if i was reading your posts thru my early bonsai years, i'd be learnin heeeeps
Hang in there Aaron, We are only discussing the basics so far. I seem to get stopped in my tracks vindicating the usefullness of these studies everytime we discuss them.
Science is very much the study of nature. The more we understand nature the better we can make our compositions look more natural.
Robert Stevens is no fan of the rules of bonsai yet he talks of studies of Leonardo da Vinci who was an Italian polymath, scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, botanist, musician and writer.
I have not read Roberts books yet, they are wrapped up ready to open Xmas morning. Yet the excerpts I have seen from Robert indicate to me he is very interested in the golden section and other studies of Nature from Leonardo da Vinci as indicated by the cover of his latest book. Yet Robert's trees are applauded for their individuality and imaginative thinking!
There is an interesting phenomenon with trees that if you look you will see that tree trunks don't taper. If you look at a tree it certainly looks like it tapers but if you study it you will soon see that no branch or trunk actually tapers. What does happen is that every time a branch leaves the trunk the trunk above is slightly less in diameter.
I recently noticed that Robert has picked up on Leonardo da Vinci's studies of this in a different way. Although Robert does not specify there is no taper he does bring point to the fact that Leonardo noticed that the sum of all the branches of a tree add up to the same diameter of the trunk.
leo.jpg
The most conjoined part of mathematics nature and the arts must be the Golden section. It is amazing to think that we are looking at this golden section all day every day in the arrangement of branches along the stems of plants and of veins in leaves, the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals.
Working in the metal industry we are constantly battling warping and ensuring things stay square. Over time you develop an eye that can detect the slightest error in proportion. It is a great feeling when your eye follows the lines of a finishes item and it does not hesitate at something that is out of order. Often checking with a square is just going through the motions because you know it is right. Some times the eye will tell you something is wrong yet it takes a long time to find it with square straight edge and ruler in hand. Some times I can not find the problem and I need to ask some one that understands better than me.
So what does all this have to do with the width to height ratio? We have been looking at the golden section all our lives and some times when we try to recreate nature our mind is telling us something is wrong with the image we have created. We can't put our finger on it as we have never documented how we know what should be. We have to ask some one "This tree looks wrong for some reason can you work out why?"
Some of the greatest artists in the world use rulers and design principles to construct their art so that they are pleasing to the eye. Do you really think if you put a ruler too your tree that it will become less of a tree or you won't be game to continue to let the imagination create.
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It's too bad your in such a hurry cause the stories I could tell you, Bushels and baskets of stories, hole crates full of stories. But if you can spare a moment I will tell you one story.