The question of measuring beauty — that is objective assessment beyond “Very nice,” “Exquisite,” “This appeals to me” — has troubled scholars and other laymen at least from the time of the Greeks.  And, beginning with the Greek philosophers, there has been widespread disagreement.

— The Golden Mean: Mathematics and the Fine Arts by Charles F. Linn (1974)

The golden mean, the divine proportion, the golden rectangle; whatever one calls it, the argument goes that the ancients discovered a ratio that was a key to beauty.  Simply put, it describes the ratio between two components (e.g. width and length) so that the shorter is to the longer as the longer is to the sum of the two (S:L=L:S+L).  This works out to a ratio of 1:1.618.  Of course, they had to get over the fact that it is not a whole number.  Neither is pi, but irrational as it is, it comes in pretty handy.

Today it is still used to varying degrees by architects, designers, even plastic surgeons.  Heck, even Donald Duck knows about it:

If you’d like to dig way deeper into the golden mean, the Fibonacci sequence, mathematics in music, patterns, and more, pick up a copy of Mr. Linn’s little book (quoted to open this post).  He shows a great sense of humor and makes a potentially dry subject pretty interesting.  To the left is a page that he uses in an experiment, asking people which building proportion they prefer.

Linn says the majority pick the bottom one, 5:3 (or 1.6:1), the closest of the four to the golden proportion.  Still, he is skeptical of folks that want to, in hindsight, find the divine proportion lurking in everything the ancients built.  In fact, he presents a rebuttal of such an argument regarding the pyramids.

So how does all of this apply to bowls, and what is that thing with the bowl in the opening photo?  The walnut bowl in that photo is one I just made, an ellipse with a length and width purposely laid out according to the golden proportion — the first time I’ve consciously done so with a bowl.  I got so caught up in the idea that I even made a simple proportional divider — two sticks of equal length with a pivot point connecting them.  In this case, the pivot point is positioned at a point that divides the length into a 1:1.618 ratio.  Whatever width they are opened to, the golden proportion exists between the wider end and the narrower end.  The same can be done for any ratio by placing the pivot point at the appropriate spot.

So…the bowl is nice.  However, to be honest, it doesn’t seem to me to have a magical attraction.  It is not glowing with a golden radiance.  Besides, the only way to view it from a perspective that reveals this special proportion is to position one’s head directly over the center of the bowl.  How often are we viewing any building or cabinet from the perspective that indicates it’s perfect proportions?  Or maybe things with good proportions look good from any vantage point.  And, with a bowl, do the handles count?

In this photo, the walnut bowl is on the right (not yet complete) and a nearly finished cherry bowl is on the left.  The outside of the walnut bowl is done to the golden proportion, while the outer dimensions of the cherry bowl are in a 2:1 ratio (which occurred by accident).  However, that includes the handles while the hollow form seems to grab the eye’s attention more.  And the hollows are different shapes, colors, etc.

Proportion is just one element in the design of any piece — bowl, furniture, figure, or other.  With bowls, the lines of a piece are as important, probably more.  I have made bowls of all sorts of proportions from round (1:1) to another 40 inches long and 10 inches wide (4:1) and all sorts of proportions in between.  I just laid out a bowl on a walnut log over the weekend.  It will be 22 inches long and 17 inches wide.  Why?  Width: because it grew that wide and I won’t waste any of that wide dark heartwood.  Length: because there were branches above and below, plus any longer and I  might not have been able to carry it!  It is up to me to come up with a good design within those dimensions.  In that way, designing greenwood bowls is different from designing furniture.

I think the golden proportion, or any proportion, can be a useful guide.  I realized after making many bowls, that the size of the bottoms I laid out by eye tended to be at a 1:3 ratio to the size of the top hollow.  So now I know I like bottoms with a certain ratio (I think there is a song about that).  In some cases proportions might even be essential or at least very important — as in painting a realistic human being.

Rather than suggest that there is one ideal proportion, George Walker and Jim Tolpin focus on methods of finding pleasing proportions using simple, whole number ratios.  Their book By Hand and Eye is a fascinating and enlightening look into all of this stuff and more.  They explain how to put proportions to work!

So, how important is the golden proportion?  How heavily was it relied on in the past?  Do all pretty faces display it?  I don’t know, but I find it interesting.  More important, I think, is to trust intuition.  Trust your eye.  A knowledge of proportions can help one to recognize why he finds something beautiful, but I think, I hope, that it is unrealistic to discover a conclusive formula for beauty.  And a little mystery is nice too.  I’m not about to approach a wooden canoe, a songbird, or my wife with calipers.  Besides, only the canoe would cooperate.