Pi day is March 14^{th} and nerds relish this day every year. Kids afraid of math must feel about pi day the way I do about dentist day. I try to have as few dentist days as possible. When I was a kid, the pi symbol on my dad’s expensive Texas Instruments calculator looked like some kind of alien hieroglyphic. My dad had special knowledge I suspected most everyone else lacked – he knew what that button was for and he even used it sometimes! It’s a very important number indeed, that little line resting atop two vertical sticks. I would later learn that pi is irrational and transcendental. Those are fancy words to let you know that smart people have thought a lot about this little number, and when you stop using numerals and start using Greek letters, you have to start using words like that. The exact value of pi is between 3.140 and 3.142 but has an infinite number of digits after the decimal point. Some have memorized pi to thousands of digits but most just remember that pi is approximately 3.14.

Pi is ubiquitous yet inscrutable. It defies our understanding with its infinite number of digits yet it pops up everywhere and describes such a simple thing – the ratio of a circle’s circumference to its diameter. Pi, written as π, is not the only famous constant. There are other intriguing numbers and they all show up in a single rock star of an equation:

The quadratic formula is quite pedestrian compared to this venerable goliath. It contains two transcendental *and* irrational numbers (e and π) , a complex number (i), and the number zero. Its simplicity is profound, but you will likely wait until calculus before learning what it means. Elegance here doesn’t mean easy. God is inscrutable. We can never fully know Him or comprehend Him because He is infinite while we are finite; His thoughts are far above ours. Yet the Bible is clear in all essential matters pertaining to salvation. This is the doctrine of perspicuity – that the Bible is clear in the important areas, though not all passages are easily understood. Frankly, a lifetime of study will not yield a complete understanding of predestination, creation ex nihilo, the atonement, or end times. Even a child can understand sin and redemption if explained in simple terms. The gospel is for all – the simpleton and the genius. Pi is used by children to find the circumference of a circle while also making an appearance in much more sophisticated math – in Cauchy’s integral formula used in complex analysis (which is the theory of functions of a complex variable) for contour integration. It shows up in Einstein’s equation for his theory of general relativity as a coefficient of the stress-energy tensor. Probability and statistics rely heavily on π in the Gaussian distribution.

Even the numerical value of π, apart from the esoteric role it plays in math and physics, is not easily understood. It is irrational and transcendental. That doesn’t mean it throws childish temper tantrums and meditates; rather, it cannot be expressed as a ratio of integers (positive or negative whole numbers) and it is not a root of any algebraic polynomial. It is fundamentally different from a number like 3 or 10 or -20. Pi is 3.14159…and never stops. If I divide 27 by 9, I get 3 and the number three stops. There are no two integers for which the ratio yields π. In algebra you might remember solving quadratic equations for x. You were finding roots of the equation which are the values of x where the function crosses the x axis. You likely found all kinds of roots like 3 or the square root of 27 or even an imaginary number like 3i, but you never got π in those solutions. That’s because π is transcendental. Pi is set apart. It’s like mathematics’ own sanctified number, separate from all other non-transcendental numbers. It has some brethren, like e, the Naperian logarithmic base, but π is very special. It’s a little teaser of God’s transcendent nature, ubiquitous in nature and even a child may understand its use for a circle, yet if you want to go deeper it will take you years and years to exhaust the depths of π in nature. Math is the language of God who hints at His nature with this special little number. It’s as if He’s saying “I’m everywhere but you will never fully comprehend Me!” A supercomputer managed to compute π out to 62.8 trillion digits but the digits keep going. There’s even a word for memorizing π to a large number of digits – piphilology, and the current record is 70,000 digits! No pattern has yet been found; the digits of π are random. We are drawn to things that are profoundly different and set apart. Piphilologists see something worth their obsession to memorize thousands of digits. God is holy and completely different than anything or anyone else. He transcends our ability to comprehend Him. His gospel message is simple to grasp, as the ratio of circumference to diameter, yet you can study weightier doctrines your whole life and still make new discoveries about God. Pi is a whisper of this truth. Love math for what it is – the language of God, and appreciate little numbers like π that whisper *God is altogether different and set apart*.

Thanks Steve for another enlightening post!