Good Odds


Gardeners may have heard it’s best to use odd numbers of similar plants in groupings and wondered why odd numbers are supposed to be more aesthetically pleasing than even numbers. Perhaps some authoritative figure in garden design plucked that rule out of the air and everyone has followed it blindly ever since. The rule doesn’t apply in situations where pairs work best, such as one columnar arbor vitae on each side of an entrance. A gardener would have to be daft to try to force another arbor vitae in there somewhere in order to obey the odd number rule, disrupting the natural harmony of pairs at entrances, gates, and arbors, where the architectural feature itself presents a third, central element.
Plumeria (Frangipani) flowers
Plumeria (frangipani) flowers in Don Tao, Si Phan Don, Laos. Photo by Basile Morin. Humans and other animals often present paired symmetries of even numbers, while plants more often than not have odd numbers of parts, as in the five petals of these frangipani flowers.

No one seems to know for sure why odd numbers in plant groupings are more pleasing, at least in an informal garden. Informality could be the key, since some people find the formality of even numbered groupings pleasing, but that appreciation doesn’t appear to come naturally to our brains, which look for a central focus in a grouping, something that presents itself naturally in odd numbered groupings. More than seven plants in a grouping starts to lose coherence and people can only vaguely get an idea of the center, rather than zeroing in on a central plant.

In a 2008 appearance on Sesame Street, Feist sings her song “1234” with help from groups of Muppets. Four is of course an even number, but you may note as you enjoy the music whether the presence of Feist herself changes the dynamic from even to odd groupings, dissimilar as she is to a Muppet. There’s certainly nothing stiff or formal about the presentation.

Experiment with different numbered groupings of similar shrubs, perennials, or annuals, and you will most likely find that without thinking about it you find odd numbers more pleasing and natural if you prefer a less formal garden, and even numbers naturally create a more formal feeling. These are arrangements nature appears to have adopted, like golden section proportions and Fibonacci spirals. The patterns most prevalent in nature seem to bypass our reason and appeal directly to our core because it’s what we are immersed in from birth, and that still begs the question of why nature prefers some patterns over others. Efficiency? Possibly that’s a part of it. Beyond that is a mystery, like the appeal of music. Many observable patterns are essentially visual representations of music, and we enjoy them because we typically enjoy harmony. When gardening, it helps to listen as well as look.
— Izzy


Seeing is Believing


“God does not play dice with the universe.”* ― Albert Einstein (1879-1955)


There are patterns throughout nature, from the rhythm of waves striking the shore, to the sand dune crests farther up the beach, to the leaves and flowers on plants and trees inland. Many of those patterns arise because of physical constraints operating through a medium, for instance the waves rise and fall regularly due to tidal influences from the Moon above and gravity from the Earth below, while sand grains in the dunes react to wind and water, and leaves and flowers allocate space for themselves in tune with the Sun and their plant neighbors.


Beauty of Coconut
The beauty of Coconut (Cocos nucifera) with its radiating pattern of fronds; photo by Krajaras.


An Italian mathematician of the 13th century named Leonardo Fibonacci, more commonly known just as Fibonacci, described natural patterns mathematically and he has since become well known for the Fibonacci sequence of numbers that add to each other infinitely, and for the Golden Ratio of 1.618, denoted in equations by the Greek letter Phi, which when employed in the Fibonacci sequence eventually yields Fibonacci spirals on a large scale. Less well known is that Fibonacci advocated the change from Roman numerals to Hindu-Arabic numerals in his 1202 book Liber Abaci, a book on calculations.


The shell of the nautilus is often cited incorrectly as a Fibonacci spiral. It is actually a logarithmic spiral. For whatever reason, the idea of Fibonacci spirals has taken hold popularly on the internet, to the point that some people appear eager to impose Fibonacci spirals on nature where patterns either hardly exist, or where they could be more accurately described with some other mathematical model. Perhaps the appeal lies in being able to ascribe patterns to a model proposed by one man, and saying “Fibonacci” has a more poetic feel than “logarithmic”. At any rate, there are many more patterns evident in nature than can be put down to chance, and that after all is the definition of a pattern.
Cottonwood one
Looking up along the deeply fissured bark of Cottonwoods (Populus deltoides) into the sunlit canopy of leaves; photo by Atiwis.

Baraka is a 1992 non-narrative film directed by Ron Fricke, with music by Michael Stearns. Fricke has described his film as a “guided meditation”. Baraka means “blessing” in a multitude of languages.

We seem to prefer patterns over chance, and order over chaos, and therefore we sometimes struggle to impose a pattern where perhaps none exists. It comforts us. It can even be a matter of belief. Some of us, maybe most of us, find it unsettling to contemplate a natural world and a universe where things happen randomly with no rhyme or reason. How can you set a schedule for yourself and your family in such a universe when you are unsure what might happen from one moment to the next? How can you plan your life, if you are so inclined? Depending on your belief in the reliability and predictability of the patterns you see in nature, you may be able to conduct your daily life with some confidence everything will go mostly as planned. With that in mind as you go about your everyday affairs, you may take time to notice how the patterns in the natural world around you guide your beliefs, whether or not you believe there is, in turn, someone or other guiding those patterns.
― Izzy