Growth at a Golden Pace
Growth at a “golden pace” of 1.6%
The Golden Spiral
I'm so excited to write about the Golden Spiral. It’s been my personal symbol for over 30 years. If I were going to get a tattoo, it would be a Golden Spiral. (And I would not be alone. Google search for Golden Spiral tattoos came up with 9,200,000 results.) It is the central motif in my logo for Art Well 4 Life.
So what’s so special about the Golden Spiral and why am I bringing it up now?
Well, I love the constant, dynamic curve that grows from its core. But it’s more than just its terrific shape. I am fascinated by its magical combination of beauty, math, nature, and spirituality. And last but not least, the Golden Spiral is a powerful, visual metaphor for slow growth. (I love metaphor if you hadn’t noticed.) Which is why I’m bringing it up now, at the beginning of the new year with all of our bright shiny intentions.
Spirals 101
Caveat: I am not a mathy person. I am an artsy person drawn to this particular aspect of math because of its relationship to art and life. If you’d like a real math explanation of spirals, I’ve got just the website for you! Click here.
The Golden Spiral belongs to the logarithmic spiral clan. These spirals have a progressive growth rate, which means they increase by the same percentage. Archimedean spirals, on the other hand, grow by the same amount. But we digress. Here’s a diagram to demonstrate the difference.
The Golden Spiral grows at the specific rate of 1.618 for every quarter turn. Memorize that number: 1.618 or 1.6 for short. It’s going to be important!
Mind Blown
Here comes the fun part. The Golden Spiral is all over the natural world: sunflower center seeds, pinecones, cabbage, the inner ear, the crest of a wave, and the list goes on and on. If you add in the almost-Golden-Spirals, like the shell of the nautilus (a relative of the squid) the list explodes!
So why is nature so drawn to this particular spiral? Here are just a few reasons. The Golden Spiral gives plants the best chance of surviving and thriving. How? By providing each petal with the maximum access to sunlight. For our friend the nautilus, it allows the mollusk to grow without fundamentally changing its shape. Very efficient indeed.
A Golden Ratio
I imagine your next burning question must be: Why is the Golden Spiral’s 1.618 rate of growth so special? 1.618, known as Phi ɸ, is a bad ass irrational number that can do all sorts of math tricks like its more famous cousin Pi 𝝿, 3.1416.
It is also the basis of the Golden Ratio, which is the mathematical proportion: 1 to 1.618. This magical ratio is often visualized with the Golden Rectangle, with the proportions 1 to 1.618.
I’ve made a handy diagram to show how great the Golden Ratio-Rectangle-Spiral is. In a nutshell, the big rectangle can split into a square and a smaller rectangle.
This smaller rectangle has the same proportions, 1 to 1.618, just in an American Girl Doll size.
Now if you divide the American Girl Doll rectangle into a square and rectangle, the new even smaller Barbie size rectangle has the same proportions, 1 to 1.618. And so on… From this progression, you can see how the Golden Spiral develops.
Psst, if you’d like the mathematical expression of the Golden Ratio, it’s a : b as b : a + b.
Let’s Save It for Another Day
There are just so much fabulous, interesting topics related to the Golden Ratio/Rectangle/Spiral. Let’s save the topic of the Golden Ratio in art and aesthetics for another blog post, because it definitely deserves its own spotlight. Suffice it to say that artists, architects, the human race has found the proportions 1 to 1.618 to be particularly pleasing and the basis for temples, paintings, all the way to Google, which used the Golden Ratio to tweak its logo.
Another topic we can explore down the line is the Golden Ratio’s staring role in “sacred geometry,” which explores the underlying links among mathematical principles, patterns, science, nature, art, humankind, spirituality and the cosmos.
The Amazing 400 Million-Year-Old Living Fossil
This blog post is about the power of slow growth. So I’ll get back on track.
One of my absolute favorite metaphors for growth is the chambered nautilus which is a mollusk related to the octopus, squid and clam. And it will come as no surprise that the nautilus shell grows in a spiral pattern very much like the Golden Spiral.
The nautilus is often called a living fossil because it’s been around, almost unchanged, since before the dinosaurs. It’s born with 4 chambers and by its maturity at age 20 years (incredible!), it can have a spiral of about 30 chambers, which is roughly a chamber a year. It lives in the outermost one, which it can retreat into when danger arises. The first chambers are so small, they are hard to see, but the positive growth trajectory has already been established. And while it has outgrown all the other chambers, it does not discard them, but rather uses the old, curved shell for balance, buoyancy, and to propel itself.
If you’re curious to learn more about the nautilus, check out this 4-minute video from the American History Museum in New York City.
5 Life Hacks from the Chambered Nautilus
So here we have this very odd looking invertebrate with its head attached to its feet (tentacle like things) that swims backwards. And at the same time, it provides us with so many interesting lessons about growth and habit formation. Here are 5 “life hacks” I’ve gleaned from the remarkable chambered nautilus —
Tiny Changes, Remarkable Results
If you need a bit more grounding from a habits professional, check out Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones by James Clear. Clear provides compelling data and practical steps for slow habit formation. It’s about tiny steps (like 1.6% shifts), systems and identity vs. habits, and trajectory vs. accomplishment.
An Inevitable Logo
So I think you can understand why I selected the Golden Spiral as the central motif for the Art Well 4 Life logo! Life, art, slow growth, a beautiful trajectory, progress, and metaphor all within this one beautiful curve.
