2. The Golden Ratio & Fibonacci Numbers: Fact versus Fiction

[@depalandepalan1911]

Its good to see elderly people learning new things, where i am located such sights are rare. You learn all the time. That mindset is precious

[@theoskylar3287]

i know im randomly asking but does anybody know a method to get back into an Instagram account..? I stupidly forgot my password. I love any tricks you can give me!

[@estebanarthur931]

@Theo Skylar instablaster ;)

[@ramunasstulga8264]

History so boring

[@raymondbermudez7163]

You know a class is properly conducted when you started out watching it out of boredom, and slowly your mind starts working, and your suddenly interested on the matter at hand. Makes me question the quality of professors in my country. Professor Devlin, thank you.

[@mjbe]

I love that after so many accomplishments Devlin still gets a big grin on his face showing adults pinecones. The joy of sets indeed. 😁

[@DonKarp]

If you construct a phi caliper (using the pentagon) then you can measure the ratio without measuring the two number lengths and dividing.

[@GeorgiaAlbert]

The Karnac Temple in Egypt is suppose to incorporates the Fibonacci sequence in its architecture. The Holy of Holies, aka the womb, begins the sequence. The buildings along the main Avenue grow in size according to the Fibonacci numbers.

[@NicknVio]

3 @ 34:37 RE: "Architects dont use the Golden ration" . Some Architects are inspired by the Golden ratio. Some use it, some do not. As of our modern buildings, i agree most of them were not inspired by the golden ratio. No problem with that. Still it is does not address the significance of the no.

[@mickboyd1634]

But the computer calculations for architecture use the golden ratio

[@Jason-sb2zh]

this man does not come across as arrogant or rude or biased. I saw the golden ratio vids on the web. good job and thumbs up!

[@benhahn8065]

At 32:10 he says there is no evidence that the Great Pyramid in Giza was built on the Golden Ratio, so he calls the claim false, but there is evidence - Robert Bauval claims that it is built on the Golden Ratio, such that it could never have a true ending point at the top, it would just go to infinity, if not capped, which it was, and if material thin enough could be made, it would just keep spiraling and going to Infinity ♾️ . Robert Bauval is an excellent architect, and a student of the Great Pyramid. I believe he has proof.

[@scurvofpcp]

I like the body language/facial expression and tones of laughter of the audience in this one.

[@kenergy5847]

All of which can be manufactured without supplying any substance.

[@timvincent8649]

Amateur traders use only Fibonacci and get it quite right (but not all the time), which is Keith's only statement about stock market and say it's just psychology. The professional traders obviously use algebra AND Fibonacci together, to get exact price patterns. Universal mathematics comes first, then psychology. The pro's know that. Greetings from a truth-seeker who makes a good living on trading :)

[@fesimco4339]

You sound like a psychopath.

[@fesimco4339]

@@BreakFix So you read his mentalist screed and your thought was: 'here's a guy I'm happy to take financial advice from!'? In that case; I happen to own a very successful toll bridge and I'm willing to sell it to you, cheap. Interested?

[@kdaviper]

Benoit Mandelbrot used Brownian motion

[@MarkusJaeger-itguy]

And he said explicitly that euclid knew about the ratio but apparently did not give it much significance. The use of ratios of low Fibonacci numbers like 8/5 is also common in architecture. His point is about scentific significance.

[@mixmasterlandberg]

About measuring the body. I found it interesting that one has 5 fingers and all but one are divided into 3 segments, the fifth finger is however divided into 2 segments. 2, 3, 5 are all fibonacci numbers.

[@matthewa6881]

Thanks, love this series. Growing a passion for mathematics as an adult, and this is helping immensely.

[@alitlweird]

I loved the Mechanical Universe series from the 1980s. 😃

[@Zukalski]

This is Bullshit mate. Listening to this clown is certainly not going to help you to understand a thing.

[@Joelthinker]

@@Zukalski lol imagine being this guy lol (you)

[@Zukalski]

@@Joelthinker en voor jou trekken ze zeker wel de rooie loper uit. Flapdrol

[@carlosalexandreFAT]

The association of the main numbers in the field of mathematics with each other, reflects numerical sequences that correspond to the dimensions of the Earth, the Moon, and the Sun in the unit of measurement in meters, which is: 1' (second) / 299792458 m/s (speed of light in a vacuum). Ramanujan number: 1,729 Earth's equatorial radius: 6,378 km. Golden number: 1.61803... • (1,729 x 6,378 x (10^-3)) ^1.61803 x (10^-3) = 3,474.18 Moon's diameter: 3,474 km. Ramanujan number: 1,729 Speed of light: 299,792,458 m/s Earth's Equatorial Diameter: 12,756 km. Earth's Equatorial Radius: 6,378 km. • (1,729 x 299,792,458) / 12,756 / 6,378) = 6,371 Earth's average radius: 6,371 km. The Cubit The cubit = Pi - phi^2 = 0.5236 Lunar distance: 384,400 km. (0.5236 x (10^6) - 384,400) x 10 = 1,392,000 Sun´s diameter: 1,392,000 km. Higgs Boson: 125.35 (GeV) Phi: 1.61803... (125.35 x (10^-1) - 1.61803) x (10^3) = 10,916.97 Circumference of the Moon: 10,916 km. Golden number: 1.618 Golden Angle: 137.5 Earth's equatorial radius: 6,378 Universal Gravitation G = 6.67 x 10^-11 N.m^2/kg^2. (((1.618 ^137.5) / 6,378) / 6.67) x (10^-20) = 12,756.62 Earth’s equatorial diameter: 12,756 km. The Euler Number is approximately: 2.71828... Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Golden number: 1.618ɸ (2.71828 ^ 6.67) x 1.618 x 10 = 12,756.23 Earth’s equatorial diameter: 12,756 km. Planck’s constant: 6.63 × 10-34 m2 kg. Circumference of the Moon: 10,916. Gold equation: 1,618 ɸ (((6.63 ^ (10,916 x 10^-4 )) x 1.618 x (10^3)= 12,756.82 Earth’s equatorial diameter: 12,756 km. Planck's temperature: 1.41679 x 10^32 Kelvin. Newton’s law of gravitation: G = 6.67 x 10^-11 N.m^2/kg^2. Speed of Sound: 340.29 m/s (1.41679 ^ 6.67) x 340.29 - 1 = 3,474.81 Moon's diameter:: 3,474 km. Cosmic microwave background radiation 2.725 kelvins ,160.4 GHz, Pi: 3.14 Earth's polar radius: 6,357 km. ((2,725 x 160.4) / 3.14 x (10^4) - (6,357 x 10^-3) = 1,392,000 The diameter of the Sun: 1,392,000 km. Numbers 3, 6 & 9 - Nikola Tesla One Parsec = 206265 AU = 3.26 light-years = 3.086 × 10^13 km. The Numbers: 3, 6 and 9 ((3^6) x 9) - (3.086 x (10^3)) -1 = 3,474 The Moon's diameter: 3,474 km. Now we will use the diameter of the Moon. Moon's diameter: 3,474 km. (3.474 + 369 + 1) x (10^2) = 384,400 The term L.D (Lunar Distance) refers to the average distance between the Earth and the Moon, which is 384,400 km. Moon's diameter: 3,474 km. ((3+6+9) x 3 x 6 x 9) - 9 - 3 + 3,474 = 6,378 Earth's equatorial radius: 6,378 km. Orion: The Connection between Heaven and Earth eBook By: Gustavo Muniz - Brazil

[@myvibe3893]

Wonderfully done.

[@theNorthernDogStar]

Whether he wrote about it or not, it is demonstrable that Bartók did use the golden ratio in quite a few of his works. Likewise the Fibonacci sequence, though he tended to use Fibonacci in different ways than the ratio.

[@eustacequinlank7418]

I enjoy Bartok (mainly piano) could you mention those pieces?

[@questioneverything42]

Every single time you have a rectangle. You caught it into three? Equal sections And every time you do that, it's always going to end up with another rectangle in the end. Forever. It's basically the equivalency of pi. Instead of Phi. It's absolutely amazing and mind-blowing that nature and beauty and things even that are scary like tornadoes. Show even the most complex Beauty in the world. Through its own secret messages that are encrypted inside of it. I love talking about the golden ratio. You know when you're in that zone, it feels really good. Stay blessed stay lifted.

[@mikedun8882]

Because the true god of the bible created all things.

[@tiesioggl]

I think statements should be made more careful. Instead of stating "false", it would be better to state that the issue is unsolved, if that's the case. That's slightly misleading use of language.

[@shaktiveda7041]

Gedas Luksas agree with your comment here.

[@Danumurti18]

But false is more proper use of word in those cases. Like golden ratio in body proportion, parthenon, pyramids, music, dna, they're all bogus. The only true but actually still unsolved is golden ratio in spiral angle of sunflowers and pinneaples.

[@poopinscoopin1404]

@@Danumurti18 all bogus? Explain how the ratios are not apart of these that you mentioned

[@Danumurti18]

@@poopinscoopin1404 those golden ratio claims are not exactly golden ratio but rather just come near to. For example 5:8 in parthenons are actually not 5:8 but 5.75 : 8, 5.25 : 8, etc. So they're just claimed to be golden ratio but false.

[@mickboyd1634]

Isn’t it amazing they used elements of the golden ratio to bring computers to life ? Normal mathematics just gives a flat screen lol

[@ianwilsongardendesign2236]

Can you spot the golden rectangle? I picked the right one. 55:28 nature examples

[@tahayameenvlogs1490]

I am of the view that golden ratio is a function of water molecule being polar.Any thing that goes to finishing in aqueous medium goes twisting in this peculiar way

[@rogermcinerny2027]

I felt so special when he revealed that I had picked the golden rectangle as my favorite

[@Uri1000x1]

Pythagorean theorem was used before Pathorgous. Reference Delin's statement about Pathorgous.

[@samuelhodges6471]

I'm not good in math. But I can learn math. I have gotten better at math by understanding math. These videos will help me better understand and do math better. What fun!

[@thisisrtsthree9992]

+Samuel Hodges agreed.

[@samuelhodges6471]

The way I see it. Math just takes time to understand what one will use a certain math formula for. Either by finding out how long or short something is or how to figure out how long it will take one to travel from one location to another or calculate time etc. So once one learn the steps to the formula(s) and what type of math will get them the answer, then math becomes easy. Check out some other ways to use math in everyday life. Counting back change for example or adding and subtracting time. I'll post some things like that to get you started. Good luck!!!!!! Thanks for the reply.

[@MycketTuff]

How's the math coming along? Enjoying the new depth and sincerity of the language? :)

[@TMB247]

Geometric reasoning was how I was taught Algebra... I went through a lot of paper in those days (checking my work Mathematically) Reason = We didn't have calculators... they existed but I couldn't afford one ;^)

[@4OHz]

In Japanese culture, a unit of measure is the “Tatami.” Similar in proportion to the golden ratio but not the same proportion.

[@Godlooksfar]

Oh more to learn about

[@TreDogOfficial]

Nice that we still see the golden ratio in nature. I have a dream of planting a fruit orchard like that.

[@TreDogOfficial]

+Dee Vigga Vectors agreed

[@shelleyaw123]

Thank You!! You've answered the question that has bothered me for 20 years. Real Algebra still exists! After being told in a College Algebra class that "we don't do it that way anymore" I'm happy to see they were mistaking Algebra with Arithmetic.

[@poemsbyomkar4405]

This is not a fibonaci number it is a matrameru ,this is a hindu maths technic, if you want learn ,use a pingla sutras -author pingla maharishi ,you find all answers ,It's just a lesson from this book, there's more to it than that

[@gardensofthegods]

@@poemsbyomkar4405 wow thank you so much I'm definitely going to look into it and I have been interested in Hinduism since I was a kid and that was 55 years ago

[@carlpen850]

In nature there's a natural feel of things... math is the language that we use to describe nature and the universe. I do teach the Golden Means... Golden Ratio... to my beginning art students to help them understand design... I also stress that they should know the rules before they attempt to break them. The best artist have an abundance of knowledge on their side... the "hacks" of the trade have very little and it shows in their work.

[@gaussianvector2093]

The language is necessary but not sufficient to define Mathematics. I define it as learning for the sake of learning. Most define it as the study of patterns. I have a inclination Noether's theorem and some assumption that learning requires invariant some how could maybe show that definition is also necessary. But I still claim mathematics is something more.

[@eustacequinlank7418]

I think there are a lot of self proclaimed ‘artists’ and ‘professors of things’ in this comments section simply looking here to add a footnote to their ‘research’. As much as I’m in the same position regarding the mathematics, I hate the disingenuous approach to ‘self validation’.

[@antimatter2380]

He said there is no credible evidence in music. I don't know if this is anecdotal but a major cord in music is the first, third, fifth, and octave eight note. And almost all rock is 3 cords... the first, third, and fifth in a scale.

[@whatabouttheearth]

Only by was of JS Bachs equal temperament. Not all people use that western standard. Many societies use microtonality which in my opinion sounds much better. And triads are very basic chord forms

[@RanBlakePiano]

Would like to read more

[@AJTalks]

G. Patrick Flanagan is brilliant a doctor that spent a great deal of time investigating the pyramids of Egypt and he proves the relation between phi and the architectural design of the Great Pyramid mathematically in his book "Beyond Pyramid Power". This professor based all of his research off of online texts instead of checking published literature or measuring for himself. I would expect more from Stanford.

[@AJTalks]

Perhaps you are not talking about the same person, the Patrick Flanagan I am talking about was a child prodigy and had a doctorate from Columbia. He published a book braking down very precise mathematical measurements that he made while he lived in Egypt. The book is called Beyond Pyramid Power. It proves without a doubt that the Egyptians had knowledge of this ratio and applied it (along with pi) to the construction of the pyramid. I have checked the facts and all of the measurements are correct. The King's chamber was not built to golden ratio length/width because it is an acousticly resonant chamber. The relationship between the three acoustic frequencies which together create resonance (standing wave) in the chamber is precisely the golden ratio. Although i'm sure you have done some research, you should not go around and make claims as if you know what you are talking about.

[@The0ldg0at]

+Alex Johnson Reading this, my understanding is there is not only 3 frequencies that will create standing waves in any room. So one can cherry picks any 3 of the many that will fits his pet theory. artsites.ucsc.edu/EMS/music/tech_background/TE-02/modes/Modes.html

[@AJTalks]

I'm glad there is someone on KZbin that knows everything and moderates the bullshit from those that are far less knowledgeable. Thanks Steve

[@LeadershipAlliance]

Alex, great insight; I also love Patrick Flanagan's work. You might enjoy my 4-minute TEDx talk on the subject, the Golden Ratio Renaissance, at this link. Cheers, Matthew Cross. kzbin.info/www/bejne/ZqWki5hspbVgfK8

[@1invag]

He says there's no evidence the Egyptians knew anything of the golden ratio but you've gotta ask why do pine cones suspiciously appear all over their hieroglyphics? He's saying there's no evidence they knew about it, but absense of evidence is not evidence of absense. To say they didn't know about it is a claim backed up by no evidence in of itself. All said, I like that he's challenging these ideas. Why is a circle seemingly arbitrarily divided up into 360 degrees? Why did the Egyptians use a base 60 number system? Why do way say there's sixty seconds in a minute 60 minutes in an hour.

[@kevingarrett8403]

The Golden Ratio in plants make sense; Nature seeks maximum growth that fits within a given structure.

[@TsTheKeyToEverything]

Notice how he keeps saying 'okay'. It reminds me of that guy from south park

[@onthehill3381]

Like...I know, right!?

[@soundsoffire5960]

this bugs that major universities point out that the golden ratio was not embedded in the monument as theres no proof...he proved himself wrong by getting the class to point out the visually appealing rectangle.. the monuments have artistic designs as they are nesnt to be visually appealing hence subconciously the golden ratio was used as it would have seemed right at the time . reguardless of if the designer was aware of it or not its apparent that humans are drawn to this ratio on a visual and at times an audio aspect..

[@rasheedlewis1]

I wouldn't call Euclid's describing the ratio as "extreme and mean" as being "unromantic".... And I mean, of course, someone has to be the first to call it "divine" or "golden." The question is why did those adjectives catch on in the general language? And what kind of class is this anyway? The slides have no LaTex, so the math is basically unreadable. He doesn't "debunk" most of the claims. And who takes a class on debunking claims like this anyway? Can he actually *teach* us how one might play around with intervals/beats/measure in a musical piece using the golden ratio, as opposed to being a pedant?

[@JohnnyJaga]

See TOOL's Lateralus to also find the Fibonacci. Spiral out... Keep going.

[@jasongravely7217]

One of my favs

[@imthemoeron]

To say that ancient humanity never used the golden ratio is willfully naive.

[@reggiearnold3032]

your a great professor and really passionate about math, I hope I can go to stanford someday

[@9Speed]

You'll want to work on your grammar before you attempt to fill out the application.

[@reggiearnold3032]

tyanks fur the advise!! I cant wit to go to STanford!.

[@kylelarson727]

Chirag R. xD

[@davidandrewwhite5147]

The spacing of primordia on meristems manifests angles related to the Phi. The angle between each primordium that allows for the optimal spacing between buds converges on Phi. But this is not actually very mysterious if you think about it. It fact it follows from a simple algorithm-like rule for initiating each new primordium as far from the last couple of primordia as possible. This only approximates Phi when the meristem is large and each primoridium is very small. For large buds an opposite or distichous phyllotaxy occurs - i.e. 180 degree angles between buds. That is a very common spacing strategy. But it is as far from Phi as one can get.

[@WarzSchoolchild]

1:24:13 , "Has anyone come up with a ratio close to 1.618. ..." A pseudo Fibonacci Series, starts:- 0, 1, 1, 2, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521...etc. next we might choose ,0, 1, 1, 2, 4, 9, 13, 22, 35, 57, 92, 149, 241, 390, 631, ...etc. Do all these corrupt series asymptotically converge on 'Phi'...??? The true series, certainly does:- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 , 89, 144, 233, 355, 610, ... It may or may not? be interesting to see how a 'corrupted' Fibonacci Series behaves. Thanks for that question Professor Keith, You have sparked my curiosity. (Edit:- First exploration, is to apply the Fibonacci 'Addition Rule' to the Prime Number series:- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109,...etc. So let's take those last two '107' & '109', we get the series 107, 109, 216, 325, 541 (Prime), 866 (2 *433), 1407, 2273 (Prime) 3680, 5953 (Prime), 9633, 15586 (2 *7793), 25219 (Prime) 40805 (5*8161), 66024, 106829, 172853 (Prime), 279682, 452535 (15*30169), 732217(Prime) and incidentally 732217/452535 = 1.61803396422... So we are converging on Phi. ...Hmmm? The distribution frequency of Prime numbers seems slightly anomalous. Take it from here guys! )

[@bobjimbobjim]

Gotta love his confidence when he raises both arms.

[@petemiller9404]

ya pick a career and... sometimes the magic works and sometimes it doesn't. if he's happy... what the heck.

[@aotearoastylagrlrepzitifre3999]

The lady laughing was golden

[@briancote7974]

I went and looked at a diagram of the Great Pyramid, took the length from the midpoint of the bottom to the edge (220 cubits) and divided it by the length of one of its faces (356 cubits) (so basically a right triangle with one side at 220 and the hypotenuse at 365). This results in 0.618... This is the inverse of the Golden Ratio (which is 1.618...). The value 0.618 is important in Pythagoreanism and likely Platonism. Anyone using the GR in design work would be familiar with it. So the professor is incorrect in his conclusion. At least in regards to the Great Pyramid. I didn’t check any of the other examples, but I’d be interested in seeing if any of the others check out.

[@mkklmann]

In music it's much easier to find the Diabolical Ratio i.e. squareroot two, i.e. the tritone (or Devil's interval) which was built into the perfect circle of fiths and the equal temperment tuning of modern instruments

[@jessruhl24]

Can you cite an example?

[@gardensofthegods]

Mikkel , I'm trying to teach myself music theory and I'm going to enjoy looking that up .

[@gravity0529]

If a definitive answer is true with only 2 answers. Therein the opposite of false is truth. by definition if more than 2 answers are available then a proof by contradiction isn't true nor wrong, it's not a definitive answer.

[@thetruthimpart]

In 1990. Jean-Clode Perez, the scientific employee of IBM, has made rather unexpected discovery in the field of genetic code. He has discovered the mathematical law controlling by self-organizing of the basis T, C, A, G inside of DNA. He has found out, that the consecutive sets of DNA nucleotides are organized in frames of the distant order called as "RESONANCES". Here "Resonance" represents the special proportion ensuring division of DNA parts pursuant to the Fibonacci numbers (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...). As already repeatedly was emphasized in our Museum, it is the same proportion, which controls by morphology of natural organisms such, as a pinecone, cactus, pineapple, etc. For example, let's consider 144 adjacent nucleotides of DNA formed from 55 basis of T and 89 basis of A, C or G; then the proportion (55-89-144) represents itself the "Resonance".

[@timloer5419]

I particularly liked the focus on the fractal population depending on scale factor and that it seemed to go well later with the discussion of optimal packing in seed heads and leaf dispersal. Enjoyed this very much! Thanks

[@mikedun8882]

It's the infinite power of the one true god who created the heavens and the earth.

[@mikedun8882]

The theistic god createdno mathematics as an infinite display of his power and glory.nothing is by chance.

[@gardensofthegods]

@@mikedun8882 Many scientists over the decades have talked about INTELLIGENT DESIGN and said it attested ( at least to them ) that there is some kind of INTELLIGENT Creator / creation out there ... and that nothing is by mistake .

[@theredeemeriam]

​​@@gardensofthegods The Father's prime initiative is for it to not be obvious that he exists. This is the whole purpose for there being free will. What the Father does however do, is bless us with the clues of his existence and the reason and logic to figure it out. The Golden ratio and the mandelbrot set are such clues.

[@Onoma314]

I have a blog where I dissect the entire series of numbers to see how it's constructed, there's a link in the header of my channel, next to the Facebook icon. I find it odd that observant Jews are forbidden from studying this sequence of numbers, even though you'd think it would be right up their alley ( being associated with Kaballah ) and Christians are entirely unaware that every single capitalized " LORD " in the Bible refers to this reduced Fibonacci sequence containing 216 numbers.

[@mckeestudio1101]

Brilliant, Glad to see someone who actually understands mathematics separate reality from wishful thinking.

[@XxPlayMakerxX131]

Are you from his course Mathematical thinking ?

[@mckeestudio1101]

@@XxPlayMakerxX131 Good afternoon, and, No, I am not. I am a professor of Art and an Artist, who has been working on a project that deals with a ratio. The Golden Ratio is something which I am deliberately avoiding, as it is definitely overhyped and as Devlin points out, it's verifiable connection to the motives and practices of historical artists is tenuous and subjective.

[@revefraser202]

Beautiful order in the universe - all around!

[@kihondosa4]

Thank you for the video. I just realized, Golden ratio is something we all tend to use with experience. One reason for it, our ability to observe nature and extract patterns.

[@BlackSmurfPunk]

~35:00 About the architect who worked just with the golden ration: Le Corbousier ;-)

[@mckeestudio1101]

One architect does not a trend make.

[@jtherrington77]

He conflated "most perfect rectangle" and "most pleasing rectangle". The perfection of the phi ratio is related to creative balance, not personal preferences.

[@renataheiberg7534]

Finally some common sense found it's way to this silliness.

[@NicknVio]

2. @ 31: RE: Greek buildings. You can verify this yourself using the Golden Grid and Caliper. Obviously, the designers are dead and we can not verify them weather they used it or not. But this is beside the point. If its there fine, it isn't it still ok, this does not affect the real significance of the no.

[@KirstenMcFarlane]

He is another generation of lecturers overlapping messing up warping and recreating whatever was originally told in ancient times, take it with a pinch of salt and lots of laughter, and try to find to positive energy buried within and draw it out and help it shine in you

[@xSCOOTERx2]

The moment they started looking at pinecones spirals for fibonacci numbers, everyone got so excited, like watching kids on a playground.

[@hamfranky]

What fascinates me is a lot of people in the comment section getting very worked up about something as arbitrary as the golden ratio.

[@richardnineteenfortyone7542]

You need to review Elliott wave theory.

[@Santathing6789]

that's because it is not arbitrary

[@geogon2007]

Aesthetics is like ideology. It responds to social traditions, values and political interests. We are born with this trained (or tamed) sight -along with hearing, smell, taste and touch-which sees beauty wherever it's supposed it should be. Everybody sees what they make them see from the beginning and if you buy that, you will try to fit the 1,618... with a hammer in nature or, unfortunately, in an "ugly" person's head.

[@hyperqbit7246]

Water molecule geometry is a possible golden triangle candidate. Though the angles between oxygen and hydrogen using measurements don’t exactly match 108 degrees, the current results are based on statistics so the 104 degree is an approximation. The geometry of the water molecule might be the reason why it keeps appearing in nature

[@Rickety3263]

Objectively false in particle physics. The uncertainty principle itself disproves your hypothesis, but it would be nice to think about.

[@KL-ii6dt]

Tldr: the golden ratio is 100% predictable as the pattern in plants, orbital patterns, and fractals. However, theres a lot of 'new age woowoo' about it being in music, human attractiveness, architecture etc, which is untrue (or at least unproven.

[@augustuswaller4962]

Why is there no mention of Pythagoras in this lecture?

[@nibussss]

Is it the most minimum energy way to pack things together.

[@griknok]

10:58 a google of "golden ratio" in 2012 gets 4 million hits, now in 2022 it's 276 million

[@reicarnationcollection8609]

This is a fantastic lecture and shows the difference between a scientist and someone who "does science". He includes examples of when it works and when it doesn't. How often does that happen? He is clearly a very talented intellectual. Did anyone else giggle at the pix of Arnie?

[@mickboyd1634]

But a snail shell is just a claim?

[@tiesioggl]

I get a sense that the lecture lacks statistics and a broader context. For example, given a daisy and it's petals count, it would be great to see how many daisies were analysed to collect data about their petal counts. It would also be great to see the numbers of petals, leaves, etc. counts compared in a context of the total of known flower kinds or compared to predicted estimate of flower kinds. Otherwise, it's the same question, why these flowers were picked.

[@GrEEnEyE089]

It makes sense that plants grow patterns based on fibonacci numbers. they grow in fractal patterns and are tuned towards optimal usage of space by natural selection which is the golden ratio.

[@fredfender8272]

Aaaah, no.

[@theredeemeriam]

@@fredfender8272 So what do you mean no fred?

[@TikkyTakMoo]

26:02 dang. Ud think the "golden rectangle" looked something close to the giant rectangle in the background containing a golden ratio object 😑

[@GPCTM]

I think all the fibonacci ratio are alternating lesser bigger lesser bigger (than the previous ratio)

[@RussDodson42]

I wonder why Keith skipped 2 when h stated the beginning of the number? It isn't 1, 1, 3 --- it's 1, 1, 2, 3...(5, 8, 13, etc.)

[@4JumbeLaShingwaya]

This is what it means when math is fun

[@omera97]

If anybody thinks this lecture is lousy and that hes just disproving the golden ratio, Just wait until 44:23 and youll realize its not

[@Silly.Old.Sisyphus]

do golden ratios appear in spiral galaxies?... something about gravity and homeostatic packing?

[@Fulely]

try antihydrogen fusion , then your close

[@ToxicallyMasculinelol]

***** dude you are so fucking stupid. you're just picking words and phrases and stringing them together to try and sound scientific, when really what you're talking about is new age spiritual quackery. not even close to pseudoscience, it's just made up garbage to trick people into spending money on "science" that will prove the existence of their preconceived spiritual beliefs. antihydrogen fusion has nothing to do with "sacred geometry" and, of course, you know nothing about it. also, "mantle dynamics" is not real

[@RonaldPatrickMarriott]

shmediaproductions you're the greatest expert I've ever heard. Go read a book . The Fibonacci sequence created from the release of high energy photons copied from the internal fusion creates the spin in the quantum field. When you criticize something that you don't know about you look really fucking stupid. Better to ask questions about this than smell like you.

[@davidandrewwhite5147]

There are many quasi-stable ratios in nature. Mostly where optimal packing in 2 dimensions occurs you get arrangement that can be construed as Golden Ratios. But optimal packing results in pentagons if the objects are evenly sized. Phi is related to pentagons. But if you pack things in 4-D, 5-D or 6-D, you get other optimal packing ratios. These ratios are not Phi. I would guess not in galaxies. For starters, stars are not evenly spaced in galaxies. Further it is obvious that there are tight and loose spirals in different galaxies.

[@RonaldPatrickMarriott]

Antihydrogen fusion wrapped in antihelium antioxygen cooling the fusion back to antihelium sealing it in is called a relativistic perturbation mantle. Trapped fusion converting antihelium to high energy photons or dark matter producing dark energy as the entire disc disappeared and returned to make a Sprite

[@johnjohns2333]

Thank you for the video! At first I though the video was about not giving credit to the amazing ration of the golden ratio. I can’t get enough of this mind blowing phenomenon! It shows there’s some kind of intelligents put into creation doesn’t it?

[@gaussianvector2093]

when you think deeply enough it does not. Thinking the rabbits, very normal behavior implies it. The same rational can be applied to the natural way thing would grow. further, it is known we are fond the familiar (google body temperature of a chicken study) so it makes sense the things we kind beautiful would be natural patterns. You cannot prove God, if you couldn't faith wouldn't be faith. I believe in something higher, but firmly believe it will never be any proof or phenomena not explainable by physics. I had a crisis of faith when I realized it was definitely plausible there is nothing more. But that's why you have to believe. Not based on any philosophical argument, not simply because why not, but because you have faith.

[@gaussianvector2093]

TL;DR No, "God" transcends logic. Faith cannot be inferred or experimentally validateable. It cannot be explained or reasoned, and why it is there cannot be due to ignorant attempts at such for an academic devout, it must come from something unfathomable and purely from within not from observation.

[@Ozymandi_as]

@@gaussianvector2093 why do you believe in God, whereas others do not? Why do so many people who claim to believe in God use their faith as a justification for acts that are self-evidently immoral. You claim abandonment of logic as proof of transcendence; and then, feeling pleased with yourself, you boast about it, under the banner of a video on number theory. Jesus!

[@1invag]

@@Ozymandi_as perspective, perspective and perspective? Place yourself inside a geometric form and youll only see the parts of the totality available to you from that particular perspective. This is how we learn, by shifting perspective. A fixed position is death. The question is why we learn

[@gardensofthegods]

.John Johns , I agree with you and over the decades a number of scientists have said this INTELLIGENT DESIGN led them to conclude there's got to be some kind of creator or creation .

[@JuliusLewis-cb2ng]

Another thing, couldn't you get a golden rectangle from ANY RECANGLE if you cut of a square from it?

[@zyzzyva57]

Be prepared to speed through half of this lecture, for example, when he goes off on measuring a pine cone, speed through it To the professor, wear a shirt that don't show arm pit sweat Also, get to your points, which many are good, but good lord, drop the puff Algebra is giving question marks letters to handle the question marks

[@NondescriptMammal]

Interesting, and the lecturer isn't terrible, but he sure takes a lot of words to get to a point.

[@mikelheron20]

This talk could have been delivered in 30 mins.

[@vincewhite5087]

Part of problem was a stupid student asked a question that showed she hadn’t taken high school math. She is out of her norm, and should go away.

[@ericashmusic8889]

@@vincewhite5087 I'd say 20 mins, & he is totally wrong about Nautilus !! .

[@pedropastador7498]

No.... it's a class not a youtube video.

[@johnpowell9174]

Good to hear a Yorkshire accent!

[@samferrer]

I love this very interactive lecture...

[@philbertbrainstain]

you've had a few Guinness and Jameson haven't you?

[@zombieregime]

for the love of god Stanford, get some stage fans!

[@afulford]

zombieregime That was to put emphasis on the golden ratio of his arms, when lifted.

[@zombieregime]

+Adam Fulford i meant that he looks like he was boiling up there.

[@afulford]

That's what I meant to LOL, most apparent when he lifted his arms.

[@harlequinharlikwin]

Omg! Yasss!

[@eyoo369]

I have come to the conclusion that people that are strictly into Math will always try to debunk it as they have no foundational knowledge in Art and how important composition and proportion is. It is only if you are well-versed in the world of Art and have a mathematical understanding of the universe is when you can truly appreciate the lovely proportion of the Golden ratio. The biggest mis-conception people have about this is that if you apply it into your art, it should supposedly make it better. This is absolutely not the case. Its the recursive ratio that has something beautiful and serene to it if you can apply it. Adding some spiral on top of your work is really not going to cut it. Study the works from Da Vinci, Van Gogh, Michelangelo and many other great minds and how subtle they have applied it.

[@davidriosg]

I have come to the conclusion that you really want to believe that there's something particularly special about the golden ratio, and there's nothing no one can say that will convince you otherwise

[@eyoo369]

@@davidriosg There is no such thing as belief in the golden ratio. Its out there in nature. Take a blank sheet of paper and write the Fibonacci sequence and do some calculations like divisions or square root and you will notice some very interesting results you will never find in other number sequences. Go take a measurement tool and go measure your own body (Vitruvian Man). Go study planetary orbits like Earth and Venus and how they have 1.618 as mathmatical relationship. These are not beliefs but universal facts.

[@ziba2660]

the golden mean spiral in two dimension of geometry is imploding and expanding circle that is spinning as radius is changing it's length in squares ratios... cool

[@jeromesims]

So how about the "claim" that photographers use the golden section? "I try to find the golden section." -Henri Cartier-Bresson who went on to inspire countless photographers. Today many cameras come with viewfinder overlays displaying the geometry of the golden ratio to help in composition. He leaves out far too much. Unconvincing as an expert on the subject. Seems like someone who at first thought it was a cool idea but then got skeptical but at no point did much actual field work one way or the other. The best evidence he gives for his claims is anecdotal, a story about interviewing architects and having them all present ideas for using the golden ratio but then saying they don't actually use it? Made no sense to me.

[@jschauer31]

It seems to me he began by wanting to present a debunking of the golden ratio. He succeeds by not showing us the true dimensions of anything at all.

[@LeadershipAlliance]

Great insight; there is F A R more to the story. You might enjoy my 4-minute TEDx talk, the Golden Ratio Renaissance, at this link. Cheers, Matthew Cross. kzbin.info/www/bejne/ZqWki5hspbVgfK8

[@mahonig9125]

1:04:50 is the only thing that i loved from this video

[@KirstenMcFarlane]

When your so glad your not stuck watching this class in university and escape is also negative. Or not. Run :-)

[@Wesgo111]

for the prof.: what does this mean for the world and nature: does it mean that the world needs the golden ratio in order to work or is it just a nice thing that we see in nature. please write back. thank you.

[@fakegandhi5577]

@Joji Joestar i think everyone in this comment section is smoking crack

[@JuliusLewis-cb2ng]

In the Nile Valley, we said : "Among these three numbers, PI3.14 PHI 1.618 AND. 618 that PHI .618 is the truest of them all. The Great Pyramid in anchored in these three numbers among many others. I trust you are not confessing to bigotry. Remember the Greek philosophers studied under us. We the black people.

[@mwmcbroom]

I found this lecture to be rather perfunctory, but then I don't think it was meant to be deeply comprehensive. It is meant more as a "survey" lecture -- an overview of the topic. And in that respect, I think it works. I first discovered the properties and significance of the Fibonacci Sequence some 16 years ago. At the time I was interested in Elliott Wave Theory as it applied to the stock market, but I never really saw how the Fibonacci Sequence was meaningfully applied using Elliott Wave principles. Nonetheless, I was fascinated by the universality of the sequence and how it could be found in so many things, especially in nature. From Sunflower seed distribution to galactic spirals. I build guitars and I decided that, with one of my projects, I was going to apply the golden ratio to one of my guitar builds. Rather than attempting to design in anything related to the ratio externally, I decided to incorporate the ratio internally. The guitar is a steel-string acoustic and I incorporated the Golden Ratio into the design of the guitar's bracing pattern. Braces were related to one another using this sequence and I even scalloped the braces such that the peak of each scallop was positioned to reflect the ratio. The result? Well, it is certainly a good sounding guitar -- but I wouldn't say it is astounding or anything. Just a solid, good sounding guitar. So I'd have to say the "experiment" worked. It's a very well-balanced, full-sounding instrument. Although I myself wonder how different it would have sounded if I would have used a more traditional bracing pattern. But what's the fun in that?

[@mantwaan]

I’d be curious to see it.

[@uilium]

That's interesting but aren't lengths represented by numbers?

[@TheDavidlloydjones]

Fer shure. But you don't necessarily know what they are, do you?

[@Dun_Did_It]

Fact is what can be proved and fiction is what cant. Due to this we have developed irational thinking. Toothfairy vs ardvark, god vs profesor, etc. I propose that unless u can prove it, keep calm and reseaech. With that said, keep faith in humanity and leaen off of one another. Be well. Ps, tnx for the info.

[@mina7572]

Anyone get the code he was blinking?

[@merops]

It's not up to him to show proof there's no connection, he just needs to show that the claimed connection is bogus (and that he did, because 1.4 or 1.8 is not in any sense the golden ratio, and because in a complex object there will always be ratios which are in that vicinity if you cherry-pick the points you measure).

Search for Modulor by Le Corbusier.

[@NicknVio]

I agree. 1. @ 24: RE: Rectangle. Its not a favorite rectangle per say but its a transition between what is known as 4-equal sided rectangle ( Square ) to a rectangle with two sides being unequal. So if i draw a square, obviously its 4 sided, if i stretch 0ne side a bit longer, we could not readily say that its longer, so we still say its a square. If it approaches 1.618 ratio however, then we begin to distinguish it as a rectangle with 2 unequal sides. The way to get statistics to this is ; 1. The participants must be unconsious of the subject 2. There must be at least more than 10 participants with varied background and ages.

[@Unkl_Bob]

At 24:00 ? If you put the time in that format it automatically makes the shortcut link

[@matthewvicendese1896]

Maths is beautiful enough. It doesn't need a whole bunch of woo. If you add all the woo, it shows you don't really understand why these numbers or ratios may pop up in nature. Also, which ratio are you talking about? The Golden Ratio is not seen in nature very often. There are an infinite number of metalic means, of which the golden ratio is the first.

[@snehas2166]

Can then come to a conclusion that whose face lengths from certain defined points is in the golden ratio is not ugly ???

[@kylelarson727]

Can't wait to show this to my math teacher lol

[@jackfever405]

The lady in the front row had 3 white stripes on her shirt and the shirt had 2 colors 3:2 ratio...Coincidence? I think not!

[@Rogue.Warrior]

Hahahaahaha.

[@johniacono4361]

great video top watch if you are having trouble going to sleep. A self graded quiz! this guy is from the late 1960's, when it was all about making one feel good about themselves without really teaching anything

[@treefrogjohnson7514]

The same way people like to jump up and claim something to be related to the golden ratio, others like to do the same whenit comes to debunking objects relations to the golden ratio. The nautilus shell, my personal favorite often has proportions that are approximate of the golden ratio and seeing as the golden ratio is an infinite, irrational number, an approximation is enough to relate the two. The Nautilus spiral cannot be constructed from the golden rectangle which seems to be the only way most skeptics and debunkers want to approach this from, but there are multiple ways to create the golden spiral. The tradional way, the fibonacci spiral is found by increasing the width of a section by Psi every 90 degrees, but the spiral can also be found by increasing it by 180 degrees, so the spiral size increases more gradually. After a 360 degree rotation, the width of the spiral from the center is Psi squared, and another full rotation we get Psi cubed and so on. There is a lot of nonsense out there, but on both sides. Some want to try and make the Fibonacci sequence and the golden ration fit every rectangle and spiral out there, but some want to react in turn by debunking everything. Math is not always as exact as people think it must be, especially when dealing with irrational numbers, and so approximations such as what can often be found in a nautilus shell do relate to the golden ratio, just not in the way other things do.

[@tinaferr]

Agree. Well said