The Square Root of Minus One

August 13, 2009 at 10:46 pm

As an engineer, I have a particular fondness for mathematics.  Indeed, Calculus and Differential Equations were required for my Bachelor’s Degree and I took additional math courses “just for fun.”  Math is the means by which humanity expresses our understanding of the universe.  Abstract symbols and equations simulating physical attributes of the real world are the very basis of science.

Still mathematics isn’t perfect.  Einstein once stated:

“As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality.”

Or as I like to put it: “Reality trumps math.”

Most of us remember back in grade school when we learned about positive and negative numbers.  The rules were simple:

positive x positive = positive

negative x positive = negative

negative x negative = positive

A little later we learned about squares (22 = 4, 32 = 9, 42 = 16, etc.) and square roots (√4 = 2, √9 = 3, √16 = 4, etc.).

Taken together we learned that you cannot have a square root for a negative number.  Here enters i, the imaginary number.  i = √-1.  It violates all those rules we learned about positive and negative numbers, but here’s the catch:  it’s really useful.

In fact, i is downright required for many scientific disciplines like vibration analysis, control systems, electromagnetism, quantum mechanics and more.  But it breaks the rules! Yes, but those rules are based on our modeling system, not reality.

So when I am told that God is just my imaginary friend by some Richard Dawkins’ acolyte as a taunt to my faith, I agree with them.  He is my imaginary friend, just as i is an imaginary number.  In either case, “imaginary” does not denote incorrect or irrational thought, but instead expresses our limited comprehension of reality.

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