In mathematics, there is a ladder of difficulty, ascending from one subject to the next. Discounting geometry, which kind of lives in a world of its own, the ladder ascends as follows—arithmetic, algebra, trigonometry, and finally, calculus. In the world of calculus, however, something strange happens. The ladder dips into the clouds, and enters the world of the infinitely big and the infinitesimally small. Let me explain.
Suppose I drew a serpentine curve on a big T-shaped grid, and I wanted to know the amount of area bounded by that curve and the two dark lines called “axes”. Can you picture it? See the serpentine curve slither across the page? Beneath it, do you see one dark line lying exactly flat across the middle of the page, and another dark line lying exactly up-and-down through the middle of the page? The lines box the area in, while the curve forms its curvy top.
Question. How would I measure the area? After all, it is not a nice shape, like a square or something, which has a nice little formula for calculating its area. If only it were squared off! Then we could multiply the length by the width and know the area for sure.
Here is where we start applying calculus. Let’s divide the area into rectangles of equal width. The height will vary, depending on how tall the curve is at that point. Good. Now we calculate the areas of all the rectangles and add them up. The answer will not be perfect, but it will be close.
Now, let’s do those steps again, only with the width of each rectangle cut in half. That will double the amount of rectangles we have, and it will also give us a more accurate approximation of the area.
But why should stop there? Cut the width in half again! And again! And again! And pretty soon, the width will start to approach the infinitesimally small, while the number of rectangles will start to approach the infinitely big. That is calculus. And it works.
But it is weird.
Earlier we pictured a curve and two axes. I can do that. But how can I picture a rectangle with a width of zero? A width of zero is a line, and a line has no area—yet somehow, when we add up all these lines with no area, we get the exact area under the curve. Welcome to the world of calculus, where the infinite messes with our minds.
The apostle Paul tells us that Moses used to put a veil over his face to hide the shame of his departing glory. Do you remember? As Moses conversed with God, his face would be begin to glow; but it would not last. It was truly a glory, but it was a fading glory. Christ, however, does not have a fading glory. His glory remains. Therefore, in comparison to the glory that remains, the glory that fades has “no glory” (2 Corinthians 3:10).
Is that claim a true statement? Did Moses have “no glory”?
Answer. He had “no glory” in comparison to the glory that remains.
What do you get when you double an infinite amount? Do you have any more?
What do you get if you take away several million? Do you have any less?
Infinity is infinity—endless is endless—whether I double it or take millions away, it is still the same.
Therefore, given that the millions did nothing, in light of infinity, the millions are nothing.
Moses had glory, but it was temporary. Christ has glory that is endless. If we try to do arithmetic here, adding the glory of Moses would add nothing to the glory of Christ, and subtract would also take nothing away. Therefore, in light of the endless glory of Christ, the glory of Moses is nothing. No glory.
And Christian, if the divine glory of Moses was “no glory” in comparison to Christ, then all our little medals, and little diplomas, and little championships, and so forth are even “less than nothing,” to borrow a phrase from Isaiah, for our medals, awards, diplomas, and championships are merely human glory. They can’t even make my face glow.
It is this thought that really intrigues me: If I should achieve anything on earth, it is a truth for me to say, “It is nothing. It is no glory.” I would be speaking the truth, and not simply feigning a false humility. I would no longer be thinking in terms of arithmetic. I would have ascended into the calculus of glory.