Why an Elephant?

The distorted impedance diagram, shown on this page, was intended to resemble an elephant, and, in doing so, evoke the lessons of the Buddhist tradition of the blind men and the elephant. The multiple loops resemble the Nyquist plots obtained in some cases for the impedance of corroding systems influenced by formation of surface films. The low-frequency inductive loop was deformed to evoke the image of the elephant’s trunk, and the capacitive loops resemble the head and body of the elephant.

The elephant has become a symbol for our group. I chose the elephant logo when I was organizing the 2004 International Symposium on Impedance Spectroscopy. Members of our group have even defined a constant-phase elephant (a bad pun), which is deployed in the second edition of our book on electrochemical impedance spectroscopy.  The elephant on the Video Room page was drawn on our lab blackboard by my student, Ming Gao, as a welcome to prospective graduate students.

Impedance spectroscopy is an application of a frequency-domain measurement to a complex system that cannot be easily visualized. The quantities measured, e.g., current and potential for electrochemical or electronic systems and stress and strain for mechanical systems, are macroscopic values that represent the spatial average of individual events. These quantities are influenced by the desired physical properties, such as diffusivity, rate constants, and viscosity, but do not provide a direct measure.

The point is that every experimental measurement we use gives us one view of a system. From the results of this measurement, we can develop a model of the system under investigation. Our confidence in the validity of the model can be improved by performing new observations of the system, often guided by the model we developed. Impedance spectroscopy is a powerful tool, but the elephant reminds us that impedance spectroscopy is not a stand-alone technique.

As a grade-school student, I learned the poem by John Godfrey Saxe (1816-1887) based on the the Buddhist parable of the blind men and the elephant.

The Blind Men and the Elephant
John Godfrey Saxe

It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind.

The First approached the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
“God bless me! but the Elephant
Is very like a wall!”

The Second, feeling of the tusk,
Cried, “Ho! what have we here
So very round and smooth and sharp?
To me ’tis mighty clear
This wonder of an Elephant
Is very like a spear!”

The Third approached the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
“I see,” quoth he, “the Elephant
Is very like a snake!”The Fourth reached out an eager hand,
And felt about the knee.
“What most this wondrous beast is like
Is mighty plain,” quoth he;
“”‘Tis clear enough the Elephant
Is very like a tree!”

The Fifth, who chanced to touch the ear,
Said: “E’en the blindest man
Can tell what this resembles most;
Deny the fact who can,
This marvel of an Elephant
Is very like a fan!?”

The Sixth no sooner had begun
About the beast to grope,
Than, seizing on the swinging tail
That fell within his scope,
“I see,” quoth he, “the Elephant
Is very like a rope!”And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!

So oft in theologic wars,
The disputants, I ween,
Rail on in utter ignorance
Of what each other mean,
And prate about an Elephant
Not one of them has seen!