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.

[1] http://mathlab.math.scu.edu.tw/mp/pdf/S30N39.pdf
[2] http://www.yeatsvision.com/Geometry.html
[3]The Lindenbaum-Tarski image is from this site http://finitegeometry.org/sc/16/logic.html