an even bigger margin in the corners. A similar plane cut can be performed in 100 dimensions. A cut along orthogonal vectors a=(1,0,0,0 ...) and b=(0,1,1,1 ...) will result in a rectangle of size of 2 * 19.9 units -- lots of unused space there. We get even more slack if we cut along (1,1,1,1 ...) and (1,-1,1,-1 ...) -- we get a square of size 14.1 * 14.1 units.

Someone: You can't just "probability zero" your way out of every problem 3blue1brown: Observe, physicist.

This is insanely beautiful! Thanks Numberphile and 3b1b! You've made my day!

This was one of the most informative videos on multidimensional geometry, quantum physics and probability. This puzzle answers the question for me that the universe when described in probabilities does not imply a multidimensional space. Thanks for the understanding… very powerful!

The man has a compass ready for the video but no rulers in sight lol

@Krekkertje

4 жыл бұрын

Rulers are easily improvised. Compasses are harder

@Cuuniyevo

4 жыл бұрын

@@Krekkertje If you don't need great precision, a compass is easily improvised as well. All you need is a pin to center the arm, which could even be made of the same cardboard as his straightedge. Poke a hole through the arm at the distance you are scribing, and place your pen/pencil/marker tip through it. A string to tie from pin to writing implement is more accurate than the cardboard, but not quite as common in most offices. The string is particularly useful in geometry though, as it can also be used to measure pi. =]

@kevinm1317

4 жыл бұрын

@@Cuuniyevo You need a pin, and to poke a hole big enough for a pencil to fit through. Far easier to just take nearly any object and use it as a straightedge.

@Jelly-ij2pw

4 жыл бұрын

@kevin M i always wear a bracelet and if you have two pencils its just as easy

@GrapefruitGecko

4 жыл бұрын

As a mathematician, it's very important to always carry an emergency compass

"I'm gonna try to make this a worse shot." Grant Sanderson fails the way Matt Parker succeeds. Of course I kid. Both of those kids put out amazing content. I always look forward to a new standupmaths or 3B1B video.

@LeoStaley

4 жыл бұрын

I'd love to see a collab with them. I'd be happy to have Matt Parker a just an audience member present in the room.

@fatsteve3120

4 жыл бұрын

@@LeoStaley Oh, I bet a collab would be amazing. Matt's dry humor and wit with Grant's mellow genius... I'd watch that.

@GrapefruitGecko

4 жыл бұрын

Lol Grant is the opposite of Matt

Pi Megami Tensei Nocturne: Featuring e from the Constant May Cry series.

@mueezadam8438

4 жыл бұрын

mariosonicfan2010 😂😂😂

I’m glad you chose zeta as the outro theme. Vincent rubinetti really did a great job composing the music of 3blue1brown. And Zeta represents that amazingly. I could go off on a long tangent on how much of the music is centered around curiosity and wonder but you just have to listen to it.

The ending was so fascinating. Talking about higher dimensions without even being in higher dimensions

@pietervannes4476

4 жыл бұрын

Its easy to talk about 2 dimensions, while our world is 3D, so why not 4D? or 6D? or 100D?

@IceMetalPunk

4 жыл бұрын

@@pietervannes4476 Graham's number D! 😁

@ozapenguin

4 жыл бұрын

@@IceMetalPunk tree(Graham's number)D

@SecularMentat

4 жыл бұрын

Grant is great at talking about these things in a mind bendy way that I don't even think about before. I think that's why I really enjoy his stuff.

2:04 "I'm going to try to make this a worse shot..." Finding failure in victory more quickly than Myles Garrett.

@benmac1977

4 жыл бұрын

Excellent comparison!

@yourguard4

4 жыл бұрын

a Parker-shot would be amazing!

@leadnitrate2194

4 жыл бұрын

Suffering from success.

@corngrohlio

4 жыл бұрын

@@yourguard4 such a Parker Shot!

@jeromeorji1057

4 жыл бұрын

Error: task failed successfully!

Super awesome video. Thought that without the animations, it would take me out of my zone (in my mind). But this puzzle had so many pieces, and I followed fully. I only regret that I would not be able to connect all those dots on my own, if I were presented the same question. But I'm practicing thanks to your help!

19:52 "Alright are you ready for the Grant finale?"

I've never seen Grant's face before. He's cute af

@AlexiLaiho227

4 жыл бұрын

he's done a few interviews on his channel if you dig through his older videos!

@dalimilmatousek4074

4 жыл бұрын

He looks like an angel!

@jedkemekt2062

4 жыл бұрын

I know! Too bad he's married

@VectorNodes

4 жыл бұрын

@@jedkemekt2062 wym too bad? I'm sure she's a cutie too O.o

@mannyheffley9551

4 жыл бұрын

@@VectorNodes too bad for us :(

"so you are not quite twice as good as someone who has no skill whatsoever" the burn :D

Great job guys. Fantastic puzzle, happy to see you two working together.

Because of my research in information theory, I already knew the formula for the high-dimensional volume, and sensed what is coming up before Grant showed us. It was still an amazing experience. Very cool puzzle with a very cool solution.

"What if the dart is landing exactly on the line" "The probability is zero, dont worry about it"

@TheLuuuuuc

4 жыл бұрын

My absolutely favorite moment

@dlevi67

4 жыл бұрын

The really nice bit is that the dart landed exactly on the same point... again. The probability is zero squared.

@anatheistsopinion9974

4 жыл бұрын

A real gem 😂

@Redskies453

4 жыл бұрын

Whereas the probability of hitting the very centre of the bull while trying to miss by as much as possible is apparently 1.

@TheLuuuuuc

4 жыл бұрын

@@dlevi67 I know this is probably a joke but I don't like reading it anyway

26:07 Brady: "you're not quite twice as good as someone who has absolutely no skill whatsoever" me af

@alveolate

4 жыл бұрын

2 x 0 = 0 cries in multiples of zero

Hello! It is I, the viewer fresh off of a calculus class! This is so cool!!!!

It’s always fun when e and pi synergize so beautifully, being the 2 most important transcendental constants.

"This is the healthy way to think of e to the x" we need more math teachers like him ;;

Woah! I watched the whole video and it felt like 10 minutes but it is 32 minutes

@-ion

4 жыл бұрын

Huh, you're right. I had to scroll up to check.

@washizukanorico

4 жыл бұрын

Long video with actual equations...got to love it!

@p.as.in.pterodactyl1024

4 жыл бұрын

Wow, I didn't even realize that's how long it was until reading your comment and checking - time flies when you're engaged!

@alenunya

4 жыл бұрын

sooo umm it was definitely a long video for me, guess it's just not my type of a content (= I'm not very smart). I felt like a two year old watching some very skilled magician doing tricks and trying to understand what's even going on. Saw everything, can explain almost nothing :( The saddest part here is that I have a bachelor degree in chemistry

@lyrimetacurl0

4 жыл бұрын

I watched on 2x and it felt like 2 hours, also 1 hour 56 minutes passed.

Boy, I love Grant. He's the kind of guy with whom you'd like to have long discussions about life.

It is always a treat to watch these videos. Thanks for sharing

I get goosebumps when I see notification of videos like this

@numberphile

4 жыл бұрын

Bless you for having notifications on. 🔔

@CK-ov6bj

4 жыл бұрын

@@numberphile bless me too😉

@devlinmcguire7543

4 жыл бұрын

@@numberphile I'm just happy to see Numberfile cares enough about it's subs to read the comments.

@leif1075

4 жыл бұрын

@@numberphile I hope you cab clarify why the probability of hitting the center is zero, because I don't think that's right.

@xybersurfer

4 жыл бұрын

@@leif1075 there are infinitely many points that can be hit, and the center is just one of them. it would be more accurate to say that the probability approaches zero

31:28 "What is the probability that the sum of all those squares is less than 1" That is the most helpful analogy for understanding higher-dimensional spheres.

@richardfredlund8846

Жыл бұрын

thought the same right there

39:33 "Which I think is beautiful and clever" and so is Greg Egan's science fiction. Go on give yourself a treat.

after rewatching this for the 4th time now... definitely one of the best NP videos ever

Grant: "I'll call this x-naught" Me: Why not

@_fangs

4 жыл бұрын

Maybe he doesn't want to

@robertwindshade7629

3 жыл бұрын

Ayayai.

@theawesomepanda1lance241

3 жыл бұрын

I am embarrassed by how long that joke took me to get

Grant, you have an amazing talent for teaching mathematics. I've watched many of your videos and have learned a ton. Brady, I've learned a ton from all of your numberphile videos you've produced over the years too. I have nothing but deep respect and admiration for you both. Thank you both for all you do for mathematics education for us common folks!

This explanation really helped me visualize the concept of e and applications of higher dimensional math better than university ever had. Thanks so much for opening my mind 🤯

This explanation was truly amazing. Thanks for the video. I really loved it!

So, obvi I knew Grant was smarter than me because I watch his math videos to be smarter, but I never imagined that he was also more attractive than me and this is really shaking my world view rn

@constracted7331

4 жыл бұрын

Who says he is smarter than you? The mind isn't a fixed muscle. It can always develop and grow to be smarter.

@bingbong2179

4 жыл бұрын

@@constracted7331 It's one thing to believe you can get better which is entirely true, but it's another thing to think that with hard-work, and being bounded by the constraints of reality and time, you can become as talented as anyone, this is simply not the case as depressing as it may seem.

@jeremywlett

4 жыл бұрын

@@TheBatch62 Obvi u new wat ay mint sew y b pehdaentik?

@z.e....3175

3 жыл бұрын

@@constracted7331 not sure but pretty sure he's somewhere 23-29 years old yet he's a fking mathematician from those very clever solutions to hard math problems. And what I know that I think during that age is still a time on achieving PhD on mathematics yet this guy has seemed to become a maths professor.

@constracted7331

3 жыл бұрын

Edin Zenon How old are you?

Always remember to hydrate when doing high-impact mathematics.

As a statistics student in university, this video blew my mind. That's because there is a relationship between probability of something happening and all that higher dimension spheres, e, pi... just amazing. Thank you so much for the great content.

The perfect crossover doesn’t exi...

I'm just mindblown by the fact that the volume of spheres "picks up" some extra pies as they increase dimensions. It's so weird! Maybe there's an interesting reason for it that you could explain in a video!

@loganstrong5426

4 жыл бұрын

While I definitely don't have an answer, I'd check out 3Blue1Brown's "Why is pi here? And why is it squared?" It has a really nice explanation why a pi squared can show up. Maybe that same chain of logic can start to be applied here.

@XenophonSoulis

4 жыл бұрын

It passes through bakeries and it gives its high numerators and denominators for pies.

@okuno54

4 жыл бұрын

I'm not sure if this is the right explanation, but IIRC, there are two independent axes of rotation in 4D space. Assuming n-space has floor(n/2) independent axes of rotation, then I think every other integral would be bounded by [0, 2π]...? It's been a long time since I did any calculus

@XenophonSoulis

4 жыл бұрын

@@okuno54 The correct explanation is the bakery I mentioned in my comment.

@vrj97

4 жыл бұрын

If you look up the formula for the volume of a torus (donut) in 3D space, it also has a pi^2. Because you can kind of think of there being two circles going on in a torus, the radial one and the cross sectional one. And then its volume is the area of the middle circle swept around in another circle. And then yes, as Okuno above me said, in 4-d space you can also have these two independent circles (say two coming from the first two coordinates and two coming from the second two) and so in some sense it makes sense that when integrating and multiplying stacks of circles to get volumes you get two factors of pi.

This guy should start a channel of his own. He could be famous

@TheEgglet

4 жыл бұрын

he does, it's called 3blue1brown

@stanley2696

4 жыл бұрын

Yea, he could teach some amazing lessons and help a lot of people with mathematic

@Jehannum2000

4 жыл бұрын

@@stanley2696 Yes, he could use those impressive animation skills to aid visualisation of complicated topics.

@stanley2696

4 жыл бұрын

@@Jehannum2000 I would love to see some introduction to Calculus by him. I have a feeling that he could do amazing geometric explanations

@Jehannum2000

4 жыл бұрын

@@stanley2696 Linear algebra too.

Wow, great video! Fascinating how higher dimensional spaces and the Taylor series of e^x pop out of this puzzle!

Fascinating lesson, Grant, thank you for the enjoyable hour!

You managed to make Grant trade in his CG animations for a dartboard, brown paper and markers. Brady you are too powerful.

Seeing his face feels like forbidden knowledge

That was one of the better math videos I've seen in a while. Loved it.

I love your channel. I would really enjoy a video about the Savitzky-Golay filtering of signals and its representation in the Fourier domain :)

As a 3blue1brown patron I've been waiting for this video. :) I've tried to solve the problem on my own for weeks and failed, so I couldn't be more excited right now!

"Infinity War is the most ambitious crossover in history" Mathematicians:"Hold my higher dimensional dart"

Really appreciate the call out that while geometric interpretations are useful, they're best not taken as only relevant for people living in a strange world experiencing that many spatial dimensions. Any collection of related measurements can and are reasonably considered "dimensions." Just a table with a few extra columns. Very practical. Nothing timey-wimey.

What a great problem and video! Ties so many concepts together neatly

Me: "you think darts is fun?" Mathematician: "Yes! you know what happens when an unrealistically bad darts player plays a totally made-up darts game?"

@unfetteredparacosmian

4 жыл бұрын

Basically all of math in a nutshell lol

@Ekevoo

4 жыл бұрын

also all games are made up

@SteveDice21

4 жыл бұрын

31:22 HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA OMG I'm a child.

The animated Pi has a good-looking live-action avatar.

After all of these years of watching and following 3Blue1Brown it was Numberphile that finally integrated a face to his voice!

I'm a second year grad student with a BSc in Physics and Applied Mathematics, and the math that appears in stuff like this still blows my mind. Math really is magical. (Also, studying physics, I'm glad to see a Taylor series not chuncated at the second order.)

"I'm gonna try to make this a worse shot" Proceeds to hit the _exact same spot_ as last time, to within a millimeter

@karolakkolo123

4 жыл бұрын

Ikr 😂

@Ultiminati

4 жыл бұрын

hitting the exact same spot is probability 0 but it is possible lulz

@Reydriel

3 жыл бұрын

*probability zero*

Wow, the two best maths KZread-channels at once?

Yes please, I would love to see a 3Blue1Brown and/or Numberphile video on higher-dimensional spheres :)

One of the best puzzle I have ever heard of ! Bravo

"Avengers Endgame is the most ambicious crossover in history" Numberphile and 3blue1brown : "Hold our beers"

@BastianGrimm2511

4 жыл бұрын

Claudio Di Biase i was looking for that one

@jesusthroughmary

4 жыл бұрын

Doh, I just left this comment

@drdca8263

4 жыл бұрын

And also (kinda sorta) Greg Egan

@MrxstGrssmnstMttckstPhlNelThot

4 жыл бұрын

"Hold our brown paper!"

30:22 reminds me of something I once read in a maths book: Spheres are pointy, and the higher you go in dimensions, the pointy-er they become.

Honestly, this guy is probably a genius. He spouts and remembers all this complex math but almost makes me understand it...almost.

This man got me through AP Calc AB and BC. Absolute Legend