Hello there [? oric ?] expressions of humanity,
Trace here, and I've been thinking
about the golden ratio.
I mean how can I not?
It's supposedly everywhere and in everything,
and somehow this mathematical concept
has been the bedrock of all nature
and human architecture since ancient times, right?
Not so much.
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Thank you so much for tuning in.
Let's talk about the golden ratio.
This video might get ratioed, but I've never actually
been super into the golden ratio, also known
as the golden section, golden mean, golden number,
divine proportion, divine section, and golden proportion.
I know it has like amazing branding, but like, oh.
The golden ratio is 1.61803398875,
and so on and so forth.
It's an irrational number, so it can't be represented
by a fraction, but it can be represented by the symbol
phi or phi, depending on if you're
more into the modern or ancient Greek.
It was created or discovered, depending
on how metaphysical you want to be,
by numerous ancient societies.
Famously, the ancient Greeks and Egyptians
both allegedly used this ratio in their architecting
of the Parthenon and the Great Pyramids at Giza, respectively.
It's got some really big names under its brand
from da Vinci to Euclid to quantum physics,
but it's more than just a meme or a button in my camera app
that I almost never use.
The ratio of 1.618 yada yada comes
from the mathematical proportion of certain rectangles.
Written out and simplified, it's A over B equals A plus B
over A. When that is equal to both
of those divided by the long side,
then you get the golden ratio.
And illustrated, it's this really easy-to-understand
rectangle.
Goldie is famous because it's easy to illustrate
in ancient construction, and it was thought by some
to be the most pleasing rectangle you can see.
But on top of that, the rectangle
is the limit for a Fibonacci sequence-- a simple set
of numbers where each number is the sum of the two
preceding it, so 1 plus 2 equals 3, 2 plus 3 equals 5,
3 plus 5 equals 8, five plus 8 equals 13,
and so on and so forth forever.
Together, the golden spiral within the Fibonacci sequence
is almost everywhere online and it's
taken on this like religious-esque love
and deference, but outside of ancient construction
and the occasional polymathic master
painting of a lady, the golden ratio
is really an interesting ratio of two things,
but nature doesn't have some underlying rule
or principle that makes it follow the sequence or the GR.
Yeah, sure, absolutely, when you look at this Romanesco broccoli
and you line it up just right, wow.
Golden ratio.
But that's just the digital equivalent of squint
and looks like [INAUDIBLE].
The Nautilus shell is the same squint, and wow.
In reality, neither are actually fitting the ratio perfectly.
The picture is either stretched or squeezed
to make sure it matches or there are
three-dimensional objects in it, and we're
looking at these from one perspective that
shows what we want to see, kind of like astrology, which
is based on constellations that only exist from our perspective
and that perspective is crafted to make a relationship.
If you change that perspective, neither the broccoli
nor Mercury's motion relative to our planet in any direction
really matter.
The GR got famous because mathematically, it's
really cool but, again, it's not a rule that nature follows.
It's a correlation.
The Goldie [? ray ?] is firmly planted
in Euclidian math, which describes
things like circles, rhombuses, spheres, and parallelograms.
Also it's fun to say--
Euclidian.
It's just fun.
This math describes simple shapes
like trying to find the area of the floor
plan of your house, which Euclidian math makes easy.
However, if you really tried to describe
all the nooks and crannies of a cauliflower, or a mountain,
or the little dips and divots on the beach,
Euclidian math ain't going to cut it.
Instead, you have to use fractal math.
Fractal math is great for calculating things
like geography, the stock market, weather patterns,
physical chemistry, galaxy distributions,
and fluid mechanics-- stuff that's complex and sometimes
appears chaotic.
It's a way to try and simplify seemingly random stuff.
Fractals are self-symmetrical calculations
with fractional parts.
They're not whole numbers but they're symmetrical.
This meme is a fractal.
This one obviously a little fractal.
A great example is snowflakes.
They can be modeled using fractal math.
Sidebar real quick.
Hi.
I'm not saying fractals describe all snowflakes.
I'm saying that if you use fractal math
and you plug-in, say, 1.26, you'll
get a snowflake-like shape.
That's it.
Describing every snowflake with a fractal
would be very tough because of complex asymmetrical influences
like, you know, wind temperatures, altitudes,
humidities, particulates, all sorts of other things,
regular temperatures--
a million things.
Fractals are a tool, not an answer.
End sidebar.
I know you probably knew that.
I had the sidebar, though, because outside
of strict statistical scientific application, the word fractal,
golden ratio, Fibonacci sequence are often
used by a sci-fi, fantasy, metaphysical crowd as some kind
of natural code secret.
While I was researching this video,
it only took me minutes to be confronted
with like my first overpromising pseudointellectual nonsense.
But, yeah, fractals are cool.
I'm here to tell you, they're not magic.
They're just math.
Or science or both.
The golden ratio, though it does describe
a very pleasing rectangle, does not cause things.
It describes them.
It describes a ratio of proportion
and it doesn't even do so that often, to be honest.
Sorry, what?
Yeah.
That's just not that common.
You can find the Fibonacci sequence and the golden ratio
if you go looking, but nature is biology and biology
is messy, so Fibbi G--
that's the golden ratio plus Fibonacci--
Fibbi G?
Uh-uh.
Pinecones, pineapples, and sunflowers
are famously Fibonacci golden ratio plants.
Personally, I think this is icky to look
at but, you know, everyone has their own preferences.
Counting clockwise and counterclockwise spirals
on the faces of some sunflowers will result in 34 and 55, 55
and 89 or 89 and 144 spirals.
Though this matches Fibbi G, it doesn't
have a known biological mechanism as to why it should.
In a crowdsourced open science study,
researchers found 20% of sunflowers
don't even fit into this pattern, though.
So while most sunflowers do follow this Fibbi G,
not all of them do.
And in fact, a 2018 study looking
at the Fibbi G and self-replicating systems
argues that the golden ratio should not
be considered a special universal constant at all.
But the constant, such as phi, appear only
in a very limited range of situations.
To study it, they assumed a self-replicating molecular
system and then did the math.
It turns out goldie and Fibbi both appeared,
but so did a bunch of other constants.
In reality, they deemed no reason
to think that phi would be best or warrant being golden at all.
There's no solid explanation as to why
Fibbi G shows up in nature.
I think we can all agree it's not because there's
some under arcane rule that all of nature
uses thanks to a benevolent and bearded creator woman.
Instead, biologists think that nature, like all biology,
often wants to be as efficient as possible,
growing and maintaining leaves or limbs and seeds.
All that takes work, so if we can grow as many as possible
in a small space, then we should do that.
If we can grow lots of leaves that all
have a high chance of seeing the sun, then do that.
But to get to this ratio in nature,
lots of flowers and trees died, and the ones
that randomly hit on this ratio over millions of years
tended to not die.
There's no reason that math should work for nature.
Nature has no responsibility to make mathematical sense,
but because of the rules of the universe, it just does.
Sometimes.
Really, the main question I have is,
why do so many people want to believe the golden ratio
is everywhere in nature, even though that's a myth?
Well, in November of 2015, one of my favorite studies
ever came out on the reception and detection
of pseudo-profound bull poopy, let's call it.
We the people love to believe things,
especially when those things make the complex simple.
Occam's razor style.
But sometimes we raised her a little much.
In the absence of understanding of the reality
or the grasping of the complexity of something,
people will focus on the bull poopy as if it's real.
As the paper's authors write quote,
"using vagueness or ambiguity to mask a lack of meaningfulness
is surely common in political rhetoric, marketing,
and even academia."
We see this all over the world all the time.
We humans want to believe in stuff.
We want Occam's razor to be real.
So when people hear about the golden ratio is perfection
in the eyes of some mathematicians, painters,
or architects, we grab it and run.
I found meaning, right?
And while the Fibbi G is a nice fit for the descriptions of how
some natural organisms do tend to organize themselves,
it's not a cause.
It's not universal, and it's not really perfect.
It's just really nice when things work out.
I love learning new things and challenging my assumptions
about stuff, like the golden ratio, especially
when that assumption is thanks to a good story,
like the documentaries on CuriosityStream.
CuriosityStream has over 2,400 documentaries short and long.
They are my favorite place to look
for interesting, thoughtful documentaries about science
and history, the environment, and technology, society
and data, and a bunch of other stuff.
It was started by the founder of Discovery Channel,
so he knows what he's doing.
If you loved that when you were a kid,
you're going to like this.
There's a really cool series called "The Joy Of"
and one episode is all about the data
that we're creating in the world,
and there is a lot of it.
I thought this episode was really good,
you should check it out.
All you got to do to get unlimited access
to CuriosityStream is go to curiositystream.com/trace.
Use the promo code-- trace.
It's easy and it only costs $2.99 a month,
plus it directly supports the making of this show,
so let me know when you do it so I can thank you.
The golden ratio is sort of like exact change
when the Netflix show ends and the credits are rolling just
as the door opens and your partner gets home from work,
or the food is ready just as you realize how hungry you are.
It's super satisfying.
Not causal.
I'll leave you with this quote about bull poopy direct
from the amazing paper that I mentioned earlier,
quote, "hidden meaning transforms
unparalleled abstract beauty."
It doesn't mean anything.
You really want it to, don't you?
And that's exactly the point.
Thanks again for watching "Uno Dos of Trace" this week.
I really hope you learned something.
Let me know if you have any ideas
or thoughts for future videos in the comments.
Make sure you subscribe, and I will see you in the future.
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