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

Will_Heath

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

Bald Cypress Forests - Part 1 by Paul Ringo, R.N.



Will

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soonami

Would it just be easier to say that odd numbers just look better? I think that fundament to Bonsai is the notion of assymetry and the each component in balance. Since bonsais are living trees, the odd number of trees are evocative of different parts of the trees competing for dominance

I appreciate all the research you do when writing these articles though, it makes not only these articles interesting but intellectual

I think this the second article you have written that has connections to Physical Chemistry - Group Theory in this one, and quantum mechanics in the tree view article

midwestbonsai

I heard once that, according to the Japanese, all even numbers, except for 2, are unlucky.
-Paul

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RonMartin(deceased)

If one finds the necessity of counting the number of trees in a forest there is indeed a problem. In most cases it is the forest planting but sometimes it is the person that needs to count.
One should be able to see the whole and not just a part of the composition. Numbers are just a small part.

midwestbonsai

I have found this
on http://www.cyborlink.com/besite/japan.htm

But I do not know if this carries over to bonsai

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soonami

yeah four sounds like death in Chinese too, a lot of hotels don't have fourth floors or room floors

Vonsgardens

As Will says:
Because it looks better

Need we say more? Hit this one straight on the head,
John

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"Wiring is simple; However, it is not easy to do it right" Boon

phithu

It must be on hell of a job to get to your room if you are on the fith floor......

__________________
Le Bugey terre de gastronomie!

Will_Heath

That is the root of the matter Ron, as I showed, even numbers actually lead us to group and count, odd numbers do not.


Numbers are actually a rather large part of the equation, see above.




Will