Poetry and Mathematics - Daffodils and Stars in Fractal Iterations

Photograph of the Milky Way Galaxy

The Milky Way Galaxy contains 300,000,000,000 stars. Stars and flowers are sometimes interchangeable in poetry.
The Milky Way Galaxy contains 300,000,000,000 stars. Stars and flowers are sometimes interchangeable in poetry. | Source

What a desolate place would be a world without a flower! It would be a face without a smile, a feast without a welcome. Are not flowers the stars of the earth, and are not our stars the flowers of heaven?


-- Mrs. Clara Lucas Balfour (1808 - 1878), British temperance leader

The Geometry of Nature in Land and Sky

The first realizations that strike me after a quick read of the poem The Daffodils by William Wordsworth is not only the fact that it is a lyrical poem of nature , but that it compares two fractal iterations :

  1. Bright stars in a field of the cosmos and
  2. Bright yellow daffodils in a field of grass.

These two are similar, but what have they to do with one another?

The concept of fractals is often taught visually with recurring patterns in nature, such as a spiral staircase mimicking the interior structure of a chambered nautilus. Another fine example is the similarity of the form and pattern of certain branch and leaf structures of tree species with the exact pattern of interior human brain structures.

Why is this important, we might ask - what of it, what does it mean?

The fractal equation is one of the dew or perhaps the only mathematical function that includes no margin at error at all. No "+/- 1", no "Confidence Interval", no "close to" or "approaching" --Change one element of a fractal equation and one gets a whole new solution, graph, structure...Some scientists and clerics apply this fact as evidence that since our universe is mathematically based, then an organized mind must be doing the mathematical organizing portion at the foundation of it. Others contend that our Universe simply happens to be a closed set based on one group of mathematics, all by chance; other universes experience different mathematics, laws of physics, and music.

ANALYSIS: Regardless of belief, the importance of this fractal notion is that a strong similarity was observed by the poet between the Milky Way and his Field of Daffodils.


Daffodils Of a Field

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The closely planted daffodils resemble the stars in the Milky Way in their density in greenspace and their bright color.
The closely planted daffodils resemble the stars in the Milky Way in their density in greenspace and their bright color.
The closely planted daffodils resemble the stars in the Milky Way in their density in greenspace and their bright color.
Source

"Daffodils", written in 1804

Second known title: I Wandered Lonely As a Cloud

I WANDER'D lonely as a cloud
That floats on high o'er vales and hills,

When all at once I saw a crowd,
A host, of golden daffodils;

Beside the lake, beneath the trees,
Fluttering and dancing in the breeze.

.

NOTE: This poem contains four stanzas of 6 lines each, all written in iambic tetrameter, one of the the first poetic meters students lean in school. This does not make it any less useful and the meter does not need to be "sing-song" given the proper wording applied to it.The rhyme is also simple: ABABCC, recurring every 6 lines. The rhyme in this poem is a bit annoying, except in the last two stanzas -- There, the rhymes sound much less like a consistent "hey hey hey" and lend themselves to a sound more thoughtful.

.

Continuous as the stars that shine
And twinkle on the Milky Way,

They stretch'd in never-ending line
Along the margin of a bay:

Ten thousand saw I at a glance,
Tossing their heads in sprightly dance.

.

NOTE: The loneliness of the unconnected (to anything else) cloud on his own in the sky is squashed to his delight by "ten thousand" bright flowers below him, remind him of the stars above him in the night sky in which he will proceed as darkness drops. He is not alone after all, but sandwiched day and night by bright millions, by velvet night and lush green space.

.

The waves beside them danced; but they
Out-did the sparkling waves in glee:

A poet could not but be gay,
In such a jocund company:

I gazed -- and gazed -- but little thought
What wealth the show to me had brought:

.

For oft, when on my couch I lie
In vacant or in pensive mood,

They flash upon that inward eye
Which is the bliss of solitude;

And then my heart with pleasure fills,
And dances with the daffodils.

.

-- William Wordsworth (b.1770 - d.1850).

.


NOTE: The poem is romantic and sparks positive emotions that ease loneliness - of happiness and joy, and of valuable, warm memories in the future. The daffodils were so joyous and lively in their dance that they out performed the rather stormy waves in the bay alongside which they grew. All nature was dancing as the poet saw these features in a walk through its wonders with his beloved sister in 1802. Her journal entries about this walk and her observations of the scenery inspired Wordsworth to write the poem, published later, in 1807, and revised in 1815; overlapping with at least a portion of years of Regency England.

Art Nouveau Portrait of the Milky Way

This interesting painting of the legend of the Milky Way carried through the sky by goddesses was painted by Frida Hanson (1855 - 1931). The repetition of female figures and folds of filmy starry fabric are also a type of fractal iterations.
This interesting painting of the legend of the Milky Way carried through the sky by goddesses was painted by Frida Hanson (1855 - 1931). The repetition of female figures and folds of filmy starry fabric are also a type of fractal iterations.

"The Milky Way" by Frida Hanson

The image above is a beautiful painting of a classic legend. The interesting story is the legend of the Milky Way, carried through the night sky by goddesses. The lovely portrait of female form and sky was painted by Frida Hanson (1855 - 1931).

The repetition of female figures and folds of filmy starry fabric create a a type of fractal iterations. Interestingly, in Asian culture, the night is female, as is the concept "yin", the night being an era of regeneration for tomorrow's actions underneath the sun, a "yang" energy.

ANALYSIS: Women are also referred to as "flowers" in the literature and poetry if the world, thus connecting all of the concepts we have as three iterations of the same theme:

  1. Daffodils,
  2. Women ("flowers") carrying the stars of the Milky Way at night, and finally,
  3. Possibilities of stars themselves being flowers in the velvety field of night.

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Comments and Analyses 15 comments

Hello, hello, profile image

Hello, hello, 6 years ago from London, UK

Fantastic hub. It was an eye opener and I learned so much from it. Thank you.


Seakay profile image

Seakay 6 years ago from Florida

Interesting and thought provoking. Love the daffodils!


freelancewriterva profile image

freelancewriterva 6 years ago

I read two of your articles today. Thank you and keep the excellent work.


lightning john profile image

lightning john 6 years ago from Florida

I really love this Patty! While reading this I noticed your, Probability Of Extraterrestial Life. I shall read it next. Thank you Patty.


FCEtier profile image

FCEtier 6 years ago from Cold Mountain

I like the entire poem and the last stanza is my favorite. It fits in well with my numerous naps! LOL

When my kids were in elementary school, they had a program where business people could visit and read a story or whatever. Every time I did that, I'd finish by reciting "Daffodils" from memory. The kids were always surprised!


G L Strout profile image

G L Strout 6 years ago from Ohio, USA

Thank you so much! I remember the dafodils poem from my own school days.

The photos are wonderful.

Your article always lift my spirit. I look forward to more!


robie2 profile image

robie2 6 years ago from Central New Jersey

Now this is just fabulous and sooooo creative. Thanks:-)


Earth Angel profile image

Earth Angel 6 years ago

Blessings to you this lovely morning Patty!!

What a GREAT Hub!! Thank you so much for sharing! Leave it to you to weave daffodils and the Milky Way, poetry and science, art and fractals together so eloquently!!

You are the BEST!! Earth Angel!!


dallas93444 profile image

dallas93444 6 years ago from Bakersfield, CA

Fractal Iterations are everywhere. It takes millions of the "Golden Ratio" geometric shapes to form a microscopic fractal. Then millions more of fractals to produce the symmetrical growth pattern in a cauliflower's natural growth design. Fractals make up everything naturally occurring on the planet, in the galaxy and the surrounding galaxies and universes, all made of fractals composed quad-zillions of tetrahedron molecules, all vibrating at different frequencies. Fractals continue on into infinity - both directions - in terms of dividing into one half, or doubling the size. The Golden Ration refers to the relationship of the sides of a rectangle. A typical business card reflects this relationship. It has been found to be the most pleasing rectangle shape... You set the bar high for hubs. Great hub. thumbs up and awesome!


How to - Answers profile image

How to - Answers 6 years ago from Ireland

What an amazing and thought provoking poem. I love the photo of the stars and Milky Way too

Thank you for sharing this


Patty Inglish, MS profile image

Patty Inglish, MS 6 years ago from North America Author

Overwhelmed with so many responses, I am pleased that readers are enjoying this Hub and the natural wonders we're discussing here. Poetry and literature, like art, like nature, can have so many patterns and layers to explore.


billyaustindillon profile image

billyaustindillon 6 years ago

Vert well done - I have always found it fascinating Fibonacci and his discovery of the natural order and fractals. The pictures make it all so real.


SafeCard 6 years ago from Charlotte, NC

I always enjoy your hubs and am curious just how you get some of your ideas on what to write about.


Patty Inglish, MS profile image

Patty Inglish, MS 6 years ago from North America Author

billy and SafeCard - I am very thankful for my ability to see patterns and similarities in the design(s) of different objects and concepts; and many request produce several possibilities. It's fun, too. But some topics, I just draw a complete blank. and so it goes...


ExoticHippieQueen 5 years ago

Hi Patty, I had never heard of fractal iteration, so thank you for making me aware of one more of millions of things I have yet to learn. Voted up and interesting!

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