A Transformation In Green

Is it possible to reinvent yourself  from the same past? Is there a certain sheath of light you can put on to  fashion the rearranging of the molecules within to emerge anew, sporting a re-engineered memory filled with assured joy? Would you rather be a sojourner, a guest in many cities or to put down roots in a familiar place? Can you be both? Looking at the other face of the same coin, can desire alone forge the necessary transformation? Most likely not — you may have to make do with knowing that a certain kind of transformation is possible, mathematical transformation, that is. So tonight I will attempt to assuage the ghost of Jay Gatsby by considering the Laplace transform that provides a means to traverse between time domain and frequency domain.

 Ordinary engineering phenomena such as the switching transient in a RLC circuit and the harmonic vibration of a beam can be described using linear ordinary differential equations where inputs and outputs are functions of time. Converting these functions into frequency domain where inputs and outputs are functions of angular frequency using the Laplace transform make them easier to solve. Instead of calculus,they can be solved by algebra.  Such transformation is possible as long as the function satisfies certain Dirichlet conditions. ^[1] 

The precision found in mathematics possesses a certain beauty. Equally appealing is the certainty conveyed in those equations. If a set of conditions are met, at least one solution for the equations exists. If I planted red tulip bulbs this past November, the borders will be ablaze with colors comes spring. An adverb describing the motion of the pomegranate flower at the entrance to a walkway in a poem read many years ago in Vietnamese never fails to make me fall hard all over again for all the poems ever written in any languages.  One should be thankful for such constancy because it escapes being transformed by time, for not all transformations are to be desired, and we are not in control as this poem ruefully points out.

The opposing force twisting down the upward course of a wayward vine reminds me of Dylan Thomas’s poem of the green fuse that drives the flower.  The extreme adjectives describing the hope coursing within the vine carry an optimism that belies the bleak soundings. That vine some day will transform again back into a root from which a new plant will emerge , the resilient seeds sown in soil once wanted will form another Eden. All you have to do is to sow a seed or two, and to be indulgent of yourself. Would you give up being in control for the pleasure of being enthralled by a resolute Eden?

Thank you for listening, dear muse.

Acknowledgement

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[1] http://sces.phys.utk.edu/~moreo/mm08/sarina.pdf.

[2] The globe is from Google Earth.

[3] The village picture is from www.overseasattraction.com .

[4] The RLC circuitry and equations are from http://www.ee.ic.ac.uk/pcheung/teaching/ee2_signals/Lecture%206%20-%20Laplace%20Transform.pdf and http://www.mathworks.com/help/toolbox/symbolic/f1-122819.html www.heritage-key.com.

[5] The tulip painting is from http://www.etsy.com.