The Golden Mean- a lecture

The Golden Mean
When did rectangles become important? It’s not an unusual question, straight lines tend to be a human thing. From an airplane or from space, seeing a straight line is evidence of humans. Crystals make for some pretty straight lines, but we are talking inches, rarely feet. Can’t think of another natural straight line, and combining straight lines into rectangles? Maybe a small crystal? Basalt formations like Devil’s Postpile?

Certainly at least the vast majority of all known rectangles are man made, and fairly recently man made at that. Some of the more ancient cities have a limited grasp of straight lines. Streets curve so much in the oldest part of Rome that you can’t see more than thirty yards ahead. And the shape of the buildings matches the curves of the street.

There is the Harappan culture of the Indus Valley, that appeared to have a solid grid with street corners at ninety degrees and homes and shops that were cubes and rectangles, roughly 3300 bc.

Most human habitation at that time followed rivers, streams, mountain trails, and other curvy formations. Is this the birthplace of the rectangle? Someplace has to be the first. And as soon as the rectangle is used, then people look at the rectangle to study the variety of ways that it may be subdivided. Probably the first natural choice is to create the perfect x and y axis lines. I can almost see the first moment that this was done. Two simple straight lines created four perfect copies, only smaller. At the time it might have seemed like magic. Four thousand years later the artist Piet Mondrian, divides the rectangle into dynamic sections by use of line, line weight, and color.

All of our current cameras render what we see with our eyes into a standard rectangle or square. Our eyes naturally have a field of vision that is almost twice as wide as it is high. It might also be said that the edges are soft and blurry as we get to the periphery of our vision,

The clear point is that the end result of using a camera is far different from the actual view of the human eye. The viewfinder, or finder for short, artificially crops off most of the world, even with the widest of lenses, what we see in the finder doesn’t match the image created by our eyes. We see this soft edged, rounded rectangle with a distance focal point, but our brain tends to give additional focus to the left/right/up/down aspect. It’s not the same focus as distance, it’s more like “importance” or “value”. The best example I can think of is a parent looking at the ninth grade class standing on the steps of the school. The parent’s eyes are riveted on their child and she is in excellent focus. The distance focus is working perfectly, the grass in front is slightly out of focus, the building behind is slightly out if focus. Photographers call this the “Depth of Field” of any photograph. Depending upon the aperature used, the depth of field contracts or expands.

Comparing a camera lens to the human eye is similar to this extent. What the lens cannot do is to give the “value focus”. In the same example of the ninth graders on the steps, what the parent sees is perfect. As soon as they bring the camera up to their eyes, most things change. The soft, blurry, rounded edges are replaced with a hard edge border. The content within the border is perfectly focused everywhere. In other words, the building, the mountain behind the building, the clouds, the grass in front of the building, and all of the children are in perfect focus. It sounds good, but if you were to show someone else the picture they would be confused. Where are they to look? Unless you physically take a marker and circle the child, the viewer is left scanning everything to find the purpose of the photo. It’s true, that by changing the depth of field range you can eliminate the clouds, the mountain, the building, and even the grass from that visual search because they would be blurry; but you still must have focus on the face if the child, and that is based upon distance, so the face of every child at that same distance will be in focus, and the viewer will still scan every face, trying to find the one face that is important. Get out the felt tip marker.

This is the dilemma of every photographer, translating what we see with our eyes into the 2D, framed rectangle (with no value focus). That’s about the simplest definition of the challenge. We can use different lenses, different settings, but in the end we can never recreate what we see with our eyes.

So, do we give up? No, there is one more tool or technique to apply that can assist in the failure of not having “value focus”, and that is using composition. What we see with our eyes does not need composing, the importance is chosen and we tend to block out everything else.

In the photograph we can chose several composing tricks to lead the viewing eye to the areas of “value”.

Back to the division of the rectangle. Early peoples began diving the rectangle with a line that was not perfectly in the middle, it was off to one side or the other, and it was different place for every size of rectangle.

The Greeks were not happy with this “touchy feely” type of rectangle division so they worked on a formula that could be consistently applied to any rectangle and the “best”, most attractive dividing line could’ve created. They had a real need in dividing temple buildings from the sanctuary and the porch. It was necessary to find the line in 3d architecture, but also in painting or later in photography. The added bonus is that any object that is on the perfect dividing line will receive extra importance. We call the dividing line “the Golden Mean”. The cool thing is the “golden mean” is both horizontal and vertical so the two perfect dividers cross, and x marks the spot. As a photographer I often place the “value focus” at one of the four available crossings of the “Golden Mean”.

So what is the formula? It’s very complicated, it involves a hypotenuse, right angles, and some geometry. It’s fascinating and very accurate, but not useful in the field. So here is the simple (and almost accurate) short cut. Divide the rectangle in eighths, count three eighths from either the left or the right. And at the same time three eighths from the top or bottom. I have a viewfinder feature that automatically grids the finder into eighths. I use it all the time. And like pi, the formula also exists in nature. The spiral of the nautilus sea shell, the spiral of some plants ( particularly some succulents, all have a formula that is expressed as either the Fibonacci Sequence of numbers or the Golden Mean.

So, remember that the camera can never capture what we see, but we can use tricks and techniques to redirect focus and attention, to get closer to the image we want.

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