Edit: 02/24/2011, to make a point about path integrals more plain.
Even though Calculus was not “discovered” until the late 17th century by Sir Isaac Newton and Gottfried von Leibniz, there is one verse in the Bible that makes a very excellent point in biblical and mathematical language that I would like to share for two reasons: 1. It’s sufficiently nerdy to have escaped common attention. 2. I have an odd interest in areas where seemingly different fields connect. So, here goes.
James 1:17 says: “Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom there is no variation or shadow of turning.” There are several possibilities about what is meant by the enigmatic phrase “shadow of turning,” as some have suggested that this refers to the orbit of heavenly bodies , which I consider at least a possible, if not certain meaning. Given that I do not believe the Bible only has one layer of meaning, though , I will discuss a mathematical meaning for this verse.
Let us begin with the assumption that as God is the ruler and creator of all things that this includes mathematics. If we concede that among the good gifts that God gives and part of the “light” of illumination that He provides is an accurate understanding of mathematics and its implications, let us then examine the mathematics and implications of this particular verse.
First, to say that there is no variation with God is to say that the dGod/dt = 0. That is, the derivative of God over time is constant. God does not change change with time–he is the same yesterday, today, and forever (Hebrews 13:8). As this very quote is stated in scripture, it is an accurate biblical statement expressed in the language of calculus.
Second, though, there is no “shadow of turning” with God. If we take variation as the first derivative, it would make the “shadow” of turning the second derivative. In other words, dGod^2/dt^2 = 0. This is an important mathematical statement for a few reasons. For one, the derivative of a function equals 0 at either a minimum, maximum, or inflection point, but additionally stating that the second derivative is 0 means that God is a straight line, completely level, with no change at any point in the existence of the universe. This is a very profound statement–a nerdy one to be sure, but profound nonetheless.
Another option, of course, is described in the article cited below  and states that the “shadow of returning” refers to rotation, which would make the dtheta/dt = 0, and would make the first derivative of both the path and the standard integral equal zero. At this point I am reminded of the difficulties I had understanding the subtleties of Green’s Theorem when I studied Calculus as an undergraduate engineering student, but this would similarly mean that God was without variation, regardless of how it is measured over time. In short, God is level–however one defines it.
The fact that God is “level” has a lot of implications. For one, it means that God is completely fair and just and consistent–something that may not be readily obvious in the fallen and corrupt world we live in but will be made very plain in His judgment. Furthermore, his standard is a just and a fair one, not an arbitrary one as is the case with mankind. God does not play favorites, but both merciful and fair. That’s a mathematical truth we can all feel joyful about.