Tuesday, May 19, 2020

Stay in Your Lane    by    Christopher Havens

Hello all! It has been a while. I'll begin writing more often, but for now, I'm giving you an article I wrote which was never accepted. I think you'll enjoy it. It will come in three parts, so please stay tuned! Please enjoy a bit about my world, titled "Stay in Your Lane".

Many of you have heard the term "off the grid" living. This is where one chooses to forsake the amenities of society. I, on the other hand am an intercity/off the grid resident.. and what I mean by that is that I am in prison.. My preferred terminology is "institutionally challenged" or "technologically handicapped" depending on how you look at it. If it seems strange that a person in my situation studies mathematics to any degree of seriousness, please rest assured that you are not alone. Because of this, I have been asked the question many a times:

What does mathematics look like in prison?

I can answer this in several ways, by telling you how on several occasions my walls get gift wrapped in paper, haphazardly held together by rolls of Scotch tape, which are then covered in symbols that inflict math anxiety on the other residents. Or how whenever my research requires the use of a computer, I must often find mathematicians to trade some of my mathematical art for computer generated lists, which upon arriving into the prison, are flagged and confiscated for having the appearance of "secret code". The prison administration refers to me as "over ambitious". "Stay in your lane", they say...

Unfortunately, none of that sufficiently describes what mathematics looks like in prison. For that, let me introduce you to the Prison Mathematics Project (PMP). The PMP is a program I built which is designed to inspire inmates to make positive life changes through the study and exploration of mathematics and the sciences.

Through time and evolution it has become the mathematical community behind prison walls. We hold meetings and mathematical events where mathematicians have attended from across the globe.. And it seems that I have become the hub for everything mathematical to the other inmates. In fact, I have so many books that it's not uncommon to find other inmates knocking on my door, mistaking me for the institution library. When I hand them Hardy's "Introduction to the Theory of Numbers" they let out a whimper and begin breaking out in hives.

The Daily Grind

On a day to day basis, I study about four different types of mathematics. I love group theory, and so even my other studies are tailored to have a group theoretic flavor to them. This is one of the ways I learn.. by having a subject as an "anchor", and then linking all of my other subjects to that anchor, making a chain of studies that lead to my anchor. For example, my linear algebra studies have a group theoretic approach. My current research has group theoretic undertones. And the group theory can be studied to include matrix groups and matrix representations.. Lie groups via matrix groups, etcetera. 

I don't know that my daily grind is unlike other students of mathematics.. I have nothing to compare it to. One thing I know for certain is that I did not follow the normal route to arrive at my current destination. I bought countless books out of the order that they should have been studied. To this day, I don't know what subjects I should have taken to ensure my foundation is well established. Also, I am unconventional.. I use old and weird techniques. For example, I use lattice method for multiplications when a calculator is not handy. I solve logarithms by a technique that turns them into continued fractions. I solve my continued fractions like breathing, and I am told that my techniques in probability are redundant.. but it works. It would be like living a dream to sit down and be able to have somebody point out my conceptual flaws and give me some tricks of the trade from time to time.

Studying mathematics in this atmosphere is hard, to say the least. If you're trying to perform legitimate research, it's even more difficult. My research is mostly in number theory. I once tried solving a problem.. which unbeknownst to me at the time, had no solution in the terms I was looking for. This took about 1 year for me to figure out! At the time, I considered this to be a mathematical failure. But since then, I have come to realize that mathematics is the subject where I find awe in my failures. Although a solution didn't exist, I had tried in every possible way I knew. One of my attempts contained some new math, which gained me a collaboration with a group in Italy. I am now a member of their research group and the resulting paper ("Linear fractional transformations and nonlinear leaping convergent of some continued fractions" by Christopher Havens, Stefano Barber, Umberto Cerutti, Nadir Murru) has recently been published by Springer's journal of Research in Number Theory.

End of the first part!!! Stay tuned. :)
Christopher


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