Monday, March 9, 2015

The Golden Ratio - golden? or merely efficient?

I've often wondered how important the so called golden ratio really is in art.
It's one of those things that "experts" love  to talk about ...but anyone who labels anything in art as a "rule" has me thinking "why?"....actually I must admit I wonder why about a lot of rules...BUT that is another issue!
As art quilt makers it's important that we know which guidelines are really useful in designing...and which are more the result of one person repeating what another said, and another repeating  that.  Like the old story of the famous grandmother's recipe for roast turkey which involved cutting a 2" slice off each end of the beast.  The family swore for years this was the secret to her perfect roasts, finally somebody asked the old lady the reason for this rule..."oh", she said, "it was to fit in the oven, I only had a small oven!".   And cooking isn't the only place where strange superstitions and practices have built up over the years...maybe we're all turning round and round before we peck at the feeder like Skinner's chickens!!!  And I want to know why?

But first....what is this Ratio anyway?

Well, here's the standard definition:
The Golden Ratio the result of dividing a line into two parts  (part a and part b) in such a way that:
the longer part (a) divided by the smaller part (b)    is also equal to
the whole length divided by the longer part (b)

There's only one number ratio that will do that and it's approximately 1.618033989...
It is exactly equal to (1+√5)/2 - if you're the mathematical kind...which I'm not...alas!

but mathematicians really love these special numbers!!!  And in mathematics the 1.618 number turns up everywhere e.g. in a pentagon - hence the "magic" of the five pointed star...but I digress.

There are many books and articles written about the importance of  this ratio in art, in architecture, in painting, in photography (photographers cling onto their Rule of Thirds almost as tightly as to their cameras), in poetry, in music and in nature.  The Greeks revered it.  Kepler said that in geometry there are 2 treasures: pythagorus and the Golden Ratio.

So last week I went to a couple of lectures by the Famous Calculus Professor (FCP), now retired and keeping his mind active by examining any claims as to the magic of numbers!!

He showed us 9 different rectangles:  which one was the most pleasing?
They were all different ratios:  1:0.75, 1:1, 1:1.25, 1:1.5, 1:1.6, 1:1.75, 1:2 etc

Take a look and see which one you think is the most attractive:

Opinion was somewhat divided but people did tend to prefer certain ones.  Scroll down to the very end to see which one is the so called "golden" one.....

So is there something to this?  Have artists, architects, musicians etc across the ages used these particular proportions to increase the beauty of their art form???  
When the the GR experts show a picture of the Parthenon with the GR lines drawn around it.  You can see, if you look carefully, that the position of those lines is largely arbitrary - done simply to create that ratio – do you include the steps or not??!!!  It’s very random.

There is some evidence that Le Corbusier actually did use the number. But images of Mona Lisa with lines drawn on it are quite arbitrary too – often they don’t include the whole face!  You could actually take any portrait and just randomly draw lines on it and sooner or later you'll come up with the right ratio.

People have spent a lifetime analyzing the number of words in verses e.e.g Vergil’s Aeniad….showing  that they agree to the GR.  But you can count up the words or  the syllables in so many ways you can create something that approximates the GR if you pick your object carefully.

They thought people like Mozart used the GR and counted up the notes, or the phrases etc etc…but a careful analysis shows the same problems with music as with poetry. Imagine counting all those notes?  and what about chords? d'you count them as 2, or 3  or 4??

Despite numerous claims that they did, one prestigious Latin professor even built his whole amazing career on revealing this in various writings - despite analyses of the art of Da Vinci and Micheangelo and Vergil and Dante and Mozart etc   most of them DID NOT use this ratio.  They simply used whatever felt right for their particular art form.

So is the whole thing about the Golden ratio a load of hooey then?  well....having thoroughly debunked its use in art, the FCP (who is definitely not an LCD!) turned to nature and the Fibonacci series.

Now you all know the Fibonacci number sequence...a lot of quilt makers have used it in designing their quilts.  This is the sequence where you simply add the two previous numbers in the row to create a third number:  0, 1, (then 0 +1 = 1) so 1 is the next number, but then 1+1 = 2, so the next number is two, and 1+2 = 3....

0,1,1,2,3,5,8,13,21,34 and on and on and on upto at least 17 thousand digits (somebody had a big computer and a lot of time on their hands!!)....

Now,  consecutive Fibonacci numbers have a particular ratio to each other....and guess what?  yes!  it's 1.618...very approximate in the smaller number but by the  time you get upto 233/144 it's spot on.

Then we looked at flower petals, and the spiral lattice you see on the bottom of pine cones and pineapples.  Counting them up we realized that there were 13 clockwise spirals and 8 anti clockwise spirals.  13/8 = 1.625  - pretty close to THE ratio!!   
But why? why does nature "choose" to use the Golden Ratio, the magic number beloved of mathematicians where artists (of whatever medium) actually haven't?  The answer is efficiency.  The best way to get the MOST little seeds into a sunflower head, or pine cone, is to create the lattice effect of two sets of spirals that are related in that particular ratio.   And if you're going to survive, you want as many of your little babies out there as possible.

So...the ratio is Golden for survival, but...really not at all crucial for art!  So don't worry if your ratios are a little off, your thirds not quite corresponding to the norm, Da Vinci didn't, the architects of the Parthenon didn't, Mozart didn't....just smile gently at the critic or the teacher who insists  on concrete, permanent, eternal rules without question!!!  

....and now for a nice cup of tea after all that hefty cogitation....if you have been, thanks for reading!

and the answer is:  number three.


Sandy said...

Hurrah! I have never quite understood this drawing of random lines on the Parthenon thing.
Not long ago we had a textile artist come to our group. She kept going on and on about the golden mean and how she uses it for her collages and wouldn't dream of not using it. But to be honest, they seemed like little tight collections of materials. The subject matter was interesting, but I think she could have had much more dynamic pieces if she had 'eyeballed' it. Or did all the tight stuff and then throw in a rule breaker.

But yes, I do agree with the Fibonacci in nature. It is there in front of your eyes. You don't have to draw lines to see it.
Thanks for thinking out loud on your blog!
Sandy in the UK

Margaret said...

With apologies to whomever -- I preferred 1, 4 and 7!

Vickie Wheatley said...

Number 6 for me. I love your smart blogs. Thanks for taking the time!

Mary Marcotte said...

I use the golden mean only as a general rule. I want my compositions to be appealing, but I also want my own voice in my work. Like so much else in life, there has to be some balance.

The Idaho Beauty said...

I'm with you on the golden mean. I tried using it when I was unsure exactly what size I wanted a particular design. In nearly every case I did not like the look of the rectangle and eventually just went with my gut - what looked right.

I've wondered how influenced we are by the standard sizes of photographs,i.e. our brains get used to a certain rectangle and so that is what looks right to us. That size changed to a square with the advent of Instamatics in the 60's, then again with the new sizing of digital photos. Now we are being influenced by the square again with on-line Instagrams.

Thanks for this informative post.

Leigh in Portland (we are not burning down) said...

In architecture that ratio is supposed to give a balanced feeling to the space of a room. I find it a convenient starting place. Sortof like when the ball of yarn has a needle size on it. It's a good place to start a swatch, but may not produce the fabric I'm looking for.

Leigh in Portland (we are not burning down) said...

In architecture that ratio is supposed to give a balanced feeling to the space of a room. I find it a convenient starting place. Sortof like when the ball of yarn has a needle size on it. It's a good place to start a swatch, but may not produce the fabric I'm looking for.

Anonymous said...

I too chose #6, for what its worth.

I read about the golden ration once and felt skeptical; glad to have it confirmed.

Beth said...

I loved it! I also picked 2 and 3.

Turtlemoonimpressions said...

Ha! Ha! Lots of good rules of thumb if in doubt but I eyeball everything and I like 4 and 7!

Unknown said...

Sent you post to my son for the golden ratio topic since he lives on such things. What a fun response from him. Check out the "consider this" at the end. Awesome.

That was neat. She goes a little hard on the anti-rules thing (and exclamation points) but other than that, really great points. Efficiency makes way more sense in nature than it does in poetry. In visual art it makes sense that it would show up as that will tend to mimic nature, where the ratio naturally occurs. It would make sense then that it would lead to number 3 being more aesthetically pleasing because it's something we see often, in nature and subsequently art. The fact that I got it wrong could bear this out. I think when we're asked to choose our favourite rectangle, we chose based on what's familiar, which is not exactly the same as what's most aesthetically pleasing.

Consider this:
You chose 3, the 1.61 ratio. I chose 2, a 1.75 ratio.
Your computer screen is 1280x800 pixels, a ratio of 1.6.
Mine is 1366x768, a ratio of 1.77.

We both chose rectangles that we look at all the time. Not perfect science, but it's a thought.

Elizabeth Barton said...

thank you for passing it onto your son!! Yes I definitely do use too many exclamation points but I must admit I tend to talk like that...I want to convey a serious lightheartedness!! very interesting his comments and undoubtedly we all do like the familiar...I wonder if they did design the screens of all these things to fit the GR? seems like the very early tvs were much squares and we've gone wider and wider ...hmm another metaphor!

The Idaho Beauty said...

Ah, Kathy - someone else with my theory of familiarity! I hadn't stopped to consider monitor ratios but your son has a good point. The eye likes what it is most familiar with.

Aly V said...

I attended the same lecture when I was a middle school math teacher and was very disappointed in his summations. Using art in a math class is an engaging way to present new topics. So what, you can zoom in or out on the Parthenon and change the ratio? In most cases no matter where you place the lines you still get 5:3 or 8:5. Those numbers are nearly the start of the golden ratio. Even 3:2 is good and the rule of threes is taught in art school.

Recognizing one rectangle as "more pleasing than the others" has nothing to do with the beauty of the golden ratio. It was a cheap and manipulative trick to make a cynical and self-congratulatory point. A better example would have been the placement of 2 perpendicular lines within a rectangle. Placement of items in any shaped rectangle with an eye towards the ratio is the point.

I agree with Sandy and Mary that it is just one element useful in making something beautiful. You frequently demonstrate how color, size, and warmth influence the eye and express beauty.

Keith Devlin may be a great mathematician and professor of higher education, but that lecture was disappointing and served little purpose. In math and in art there areas for exploration and avenues that connect the two. Why not appreciate the beauty inherent in both?

Alyson Vega (math teacher turned artist following left-hemisphere brain damage)

P.S. I just discovered your art via Pinterest. It is beautiful.