Why Do We Use An Odd Number Of Trees In A Forest?

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I wrote and posted the following almost exactly two years ago and I thought it might make for some interesting discussion now...


Why Do We Use An Odd Number Of Trees In A Forest?

In bonsai, we are often told that we should use an odd number of trees when creating a forest that contains less than 10 trees. I am a firm believer in this “rule” and I will attempt to explain why in the following article.

First, we as humans tend to group objects into sets subconsciously when we view them. I’ll leave the question as to if this is a learned behavior or an instinctive one to the experts and explain how we count and perceive the number of objects.

We could get into Group Theory here and state that Every group “G” is is isomorphic to a subgroup of “SG”, the group of permutations of the elements of G. If G is finite and has order n, then G is isomorphic to a subgroup of Sn. However, I think it is best to say that we as humans have learned to “group” objects together and it is far easier to do this with even numbers than odd numbers, hence it is “easier to view an odd number of trees in a forest without subconsciously grouping them into subgroups. This allows for the “whole” of the forest to be seen and not the “parts.”

There is an inherent pattern in numbers, in prime numbers patterns seem to pop up everywhere. There is also a beauty in mathematics that is not often appreciated. As I wrote in another article, math and numbers have led to some very interesting advances in art.


Odd numbers are thought of being more aesthetically pleasing to the human eye in many other forms of art and expression as well. Models, container gardeners, and even landscapers all recognize this concept. Searching on odd numbers brings up page after page of their use and the thought that they are aesthetically pleasing is dominate.

The use of odd numbers in art predates all of us, Picasso, Monet, and Van Gogh all knew this from instinct or instruction. It is mentioned often, shown more, below are a few examples.

Monet
Monet
Van Gogh
Van Gogh
Van Gogh

Why do odd numbers work best for forests? This is a tough one in all art forms, take the book, "Drawing For Dummies" for example, it states in the chapter, "Focusing on the Elements of Composition in Drawing" that "Placing an odd number of objects into a grouping (rather than an even number) makes a composition more artistically pleasing. Balancing three objects on one side of a composition and five on the other is much more interesting than a static arrangement of four on either side." In fact this chapter could very well be written about designing bonsai.

There are many reasons for the odd numbered trees in a forest "rule." Some say it is a Japanese idea. "Within the East Asian artistic tradition, China has been the acknowledged teacher and Japan the devoted student. Nevertheless, Japanese arts developed their own style, which can be clearly differentiated from the Chinese. The monumental, symmetrically balanced, rational approach of Chinese art forms became miniaturized, irregular, and subtly suggestive in Japanese hands. Miniature rock gardens, diminutive plants (bonsai), and flower arrangements, in which the selected few represented a garden, were the favorite pursuits of refined aristocrats for a millennium, and they have remained a part of contemporary cultural life.

The diagonal, reflecting a natural flow, rather than the fixed triangle became the favored structural device, whether in painting, architectural or garden design, dance steps, or musical notations. Odd numbers replace even numbers in the regularity of a Chinese master pattern, and a pull to one side allows a motif to turn the corner of a three-dimensional object, thus giving continuity and motion that is lacking in a static frontal design."


The Japanese connection is an important one as we have been influenced by Guiding Thoughts in Japanese Aesthetics "Guiding Thoughts in Japanese Aesthetics Shizen (naturalness, absence of pretense) - Gardens (and arguably any aesthetic object) should be natural. Design with the intention of making your creation look as though it had grown that way by itself. If you have obviously man-made objects involved, do not try to disguise them. (ex. Cement mortar or brick looks better untouched than painted.) Choose simple objects which will fit in with the natural surroundings.

Odd Numbers - When placing elements in a composition, use odd numbers such as one, three, and five. This will better result in a sense of natural asymmetry."


Yet this goes beyond the Japanese, as I pointed out earlier, great artists such as Monet, Van Gogh, and such all recognized that odd numbers were more visually pleasing than even numbers and their works reflect this.

But besides the extreme lack of even number forests, what other artists besides those already mentioned recommend the use of odd number trees?

John Ainsworth in his "The Secret Art of Bonsai Revealed" notes the importance of odd numbers but also references this belief to the Japanese.

Elizabeth Chute in her "The Ancient Art of Bonsai" states the same but goes on to say that visually pleasing group plantings are much easier with odd numbers.

Odd numbers simply work. The fact the there are very few actual bonsai forests with less than ten trees that contain even number of trees shows that it may very well be a futile effort.

Although Saikei are often confused with forests lately, they are not the same thing. Most Saikei have other objects that make up an odd number when counted with the forest trees. And they do go by a different set of design principles.

In closing, I feel it is quite clear why forests should have an odd number of trees. It is more aesthetically pleasing and therefore more artistically sound.

In other words...to answer the question, "Why Do We Use An Odd Number Of Trees In A Forest?"

Because it looks better.


Some links on forests..

Creating a Forest Bonsai by Brent Walston

Bonsai Forest by Ruth Staal

A Bonsai Close-up on Forest Plantings by Pauline Muth

The History of Goshin

Restoration of Peace Forest

Forest Bonsai - Design & Construction

Some Short Notes On Creating A Forest by Jim Smith



Will Heath



Will
 
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Dwight

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Interesting....Vance delving into the psyche of humans is a rather frightening concept. I remember reading ( while going through a gifted/tallented certification ) that the smaller an object is , the more we notice symetry. Examples were ancient temples in S. America and Egypt. The temples themselves were so big the symetry was almost natural but the hygroglyphs on the temple walls are almost totally asymetrical. One egg head said it had something to do with the asymetry of our brains. Contrary to what most seem to think our brains are very definately asymetrical from the gross structure down to functionality. Ever notice how a face that is very symetrical is not as attractive as one that is just slighhtly off ? We seem to be drawn to asymetry ( odd numbers being an example ) on the personal scale while symetry on a grand scale is OK. Even there , asymetry has it's place. Ask an archetect and he'll probably say an asymetrical appearance on a building of moderate size is more pleasing than a symetrical appearance ( think " Falling Waters ).
 

Vance Wood

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Interesting....Vance delving into the psyche of humans is a rather frightening concept. .

Interesting indeed! I don't remember having made a comment to this string before now. But now that my name has been brought into it look at music. There is a difference between formal and military music in that most of the above is symmetrical in two's and four's where as informal and "playful music" is in three's; at least from the stand point of early music. Uneven music has the flavor of being unstructured and more natural; random. Symmetrical music is contrived, purposeful, controlled and controlling.

As far as uneven numbers and the bonsai Forrest; the uneven count seems more natural and not contrived by the hands of man, which is after all the goal of all good bonsai.
 

Walter Pall

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I use EVEN numbers for forests if I even care to count the trees. I do this as a statement: The rules are misunderstood, they are not phrased in an artistic way.

A gardener would say: "don't use even numbers on forests and groups."
An artist would say: "Try to avoid symmetry, and try to get some dynamic balance into your design"

With larger groups and very much difference in diameter and height and slight difference in character of the trees it is perfectly possible to achieve what the artist wants.

I use even numbers most of the time to prove exactly this point.
Why listen to gardeners if you work artistically?
 
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Hans van Meer

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I use EVEN numbers for forests if I even care to count the trees. I do this as a statement: The rules are misunderstood, they are not phrased in an artistic way.

A gardener would say: "don't use even numbers on forests and groups."
An artist would say: "Try to avoid symmetry, and try to get some dynamic balance into your design"

With larger groups and very much difference in diamter and height and slight difference in character of the trees it is perfectly possible to achieve what the artist wants.

I use even numbers most of the time to prove exactly this point.
Why listen to gardeners if you work artistically?

My thoughts exactly! Although I must admit that because of the leg of useful material I have not made a lot of forest groups up til now, I could not care less about how much trees are in my compositions! As long as it looks good...who is counting! It is all about open spaces, dept, rhythm and the evoking of feelings, it has nothing to do with using a calculator for your design! And yes just like in the paintings posted here by Van Gogh, in witch he deliberately works with even numbers (count them your self) and even poets a tree smack in the middle of the canvas, just to make the analytic criticasters go mad, just Like Walter is explaining! Although it is fun to discuss this numbers topic, it has not much relevance in creating a successful forest! Mathematics those not create beautiful bonsai, only feelings do!
Regards ,
Hans.
 
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Why listen to gardeners if you work artistically?


Because artistically, odd numbers work, be it in the great masterpieces, or in gardening...

While it may be possible to create a visually pleasing and artistically balanced forest with even numbers (with less than 10 trees), it is not always feasible and often is very difficult. Examples of such are incredibly rare.

Walter, if you can, post some of your examples for discussion please.

Hans?



Will
 
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Vance Wood

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I use EVEN numbers for forests if I even care to count the trees. I do this as a statement: The rules are misunderstood, they are not phrased in an artistic way.

A gardener would say: "don't use even numbers on forests and groups."
An artist would say: "Try to avoid symmetry, and try to get some dynamic balance into your design"

With larger groups and very much difference in diameter and height and slight difference in character of the trees it is perfectly possible to achieve what the artist wants.

I use even numbers most of the time to prove exactly this point.
Why listen to gardeners if you work artistically?

With all due respects I have a problem with you doing anything just to prove a point. There is no doubt that you can pull it off, I think you could make a good bonsai out of a bowl of corn flakes, even though I have not seen one of your forest projects and would very much like to just to see how you align the elements, doing so just to tweak the concepts of rules does not seem to follow what I have come to believe as your artistic iconoclastic instinct. I have always thought that your philosophy was one of doing what looks good, this seems to say do what violates convention and make it look good. I am somewhat surprised! To me anyone who seeks to violate all the rules is just the flip side of the coin to those who seek to follow all the rules. No offence intended, I respect your work immensely, it is a breath of fresh air in an over-used out-house. But respectfully, just because you have said it does not necessarily mean I have to buy it.
 
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Behr

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I am one of the 'counters' when creating forests, and intentionally try my best to avoid using 'odd numbers' of trees, rocks, or any other 'artifacts' when possible...The main reason for my efforts in this is to give those that are so determined to 'judge' a landscape by the 'numbers' an 'easy' method to 'critique' the composition...This allows them the freedom to move on to something that better follows the 'rules', and find something that even they can enjoy and appreciate...

For those that have the ability to appreciate a composition for the 'artistic' beauty or value without judging it by the 'numbers' or 'rules', there needs to be a few people like Mr. Walter, Mr. Hans, and I who just enjoy doing things to make a statement...

Regards
Behr

:) :) :)
 
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I understand, but even if a person does not count consciously, humans have a natural tendency to group objects together, it is our nature, odd numbers are harder to group, hence a more natural appearance.
 

irene_b

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If the scene flows to convince of the forest or a small section of a forest who cares how many trees are there?
Why would you worry about the numbers if it works?
To me that is like the paint by numbers!
Irene
 
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To me that is like the paint by numbers!
Irene

Why? Paint by numbers is a faux-art for little children. I would hate to think you meant anything of the sort.

I thought the point about the mind's tendency to form groups was fascinating. I know this from psychology as the phenomenon of "chunking" where we break large groups into smaller groups in order to remember them: eg phone numbers are written as ###-###-#### and not ##########.

To all of the "non-counters" or people who don't like this "rule", could you please post a pic of a convincing group of 4 trees to illustrate your point? I've seen lots of great odd numbered groups, but I've never even seen a even numbered group. Please change my mind.
 

grouper52

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To all of the "non-counters" or people who don't like this "rule", could you please post a pic of a convincing group of 4 trees to illustrate your point? I've seen lots of great odd numbered groups, but I've never even seen a even numbered group. Please change my mind.

"Convincing" may be in the eye of the beholder, but this group is what started this discussion, and at least a few folks seem to have found it convincing.

http://bonsainut.com/forums/showthread.php?t=903
 
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"Convincing" may be in the eye of the beholder, but this group is what started this discussion, and at least a few folks seem to have found it convincing.

http://bonsainut.com/forums/showthread.php?t=903

Very nice and yes, convincing.

However, I think we might not all be talking about the same thing. The rules of penjing are very flexible about what can go in the pot: rocks, sticks, rivers, sand, more than one type of tree in the planting, clay figures, etc, etc. Example, right away when I looked at the tree on the left and saw it as a group of 2 OBJECTS if not 2 trees. Take that rock out and then see how convincing it looks. I've seen penjing with two trees before and it was very nice, but I'm pretty sure if found that picture again I would find a odd number of visual elements (objects).

Bonsai, as I'm thinking of it, differs in that respect. Only trees go in the pot. I haven't seen a convincing planting of four trees and only four trees.

And I love the pot you have it in! :)
 

grouper52

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Very nice and yes, convincing.

However, I think we might not all be talking about the same thing. The rules of penjing are very flexible about what can go in the pot: rocks, sticks, rivers, sand, more than one type of tree in the planting, clay figures, etc, etc. Example, right away when I looked at the tree on the left and saw it as a group of 2 OBJECTS if not 2 trees. Take that rock out and then see how convincing it looks. I've seen penjing with two trees before and it was very nice, but I'm pretty sure if found that picture again I would find a odd number of visual elements (objects).

Bonsai, as I'm thinking of it, differs in that respect. Only trees go in the pot. I haven't seen a convincing planting of four trees and only four trees.

And I love the pot you have it in! :)

Yes, I agree about the rock, and about a straightforward 4 tree non-penjing style planting - it might be possible to do a convincing job of it, but I don't recall seeing any either.

Glad you like the pot - a local non-bonsai nursery here imported a bunch of these monsters a few years ago, then put them out at fire sale prices for some reason. Jason and I snatched up almost all they had!

Last evening when I got home there was just enough light left to lower the top of the left tree a bit and trim the two visually "touching" branches as folks suggested - it looks much better now, and I may take another photo this weekend. Thanks to those who guided me to make those changes.
 

agraham

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bonsai? penjing? even? odd?

It makes no difference...beautifully done.And as someone who doesn't walk in many forests....it makes me wish I could.

andy

wow..screwed that up

this post was in reference to Groupers 4 tree forest http://bonsainut.com/forums/showthread.php?t=903
 
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