An Engineer's Literary Notebook

Exploring the real and surreal connections between poetry and engineering

Posts Tagged ‘Gardening’

Sequence Everlasting

Posted by xbanguyen on July 8, 2012

The scent of lilies at night made me feel like a voyeur as I walked along someone’s garden on the way back to the car after the  fireworks ended. I spied the thick petals rising over the ferns to bathe in the night air, the greenness of the ferns a perfect foil. This being July, the unfurling was mostly done, but the knowledge that the unfurling patterns followed the Fibonacci sequence made the world of numbers come alive in spite of a lack of moonlight. As you know. each number in Fibonacci sequences equals to the sum of the two preceding numbers.  Mathematically,  Fn = Fn-1 + Fn-2. The Fibonacci sequence of order 2 (n =2) includes 0, 1, 3,5,8,13,21 … This series abounds in nature: the calla lily has one petal, euphorbia two,  buttercup five, delphinium eight, black-eye susan thirteen, aster twenty one. Is it the number of petals in the flowers that make them pleasing to the eye, or is there something else?  Perhaps, because the sun flowers actually have their seeds packed that way to maximize the number of seeds in that space with the angle between the appearance of each seed exactly the one that is least approximated by a fraction, the golden angle calculated from the golden means which is the ratio of two successive numbers in a Fibonacci sequence [1] .  It is the golden ratio Phi that creates the enduring beauty of the Parthenon, and underpins the face of the beloved.  How does a specific mathematical proportion cause a universal perception of beauty in the mind?  Will this poem shed some light on the bridge that links mathematics and beauty in the mind?

The tension in alternating the mind as both subject and object, enchanting and enchanted leaves me optimistic, especially the last line because by changing, the mind can create changes. By applying the golden ratio observed in nature to man made structures, we create beauty. That there are mathematical sequences behind beauty is encouraging because they add to the understanding of how we come to be and how we endure without depending on the existence of God, even though the comfort of believing in a greater being beckons as I mourn my mother. This series of posts has never been intended to be a journal, but I must mark her passing this past April. It took me several months to write again. This post is for you, mama, you who taught me how to solve for x by working out simple ratios, you who bought me many books of poems, explained to me the two-seven-six-eight meter in ca-dao, made potpourri for me from the roses in your garden, and most of all you who loved me unconditionally. I do not know if there is an afterlife, but I am grateful that your love of languages and things of beauty live on in me.

Thank you for the inspiration, dear muse.

Acknowledgments

1. http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
2. The composite graphics of the sun flower is from http://www.mi.sanu.ac.rs/vismath/lends/ch2.htm and http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html
3. The fern photo is from http://www.flickr.com/photos/22887580@N06/2198052702/?reg=
4. The Fibonacci diagram is from http://www.learncpp.com/cpp-tutorial/710-recursion/
5. The Parthenon photo is from http://alexorbit.com/fibonacci/golden-ratio.htm

Posted in Fibonacci, Golden Ratio, Marianne Moore | Tagged: , , , , , | Leave a Comment »

A Duality in Domains

Posted by xbanguyen on May 2, 2010

Lately I have become hesitant in thinking of  numbers as austere things, well-defined and finite. It used to be that numbers had a different kind of charm, mostly because I knew where I was with them – one mole contains one Avogadro constant, 6.0221415 × 1023, of molecules –  exactly the number of atoms in 12 grams of carbon. There are 1000 meters in one kilometer, 149,597,871 kilometer in one astronomical unit , and one astronomical unit  separate the center of the sun from the center of the earth.  I used to think that comfort could be found in numbers because they carried no apparent ambiguity. Then I ran into this book, “The Solitude of Prime Numbers”, and my perception was shaken. Consider the solitary  3 and 5, 17 and 19, so close together but will never meet. There is a quality of timelessness in this exclusion zone where each prime number exists. That irrefutable distance makes these numbers appear forlorn and makes me yearn for time, time as a medium, intangible but could be used to track other things such as different types of  signals.  It is useful to be able to pick out a particular signal among others, for example, a human voice in the midst of a noisy transmission.  An electrical signal varies over time, and its magnitudes at instances in time differentiate it from other signals.  In time domain analysis, a signal is expressed as a function of time, made visible via an oscilloscope.  Since time and frequency are complementary in nature, the same signal can be converted into frequency domain as Fourier’s theory states that any waveform in time domain can be described as a sum of sine and cosine waves of different frequencies.  The same signal exists both in the domain of time and the domain of frequency, just like the same shade of blue exists on the petals of the himalayan poppies and in my memory of this flower one summer ago.

Now it is spring. This afternoon as I worked in the garden I saw beauty anew in the color of the geranium. Despite its red boldness, it unfurled its petals gently away from the chartreuse buds.  This brings to mind a fragment of an Eleanor Wilner’s poem:

… beauty had no figure, no sacred

symmetry, centripetal, slowly opening

To a half-glimpsed nuclear core –

hot enough to melt the artic,

icebound heart of God,

One flower in Eden

and they would have known

beauty, and knowing that,

would know how beauty fades.

Why is it not incongruous to detect a trace of melancholy here? Perhaps because when happy, it is best to leave a bit of pleasure unenjoyed, lest the gods are jealous, as if we had a choice.  That is how I feel about the anatomy of melancholy tonight. Come to think of it, we always have a choice, and the act of making choices in itself is an adventure.  Thank you, dear muse.

Acknowledgement: The waveform graph is from zone.ni.com


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Posted in Analog, Gardening, Memory | Tagged: , , , , , | Leave a Comment »

Clock Trees

Posted by xbanguyen on December 13, 2009

Leaning over the fallen monkshood, the daphne stiffens. It is early December but winter is already entrenched in my garden. The earth smells sharp with the scent of inevitability as I gather the rose hips and remember how lush the summer was. I have many rose shrubs but no trees. Perhaps that’s why the five poplars that marched up the hill toward a cottage in Dingle of long ago are still on my mind. But the lack of trees notwithstanding, I ought to be more content because there are many kinds of trees, not least are the clock trees in my other world of ASIC design. Not everyone gets to synthesize such intricate trees except we ASIC engineers. A dubious pleasure, you may beg to differ, if you are familiar with that perilous realm fraught with forbidden windows that send unwary signals into abject oscillation. I suppose that it is easy to be flippant now because the havoc that large clock skews could wreak on an ASIC is temporarily a thing of the past. Why is it that everywhere I turn, I see the impact of time? Why not turn the table? Why not consider the baring of their branches a way for the poplars to consume time? Yet, would it be better not to resist but to learn the rhythm of time to get some peace? There are many things to learn.   Ask Louise Bogan.

Knowledge

Now that I know
How passion warms little
Of flesh in the mould,
And treasure is brittle,–

I’ll lie here and learn
How, over their ground
Trees make a long shadow
And a light sound.

Louise Bogan

I can’t very comfortably lie down on this frigid piece of earth now.  But if I could, would I be able to hear Persephone pacing the grand halls of the underworld?  Would I be able to see Demeter’s tears like a waterfall glistening in the moonlight?


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