The Value of Abstract Thought

September 10, 2024
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October 1, 1915

“How did you pick up this job? When did you learn to land survey?” I asked du Bois.

“My last year of school. I’m good at math, trigonometry, geometry and such. My instructors insisted I try it for a trade. It came easily and apparently there is a surveyor shortage in Steamboat Springs.”

“I hit the math wall at calculus,” I confessed.

“Oui, abstract though is necessary but mostly it is learning the tricks of math.”

“How so?”

“What’s the sum of all the numbers from 1 to 100?”

“I don’t know. I would have to figure it out with pencil and paper.”

“The trick is 1 plus 100 is 101 and 2 plus 99 is 101, 3 plus 98 is a 101 and so on for fifty pairs of numbers. So, fifty pairs times 101 equal 5050. That’s a famous calculus formula.”

“By golly I’ve got it. One plus 10 is 11 times five pairs equal 55.”

“Indeed, it will work for any continuous sequence of paired numbers.”

“What happens with an odd group of numbers like 1 to 9?”

“That’s why we have zeros.  zero plus 9 equals 9, you still have five pairs times 9 equal 45.”

“I’m glad I got out of bed this morning. I learned a math trick.”

“More importantly, you realized abstract thought,” du Bois chuckled. “Apply it to solve the problems of life by coloring or thinking outside the lines. Find your trick.” He turned the transit to check his back site, set the cross hairs on it and then turn the instrument one hundred and eighty degrees. “Julius, help me measure out one hundred and fifty feet and pound in this wooden stake in the ground. That’s the next corner of this Yahmonite lot.”

We measured and I put the stick to the ground. He looked through transit telescope. “It needs to go to your left to be on the lot line. Oh, too much, back a bit, good there, pound it solidly in the ground.” He rolled the measuring tape back onto the reel and walked to me saying, “JJ only wants the money, a concrete thought. Corina wants freedom and justice, abstract thoughts. Julius won’t eat his peas, he thinks he doesn’t like them, but he tries a bite and discovers he loves them. You can’t measure love.” He held the tape with both hands, “You have to feel it.”

Arthur, du Bois’s work partner returned from relieving himself in the bushes. “Hey, are you trying to take my job?” he joked.

“No, Arthur he’s just learning to be abstract. Next, he’ll learn the difference between accurate and precise.” They both laughed. I gave du Bois a questioning glance. “Precise is exactly on the nose. Accurate is measuring to get close and perceiving how near you need to be to someone,” he paused for effect, “or something.”

Arthur looked at the stake saying, “Relax Julius, if you work more with us, you’ll pick it up quick enough.

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