Sunday, January 21, 2018

The Golden Ratio: Fact or Fiction—And Does It Really Matter?

Golden Ratio and the Nautilus Shell
(The red shows a curve based on the Golden Ratio.  The blue shows a shell,
the growth pattern of which is not based on the Golden Ratio but on a logarithmic curve.)

Most of my students are familiar with the mathematical concept of the Golden Ratio, even before I bring it up in my workshops.  They’ve read that you can find it in shells and hurricanes, that it was used by the ancient Greeks in architecture and by Da Vinci in his “Vitruvian Man” and...well, you can read all about it on the Internet.  Apparently, it is found in everything from sunflowers to spiral galaxies.  Some deem it the magical ratio that holds the universe together.

Da Vinci's "Vitruvian Man."
Did Da Vinci use the Golden Ratio to draw this?
Or did people who came after Da Vinci see a design that isn't there?
Personally, I don't see it.

But recently, I learned that there are Golden Ratio deniers.  One is Keith Devlin, a mathematician and Executive Director of the Human Sciences and Technologies Advanced Research Institute at Stanford University and National Public Radio's “Math  Guy.”  His article on it is fascinating.   Basically, Devlin's thesis is that the Golden Ratio isn't all that prevalent.  There are many others in his camp, and you can spend hours reading arguments, both pro and con.

Basically, the Golden Ratio is simple.  But rather than give you a mathematical formula, I offer the diagram that’s usually given, superimposed over a nautilus shell, at the top of this post.  You've all seen something like it.

Painters who use the Golden Ratio may use it to draw a grid on their canvas to identify what one might call “pleasure points” or “power lines,” where important parts of a design might be placed with the goal of making a more attractive and powerful painting.

Center of Interest Based on Golden Rectangle
(The Golden Rectangle is based on the Golden Ratio)

There’s a difference, of course, between trying to discover the Golden Ratio in a design and purposefully creating a design with it in mind.  We humans like to impose order on what we perceive as a sometimes chaotic world, so we often see order where there is none; or we create nicely ordered designs to satisfy our need for order.

For us artists, it all boils down to:  “Does the Golden Ratio really matter?”

No, it doesn’t.  There are many ways to divide up a canvas or organize a design in a pleasing and powerful way.  The Golden Ratio is just one.  It doesn’t matter if it is the magical formula upon which all Creation is based, or not.  With ruler and compass, you come up with  many attractive ways to organize two-dimensional space.

I believe that we all have an intuitive sense as to what makes a pleasing design.  Designer Arthur Wesley Dow believed one could fine-tune this intuition simply by looking at good art, as described in his wonderful book, Composition:  Understanding Line, Notan and Color.

Much of our intuition, however, isn't innate but is instilled by our culture.  This was made clear in the 19th century when Japanese exports of woodblock prints arrived in Europe after trade was re-established with that country.  The Japanese sense of design was very different from the European one, and it profoundly changed the way the West looked at design.  In his book, Dow draws heavily on what was for his generation a new influence.

So, go look at some good art and get busy!

No comments: