An Engineer's Literary Notebook

Exploring the real and surreal connections between poetry and engineering

Archive for the ‘Yeats’ Category

A Geometric Diversion

Posted by xbanguyen on June 6, 2010

If one fine morning you were to find yourself alone in the Louvre’s Salle des États facing the Mona Lisa without the bulletproof glass, would you fall under her spell?  But this is Seattle, not Paris, and all I have in front of me is a digitized version. Nevertheless,  those eyes still beckon. Looking at the curves of her face and the subtle way she turns toward me, I have to step back to realize that everything I see was geometry.  Aerial perspectives were used to create the illusion of space and distance on a two-dimensional canvas, and Leonardo DaVinci applied them with such masterful precision that the result is an enduring artwork.

As a part of me works out the strategy of superimposing a series of lines, rectangles and circles upon the painting to reveal the geometric structure beneath, the other part of me delights in the luminescence of her eyes and the seemingly unfathomable depth within.  The visual pleasure offered by things of beauty complements the analytical appreciation. It has been said that geometry is the field of mathematics whose main source of intuition is human visual perception [1], and mathematically speaking, linear algebra is to geometry as boolean algebra is to logic.  If harmony can be found in the link between mathematics and arts, then it is not surprising that the ability to scientifically represent 3D images had been contemplated by one of my favorite poets, Yeats [2].

What of the geometry of intangible things? Does happiness have a shape? Does sorrow? These questions occurred to me as I came across this poem of Young Smith and felt an immediate affinity.

She Considers the Dimensions of Her Soul

(Mrs. Morninghouse, after a Sermon Entitled,
“What the Spirit Teaches Us through Grief”)

The shape of her soul is a square.
She knows this to be the case
because she sometimes feels its corners
pressing sharp against the bone
just under her shoulder blades
and across the wings of her hips.
At one time, when she was younger,
she had hoped that it might be a cube,
but the years have worked to dispel
this illusion of space. So that now
she understands: it is a simple plane:
a shape with surface, but no volume—
a window without a building, an eye
without a mind.
Of course, this square
does not appear on x-rays, and often,
weeks may pass when she forgets
that it exists. When she does think
to consider its purpose in her life,
she can say only that it aches with
a single mystery for whose answer
she has long ago given up the search—
since that question is a name which can
never quite be asked. This yearning,
she has concluded, is the only function
of the square, repeated again and again
in each of its four matching angles,
until, with time, she is persuaded anew
to accept that what it frames has no
interest in ever making her happy.

Young Smith

It’s best to avoid pondering about said affinity.  Let’s just be content with the lyrical stoicism found in the poem and accept the recurrence of the four angles to find solace in the perfection of their equality. At times,  when contentment is elusive, Emily Dickinson’s playfulness is comforting because “To make a prairie it takes a clover and one bee,/-One clover, and a bee,/And revelry,/The revelry alone will do/If bees are few.”

Thank you, dear muse.

[3]The Lindenbaum-Tarski image is from this site

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A Certain Uncertainty

Posted by xbanguyen on February 15, 2010

So I thought I would cross the bridge to write a poem.  It was hard.  The unadorned volumes of e.e cummings, the gilded spines of W. H. Auden’s Collection, the frayed fabric of Rainer Maria Rilke’s works on my bookshelves stood patiently as if to reassure me but failed to impart any help. It was like gazing at the  glass cases in  a Parisian pâtisserie.  I can first admire then devour those delectable concoctions with aclarity and pleasure but can never make them, no matter how many Jacques Pepin’s cookbooks are strewn in my kitchen.  Truly the sensation I get when reading certain poems are physical.  I  remember writing to my English professor to explain that I could appreciate but could not create some years ago.  Alas, it is still true. I know full well that there are no equations that, when properly applied, would produce a poem.   Rhythms and meters are recourses but using them, or not, effectively requires something elusive.  I did try. My logical mind took over as soon as I put down one sentence and insisted that it had to be, well, logical. Unfortunately it was also stilted.  I had wanted to reach back to collect the shivers that ran through me as I read Emily Dickinson’s “A Certain Slant of Light” and saved it in another poem.  However, that desire itself is not born of logic so why apply logic to fulfill it?   For this reader, what makes poetry compelling is the perception of its uncertainty and the elements of surprises as the words turn.  Paradoxically, some poems  also offer the certainty of the beauty evoked by the images they convey. Consider the following lines.

I will arise and go now,
And go to Innisfree,
And a small cabin build there,
Of clay and wattles made;
Nine bean rows will I have there,
A hive for the honey bee,
And live alone in the bee-loud glade

W. B. Yeats

I can always count on the melancholy pleasure evokes by reading that poem even when I am uncertain why it is so.   At the same time, I can always count on the certainty that when a block of VHDL code simulates without errors and passes timing, its synthesized version will function correctly.  But is it truly a certainty? Perhaps not always. In fact, uncertainty is not only abound in poetry, but also in science and engineering.  The Heisenberg uncertainty principle states that at any point in time,  pairs of properties of a particle can not be known exactly – for example, the more precise its momentum is known, the more uncertain its position is.  In other words, “When you say that the electron acts as a wave, then the wave is the quantum mechanical wavefunction and it is therefore related to the probability of finding the electron at any point in space. A perfect sine wave for the electron wave spreads that probability throughout all of space, and the “position” of the electron is completely uncertain.”

I appreciate the irony of finding the word inescapable during this brief excursion into the realm of quantum physics.  There is an air of human resignation in this word that makes me feel a kinship to all engineers and poets.  The desire — more than that, the need to be certain must be the driving force in much of engineering work.  And yet, the measured acceptance of uncertainty is also a necessity. The duality of such realization accentuates my enjoyment of these stanzas from Mariane Moore’s Nevertheless.

The weak overcomes its
menace, the strong over-
comes itself. What is there

like fortitude! What sap
went through that little thread
to make the cherry red!

Acknowledgement: Information and waveforms describing the Heisenberg principle was from this site:

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