Nonlinear Transformations: A Well-Rounded World
Nathan Kimbrell has found purpose and direction from studying math while incarcerated. He hopes to pursue a graduate degree in the future.

I have been part of a pretty cool program for nearly two years now. It allows me to have these things called extended family visits. These take place in a duplex on the compound. Every other month or so, my family comes to spend an entire weekend with me. These are great!
It is the same crew every time. I look forward to my mom’s home-cooked meals. There is never a dull moment when my stepdad is around, too. My little brother and my daughter are only a year apart at 15 and 14, so the teenage shenanigans only cease when they leave. Of course, I am a delinquent and encourage such behavior. Sometimes, I wonder how my mom deals with us.
This last visit was a blast. Friday was all about smashing some Dorito bowls and binge-watching a show called Tulsa King. We started watching it at about 2 pm, and before we knew it, it was 10 pm. We all laughed at how sucked in we all were, but only before binging again until 3 am.
What was special to me about this visit was Saturday. After finishing the first two seasons of Tulsa King, my parents fell asleep while the rest of us watched the Captain Underpants movie. Afterwards, the general, unfiltered conversations began. I mean, there were pillow fights and other rambunctious behavior, too, but only intermittently.
We talked about everything under the sun, and I always encourage the kids to express themselves freely around me. We were talking about school, politics, and history before Christopher Columbus came up. They had this notion that Columbus thought the world was flat, and mentioned how some people still think that it is flat. I would not let this stand.
I explained to them that a man named Eratosthenes discovered that the world was round over a thousand years before Columbus ever set foot on Hispaniola. He did not have a cell phone. There were no satellites. It was purely through his powers of reasoning. This excited them, and they wanted to know more.
It required some digression. First, I had to show them how the ancients were able to measure the heights of things like pyramids. Take a rod of known length, measure its shadow, and take the ratio between the two to get a constant. Go to your nearest pyramid, measure its shadow, and now you can use the constant to find its height. Voilà!
This alone set them into a frenzy. My little brother let out an f-bomb, and my daughter’s jaw dropped. They wanted to know why people were not this smart anymore. I smiled before letting them know that they just weren't talking to the right people. My daughter and I had fun with a couple of algebra problems before we continued.
It was time to let them know the truth. A letter came to Eratosthenes from a man in Syene claiming that there were no shadows on the equinox. He first assumed that light rays are parallel. Then he reasoned that since shadows existed where he was in Alexandria on the equinox, it must be the case that the surface of the earth is curved. I drew this out for them, emphasizing the parallel lines and the transversal.
My daughter was able to make out the next important step. Our friend Eratosthenes then used the theorem that alternate interior angles are equal to find an angle between Alexandria and Syene. He paid a surveyor to find the distance between the two, and from there, he calculated the circumference of the earth to within two percent accuracy.
It was 2 am at this point. The kids had loads of questions. It was so much fun answering them. We debated what beauty is and whether or not math fits into the category. I told them about my theory of white holes. We also spent some time hitting each other with kitchen utensils.
It went on like that until 6 am. This was my favorite visit thus far. They're growing up to be their own people now. It kills me that I only get to see snapshots. Here I am, though.
Header image by The New York Public Library on Unsplash.


