An Engineer's Literary Notebook

Exploring the real and surreal connections between poetry and engineering

Posts Tagged ‘summer’

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

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The Integrals In Things Past

Posted by xbanguyen on October 24, 2009

The integral sign \intreminds me of the salt water taffy machines in the  sweet shops of the Oregon coastal towns we  visited during the summers of my girlhood. I remember pressing my nose against the glass partition to watch  the machine pulled the strands of candy in a mesmerizing pattern over and over,  stretching them into almost living things – supple and touchable.  As I look back, those summers appear pleasantly long and unfocused like the desultory walks along the beaches, trading taffy flavors and seashells with my sisters.   The fact that a mathematical sign can invoke such nostalgia made me reach out for an old textbook tonight.  Full of equations yellowed out with highlighters by my former self, it patiently repeats to  me that the Volterra series has the ability to capture the effects of memory.  Differing from the Taylor series that approximates the response of a non-linear system such that the output is solely dependent on the inputs at a particular time, the Volterra series calculates the output using the inputs at all other times.  Specifically, it is a series of infinite sums of multidimensional convolutional integrals and can be used to calculate the intermodulation effect of audio signals.

The integral of rational functions can also be used to calculate the drag force effect on the free fall of a sky diver.  But this fact was of no use to John Gillespie Magee whose parachute failed to open one summer day in 1941.  But how he had lived!

High Flight
by John Gillespie Magee, Jr.
Oh, I have slipped the surly bonds of earth,
And danced the skies on laughter-silvered wings;
Sunward I’ve climbed, and joined the tumbling mirth
Of sun-split clouds…and done a hundred things
You have not dreamed of…wheeled and soared and swung
High in the sunlit silence. Hov’ring there,
I’ve chased the shouting wind along, and flung
My eager craft through footless halls of air.
Up, up, the long, delirious burning blue
I’ve topped the windswept heights with easy grace
Where never lark, nor even eagle flew.
And while with silent, lifting mind I’ve trod
The high untrespassed sanctity of space…
…put out my hand, and touched the face of God.

High Flight

by John Gillespie Magee, Jr.

Oh, I have slipped the surly bonds of earth,

And danced the skies on laughter-silvered wings;

Sunward I’ve climbed, and joined the tumbling mirth

Of sun-split clouds…and done a hundred things

You have not dreamed of…wheeled and soared and swung

High in the sunlit silence. Hov’ring there,

I’ve chased the shouting wind along, and flung

My eager craft through footless halls of air.

Up, up, the long, delirious burning blue

I’ve topped the windswept heights with easy grace

Where never lark, nor even eagle flew.

And while with silent, lifting mind I’ve trod

The high untrespassed sanctity of space…

…put out my hand, and touched the face of God.

John was nineteen when he died.  It was a farmer who saw him falling from the plane. The same force must have acted upon Icarus of the Grecian myth, another boy who fell out of the sky.  W. H. Auden offers some commentaries on how  these tragedies were perceived and interpreted by arts.

Musee des Beaux Arts

About suffering they were never wrong,

The Old Masters; how well, they understood

Its human position; how it takes place

While someone else is eating or opening a window or just walking dully along;

How, when the aged are reverently, passionately waiting

For the miraculous birth, there always must be

Children who did not specially want it to happen, skating

On a pond at the edge of the wood:

They never forgot

That even the dreadful martyrdom must run its course

Anyhow in a corner, some untidy spot

Where the dogs go on with their doggy life and the torturer’s horse

Scratches its innocent behind on a tree.

In Breughel’s Icarus, for instance: how everything turns away

Quite leisurely from the disaster; the ploughman may

Have heard the splash, the forsaken cry,

But for him it was not an important failure; the sun shone

As it had to on the white legs disappearing into the green

Water; and the expensive delicate ship that must have seen

Something amazing, a boy falling out of the sky,

had somewhere to get to and sailed calmly on.

W. H. Auden

It is cold comfort to be offered the permanence in the nature of gravity.  Looking at the poems from another angle,  I see that there are worse things than to be desensitized by arts. After all, having a susceptible heart  I need  all the help I can get to be inoculated against the rampant pain radiating from too many tragedies, both real and mythical.


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A Time To Measure

Posted by xbanguyen on August 4, 2009

Somehow the idea that we can measure a very small amount of time, a femtosecond for instance, really appeals to me. It does not matter that it is not I who can do the measuring. Paradoxically I also take pleasure in knowing that the electrons will go their own ways regardless whether or not they are used as the tools for such measurements. The idea that tiny particles are now going about their business in the void that is my body is compelling.  For me, time has often been a scarce commodity.  So it’s fitting to begin my first post this way. Rereading what I wrote pre-blog, my haphazard collection of essays and the overwrought poems  stuck in a directory somewhere on this hard-drive makes me think that I need to deal with time first and it won’t be the last time. So how do I deal with time? Why am I blogging now instead of sleeping? It’s past midnight here in my part of the world.

Let’s throw time into the soup made up of one part beauty and two parts faith (no, not that kind, perhaps later).    I’ve found that sometimes beauty shows up at unexpected places.  Take simulation waveforms, for example.  In my  work as an an engineer for  a company that makes medical devices, I often use waveforms to trouble shoot logic problems.  The waveforms are often green — I want to say chartreuse green because I like the word chartreuse, but it would not be accurate.  So they are green against the default black background.  Pages full of waveforms can weave themselves into striking patterns as I zoom in and out in search for clues.   There are always clues.  One has to believe in logic, with passion at times, that the causes that manifest themselves in a particular bug will be found even if it appears confounding.  At the same time one has to proceed with dispassion, methodically, to find the pesky thing.  And simulation waveforms are displayed in units of time, mostly nanoseconds.   How many nanoseconds has it been since Andrew Marvell wrote these lines?

But at my back I always hear

Time’s winged chariot hurrying near

Most of the time I forget about the amorous intention of the poet and only hear that relentless chariot  gaining on me.  But what would happen if it catches up with me?  What am I really afraid of?  That there will not be another summer as delightful as this one has been?  While I don’t disagree with Henry James that summer afternoon are the two most beautiful words in the English language, I think that summer morning are possibly better.  Just the potentials alone make it so.  The summer morning sky takes on such impossibly vivid blue that colors the coming day with a sheen of possibility.  Even the early summer morning air feels different, fresh with not only a hint of promises but also seductive with the certainty of promises fulfilled.  Get up really early tomorrow morning, stand in front of  the open window and breathe in deeply.  You’ll know what I mean.

Come to think of it, there is something melancholy about a summer afternoon, the charm of having a cream tea completed with cucumber sandwiches and scones notwithstanding because dusk approaches and with it comes darkness.    But what about the stars?  What about the scent of jasmine? What about the fireflies and other things of beauty that accompany twilight?  Perhaps I am missing the point while seeking an illusion of permanence.


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Poetry in Engineering?

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