The Mathematics of Flowers
“The Mathematics of Flowers”
by Gina Margolies
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The word mathematics typically brings numbers to mind. More than numbers though, mathematics is a language, a vocabulary of symbols and words used to express concepts. Flowers also speak a type of language. Officially called floriography, the language of flowers refers to the idea that each flower holds a meaning or message which can be used as a way to communicate certain sentiments. What happens when the two collide? You get the mathematics of flowers, of course. (Would that be florionumery?) What does math have to do with flowers? More than you would think.
The golden mean
Many math concepts are over my head and Fibonacci numbers are no exception. Fibonacci sounds to me like a funny way to say that someone told a few too many white lies, but it is in reality a mathematical concept. The word Fibonacci refers to a nickname given to an Italian mathematician. He did a lot of amazing work including the Fibonacci numbers. This term refers to a sequence of numbers called, naturally, the Fibonacci sequence, in which every number is the sum of the two numbers before it. This would be a Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
One plus one is two, one plus two is three, two plus three is five, three plus five is eight, and so on. The Fibonacci sequence is thought to approximate something called the golden ratio or the golden mean. This is yet another mathematical concept that refers to a relationship or proportion, i.e. ratio between two numbers. The Fibonacci numbers have been used in design fields such as art and architecture because the proportion, i.e. the golden mean, is thought to result in aesthetically pleasing work. Interestingly, this occurs naturally in many aesthetically pleasing things, including flowers. It turns out that the Fibonacci numbers can really be considered nature’s numbers.
The arrangements of leaves on a plant stem and petals in a flower head represent successive numbers in the Fibonacci sequence. For example, seeds on the head of a sunflower are arrayed in two sets of spiral rows in a glorious Fibonacci sequence. Look closely and you will see what is so glorious about it.
Plants grow the way they do in order to maximize efficiency. In flowers, the arrangement of the petals is set to maximize the amount of space for each petal or to make sure that each petal has sufficient exposure to sunlight. Many flower heads are densely packed with petals, making these arrangements critical to the success of each individual petal and thus the success of the flower as a whole. The arrangement of the petals on a black-eyed-Susan or the scales on a pineapple is not random. It is a precise mathematical arrangement that allows all of the elements to work together to ensure the success of the whole by achieving the golden mean. I might not be able to discover high-level mathematical concepts or produce a profound sequence of numbers, but I can appreciate the beauty these arrangements communicate. Mother Nature could have shown Signor Fibonacci a thing or two.
Flora’s Clock.
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Another mathematical concept reflected in nature is that of time - time of the day, time of the month, and time of the year. Time seems such a simple idea, just a numerical system or way of measuring the passage of, well, time. Before the invention of mechanical clocks, hourglasses, sundials, and iPhones, people needed some way to mark or note the time in order for society to function. One could not arrange a meeting without some way of denoting what time the get-together would be held. Before machines were invented, people used what was available. To tell time they relied on nature.
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The most obvious way nature indicates the passage of time is with the sun. The sun rises and sets in a predictable pattern. However, the sun is a less than precise way to denote time, so people looked for more exacting ways to do so. There were many different ideas and thoughts on how to do this and, as necessity is always the mother of invention, many brilliant ideas. One that I love is called Flora’s Clock.
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Flora’s Clock was created by an amazing Swedish chap named Carolus Linnaeus. Doctor Linnaeus is famous as a botanist, amongst other things. He is known for normalizing the modern system of naming organisms called binomial nomenclature. He also conceived of the idea that became Flora’s Clock. Flowers were used to mark time, in hours, weeks or months, according to when they bloom. Some flowers open their petals at a particular hour each day. Linnaeus decided to make a list of these. Using this list, we can reckon the hours in flowers.
Linnaeus’ basic concept was to plant a garden that, based on the time of day the various plants opened and closed their flowers, would tell time. Linnaeus named his idea the flower clock, often called Flora’s Clock after the Roman goddess of flowers. Many plants flower on a circadian rhythm. The term refers to a biological process that takes about twenty-four hours. Some flowers have a particularly strong circadian rhythm and open at the exact same time every day. Linnaeus created a list of flowers that exhibited this quality and arranged them to mark the passage of twenty-four hours, just like a clock does for us today.
There are different lists of the flowers that make up the clock. The one I like best is found in the book The Flowers Personified by J.J. Grandaville. According to this book, the flowers that Linnaeus determined to work best for his clock were:
midnight large-flowered cactus
one o’clock alpine sow-thistle
two o’clock yellow goats-beard
three o’clock scammony convolvulus
four o’clock smooth crepes
five o’clock day lily
six o’clock hawkweed
seven o’clock small-cape marigold
eight o’clock red pimpernel
nine o’clock field marigold
ten o’clock Egyptian fig marigold
eleven o’clock star of Bethlehem
noon ice plant
one o’clock profuse-flowering pink
two o’clock mouse-ear hawkweed
three o’clock dandelion
four o’clock madwort
five o’clock marvel of Peru
six o’clock geranium
seven o’clock naked-stalked poppy
eight o’clock upright bindweed
nine o’clock flax-leaved bindweed
ten o’clock cypress vine
eleven o’clock night-flowering catch-fly
Linnaeus made a garden plan which indicated where each flower should be planted in order to “tell” the time of day. There was one rather obvious problem with Flora’s Clock. The opening and closing of a flower is generally related to sunlight, weather, and the seasons. The geographical location of the garden would impact upon the flowering times and hence Linnaeus’ clock. Apparently, this did not stop some gardeners from trying to follow Linnaeus’ plan to construct a Flora’s Clock and some even seem to have had some success at it.
Floriography and Flora’s Clock
There has been no need to rely on nature to mark time since the mechanical clock was invented, but I still like the idea of doing it. I am not the only one. During the Victorian Era, the language of flowers, also called floriography, became very popular in Europe and the United States. This language was based on the belief that each flower has a hidden meaning or message. If one knew all of the hidden meanings, one could use flowers to send secret messages. The Victorians did just this. Books like Grandaville’s listed the meanings of the flowers and people used them to decode the bouquets they received. While the Victorians had mechanical clocks to tell the time, Flora’s Clock was used to mark the time in secret messages. If your bouquet contained a profuse-flowering pink, you could use Flora’s Clock to determine that your secret tryst was set for one o’clock in the afternoon. A large-flowered cactus meant meet me at midnight. Microsoft Outlook events seem quite boring in comparison.
Flora’s Calendar
Flowers also helped the Victorians mark the time of year. For example, The Flowers Personified also held a Flora’s Calendar. The idea of it is perfectly simple. Nature herself has arranged this part of the calendar by causing particular plants to bloom at certain times of the year. The Flowers Personified provided this list:
January Black Hellebore
February Mezereon
March Alpine Soldanella
April Early dwarf Tulip
May Common Dropwort
June Cornpoppy
July Centaury
August Scabious
September European Cyclamen
October Chinese St. Johnswort
November Serrated Pallasia
December Smooth Lopezia
One could indicate that one would return in April by sending an early dwarf tulip or that one would not wait past the end of the year by including a smooth lopezia, a flower that is much lovelier than its name suggests.
Math + Nature = Beauty
Whether it is the arrangement of the seeds on a purple English daisy’s gorgeous flower head or the fact that the marvel of Peru is also known as the four o’clock because of the time it opens every day, the collision of mathematics and flowers produces not only efficiency in nature, but wonder and amazement in human beings. Even if you cannot remember what you just read about Fibonacci, your eye can tell you that the precise arrangement of the petals on your favorite cabbage rose is a beautiful thing to behold.