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A Lesson In Practical Geometry

Ray Blain is a retired pediatrician and medical consultant, and author of a forthcoming autobiography Becoming A Doctor; My Dreams and Nightmares.

I have always loved mathematics from learning times tables in elementary school to algebra, calculus and geometry in high school.

One of the first things I learned in geometry was that the shortest distance between two points is a straight line. This simple rule became more complicated when I learned in college that space is curved, so the straight line we draw on any surface is really slightly curved in space; a true straight line is only imaginary.

In my curious mind that raised the bizarre question of what is the longest distance between two points. One possibility is that it is the distance from one point around the entire universe until it finds the second point — assuming the universe is a like the surface of a ball. Believe it or not, I had discovered a simpler answer as a teenager on a trip up the Quaboag River in Massachusetts between Brookfield and Quaboag Pond.

My older brother and I loved to canoe. We had both been Boy Scouts. Bob learned to swim like a fish and I swam like a rock. We didn't use life jackets in those days so we usually picked narrow rivers in our state or stayed close to shore in larger bodies of water and avoided any rapids or stretches where we knew there were dams.

We were able to borrow a wooden canoe from our old friend and Scoutmaster. We always used a wooden craft because, even if filled with water, it stayed near the surface unless overloaded with cargo. As long as I was with the canoe I would be safe if any mishap occurred. I don't know what the Quaboag is like now but 70 years ago it was a scenic, gentle waterway with several long curving stretches as it approached the pond.

We parked the old, black, stick-shift Chevy in a small area with trees off highway 148 near the bridge over the river just before reaching the outskirts of Brookfield. We lifted our very heavy transportation off the roof of the car, loaded our supplies, and launched the canoe into the beautiful slowly flowing water. The pleasure of riding in a canoe under idyllic circumstances is hard to describe in words.

Several of our ancestors were Huron, Algonquin and Mohawk First Americans from south-eastern Canada and the New-York/New England area. They used wood and birchbark canoes as their principle water vehicle. We were experiencing the joy they must also have felt voyaging in and enjoying nature at its best.

We made excellent progress upstream for the first miles of passage. Then we came to the flat swampy area of the curves. The areas between the water channels were inhabited by mounds of grass protruding above clear water. It was probably near noon by this time so we decided to take a shortcut through the grasses so we could find a place to stop and have a brief lunch at the pond in the distance.


The passage was slower, but the distance much shorter, so we were optimistic and overconfident as teenagers sometimes are. The grass mounds had different goals. They became closer and taller as we proceeded, sometime rising four to six inches above the water. The mounds became too congested for us to get out and push. We were about mid-point by then.

There was nowhere to turn around, so our fate was sealed. In order to advance toward the river channel that lay ahead we had to use our paddles to push against the grass mounds and even downward to decrease the friction. After hours of hard work we again reached open water and moved rapidly toward the pond since darkness was rapidly approaching. We came to a small beach area on the right but decided it was too open for a campsite. At dusk we found a wooded area further on with sufficient coverage, so we beached the canoe, put a tarp over a patch of foliage, spread our sleeping bags, and fell asleep.

Morning arrived to find us on a tarp spread over a patch of poison ivy. The tarp saved us from contaminating our sleeping bag and skin surfaces. We exited as carefully as possible, sat by the canoe, had a cold breakfast, loaded our equipment into our craft and started the return trip. As we passed the beach that looked so inviting on the way in, we saw it occupied by a group of cows munching grass or drinking pond water. What a surprise that would have been if we had slept there.

We followed the river down stream around all its bends rather than challenge the grass clumps to another dual. As we started to lift the canoe onto the car roof I made the remark that our trip through the swampy grass had answered my question about the longest distance between two points — it's the short cut. We laughed so hard about this insight that it took several attempts before we got the canoe in place, tied it down, and drove away.

It is a lesson that I have never forgotten. If a shortcut is really the shortest or easiest way to get from here to there or to complete a task, intelligent people would have already made it the most traveled route before I got there, with only rare exceptions. Avoid short cuts and avoid unnecessary harder work or peril. I still avoid this longest distance between two points in life whenever possible.

~ Raymond Leo Blain, M.D.















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