The Golden Ratio: Nature's Favorite Number

Aperture
5 Mar 202114:44

Summary

TLDRThe script delves into humanity's innate fascination with patterns, particularly the golden ratio, an irrational number approximately equal to 1.618. It explores the ratio's prevalence in nature, such as in sunflower seed arrangements and the Fibonacci sequence, and its purported influence on aesthetics, from facial beauty to architecture. The video challenges the golden ratio's divine status, questioning its true impact on design and biology, suggesting that our obsession may stem from a desire to find patterns that make us special. It concludes by pondering the nature of mathematical discovery versus invention, hinting that the golden ratio's allure may be more about human perception of beauty than an inherent universal truth.

Takeaways

  • 🧩 Humans are naturally inclined to seek patterns, which provide comfort and meaning, even in complex subjects like string theory and quantum mechanics.
  • 🔍 Nature and mathematics are at the forefront of pattern-seeking behavior, with humans having evolved to notice patterns and detect anomalies.
  • 🌟 The golden ratio, symbolized by the Greek letter Phi (∅), is a pattern that has fascinated mathematicians and people for centuries due to its unique mathematical properties.
  • 📏 The golden ratio is defined by dividing a line into two parts such that the ratio of the whole line to the larger part is the same as the ratio of the larger part to the smaller part, resulting in a value of approximately 1.618.
  • ∞ The golden ratio is an irrational number, similar to pi, with a non-terminating and unending decimal expansion.
  • 💐 The golden ratio and Fibonacci sequence appear in nature, notably in the arrangement of seeds in sunflowers and other plants, where it helps maximize sunlight and rain for optimal growth.
  • 🎨 The aesthetic appeal of the golden ratio is often associated with beauty in human faces and body proportions, as well as in art and architecture, although these connections are not scientifically verified.
  • 🏛 Claims that historical structures like the Egyptian pyramids were designed based on the golden ratio lack substantial evidence.
  • 🤔 The fascination with the golden ratio may stem from a desire to find patterns that make us feel special or to impose a sense of beauty and perfection onto the natural world.
  • 🧬 Recent research suggests that the golden ratio may have a biological significance, with studies finding it in the cardiovascular system across different ethnic groups.
  • 🔬 Despite the allure of the golden ratio, it is essential to approach claims about its prevalence and significance with skepticism, recognizing that our perception of beauty and patterns may be influenced by familiarity and cultural narratives.

Q & A

  • What is the golden ratio and how is it mathematically defined?

    -The golden ratio, often symbolized by the Greek letter Phi (Φ), is a mathematical concept where a line is divided into two parts such that the ratio of the whole line to the larger segment is the same as the ratio of the larger segment to the smaller one. Mathematically, if you have a line divided into two segments, 'a' and 'b', where 'a' is the longer segment and 'b' is the smaller segment, the golden ratio is satisfied when (a+b)/a = a/b, which approximates to the value 1.618...

  • Why is the golden ratio also referred to as 'the divine proportion'?

    -The term 'divine proportion' implies a special or extraordinary property attributed to the golden ratio, suggesting that it holds some form of aesthetic or natural significance. This name reflects the historical and cultural fascination with the ratio due to its prevalence in nature, art, and architecture.

  • How does the golden ratio manifest in nature, specifically in the arrangement of seeds in a sunflower?

    -In nature, the golden ratio is evident in the way seeds are arranged in sunflowers. The angle at which new seeds are added in relation to the previous ones, known as the golden angle (approximately 137.5 degrees), creates a spiral pattern that maximizes space and ensures that seeds are packed efficiently to receive sunlight and nutrients.

  • What is the Fibonacci sequence, and how is it related to the golden ratio?

    -The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. This sequence is intimately connected to the golden ratio because as you progress through the sequence, the ratio of two consecutive Fibonacci numbers approaches the value of the golden ratio, Phi.

  • How is the golden ratio thought to influence human perception of beauty, particularly in facial features?

    -The golden ratio has been associated with the perception of beauty in human faces, with the idea that facial proportions close to the golden ratio are more aesthetically pleasing. This concept suggests that harmony and balance in facial features, as defined by the golden ratio, contribute to attractiveness.

  • What are some criticisms or limitations regarding the claims of the golden ratio's influence on aesthetics in architecture and human faces?

    -Critics argue that attributing aesthetic appeal to the golden ratio in architecture and human faces often lacks scientific rigor. For architecture, it's not enough for a structure to have the golden ratio; it must be meaningfully incorporated. For faces, without clear definitions of facial features and their measurements, claims of the golden ratio's influence are hard to verify.

  • What does the script suggest about the psychological reasons behind the fascination with the golden ratio?

    -The script suggests that the fascination with the golden ratio is rooted in our innate desire to find patterns and seek a sense of order and meaning. This pattern-seeking behavior can sometimes lead us to attribute significance to patterns like the golden ratio, even when the evidence for such significance is not conclusive.

  • How does the golden ratio relate to modern design practices, particularly in UI/UX design?

    -In modern design, especially in UI/UX, the golden ratio has become a staple, with designers often using it to inform the layout and proportions of elements within a design. For example, headings might be 1.6 times the size of body text, and golden rectangles are used in layout compositions.

  • What biological evidence is presented in the script that suggests a deeper significance of the golden ratio in human cardiovascular health?

    -The script presents research indicating that the golden ratio is closely related to the dimensions of the human heart's left ventricle. Studies have found that the ratio of the left ventricle's horizontal to vertical lengths in a large sample of subjects was approximately 1.618, and deviations from this value were associated with poorer heart function.

  • How does the script address the philosophical question of whether mathematics is invented or discovered?

    -The script explores the idea that mathematical phenomena, like the golden ratio, exist independently of our understanding or recognition of them. It suggests that while we may name and define mathematical concepts, the underlying properties of these concepts remain unchanged and exist whether or not we are aware of them.

  • What is the conclusion presented in the script regarding the 'divinity' of the golden ratio and our pursuit of beauty?

    -The script concludes that the 'divinity' of the golden ratio is not an inherent property but rather a construct of our perception of beauty and perfection. It suggests that our search for beauty in the universe is ongoing and that the golden ratio, while fascinating, may not be the ultimate symbol of perfection we seek.

Outlines

00:00

🔍 The Golden Ratio: A Mathematical and Aesthetic Pursuit

The first paragraph delves into humanity's innate desire to find patterns, which brings comfort and meaning. It highlights the golden ratio, a mathematical constant represented by the Greek letter Phi (approximately 1.618), and its irrational, non-terminating nature similar to pi. The golden ratio is found in nature, particularly in the spiral arrangement of seeds in sunflowers and other plants, which optimizes sunlight and rain exposure for survival and reproduction. The Fibonacci sequence is also mentioned, showing how the ratio between successive numbers approaches Phi. The paragraph also touches on the aesthetic appeal of the golden ratio, suggesting that visually pleasing faces and the human body, including famous works like Da Vinci's 'Vitruvian Man,' have proportions close to this ratio. However, it questions the extent to which the golden ratio is genuinely present in architecture and other human-made structures, hinting at a possible overemphasis on its significance.

05:02

🎨 Debunking the Golden Ratio's Aesthetic Claims

The second paragraph critically examines the claims surrounding the golden ratio's role in aesthetics, particularly in facial beauty and design. It points out that for the golden ratio to be meaningfully incorporated, it must be a deliberate choice that adds value. The paragraph challenges the validity of internet claims that superimpose the golden ratio onto celebrity faces without clear definitions of facial features. It also discusses experiments involving golden rectangles, which show that people tend to prefer rectangles with proportions slightly different from the golden ratio, thus casting doubt on the idea that the golden ratio is inherently more attractive. The text also explores the influence of familiarity with the golden ratio and how it might bias perceptions of attractiveness. It concludes by questioning the origins of the golden ratio's popularity in modern design and suggests that its perceived divinity may be more about human perception than any inherent property.

10:03

🌿 The Golden Ratio in Nature and Its Human Obsession

The third paragraph explores the presence of the golden ratio in the cardiovascular system, suggesting a deeper biological significance. It discusses research findings that show the left ventricle dimensions of hearts from Swedish and Chinese subjects closely match the golden ratio, and how deviations from this ratio are associated with poorer heart function. The paragraph also mentions the golden ratio's connection to the growth rates of fetal hearts and the decline of cardiovascular health with age. It acknowledges potential biases in the choice of units for these measurements, which could exaggerate the golden ratio's significance. The text reflects on the human tendency to seek patterns that make us feel special and questions whether the golden ratio's appeal is due to its genuine properties or the human desire to find meaning and beauty in the universe. It concludes by suggesting that the golden ratio's perceived divinity is more about human perceptions of beauty and perfection rather than any inherent transcendental property.

Mindmap

Keywords

💡Patterns

Patterns refer to regularities or recurring structures that can be found in various aspects of life, from natural phenomena to human behavior. In the video, patterns are highlighted as a fundamental human quest for comfort and meaning, ranging from complex theories like string theory to everyday interactions. The script emphasizes how humans have evolved to recognize patterns and seek them out, which ties into the broader theme of the video about the allure of the golden ratio and its prevalence in nature and human constructs.

💡Golden Ratio

The golden ratio, often symbolized by the Greek letter Phi (Φ), is a mathematical constant approximately equal to 1.618. It is an irrational number, much like pi, and is characterized by its unique property where a line divided into two parts has the whole line to the larger part as the larger part to the smaller part. The video discusses the golden ratio's significance in both mathematics and aesthetics, suggesting it has a 'divine proportion' and exploring its presence in nature, such as the arrangement of seeds in sunflowers, and its purported influence on human perception of beauty.

💡Fibonacci Sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, typically starting with 0 and 1. It is closely related to the golden ratio, as the ratio of consecutive Fibonacci numbers approximates the golden ratio as the sequence progresses. The script uses the Fibonacci sequence to illustrate the golden ratio's prevalence in nature, particularly in the spiral patterns of seeds in sunflowers and the arrangement of petals in flowers.

💡Aesthetics

Aesthetics pertains to the study of beauty and the principles that underlie it. The video script delves into the aesthetic appeal of the golden ratio, suggesting that it plays a role in what humans perceive as beautiful, such as in facial proportions and artistic compositions. It challenges the notion that the golden ratio is inherently aesthetically pleasing by presenting evidence from experiments that people may prefer rectangles with proportions slightly different from the golden ratio.

💡Irrational Numbers

Irrational numbers are real numbers that cannot be expressed as a simple fraction – they have non-terminating, non-repeating decimal expansions. The golden ratio is an example of an irrational number, as mentioned in the script. This concept is important in the video as it underscores the unending and unique nature of the golden ratio, which cannot be precisely represented or fully written out.

💡Golden Angle

The golden angle is the angle associated with the golden ratio when applied to the arrangement of objects in a spiral pattern, such as seeds in a sunflower. The script explains that the golden angle is approximately 137.5 degrees, which is the angle at which new seeds are placed in a sunflower to maximize efficiency and space utilization. This concept is integral to the video's exploration of the golden ratio's role in natural patterns.

💡Da Vinci's Vitruvian Man

The Vitruvian Man is a drawing by Leonardo da Vinci that is often cited as an example of the golden ratio's application in human proportions. In the video, it is mentioned to illustrate the historical fascination with the idea that the golden ratio contributes to the perceived beauty and harmony of the human body. The script uses this example to discuss the cultural and aesthetic significance attributed to the golden ratio.

💡Cardiovascular System

The cardiovascular system, which includes the heart and blood vessels, is highlighted in the video as an area of biological interest in relation to the golden ratio. The script mentions research findings that suggest a connection between the dimensions of the heart's left ventricle and the golden ratio, indicating a potential universal biological significance of the ratio that extends beyond cultural or aesthetic preferences.

💡UI/UX Design

UI/UX design refers to the user interface and user experience design, respectively, which are important aspects of modern graphic design. The video script notes the influence of the golden ratio in design practices, with examples such as website layouts and font sizes that incorporate the golden ratio. This illustrates the ongoing fascination with and application of the golden ratio in contemporary design.

💡AtlasVPN

AtlasVPN is a virtual private network (VPN) service mentioned in the video's sponsorship section. While not directly related to the main theme of the golden ratio, it serves as an example of modern technology that can provide users with access to content that might be restricted based on their geographical location. The script uses AtlasVPN to demonstrate how VPNs can bypass regional limitations on platforms like Netflix, Hulu, and Disney+.

Highlights

Humanity's innate pattern-seeking behavior provides comfort and meaning.

The golden ratio, symbolized by the Greek letter Phi, is a pattern of fascination in mathematics and aesthetics.

The golden ratio is defined by a line segment divided into two parts maintaining a consistent ratio.

The golden ratio value of approximately 1.618 is an irrational, non-terminating number, similar to pi.

The golden ratio is also known as 'the divine proportion', implying a divine or extraordinary property.

The Fibonacci sequence and the golden ratio appear in natural phenomena like floral seed arrangements.

Sunflowers exhibit the golden ratio in their seed spirals, optimizing sunlight and rain exposure for genetic survival.

The number of spiral arms in sunflowers and other plants often corresponds to Fibonacci numbers.

Aesthetically pleasing human faces and bodies are often associated with proportions close to the golden ratio.

Claims of the golden ratio's influence in architecture, such as the Egyptian pyramids, lack substantial evidence.

The golden ratio's aesthetic significance is hard to verify and often relies on perception and familiarity.

Experiments show that people may prefer rectangles close to, but not exactly at, the golden ratio.

Modern design, especially UI/UX, has adopted the golden ratio, although its desirability is debated.

Biological research suggests the golden ratio may play a role in the cardiovascular system's efficiency.

Heart function and cardiovascular health metrics have been found to be closely related to the golden ratio.

The golden ratio's perceived divinity may stem from a human desire for patterns and a sense of specialness.

The golden ratio existed before human cognition and its mathematical properties remain constant regardless of our understanding.

The search for beauty and perfection in the universe is ongoing, reflecting the irrational, unending nature of Phi.

The video was sponsored by AtlasVPN, which provides a virtual private network to mask online identity and bypass regional restrictions.

Transcripts

play00:00

Humanity has always been in search of patterns.  They make us feel comfortable. They give us  

play00:06

meaning. Whether they be in the deepest, most  conceptually difficult topics like string theory  

play00:11

and quantum mechanics, or even in simple  things like the behaviour of the person we  

play00:15

are talking to, we love to seek patterns, and  do so sometimes against our better judgement.  

play00:21

Nature and mathematics are no exceptions to  that list when it comes to pattern-seeking.  

play00:25

In fact, it is at the forefront of it. We have  

play00:28

evolved to notice patterns and be  alerted when something isn’t right.

play00:32

One of these so-called patterns that has  fascinated mathematicians and individuals  

play00:36

alike for centuries is the golden ratio.  Also known by the Greek letter Phi,  

play00:41

it can be defined by taking a line and  breaking it into two separate pieces.  

play00:45

If the ratio between these two new portions is  the same as the ratio between the original line  

play00:50

and the now larger piece, the portions  are said to satisfy the golden ratio.

play00:55

The value that satisfies this equation is  roughly 1.618… It’s an irrational number,  

play01:01

meaning we don’t know how to represent it using  the ratio of 2 whole numbers. In fact, we can’t  

play01:06

even write the number fully, it’s unending.  It’s effectively the same as pi in that regard,  

play01:12

and so we instead use the dots to represent  the non-terminating nature of this number.

play01:16

But what makes this ratio so golden? Well, I  should point out, the ‘golden’ part of the name  

play01:20

is rather modern. The more original name that was  given to this ratio was ‘the divine proportion.’  

play01:26

And right away, you can see that the  term implies some sort of divinity - an  

play01:30

extraordinary property that people must have  noticed when they were dealing with this number.  

play01:35

To further explain this fascination,  

play01:37

we should begin by dividing the fascination  into two parts - mathematics and aesthetics.

play01:43

The golden ratio and the fibonacci sequence  appear in nature every day, and arguably the  

play01:48

strongest evidence of “goldenness” in the golden  ratio is in the floral arrangement of seeds.

play01:54

Take this for example: if you were a sunflower,  how much of a turn would you make before you make  

play01:59

a new seed? If you don’t turn at all, well you  just continue making a straight line of seeds,  

play02:08

kinda boring. If you make half a turn, or a  180 degree turn each time, well now you have  

play02:14

a line of seeds, but in opposite directions. 120  degrees gives you 3 lines, 144 degrees gives you  

play02:21

5 lines. There should exist some angle, some  number of turns that, if properly executed,  

play02:28

produces a pattern of seeds that is closely packed  together with no gaps between them. Something like  

play02:33

this, this seems more natural to nature, right?  The number of “turns” needed to produce a spiral  

play02:40

design like this is… well, the golden ratio.  One seed placed every 1.618 turns, or every  

play02:48

137.5 degrees. This is known as the golden  angle, and it is seen all throughout nature.

play02:56

The idea is to arrange seeds in a way that can  maximize the sunlight and rain that they receive,  

play03:00

so that the genetic material can successfully be  passed on to the next generation. If you don’t do  

play03:05

this efficiently, evolution won’t be very kind to  you. If you pack in the seeds too tightly, all the  

play03:11

seeds won’t get the nutrients they need. If you  pack them too sparsely, you’re just wasting space.  

play03:18

This happens with not only sunflower seeds, but in  plant leaves, tree branches, and more. In fact, it  

play03:24

goes even deeper. If you were to count the number  of spiral arms in both directions, left and right,  

play03:30

you’ll find that they aren’t equal; however,  they will both always be fibonacci numbers.  

play03:36

The higher and higher the numbers go, the closer  and closer the ratio between them approaches Phi.

play03:43

The beautiful spirals that result are purely a  creation of nature. These spirals are consistent  

play03:48

across different flower types, and even  the numbers of petals seem to be related  

play03:51

to the golden ratio. The sunflower example is  particularly interesting because it actually ties  

play03:57

the aesthetic element of the golden ratio to the  mathematics behind it; there is a reason why the  

play04:02

golden ratio is used in flowers, and any other  value doesn’t seem to work very well. But what  

play04:07

does that really tell us about the underlying,  and possibly grand design of the universe?

play04:12

We are all somewhat familiar with the  aesthetic elements of the divine proportion.  

play04:16

The idea is that visually pleasing faces tend  to have proportions that are somewhat close  

play04:20

to the golden ratio. The closer you are to  it, the more beautiful your face should be.  

play04:26

This inclination of harmony extends to the rest  of the body as well, with many claiming that Da  

play04:30

Vinci’s ‘Vitruvian Man’ demonstrates that the  human body owes its beauty to the golden ratio.  

play04:36

The phenomenon also has its place in architecture,  with claims thrown around that structures as old  

play04:40

as the pyramids of Egypt are in some way shape  or form inspired by the golden ratio... except  

play04:46

for the fact that there’s hardly any evidence  that the Egyptians even knew this ratio existed.

play04:50

All of these beliefs contributed to the idea of  the golden ratio and made it what it is today. The  

play04:56

mathematical beauty is undeniable, it’s proven;  however, it’s generally hard to verify any of  

play05:02

these claims regarding it’s aesthetic purpose in  our lives. For one, it is not sufficient for a  

play05:08

structure to just have the golden ratio somewhere.  It must be meaningfully incorporated and be the  

play05:13

result of someone’s conscious or subconscious  choice. What does meaningful incorporation entail?  

play05:19

Why would you choose the ratio of, say, this  pillar with that one, and not with another? Then  

play05:25

there are questions of measurement. Oftentimes,  you see pictures thrown around the internet with a  

play05:30

famous celebrity’s face with random lines drawn on  them that claim to satisfy the divine proportion.

play05:35

Long story short, they’re reaching pretty hard.  Without proper definitions of the facial features  

play05:41

they are referring to, like what a cheek  bone is, where it starts and ends and so on,  

play05:46

there is basically no scientifically  verifiable structure to what they’re claiming.  

play05:50

Even if you do find that a certain  arrangement and placement of measurements  

play05:53

do wind up representing the golden ratio  very well, it’s never quite exactly that.

play05:58

Phi, the golden ratio value, is irrational.  It’s unending. You can come close, but you  

play05:58

can never truly achieve it  just by drawing some lines.

play05:59

Despite these claims, however, one could still  argue about the idea of facial beauty and the  

play06:03

importance of the golden ratio in it. All  that matters is our perception of something.  

play06:08

If the ratio of some facial feature  is close enough to the golden ratio,  

play06:12

so much so that we’re unable to distinguish it  from the actual ratio itself, and we find it  

play06:17

pleasing, wouldn’t you say that the aesthetic  element of the golden ratio is justified?

play06:22

To investigate this point, experiments have been  conducted relatively recently using a geometric  

play06:27

object that has the golden ratio written  all over it. It’s the golden rectangle.  

play06:32

It’s any rectangle that has sides a, b  that satisfies the relationship I just  

play06:36

described at the start of the video, except  this time it’s a shape and not just lines.

play06:42

The experiments include showing participants many  different rectangles of different proportions,  

play06:46

with one or more of them being golden rectangles.  

play06:50

They were then asked to choose which rectangle  they felt represented the ratio best.  

play06:54

If the hypothesis that things with the golden  ratio embedded in them are more attractive to  

play06:58

us is indeed true, you would expect to see a  significant number of participants choosing  

play07:02

the golden rectangles. But, turns out, the  evidence is not very great on this one.

play07:08

Instead of choosing the golden rectangle,  

play07:10

participants seem to prefer rectangles  around that number, like 1.5 or 1.75.  

play07:16

It’s close, but it already somewhat disproves the  idea of the golden ratio. If a rough value around  

play07:22

the golden ratio is so good, then the golden ratio  itself isn’t so golden after all. But even if,  

play07:28

say, the preferences do seem to be around that  golden ratio, there are theories as to why that  

play07:33

might be. People who are more aware of the golden  ratio might be predisposed to having a preference  

play07:39

toward it because of the place it holds in history  and in mathematics. Besides, if you spend a lot of  

play07:44

time staring at a screen with aspect ratios  relatively close to that of golden ratio,  

play07:48

something like a 16:9 monitor, you will  unintentionally find them more attractive.  

play07:54

But now it would be a fair question to  ask, well what started this golden trend?

play07:59

There does seem to be a sincere focus on the  golden ratio in the modern design language,  

play08:03

especially with UI/UX design. While no designer in  their right mind would swear by one single rule,  

play08:09

the golden ratio has seemingly become a  mainstay in graphic design. For example,  

play08:15

a lot of websites tend to have headings that  are 1.6 times the font size of the general text.  

play08:20

Website layouts also incorporate golden  rectangles. Again, once something like the golden  

play08:25

ratio has been generally accepted as something  divine, it’s very hard to distinguish whether it’s  

play08:29

desirability stems simply from its familiarity  in our lives or from some deeper meaning.

play08:35

But it just so turns out that there is some  deeper meaning, deeper inside us. There’s a  

play08:40

body of research that focuses instead on deeper  biology and how the golden ratio plays a crucial  

play08:45

role in it. The cardiovascular system is of  keen interest in this regard. This is because  

play08:50

it is one of those biological systems that has  very small differences across ethnic groups.  

play08:55

So, if the golden ratio were to be found in such  a system, we could claim that it is indeed a more  

play09:00

universal phenomenon, rather than existing  simply due to some ethnic variation or bias.

play09:06

The cardiovascular system is  deep in us, it runs our lives.  

play09:10

There is no element of fabrication down  there. Evidence found here would much  

play09:14

better support the idea that there is some  natural significance to the golden ratio,  

play09:19

and in fact, there is. Your heart has many moving  parts that help keep your body functioning.  

play09:25

One of them being the left ventricle, it’s what  helps pump oxygen throughout your body. Now,  

play09:30

the average ratio of left ventricle horizontal and  vertical lengths of over 1,400 Swedish and Chinese  

play09:36

subjects was found to be 1.618 – awfully close  to the golden ratio. Patients with left ventricle  

play09:42

ratios that were further away from this value  were deemed to have poorer functioning hearts,  

play09:46

and they were. And as we age, our hearts tend to  lose some of their power. Over time, your blood  

play09:50

begins to pump slower and slower throughout your  body. Even the age-related cardiovascular decline  

play09:56

was related to the golden ratio, with an early  diastolic velocity decline of 1.6 cm/s per decade.

play10:03

On the other side of the spectrum, the early  diastolic flow velocity of muscles in the  

play10:07

heart of a growing fetus increases by 1.6 mm/s  per week. It’s remarkable how these and other  

play10:13

metrics of cardiovascular health hover close to  this special value. But even in these examples,  

play10:19

there’s still a bias in choice of units. For  example, why is this particular metric in mm/s  

play10:25

and not inches/s? Such choices could alter these  quantities and take away the divinity in them.

play10:32

But why? If there isn’t so much evidence  behind the divinity of the golden ratio,  

play10:37

why do people have this obsession over it? Well,  it’s the same reason why we once believed the  

play10:42

earth was the center of the universe. We  want to believe these things. Of course,  

play10:47

people have moved on from those particular  beliefs to more modern and sophisticated ones,  

play10:51

like how the earth is flat and all. But  the core philosophy remains the same.  

play10:56

We love patterns, and we love them  even more if they make us seem special.  

play11:01

Why did the golden ratio only have to do with  our faces and not those of other animals?  

play11:05

What about the body proportions of a snake?  It’s only human to only care about ourselves.

play11:11

This also highlights the age-old question  about whether math is invented or discovered.  

play11:16

You see, the phenomenon of the golden ratio  existed long before we had any idea of it.  

play11:22

The flowers arranged themselves without us  having a cognition of numbers or mathematics.  

play11:26

Even when we tried forcing our hand on  certain elements of the golden ratio to  

play11:30

suit our narratives of existence, the  golden ratio itself did not change.  

play11:35

If the golden ratio were from a different  time and it were named differently,  

play11:39

we would still be talking about the  same thing, only with a different name.  

play11:43

It was what it was, and it will always be,  whether we have any cognition of it or not.  

play11:50

There are things, properties of math and  science out there that exist currently,  

play11:55

right in front of us perhaps, and  we have zero idea what they are  

play11:59

or what they entail. We may define things along  the way, just as we have given the ratio a name,  

play12:05

but the underlying mathematical  properties remain unchanged.

play12:09

In truth, the divine proportion owes its divinity  not to some all-pervading transcendental property,  

play12:15

but rather to the idea of beauty and  perfection that we’ve imposed on it.  

play12:19

This beauty we seek is quite possibly  not concentrated in one golden number,  

play12:23

and even if it is, the golden  ratio is probably not the one.  

play12:28

In trying to find perfection, we could nonetheless  keep defining Phi. But remember, it’s irrational.  

play12:35

Phi does not end, and neither does our  search for beauty in the universe we live in.

play12:48

This video was sponsored by AtlasVPN. AtlasVPN  gives you access to a virtual private network;  

play12:55

basically, it masks your identity  while you’re connected to the internet.  

play12:59

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but little do you know that you actually can’t  access most things on it. The same goes for Hulu,  

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Disney+, and many other subscription based  platforms. You’re paying for subscriptions  

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to these services, and they’ve locked away  things from you simply because of your location.

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But with AtlasVPN, you can get rid of these walls  that have been put up, and can give you access to  

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everything you’ve been missing out on. If you’re  on Windows PC, a Mac, an Android phone, or  

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an iPhone, it doesn’t matter, AtlasVPN is  available for you to use on almost any device.

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AtlasVPN actually has a huge discount on their 3  year deal, it’s only $1.39 a month. It’s really  

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cheap, and you can try out AtlasVPN by clicking  the link at the top of the description. If you  

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find that you don’t like it, or you don’t use it  much, they have a 30 day money back guarantee.

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In 2021, I’d say that mostly everyone should  be using a VPN, so I’d definitely check  

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out AtlasVPN. You’ll be protecting yourself  and supporting my channel at the same time.

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