by Warren Criswell

"Isn't it beautiful? Don't you think the beauty and symmetry of the
mathematics echoes that of the natural phenomena they describe?"
.........................................................................................(Page 9)

In those distant days before PCs and Macs and iPhones, before Steve Jobs gave us an app for everything, if you wanted to know how the world worked you had to figure it out for yourself. Some might call this reinventing the wheel, but how can you really know how a wheel works without reinventing it? So we did it the old-fashioned way--we learned it.

When I say "we," I'm referring to me and my friend Ray Durrance, whom I met in nursery school where we clobbered each other with wooden alphabet blocks and struck up a life-long friendship. (Ray is the other transient in Two Transients, the hero of The Gift, and the leader in Two Men on Stilts.) And so when in June of 1987 I received an urgent request from my friend to help him formulate a quick way to predict, without the help of a newspaper, sunrise and sunset in any given location, which he thought would impress women on an upcoming camping trip, I naturally answered the call of duty and sprang into action.

At least that was the way I remembered it until Ray read this and set me straight:

"Yeah, but you forget that we worked on that problem for almost a year, sending letters back and forth (no email then) filled with drawings, data from observations made at various locations, with hand-held compasses and wind-up watches."

He grudgingly concedes that "You were the first to finally derive a formula that worked. I have a note in one of my journals where I admit that it worked. But you didn't just pull it out of your ass the next day after we started - it was a long process."

He also corrects my memory of our motivation, saying that it was on a "higher level" than the one to which I attributed it. It was in the pursuit of pure knowledge, not carnal knowledge, and that if we hoped it would impress women, those women must have been our wives. We are both the same age, Ray and I, so I'll leave it to the reader to judge which old fart's memory has deteriorated the most. But I'm just saying … if Kepler had discovered the elliptical orbits of the planets to impress his girlfriend, would his achievement have been any less brilliant? Isn't it all a quest for beauty?...

We grew up in south Florida but now Ray was living in Michigan, where he was teaching library science at U-M and I was working in a print shop in Arkansas where our bus broke down. Ray and I had collaborated earlier on another astronomical project - determining the height and position of meteors during a Leonid shower - or a Perseid, I forget which - by triangulation, using the great circle segment from Ann Arbor to Benton as the baseline, synchronizing our sightings and using our fists to measure the altitudes (1 fist held at arm's length subtends 10 degrees of arc as every star-gazer knows).

At least that was the plan, and we were sure it would have worked if only the weather had cooperated. We have always considered ourselves authorities on any activity that we have discussed many times, even though we may not have actually done it. Like lancing wild hogs in the Everglades. "You've done that?!" someone would ask. "No, but we've discussed it many times."

So anyhow, the following is a copy of a letter to my friend in the form of a technical treatise summing up our months of research. It contains the christening of "Criswell's Triangle" and "Spiritual Trig" (which is a higher form of spherical trig). I'm sure it works as well today as it did in 1987, and though it may not impress women anymore, especially those with iPhones, it may still have some value on that higher plane Ray invoked.

Warren Criswell, 2011


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