Calculus – the Math of Change

A lot of people are afraid of math.  That’s too bad because math is the language of God and when He spoke creation into existence, His thoughts were mathematical as He ordained the laws by which our universe would abide.  Since God wants each of us to have a relationship with Him and to enjoy Him, He left His mark throughout creation.  Not only do we have the Bible, but we also have a code for the order He established that underpins everything – mathematics.  Hebrews 1:3 tells us that God upholds all things by the word of His power and this is precisely why math works.  If the universe ran by inconsistent laws, math would not work.  The same laws of physics that work here on earth will work on planets far away and those laws are described by mathematical equations.  Truth is truth no matter where it is revealed.

One branch of mathematics called calculus treats change in physical systems.  Rates of change include things like velocity and, in fact, if you’ve ever said “At this rate”, you’ve already used the math of change in your daily language.  Calculus is the mathematics of change.   Motors and engines exploit the principle of magnetic induction which is described by calculus equations.  Economists use calculus for optimizing cost functions and musicians rely on DSP techniques to create music which is all based on calculus.  Simply put, things change and we need rigorous methods to describe those changes.

God’s attributes are continually demonstrated in the physical realm because His image is imprinted on all of creation.  God does not change and we see this mirrored in the law of conservation of energy and the consistency of elemental matter throughout the universe as well as the constancy of the laws of physics everywhere.  God does not change.  But we are not like him and we do change.  Everything that is, or was, created changes.  He ordered all things such that change can be managed and predicted.  The unchangeable one codified the treatment of everything that is not like Himself – the mathematics of the mutable.  Imagine for a moment that you’re driving in an accelerating car.  If the velocity is increasing linearly, the acceleration is a constant value.  A mathematician would say that the derivative of linearly increasing velocity is constant acceleration.  If your velocity is constant, then its derivative is zero because there is no acceleration.  When there is no change, the derivative is zero.  Because God does not change, the derivative of His attributes is always zero.  Another type of change is turning or spinning.  Things in nature which turn will always have nonzero derivatives.  When you turn your car, things slide toward the far side door because your direction is changing.  Any curve has a nonzero derivative and only things that are straight don’t vary.  The derivative of straight-line motion with constant speed is zero.  God doesn’t change His path or pull a 180 on us.  He decreed His will at the creation of the world and has moved without changing ever since.

Calculus also brings the infinite together with the infinitesimal.  It is used to calculate areas under curves by imagining the insertion of many skinny rectangles underneath those curves since we can easily find the area of a rectangle.  Like a puzzle, calculus tries to match rectangles of differing height to the curve and the approximation gets better as the rectangles become skinnier.  As the width of each rectangle tends toward zero, the number of rectangles tends toward infinity and the approximation becomes exact.  The height of each rectangle is the value of the function at each point, and if you multiply the height by the infinitesimal width, you get the area for each rectangle.  Sum these all up and you have the area under the entire curve and that is integral calculus.  Calculus requires taking the limit to infinity and zero simultaneously.  God is infinite and exists in the realm of limits.  Imagine trying to be holier than any living person.  You might achieve it, but still miss the holiness of God by an infinite gap.  God is infinite and we are finite.  Calculus enables manipulating quantities that change, with limits tending toward infinity.  We cannot achieve infinite holiness or righteousness – we need the Savior, Jesus Christ, who is perfect and is the exact representation of our Heavenly Father.  No matter how hard you try on your own, you will never match the limitless holiness of Jesus Christ.