The Golden Ratio: Nature's Favorite Number
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
- 𧩠Humans are naturally inclined to seek patterns, which provide comfort and meaning, even in complex subjects like string theory and quantum mechanics.
- đ Nature and mathematics are at the forefront of pattern-seeking behavior, with humans having evolved to notice patterns and detect anomalies.
- đ The golden ratio, symbolized by the Greek letter Phi (â ), is a pattern that has fascinated mathematicians and people for centuries due to its unique mathematical properties.
- đ 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.
- â The golden ratio is an irrational number, similar to pi, with a non-terminating and unending decimal expansion.
- đ 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.
- đš 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.
- đ Claims that historical structures like the Egyptian pyramids were designed based on the golden ratio lack substantial evidence.
- đ€ 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.
- 𧏠Recent research suggests that the golden ratio may have a biological significance, with studies finding it in the cardiovascular system across different ethnic groups.
- đŹ 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 (Ί), 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
đ 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.
đš 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.
đż 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
đĄPatterns
đĄGolden Ratio
đĄFibonacci Sequence
đĄAesthetics
đĄIrrational Numbers
đĄGolden Angle
đĄDa Vinci's Vitruvian Man
đĄCardiovascular System
đĄUI/UX Design
đĄAtlasVPN
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
Humanity has always been in search of patterns. They make us feel comfortable. They give us Â
meaning. Whether they be in the deepest, most conceptually difficult topics like string theory Â
and quantum mechanics, or even in simple things like the behaviour of the person we Â
are talking to, we love to seek patterns, and do so sometimes against our better judgement. Â
Nature and mathematics are no exceptions to that list when it comes to pattern-seeking. Â
In fact, it is at the forefront of it. We have Â
evolved to notice patterns and be alerted when something isnât right.
One of these so-called patterns that has fascinated mathematicians and individuals Â
alike for centuries is the golden ratio. Also known by the Greek letter Phi, Â
it can be defined by taking a line and breaking it into two separate pieces. Â
If the ratio between these two new portions is the same as the ratio between the original line Â
and the now larger piece, the portions are said to satisfy the golden ratio.
The value that satisfies this equation is roughly 1.618⊠Itâs an irrational number, Â
meaning we donât know how to represent it using the ratio of 2 whole numbers. In fact, we canât Â
even write the number fully, itâs unending. Itâs effectively the same as pi in that regard, Â
and so we instead use the dots to represent the non-terminating nature of this number.
But what makes this ratio so golden? Well, I should point out, the âgoldenâ part of the name Â
is rather modern. The more original name that was given to this ratio was âthe divine proportion.â Â
And right away, you can see that the term implies some sort of divinity - an Â
extraordinary property that people must have noticed when they were dealing with this number. Â
To further explain this fascination, Â
we should begin by dividing the fascination into two parts - mathematics and aesthetics.
The golden ratio and the fibonacci sequence appear in nature every day, and arguably the Â
strongest evidence of âgoldennessâ in the golden ratio is in the floral arrangement of seeds.
Take this for example: if you were a sunflower, how much of a turn would you make before you make Â
a new seed? If you donât turn at all, well you just continue making a straight line of seeds, Â
kinda boring. If you make half a turn, or a 180 degree turn each time, well now you have Â
a line of seeds, but in opposite directions. 120 degrees gives you 3 lines, 144 degrees gives you Â
5 lines. There should exist some angle, some number of turns that, if properly executed, Â
produces a pattern of seeds that is closely packed together with no gaps between them. Something like Â
this, this seems more natural to nature, right? The number of âturnsâ needed to produce a spiral Â
design like this is⊠well, the golden ratio. One seed placed every 1.618 turns, or every Â
137.5 degrees. This is known as the golden angle, and it is seen all throughout nature.
The idea is to arrange seeds in a way that can maximize the sunlight and rain that they receive, Â
so that the genetic material can successfully be passed on to the next generation. If you donât do Â
this efficiently, evolution wonât be very kind to you. If you pack in the seeds too tightly, all the Â
seeds wonât get the nutrients they need. If you pack them too sparsely, youâre just wasting space. Â
This happens with not only sunflower seeds, but in plant leaves, tree branches, and more. In fact, it Â
goes even deeper. If you were to count the number of spiral arms in both directions, left and right, Â
youâll find that they arenât equal; however, they will both always be fibonacci numbers. Â
The higher and higher the numbers go, the closer and closer the ratio between them approaches Phi.
The beautiful spirals that result are purely a creation of nature. These spirals are consistent Â
across different flower types, and even the numbers of petals seem to be related Â
to the golden ratio. The sunflower example is particularly interesting because it actually ties Â
the aesthetic element of the golden ratio to the mathematics behind it; there is a reason why the Â
golden ratio is used in flowers, and any other value doesnât seem to work very well. But what Â
does that really tell us about the underlying, and possibly grand design of the universe?
We are all somewhat familiar with the aesthetic elements of the divine proportion. Â
The idea is that visually pleasing faces tend to have proportions that are somewhat close Â
to the golden ratio. The closer you are to it, the more beautiful your face should be. Â
This inclination of harmony extends to the rest of the body as well, with many claiming that Da Â
Vinciâs âVitruvian Manâ demonstrates that the human body owes its beauty to the golden ratio. Â
The phenomenon also has its place in architecture, with claims thrown around that structures as old Â
as the pyramids of Egypt are in some way shape or form inspired by the golden ratio... except Â
for the fact that thereâs hardly any evidence that the Egyptians even knew this ratio existed.
All of these beliefs contributed to the idea of the golden ratio and made it what it is today. The Â
mathematical beauty is undeniable, itâs proven; however, itâs generally hard to verify any of Â
these claims regarding itâs aesthetic purpose in our lives. For one, it is not sufficient for a Â
structure to just have the golden ratio somewhere. It must be meaningfully incorporated and be the Â
result of someoneâs conscious or subconscious choice. What does meaningful incorporation entail? Â
Why would you choose the ratio of, say, this pillar with that one, and not with another? Then Â
there are questions of measurement. Oftentimes, you see pictures thrown around the internet with a Â
famous celebrityâs face with random lines drawn on them that claim to satisfy the divine proportion.
Long story short, theyâre reaching pretty hard. Without proper definitions of the facial features Â
they are referring to, like what a cheek bone is, where it starts and ends and so on, Â
there is basically no scientifically verifiable structure to what theyâre claiming. Â
Even if you do find that a certain arrangement and placement of measurements Â
do wind up representing the golden ratio very well, itâs never quite exactly that.
Phi, the golden ratio value, is irrational. Itâs unending. You can come close, but you Â
can never truly achieve it just by drawing some lines.
Despite these claims, however, one could still argue about the idea of facial beauty and the Â
importance of the golden ratio in it. All that matters is our perception of something. Â
If the ratio of some facial feature is close enough to the golden ratio, Â
so much so that weâre unable to distinguish it from the actual ratio itself, and we find it Â
pleasing, wouldnât you say that the aesthetic element of the golden ratio is justified?
To investigate this point, experiments have been conducted relatively recently using a geometric Â
object that has the golden ratio written all over it. Itâs the golden rectangle. Â
Itâs any rectangle that has sides a, b that satisfies the relationship I just Â
described at the start of the video, except this time itâs a shape and not just lines.
The experiments include showing participants many different rectangles of different proportions, Â
with one or more of them being golden rectangles. Â
They were then asked to choose which rectangle they felt represented the ratio best. Â
If the hypothesis that things with the golden ratio embedded in them are more attractive to Â
us is indeed true, you would expect to see a significant number of participants choosing Â
the golden rectangles. But, turns out, the evidence is not very great on this one.
Instead of choosing the golden rectangle, Â
participants seem to prefer rectangles around that number, like 1.5 or 1.75. Â
Itâs close, but it already somewhat disproves the idea of the golden ratio. If a rough value around Â
the golden ratio is so good, then the golden ratio itself isnât so golden after all. But even if, Â
say, the preferences do seem to be around that golden ratio, there are theories as to why that Â
might be. People who are more aware of the golden ratio might be predisposed to having a preference Â
toward it because of the place it holds in history and in mathematics. Besides, if you spend a lot of Â
time staring at a screen with aspect ratios relatively close to that of golden ratio, Â
something like a 16:9 monitor, you will unintentionally find them more attractive. Â
But now it would be a fair question to ask, well what started this golden trend?
There does seem to be a sincere focus on the golden ratio in the modern design language, Â
especially with UI/UX design. While no designer in their right mind would swear by one single rule, Â
the golden ratio has seemingly become a mainstay in graphic design. For example, Â
a lot of websites tend to have headings that are 1.6 times the font size of the general text. Â
Website layouts also incorporate golden rectangles. Again, once something like the golden Â
ratio has been generally accepted as something divine, itâs very hard to distinguish whether itâs Â
desirability stems simply from its familiarity in our lives or from some deeper meaning.
But it just so turns out that there is some deeper meaning, deeper inside us. Thereâs a Â
body of research that focuses instead on deeper biology and how the golden ratio plays a crucial Â
role in it. The cardiovascular system is of keen interest in this regard. This is because Â
it is one of those biological systems that has very small differences across ethnic groups. Â
So, if the golden ratio were to be found in such a system, we could claim that it is indeed a more Â
universal phenomenon, rather than existing simply due to some ethnic variation or bias.
The cardiovascular system is deep in us, it runs our lives. Â
There is no element of fabrication down there. Evidence found here would much Â
better support the idea that there is some natural significance to the golden ratio, Â
and in fact, there is. Your heart has many moving parts that help keep your body functioning. Â
One of them being the left ventricle, itâs what helps pump oxygen throughout your body. Now, Â
the average ratio of left ventricle horizontal and vertical lengths of over 1,400 Swedish and Chinese Â
subjects was found to be 1.618 â awfully close to the golden ratio. Patients with left ventricle Â
ratios that were further away from this value were deemed to have poorer functioning hearts, Â
and they were. And as we age, our hearts tend to lose some of their power. Over time, your blood Â
begins to pump slower and slower throughout your body. Even the age-related cardiovascular decline Â
was related to the golden ratio, with an early diastolic velocity decline of 1.6 cm/s per decade.
On the other side of the spectrum, the early diastolic flow velocity of muscles in the Â
heart of a growing fetus increases by 1.6 mm/s per week. Itâs remarkable how these and other Â
metrics of cardiovascular health hover close to this special value. But even in these examples, Â
thereâs still a bias in choice of units. For example, why is this particular metric in mm/s Â
and not inches/s? Such choices could alter these quantities and take away the divinity in them.
But why? If there isnât so much evidence behind the divinity of the golden ratio, Â
why do people have this obsession over it? Well, itâs the same reason why we once believed the Â
earth was the center of the universe. We want to believe these things. Of course, Â
people have moved on from those particular beliefs to more modern and sophisticated ones, Â
like how the earth is flat and all. But the core philosophy remains the same. Â
We love patterns, and we love them even more if they make us seem special. Â
Why did the golden ratio only have to do with our faces and not those of other animals? Â
What about the body proportions of a snake? Itâs only human to only care about ourselves.
This also highlights the age-old question about whether math is invented or discovered. Â
You see, the phenomenon of the golden ratio existed long before we had any idea of it. Â
The flowers arranged themselves without us having a cognition of numbers or mathematics. Â
Even when we tried forcing our hand on certain elements of the golden ratio to Â
suit our narratives of existence, the golden ratio itself did not change. Â
If the golden ratio were from a different time and it were named differently, Â
we would still be talking about the same thing, only with a different name. Â
It was what it was, and it will always be, whether we have any cognition of it or not. Â
There are things, properties of math and science out there that exist currently, Â
right in front of us perhaps, and we have zero idea what they are Â
or what they entail. We may define things along the way, just as we have given the ratio a name, Â
but the underlying mathematical properties remain unchanged.
In truth, the divine proportion owes its divinity not to some all-pervading transcendental property, Â
but rather to the idea of beauty and perfection that weâve imposed on it. Â
This beauty we seek is quite possibly not concentrated in one golden number, Â
and even if it is, the golden ratio is probably not the one. Â
In trying to find perfection, we could nonetheless keep defining Phi. But remember, itâs irrational. Â
Phi does not end, and neither does our search for beauty in the universe we live in.
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