Last week I referred to some horse barns that the family construction company built in the 1960s. I made a guess bout the size of the barns, but invited The Main Cheese to weigh in regarding the accuracy of my estimate. Here is his response:
“…today I have taken some time out of my busy schedule to try and estimate the size of and the number of block to build those five barns. Like you, I have always visualized them to be @ 100′ by 25′ or so. Now I’m thinking bigger. I’m thinking the depth of a horse stall had to be 10′ and the width at least 8′. The width of the aisle down the center had to be 10′ to 12′, I’m trying to visualize that. 10 stalls plus a tack room on each end at 8′ each plus 8″ for each of the 11 dividing walls adds up to almost 104′, so we’re close there. I went to the Internet and zeroed in on the barns and tried to get a sense of the proportions that way, even used a ruler. So I’m saying 104′ by 32′ by 8′ high by another 3 courses of block below ground =roughly 5500 block per barn…. What was even more fun was the construction of the clubhouse, where 8″ by 12″ by 16″ block were used: a bit heavier if you remember.”
The Main Cheese was the guy I worked for from about age 13 during summer breaks and school holidays, through college, and then for 9 years after college. Also known, of course, as “Dad.” I think my brother came up with “The Main Cheese” thing.
Now, Dad’s calculations are typical of something that is simple, but rather difficult to express. You see, when one’s livelihood involves making something tangible, that has to have certain functions and be composed of specific materials and occupy a defined space, you get rather caught up in the whole enterprise of what Tom Sawyer and Huck and Jethro Bodine called cipherin’. I did not have many difficulties with cipherin’ until 9th grade, when they introduced a unit that truly was a cipher to me: X. Formulae involving X were the darkest of mysteries to me. It did not help that the algebra teacher (here I use the word to describe his role, though not his profession or metier) was an arrogant egotistical lout, but we’ll make that the subject for some other day after I’ve elucidated the entirety of all the world’s myriad wonders and glories.
When one’s job involves carrying about half of those 5500 30-pound blocks of concrete (younger bro’ did the other half), you start thinking a lot about how things that are 8″x8″x12″ stack together into that specific shape and function of a horse barn. That’s about the most simple form of practical geometry there is, and people seemed to have figured out stacking bricks to make buildings just after they found out that certain rocks could be sharpened for greater effectiveness against big fast animals loaded with tasty meat. (labels read: “Flint has been shown to be an effective, hunger-preventive mechanism when used in a conscientiously applied program of stone-working and regular hunting practices.”)
Once you get to the roof of the barn or any roof, the geometry gets more involved. You’re going to cut wood of certain dimensions with appropriate angles at either end to join together to make the roof at a specific angle. If you want a roof that’s going to be 16 feet to the center, using the Cheese’s figure, and it’s going to have a pitch of 3 feet in every twelve, it’s going to be 4 feet tall in the center. So, now you get to figure the angles at each end to complete the hypotenuse of a triangle that has vertical and horizontal limbs of 4′ and 16′, respectively. Kazango! Algebra! If you do that sort of thing for enough times (and in a 104′-long building, with roof trusses every two feet, you’re going to do it about a hundred times, given the two sides to the building), algebra starts to be less of a mystery and more of something you live with. It’s experiences like this that turn people into engineers.
Now, I know for a fact that the same fascination with this still-simple geometry and algebra took hold of my grandfather, too. He was still in charge of the family operation in those days, and I’m pretty certain that it was on this same job at the fairgrounds that he first told me one of his favorite stories. I was cutting some of those angled ends for rafters and he asked me if I was certain that was the right angle. He told me that when he was a kid, working for his father, he had just “mastered” geometry, figured out the angles for a roof and cut a whole lot of rafters, confident in his measurements. When they hauled them up and started putting the roof together, they were several inches too short. He loved to tell that story, probably because my great-grandfather never let him forget it.
The ultimate, unforgettable advanced geometry lesson I ever saw in action was also at that same fairgrounds, a couple of years later. The fairgrounds had a half-mile horse track. They wanted to widen the home stretch, and that meant moving the inner rail over toward the backstretch, and recalculating the curves and redoing all the posts and railings (which were highway guardrails: this was a harness track): hundreds of holes to be dug, posts set, and guardrails reattached. Before that could happen, Dad and my grandfather had to calculate those new curves of the rail along the two 180-degree turns. So there, in the humid July sun, standing in the infield, I listened to them discuss whether they would determine the center point of a circle and project a regular circle of a certain radius, or whether — as my grandfather maintained — there was a logarithmic calculation that would give them a simpler method. For a kid still wrestling with a-squared plus b-squared equals c-squared, this was mind-blowing. (I happen to know I was just about to turn 16 that summer, because, being on an empty horse track, having to move the equipment along the half mile of railing, I sometimes got to drive my grand-dad’s 1950 Chevy pickup with the footswitch starter, one of my first driving experiences.)
I wish every kid laboring in that terrible pit of toil, facing that elusive, damnable “X” could have the same chance I did, though: to be able to go somewhere that the reason for even knowing how to solve for X matters, and then to get a living, visceral demonstration of how it’s done. It would also be nice if one didn’t have to carry thousands of heavy blocks or saw several thousand pieces of wood, but maybe that’s part of the magic.
And if every kid could have something like my experience of standing out in the infield of that racetrack, watching the Old Guys do something I could barely understand, then everyone would be rich.