When I was learning calculus, back in the dark ages, I remember having great difficulty grasping the very basic concept of “the slope of a point.” It sounded completely illogical, then and now. After all, didn’t Euclid define a point as having location, but not dimension (no length, width, or size). Without at least length, how can it have slope, which describes a direction (up, down, left, right, angled…)?

Well, calculus and its sloping points turn out to have lots of valuable uses. (I’d list them now if I could remember any.)

But I do recall the procedure for demonstrating and determining the slope of a point. It involves gradually vanishing “limits”. A limit (if I remember correctly, or even approximately) is the slope or angle of the smallest possible section of a graphed curve in the area of the point in question. You start with one inch on either side of the point, and measure the slope of that two-inch line between them. Then you repeat the process with half that distance, then keep halving it. Eventually, the series of those slope-measurements closes in on the slope of the particular point. Voila! Cool, no?

(Well, anyway, that’s how I remember it. If I have gotten it wrong, I hope some helpful mathematician or engineer or calculist will write a comment straightening me out. I’d hate to misinform my faithful readers.)

I said above that this all has many valuable uses, which I knew once long ago. But I have recently found a new one, for my prayer life.

Prayer takes place in time. We sing of the “Sweet Hour of Prayer.” We recite prescribed prayers (Ave, Our Father, Memorare, the Rosary, etc.); these prayers are of definite length in words spoken and therefore in time. Monks and nuns pray at specific times throughout the day.

But this implies that the rest of our time is spent in non-prayer. Many of us seek to increase our time spent in prayer. Extending prayer time of course reduces our non-prayer time. But is there another way to increase prayer by converting non-prayer time into prayer time (NPT into PT, as it were)? Continue reading