That's Not How the Golden Ratio Works

[@AnotherRoof]

⬣ *CORRECTIONS, CLARIFICATIONS, AND COMMON COMMENTS* ⬣ 1. 2:29 I say this graph looks like the Riemann-Zeta function. It isn't! This is a graph of the Gamma function. This is why I dropped analysis in favour of algebra... 2. 8:37 the table showing bone lengths: the index metacarpal should be 490.7, giving a ratio of 1.721. Still not the golden ratio! 3. 18:29 line four there is a q^2 denominator when it should just be a q. The funny thing about this is that one of my patrons caught the mistake in an early draft -- I fixed the q on the line above but forgot to fix this one! >_< 4. 19:19 I'm using "size" to refer to "absolute value" here, and then I misspeak, saying: "...so this whole thing is an integer which has size less than 1 [...] so it must be 0; that's the only integer less than 1." I meant to say "that's the only integer with *size* less than 1." Clearly, if n is an integer with |n|

[@asdsdvb6408]

at 19:33, you say "this must be 0, that's the only integer less than one". but you can also have negative integers. i'm not a mathematician so sorry if i'm wrong but that didn't seem right to me

[@Onoma314]

That movie also incorrectly stated " qedem " is the Hebrew word for " garden ". which it's not. " Qedem " in that verse he mentions is used to mean " east " , while the Hebrew word for " garden " is " gan " which is a direct Sumerian loanword ( Cf. The GAN_2 system of area measurements for more ). " Eden " is also a direct Sumerian loanword ( Edinu in Akkadian ) Great video btw ! ETA: Hebrew ( And Koine Greek ) numerals are taken from Egyptian Hieratic numerals, there's nothing special about them at all, and " gematria " actually means " earth " ( ge ) + " measure " ( metria ). Earth measure is essentially geodesy, and geodetic measurements were taken and used by Egyptians for the purpose of building and aligning temples like the one at Karnak, and the writing was predominantly in Hieratic, the main script of math / science / religious texts. There's really nothing woo about it, it's just that religious people don't know real history. They want to make up bizarre explanations for things that don't need them 🙂

[@AnotherRoof]

@@asdsdvb6408 I've updated the pinned comment to address this, thanks!

[@asdsdvb6408]

@@AnotherRoof thank you for replying to my comment and for the correction! great video btw!

[@themathhatter5290]

8:37 The X-ray number for index metacarpal is not accurately input into the table. And I would argue the ratio of First to second phalange of your middle finger is quite close to the golden ratio!... so if anyone asks for an example of a golden ratio in the human body, you can flip them off. :D

[@fluffiddy6515]

Zeppeli family is gonna hate this

[@evansherburn4157]

The golden ratio isn’t a number, it unlocks tusk act 4

[@FeeshUnofficial]

EXACTLY

[@kylewood4001]

Anti JJBA part 7 propaganda

[@BetterCaulipowerSall-vq9yn]

gyro is extremely disappointed

[@MassiveDestructionSP]

Bah! Next you're gonna tell me that I can't use a horse to channel the Golden Ratio into my nails.

[@someonehavinganidentitycrisis]

I've been looking for this

[@IdiotSandwich-kr7vc]

This comment is so bizarre

[@hauntedhoody2976]

What an adventure you must have

[@Kram1032]

ViHart has also covered how plants are doing golden ratios - as have many before and after her. But her exploration goes one step further: It also shows how they actually are able to do this. Like, how does a plant actually measure the golden angle? And the answer is that it kinda doesn't. It involves the following of chemical gradients in a way that just so happens to *usually* (but due to inherent randomness actually not quite always!) causes the tightly fitting spiral patterns we see in sunflowers, pine cones, and some (but far from all) plants' leaf growth patterns.

[@ABaumstumpf]

And to make it funnier: those patterns are mostly just any arbitrary logarithmic spiral and not the "golden" spiral.

[@2stral]

i think vihart is why i love math. along with numberphile

[@ZackC]

In plant leaf growth, though, when there is a logarithmic spiral, it is tending towards the “golden.” Similarly to the seed packing, a plant whose leaves exhibit a golden ratio in their distribution around the stem will have the potential to receive more sunlight than leaves in another distribution which would more likely be shadowing one another.

[@Kowzorz]

​@@ZackCvihart examines that sunlight line of logic too and concludes its misguided.

[@Baptized_in_Fire.]

It's pressure mediation. Typically 137.5°.

[@jasonmp85]

Also, Pi is essentially a student film, the kind of indie film that no longer sees mainstream breakout. It cost $130k to make. They weren’t going around paying mathematics consultants.

[@thevoteman]

they could have at least gotten pi correctly but yeah, good poont

[@thevoteman]

@@topherthe11th23 you make a good poont

[@atomic_xfire]

​​@@topherthe11th23poont taken

[@FFKonoko]

​@@topherthe11th23 2 minutes to copy and paste pi from altavista or such, but presumably the real reason is that whoever they outsourced the opening to knew keyboard mashing was easier.

[@j.0x00n4]

Finally someone said it. I'm an artist and I'm dead tired of seeing people disregard others work for not fitting into some ratio or formula, as if a beautiful composition actually relies on pseudo science and not every other choice in the frame or composition.

[@realdragon]

People do that?

[@j.0x00n4]

@@realdragon Unfortunately it's all too common in traditional art studies.

[@KatSpicert]

Why is it that there's so many people in traditional art studies who seem so overly pretentious and pseudo-intellectual? What is it about art that inflates people's egos?

[@FFKonoko]

It isn't pseudo science, it's misapplied maths

[@FFKonoko]

​​@@KatSpicert it's called college students learn about it and then want to use it, they get too excited about knowing that thing that apparently not do many use or know about and it makes them feel special. Possibly combined with a bit of hipsterness, because they are doing things the hard way, without undo.

[@opensocietyenjoyer]

"golden ratio is when spiral" is what 99% of the public take away from 99% of "golden ratio" videos

[@AmmoGus1]

How do you know? Are you some 160 iq genius who knows what everyone else thinks?

[@opensocietyenjoyer]

@@AmmoGus1 do you think that me knowing what people think means i can read minds?

[@we_hate_things]

​@@opensocietyenjoyer Damn bro read my mind

[@bigboy-gw8me]

@@AmmoGus1 no, a 160 iq genius would not be good at knowing what other people think.

[@frauleinhohenzollern]

Ok

[@ciaranheikeclark]

I enjoyed the beautiful sunflower joke :)

[@erikziak1249]

0:10 As a mechanical engineer, I feel physical pain when seeing images like that, especially if all the wheels are the same size and the shape of the tooth is what it is. Ouch!

[@japedr]

Well, to ease a bit your pain, you could imagine they are not all at the same depth level.

[@key_bounce]

@@japedr Or, I suppose, the 3d (slanted) gears that actually do work when placed like that.

[@milanstevic8424]

No, this is exactly what they *had in mind* . With a slogan of "Making the city work together" and a picture of gears in a deadlock there is a deep subliminal message there, could also be subconscious.

[@mal2ksc]

@@milanstevic8424 Maybe it's what the artist that created the sign intended. I can believe they'd be intentionally subversive, especially if it didn't jeopardize getting paid. Then the government that commissioned it didn't put it in front of anyone who knew better, so there it is for all to laugh at.

[@trueriver1950]

​​@@mal2ksc Close, but as a detail it was the local government not at national level. The ad is from my home city of Manchester, England, and was the second as in a series announcing the introduction of route 3 of the shuttle service run around the city centre. The irony was that the free buses were supposed to reduce gridlock (there was a stop by most of the car parks) and encourage drivers to abandon the car for travel within the city. Instead what the ad actually showed us that careless design means that a third route could actually cause gridlock not stop it. So yes, subliminally eye catching, but with exactly the reverse effect of that intended.

[@stjernis]

Blackboard fills itself in and even animates a bit, 3b1b style. Nice touches.

[@GeoPuff]

Hey, just wanted to say that your video quality has noticeably improved over time, and this was one of my favorite ones so far! From the sunflower joke, to the misleading the audience to prove your point, I just love all the different ways your videos keep me engaged. This is one of my favorite channels!

[@AnotherRoof]

I want to keep improving and growing so thanks for the kind words!

[@_devotio_]

I can't believe gyro zeppeli lied to me

[@brandontylerburt]

The woo surrounding the Golden Ratio often seems to act as a thought-stopper for many people-that is, people will memorize the "fact" that it's got something to do with the chambered nautilus and the Fibonacci sequence and beauty ... and then they'll lose any desire to find out what it actually is or anything more about it. And now we're all doomed to hear somebody expounding at length on how the Golden Spiral is just everywhere, man, at least once a year at a party, so transported by an unoriginal idea they don't notice our eyes glazing over as we nod politely and try to summon the desired level of feigned astonishment. Nothing travels at the speed of stupidity, so I don't think this video will be enough to stamp it out. But thank you very much for a well-conceived and nicely presented explanation.

[@TheFrozenthia]

Inappropriate to call it stupidity. That's not helpful and doesn't encourage curiosity.

[@danielsmokesmids]

Your sense of superiority is showing

[@krimbus1236]

@@brandontylerburtthis is a KZbin comment section. You’re not gonna get a medal

[@brandontylerburt]

@@krimbus1236 Oh, really? (Pulls out KZbin comment medal) Are you SURE about that?

[@brandontylerburt]

@@danielsmokesmids Look, I don't write with any kind of sense of superiority. I have fun writing KZbin comments and, I mean, that is just the way that I write. I was an opinion columnist for a lot of years and then the newspaper industry tanked and right now I'm unemployed, and I guess that's why I've been hitting the comments section too hard. So maybe I need to dial it down a little bit, and I should be careful not to come across as overly critical. And if I don't I guess I can't afford to get my feelings hurt when somebody accuses me of having a sense of superiority. If you knew me, though, you'd realize a superiority complex is pretty much the opposite of my neuroses. Please, if you don't mind, give me the benefit of the doubt here. I really would appreciate it.

[@FeeshUnofficial]

The only ones who know how to apply the golden ratio properly are the Zeppeli family and Johnny Joestar

[@rtg_onefourtwoeightfiveseven]

19:19 Clarification for the confused (like I was): when Roof says "it's the only integer (with size) less than 1", he means "...with absolute value less than 1", which is relevant because the original quantity was less than 1 when wrapped in an absolute value.

[@pyrotas]

I am a Physicist. And about this dephinite subject there are countless examples of disinformation and bad science communication. This on the other hand is probably the most lucid and most directly explained content out there. This channel is criminally under-rated!

[@RecursiveTriforce]

​​@PaxAlotin-j6r It's a joke about the subject of the video. It's about the golden ratio (phi).

[@jamesworley9888]

What most people call bad science are actually mostly approximations. It's unfair to discredit Ancient scientists just because their measurements had to be rough estimations. I think neither the spiritual nor scientific people are treating these numbers in the way they should be treated. Each calculation towards more accuracy is a footstep in the latter to infinity and just because the first step is bent out of shape from people overusing it doesn't mean it isn't part of the evolution.

[@publiconions6313]

Love the Numberphile shout-out... Ben is the best and that is one of his best episodes

[@popcorn485]

12:00 the way you casually do by hand what most of us did with Python or Mathematica … is what I’m here for! So refreshing!

[@CiaoRooster]

The Pi expansion is also wrong on the math club banner for Pi Day in Drew Barrymore’s “Never Been Kissed.” I think they strayed after 3.1415 or there about, super early. Spotted it in theaters. Drove me crazy.

[@aldasundimer]

This is one of my favorite movies and i was also obsessed with it in my early twenties. I even made an electronic song where I used samples from the movie. I think the statements about pi being found everywhere in nature is opposed by the speech of Saul where he states that this is basically numerology. For me the movie is more about the urge of human to understand life in it's whole, to find the ultimate truth and the inability to achieve this through science.

[@timbeaton5045]

Yep. I remember seeing this on TV a long time ago, and was knocked out by it. Such a concentration of tense moments, clever photography, and a brilliant intense feel. I also liked The fountain, too, although not many other people, seemingly did. Requiem for. Dream also, but I found it difficult to watch a second time.

[@almanacization]

I'd say it's much more likely that it's the gamma function at 2:29 . The absolute value seems to be increasing rapidly as the real part of the argument goes to infinity.

[@neckbeardeater682]

It is the gamma function

[@lapiscarrot3557]

Was gonna say the same thing

[@jessehammer123]

Yeah, I too was like “isn’t that gamma rather than Riemann-Zeta?”

[@iskrabesamrtna]

'When I was 6 years old my mom told me not to stare at the Sun - and I did' So was I, and all sorts of weird things happened, many portals opened. Thank you for mentioning the movie Pi, it's a masterpiece.

[@SpeakerWiggin49]

/s

[@not_David]

I just have to comment that the animations at 3:16 are slick. If I did a screen shot I'd be sure they are physically drawn on. I have no clue how you did that haha.

[@diribigal]

Alex: Nurtures our understanding of mathematics, responsibly puts out polished videos regularly, and cares about people who might be misled by films. Also Alex: I'm not "Caring, nurturing and responsible."

[@emilyrln]

Bruh you saw how mean he was to the camera guy smh

[@alansillitoNYC]

I love maths and I love the film Pi, as a film. Imagery, ideas, and Drum & Bass tracks - brilliant.

[@quantumgaming9180]

Amazing video as always. FINNALY someone talking about the falso claims about the golden ratio. Also not just some repetitive video review on some movie but an actual personality rich video essay finding deep details of the stage director in planning a movie.

[@yew7607]

Small mistake at 18:32 with the denominator of 2*delta / q^2 being squared even though it's not in reality.

[@enpeacemusic192]

thank you so much this has bugged me forever because clearly these people really do not know what they are talking about sometimes..

[@kinyutaka]

One thing that I noticed in the video is that the old man tells him that a mathematician that goes too far is a numerologist, I think that was the whole point of the film. He studied so hard about the Golden Ratio and the weirdness of it that he lost touch with reality. The obsessive compulsive door locking, the routine use of drugs, the disconnect between him and the girl that likes him, all because he can't see the forest for the trees.

[@degariuslozak2169]

Interesting thing about the Parthenon The columns aren't vertically straight, they're actually angled inwards, however the the varying thickness of the bases of the columns creates the illusion of it being vertically straight

[@Aaaaaaarrrpirate]

Wow it’s almost like the creators had actual ways of making things look big and nice

[@kmjohnny]

I got more excited for this video, but not for the reason you think. I actually started working with Manim to make some videos around the golden ratio this week, potentially turning it into a KZbin video in the future. There's just some beauty in this ratio that I haven't seen explained completely, and now I'm working on a different approach. But enough tldr, thanks for the video Alex.

[@julioaurelio]

That sounds awesome, I'll stick around your channel. +1 subscriber.

[@sharcraz211]

How could Jojo's bizarre adventure lie to me!? /s

[@joels310]

I just found your channel! You got me working parts of my brain that haven't been dusted off in 15 years since university. Ty for making this amazing video, I can't wait to see what other stuff you have.

[@sparrrorow]

based on the thumbnail alone i thought this was an art tutorial video, but sure, i'll stay for a math video essay

[@jarlsparkley]

I honestly think that we should just standardize the mile to be equal to golden ratio kilometers

[@emilyrln]

Deeply satisfying idea; now we just need to find a wealthy eccentric to pay for replacing all the signs.

[@_..-.._..-.._]

This is a video where I understand about 1 out of every 1.6 things said. I can hope to watch a few times to understand more. I appreciate that you haven’t dumbed it down too far. It’s well presented, but allows the viewer to pause and google some of the terms and equations to get a better understanding. Subscribed!

[@ludvercz]

I strongly agree with your conclusions. This is a cinematic masterpiece I love and hate so much. Clint Mansell's score is a work of genius, the cinematography is brilliant, the cluster headache scenes for example are so powerful you can almost feel it yourself. Like, they should be teaching this stuff to new generations of filmmakers, this is how you "show, not tell". And then the movie goes on to "tell" us all this nonsense about mathematics. Just the fact that it's called Pi but is actually about Phi(?) which it then calls Theta, is enough to break my little maths-nerd heart. I've never felt this conflicted about anything else until I heard your closing pun.

[@SineN0mine3]

Now that you mention it, it seems a little unlikely that the filmmakers wouldn't have realised that the title of the film and the name they give the symbol in the script were different. Maybe it's supposed to be a sign of the main character's madness? Or a sign that the universe is inherently chaotic or something? I haven't seen it in ages but I wouldn't be surprised if they put in little details like that rather than make such an obvious mistake.

[@ToyInsanity]

Clint Mansell from PWEI???

[@ludvercz]

@@ToyInsanity the one and only

[@Geek37664]

Pi is one of the best films ever made despite the inaccuracies found within it. It’s dark, demented and dreary and yet it’s a suspenseful, engaging watch. It helped me get into mathematics when I decided on a degree when I went to college the year after it came out, so it holds a special place in my being. Thank you for reviewing this wonderful film.

[@JKTCGMV13]

If I’m a beautiful sunflower then so is the camera man 😤😤😤

[@j.thomas1420]

Great content, I've subscribed. You deserve way more subscribers...! ⬡

[@leyasep5919]

The quality remains very high ! This is accurate, thorough yet still quite approachable, not too long... I admire your work !

[@pink_plasticbag]

man, this channel is so underrated. this is amazing

[@Jenthura]

8:26 "...8th fracture..." 28:55 "Ow" Hmm, I wonder why?

[@X22GJP]

A really interesting video, especially since I’ve never heard anybody pronounce epsilon like that, and I’m a fellow Brit!

[@AABB-px8lc]

13 km - that was really funny.

[@Neptoid]

Thanks this helped me process some of the feelings and thoughts I have about the movie. I wanted despiratly to have a movie about math and a genius. Those are rare and usually tied to stereotypical and unhelpful explainations. The pseudoscience part has me going mad, yet I am facinated by the occult and pattern recognition in general. I was suprised how you showed it could be used as just memory aids and didn't need to have an irrational and superstitious basis. Even though superstitions are not too harmful and can even be helpful. Often indirectly, but many times they bring furfillment and profound realizations. Stuff that makes us process and realize things aren't all that bad. Movies where willpower transcends over all hurdles and breathing controls life are protoscientific, but they still give us powerful effects. Flames on stage aren't powerful even though the music is to us, perhaps for misplaced trust in their true effects

[@ModusTollendoTollens]

Nice video. Also The Dear Hunter is a nice choice (even thought Act IV is my favourite).

[@Matheus_vs64]

Amazong Video, especially the prt where you explain why phi is that infinite fraction of ones and therefore its connection to being the most irrational number. 10/10 video❤

[@dojelnotmyrealname4018]

11:04 I love the dedication of having the autocue be correct.

[@dinoscheidt]

Phew… don’t want to know the effort to get to this production quality. Great work!

[@hofh]

I take the "discrepancies" in the movie as a sign that the story takes place in an alternative universe: a universe in which phi is called theta, and pi equals to whatever they made it be, etc - and it makes the story much more immersive for me, as I can entertain the idea that our main character is obsessing over something real - I no longer know how their world truly works, but I know for sure that it works differently from mine; it might as well all be real and not solely in his head, in-universe c:

[@serb4446]

It is a testament to both this video and its comment section that I have not seen a single person even mention JoJo's

[@erie3936]

Outdated info

[@someguywithatophat7599]

Well there are some now at least But also in making this statement, your statement becomes false

[@someguywithatophat7599]

@@erie3936 actually i checked a few comments, the funny thing is it was wrong from the getgo, i found jojo comments from 14 days ago, while this comment is only from 10

[@jaredcramsie182]

24:54 You mention that Max's computer was named 'Euclid', this may be another reference to the golden ratio. Euclid's algorithm for computing the Greatest Common Divisor has a computational complexity of roughly O(log_{phi}(n)). This means that, in the worst case, we can expect the number of iterations of Euclid's algorithm to increase proportional to 'the base-phi logarithm of n', where n is the smaller number. This is derived by noticing that sequential numbers of the Fibonacci sequence are the worst possible input for Euclid's GCD algorithm. 1. Taking the modulus of the larger number will never reduce the result by multiple of the smaller number. 2. The remainder is the next smallest number in the Fibonacci sequence, which means we never prematurely terminate. F_{n+1} mod F_{n} = F_{n-1} This corresponds to the continued-fraction definition of phi (seen at 14:50 in the video).

[@ruilopes6638]

Loved this one, as the golden ratio claims always bother me as well One thing I would add about Fibonacci/phi relation is that it has nothing to do specifically with the Fibonacci seeds but just the recursion formula.(as it’s clear by the proof where the seeds are nowhere to be seen). The Lucas sequence which stats at 2 and 1 instead is much more “golden” than Fibonacci’s (and the relations between the two sequences are beatiful on their own ) (And nice to know another dear hunter fan)

[@Geek37664]

At 21:40, you give reasoning for I like exploring sacred geometry symbols such as the Flower of Life without having to go into woo land. The geometric properties alone within it are both beautiful and fascinating. You can geometrically construct many square roots of integers and discover Pythagorean style relation for 60° and 120° angles. I personally think such symbols are why we have isometric graph paper available for drafting.

[@kylecow1930]

excited for you to cover Zorn's Lemma (1970)

[@daanwilmer]

Aww, Another Cameraperson Under Another Roof, I do think you're a special sunflower! 🌻

[@עמיתלרמן]

God I always hate it when in films and stuff the plot tries to show someone as intellectual by fake math so this series speak to me. However I didn't know about that nice property about the flowers, I always assumed its the same rubbish as "phi is everywhere in nature" kind of stuff. But as soon as you said that it goes like a logarithmic spiral it was clear to me, I just couldn't make that assumption without prior knowledge and never thought of that so deeply.

[@antarcticbirdenthusiast]

Zeppeli family been reeeeal quiet sence this dropped

[@DustinRodriguez1_0]

When Pi originally came out, I had to find a theater where it would be shown and travel a bit to get to one. I ended up, funnily enough (if you've seen it), finding a small theater in a Jewish neighborhood with a large orthodox population. At the time, the central underlying idea of the film, that there is an intricate pattern underlying all of reality (and that understanding the pattern would destroy you) was fairly novel. It's surprising how poorly the film has aged. Now those ideas have been woven into so much media in so many different forms that it seems kind of trite. It does also draw a bit on some Jewish mysticism type stuff (Kabbalah) which I've gone on to learn a bit more about... I don't subscribe to any sort of religious belief, but I think there is actually some instructive stuff about how the brain works, how we process language, etc that can be garnered from the practices they do. Not the beliefs themselves, but the practices. I imagine back when written language was first invented, many of its features that we entirely take for granted were seen as quasi-magical back then. Things like reading one passage, then reading a passage about a completely different situation but recognizing a common pattern to their structure.... that is something that simply was not possible prior to the development of written language. When it was brand new, when it was knowledge held by only a very small number of people, where they couldn't even explain to others what they were talking about (because they didn't have words like 'metaphorical' or 'symbolic' yet), etc, it almost HAD to seem magical. Which would naturally lead people to looking for more patterns, and eventually might lead on to development of new ideas and insights... I could see that sort of thing playing a real role as our brains were adapting to a language more durable than our own minds. Our language has deeply profound effects on how we perceive the world and think, stuff like cultures who read left-to-right seeing themselves as walking forward into a visible future, while those who read right-to-left see themselves as always looking at the past, walking backwards blindly into the unknown. That's just one example, there are hundreds.

[@ambrosia777]

The animation in this video is a big mark up! Well done!

[@leyasep5919]

14:56 that's an insanely good explanation !!! thanks so much ! 😀

[@timseguine2]

As a programmer, the number of significant digits that are correct makes me highly suspicious that they used the value of pi as given by the constant in some programming language that was returned as a standard 32-bit floating point number. The accuracy of that format is about 7 or 8 significant digits in most cases. If I had to guess, they wrote a program that took the value of pi according to that constant, then kept subtracting the integer part of the number and multiplying the remaining value by ten. I didn't completely verify, but if that theory is true, you would expect it to be periodic after a while. And it does look like it might be (in any case I did find some pretty long sequences of repeated digits before getting bored with the task to write this response).

[@RFC3514]

If I had to guess, someone gave a graphic designer a printout of pi, he started copying the digits, then decided no one would notice, and just punched his keypad randomly.

[@timseguine2]

@@RFC3514 That is also a very realistic possibility.

[@matthewschwartz8730]

Omg I can't believe u mentioned the movie pi! I didn't know if it was a hallucination I had from back in the day but I swear no one else has ever heard of that movie.

[@dominikmuller4477]

phi is the most irrational number because its continued fraction has only 1 in the denominators. That proof about fractional approximations you gave is beautiful, but if you want to use it to prove that phi is the "most" irrational number, you need to prove that no other number (other than rational multiples of phi + rational constant) breaks the approximation for larger A.

[@LordMarcus]

Was gonna say this myself. 😅

[@nuggetoftruth865]

To be fair though, it does still prove that no other irrational can be *more* irrational. If anything, the best you can get is another irrational number that’s equally irrational. But I think you can make the logical assumption that if any other irrational also breaks when reducing the approximation by an infinitely small amount, that other irrational must be the same as phi since there is literally no space between them for another number. If there was room, then an irrational could fit in between them, and that would break the definition.

[@LillianRyanUhl]

That wasn't what he actually set out to prove though: he only set out to prove that phi is a counter example to any larger constant in the denominator

[@ZakNouar-cn2hg]

That was a fantastic video, I greatly enjoyed that

[@JoshPrandel]

24:43 what a speech, I can't stop thinking about it

[@havenp]

It’s heartening that the sunflower example is by far the most common one that I’ve heard

[@oasntet]

Every time I see an argument about the Monty Hall problem I get so frustrated. It's not that hard to just simulate it a few dozen times and see the results of the two strategies, and in doing so the reason it works becomes far more obvious. Don't argue about it, just test it!

[@Valkhiya]

My favorite way to understand it is to change the problem to have 100 doors instead: You choose one, then the host reveals 98 doors that don't have a car behind them and asks if you want to switch to the last remaining one that you didn't pick.

[@KSignalEingang]

I think one possible cause of these arguments is that some people aren't approaching it as a mathematical problem, whether they realize it or not. One of the key facts of the problem is that Monty knows what's behind all three doors - he's never going to inadvertently open the door with the car. What's not typically specified is, does Monty *always* open a door? Or is he making a strategic choice to do so or not? If Monty is choosing whether or not to reveal a goat, now we have more of a psychological/game theory question than a mathematical one. Of course some of us might just prefer having a goat to a car. Goats are pretty cool.

[@robertpearce8394]

For me, it's a mathematical versus an emotional argument. You have a 1 in 3 chance of picking the correct box, but if you pick the correct box and then switch, you are probably going to be more upset than not switching and losing.

[@mariozehren4666]

​@@ValkhiyaThat was my favourite way to understand it as well for a long time. Recently I came across another way to explain it that feels even more intuitive to me and works without imagining 100 doors (Honestly, I was shocked that I hadn't heard that exact explanation more often before). Imagine you choose one of three doors and then you can make a decision: Either you get what's behind the one door you chose or you get what's in both of the other two doors combined. In that situation, you obviously should switch to the two doors as your chance to win the price will be 2/3 with them and only 1/3 with the single door you chose initially. But notice that by choosing the two doors you are guaranteed to get at least one empty door. You can imagine the game show proceeding like this to build suspense: You made the choice to switch to the two doors. Now the showmaster opens the one empty door which is definitely among these two. At this point, two doors are still closed - one of the two that you chose and the third one you chose initially but then switched from - and you still don't know if you made the right decision by switching. But obviously that doesn't change the fact that your winning chance by choosing the two instead of just one door was and still is 2/3. Ultimately, the showmaster opens the other of the two doors you chose and now you know if you made the right decision and won or not. Now what the Monty Hall Problem does, is that it changes the order of the events described above by first opening an empty door - which is equivalent to the one of the two doors that is guaranteed to be empty and that the showmaster opens first in the scenario above - and then letting you choose if you want to stay with your initial pick or switch. But that change in the order of events changes absolutely nothing about the information that you have: Making the choice having seen one empty door being opened is completely equivalent to making the choice knowing that one of the two doors you choose will then be opened and be empty. Actually seeing an empty door you already know is there gives you no additional information. So essentially, the Monty Hall Problem is just the showmaster asking you if you want to stay with your initial choice or switch to the other two doors combined, thereby obviously upgrading your winning chance to 2/3. The only thing that makes it confusing is that one little change in the order of events compared to the completely obvious case that somehow seems important to the human mind at first but actually makes no difference to the information that you have.

[@inutamer3658]

The easiest explanation I find is... on your initial choice you have a 1/3 chance of picking the winning answer. Monty will always reveal one goat and never the prize. Therefore when given the option to switch you are being asked "was my original choice wrong?" Which is 1/3 to be correct and 2/3 to be wrong and need a switch

[@haraldclark6206]

Fantastically enjoyable, thank you!

[@letsmakeit110]

between you, numberphile, cracking the cryptic, and the game show "Countdown" british ppl are really good at math.

[@ToyInsanity]

maths*

[@_..-.._..-.._]

I’m so happy to hear that the 3 lines thing is completely made-up. I always felt that it was arbitrarily applied to anything that fit, but so many “smart” people had told me it was an important detail. 🤦‍♂️

[@SineN0mine3]

2:24 I'd say two things are responsible for this, firstly that the films title sequence is usually made by somebody other than the rest of the film and secondly that audiences hadn't developed the habit of watching movies frame by frame on pause and scrutinizing every visible detail. So a graphic designer, who probably knew they could look up the digits, considered how long it would take to type them out and just said "nah, nobody will notice!".

[@brun4775]

The actor who plays Sol rings a bell.

[@3Max]

Don't blink, or you might miss the connection.

[@MathNerd1729]

Great video! I was very excited when you looked into the result in the thumbnail about Phi, being the most irrational number, “breaking” a slightly modified version of an inequality :) Also, 22:11 to 23:05 is especially funny to me because my birth name has name number 6 but my preferred name has name number 3. I can confirm that I'm not that responsible or sociable either 😂 (maybe it has something to do with my autism)

[@quantumastrologer5599]

You could argue that the movie isn't about math or related concepts but about a person experiencing some form of schizophrenia and insufferable headaches (a friend of mine had these kinda cluster-headaches and they are truly a nightmare, even if you only sit there and watch the person experiencing them). So the errors make perfect sense since inexact / confused thinking is kinda normal then (which can be a blessing since it opens up unexplored ways of thinking about problems and a curse because it can suck hard). Following this line of thinking taking apart the math of the movie completely misses the point.

[@mutantdog.]

I think you were too generous with your placement on the ‘accuracy’ axis here. I’d have put it closer to 0 and deducted points for not really having anything to do with pi itself. Are negative values allowed in your ranking system?

[@vagarisaster]

As a Saw fan, had to pause and like after the Spiral joke. 💀

[@uselesscommon7761]

21:55 it's funny, because an eastern numerologist would tell you that 4 is a number of death

[@ttmfndng201]

7:14 Fun fact: ln(5) is an even better approximation. Phi is accurate to 2 S.F. while ln (5) is accurate to 4 S.F.

[@timseguine2]

I like to "well actually" the odd number of gears thing in the devil's advocate direction when people point it out. Maybe it's an accurate orthographic projection of a three dimensional gear train where not all the gears are the same thickness or coplanar.

[@octavianova1300]

I wish I had known about this property of phi sooner, because that "most irrational" property sounds like it would come in handy for an idea I was playing around with, a while back, but kinda hit a wall on. I wanted to create a musical scaling system designed to be maximally discordant, and thus to steer as widely of approximating any small whole number ratios of frequencies. The issue I ran into is that the two parameters involved that were trying to be simultaneously optimized - distance from small whole number ratios, and the "smallness" of the whole numbers in said ratio - proved to have a direct tension between them, and I failed to find a particularly natural way to optimize a balance between them. I'm not sure how I would work phi into this particular problem, but its mentioned property would seem to suggest it could hold the key to this particular project.

[@emilyrln]

15:17 chalkboardception 😂 also your handwriting is very clear and pleasant to look at! Do you always write like that or is it just for the boards?

[@LunalyteZyxienne]

as a math nerd and witch, I appreciate the educational video without being dismissive of magic. magic specifically cannot stand up to the standards of the laboratory, the law of large numbers, or the blackboard

[@gcewing]

25:11 Watch for Alex's upcoming spinoff series, MACMS -- Mathematical Accuracy in Cracked Mirrors.

[@diechort]

So Donald in Mathmagic Land was lied to me? My whole life has been a lie.....

[@McConnor28]

This is your funniest video yet.

[@HexDeck]

Genuinely 0 overlap with the Mona Lisa one, I thought it was satire

[@amirilan4435]

Have you thought about looking at the movie "The number 23"? though its a more numerological one than a mathematical one, it is still quite an amusing one.

[@ScrimmyBingus42]

Cool to see how nature was inspired by Maynard James Keenan, who invented math to write the song Lateralus.

[@quinterbeck]

Enjoyed the discussion of the difference between mathematics and numerology! As I see it, there's a literary use of numbers as symbols in the Jewish & Christian scriptures, where authors intentionally use them to draw connections, build on themes. But the understanding of those symbols was shared between the author and the original audience. Maybe you wouldn't count that as numerology. I see it as a little different from the kinds you cover in the video

[@hw2007]

16:37 The alarm went off in my head before he said the last name xD

[@LNHofficial]

I thought this was a steel ball run video

[@magnumxchiptunes]

You are great at explaining proofs.

[@weavehole]

My favourite clip too! :)

[@kyleolson8977]

I would be willing to believe the "Golden Ratio Everywhere" idea gained far more traction thanks to Disney's "Donald in Mathmagicland". I watched it on film in school in the 1980's. The pool section is good.

[@alexdamman6805]

Quality episode, my man. Slider on a chalkboard! HA HA

[@Blitterbug]

As an English engineer of some 6-odd decades, I've never heard anyone (Brit or otherwise) mangle that poor Greek letter as ep-'sy-lon, only 'ep-si-lon (where the quote mark is which syllable to stress)... ;)

[@havenp]

Cambridge dictionary does list ep-‘sai-lon as the British pronunciation, but Oxford dictionary has stress on the first syllable for all dialects. Weird, I’ve also never heard it said in the way he does.

[@Blitterbug]

@@havenp Yep, the Cambridge dictionary is actually, empirically wrong. Astonishing!