On Clemency and Transformation
An in-depth interview with Christopher Havens
I'm not easily convinced that something of this nature will really happen, but the reality is that I must now prepare for this. The world is so different.
Ahead of his clemency hearing, PMP founder Christopher Havens joined us (virtually) for an interview about the upcoming events and possible changes in his life. In our conversation, Christopher delivers important reflections on learning, self-rehabilitation, the clemency process, and on imagining freedom and the "real world” outside prison.
He also poses a challenge and a problem, don’t miss it! You might be able to solve it.
Since our interview, Christopher received a positive recommendation from the State of Washington's Pardons & Clemency board. We will learn more about the fate of his petition in December, as the final decision will be made by the governor.
Recently, Christopher also published a textbook on continued fractions with fellow researcher Carsten Elsner—you can find it here.
We will soon publish a follow-up, given the positive hearing outcome.
In the meantime, let’s dive into our interview.
Q: This might be a very random question, but we are wondering... what is your favorite number and why?
CH: I remember my first steps into number theory, when I first started learning about continued fractions. I was so amazed at how our most celebrated irrational constants, like Euler’s number $e$, the circular number $\pi$ or the golden ratio $\phi := \tfrac{1+\sqrt{5}}{2}$, could be expressed in beautiful and predictable ways using continued fractions. It made me wonder whether I could go backwards, starting from a really beautiful continued fraction and express it in exact and finite terms using well known mathematical constants. I tried to find the exact value for $$1 + \dfrac{1}{2 + \dfrac{1}{3 + \dfrac{1}{{4 + \ddots}}}}$$ It’s simple and beautiful, and its decimal value is 1.4331274267223… My investigations into this number led me to make my first discovery in mathematics and resulted in my first published research project. It became my number, since it had no name.
After I met my current research partner Carsten Elsner, he joked with me for referring to it as my number, and we decided to give it a name after writing a whole research project about it! We named it the Zopf number (Zopf Zahlen, in German). The word Zopf translates directly into the English words braid or pleat. In German folklore, there is a story about a traveling nobleman who becomes stuck in a swamp and begins sinking, deeper and deeper, until the muck has nearly swallowed him whole. To escape the fate of being consumed, he lifts himself out of the bog with his remaining strength using his own braid.
The continued fraction $z = [1, 2, 3,\ldots]$ was given the name Zopf, not only because of how its elements (the natural numbers) seem to twist around unity, but also because of how the number has played such a pivotal role in my own life from my first days in mathematical research, and how it has since shaped the trajectory of my path.
Thus, the Zopf number is a symbolic representation of the braid from my own journey. For if it weren't for my braid, I would still be stuck in the muck, having never experienced such an incredible adventure.
I use mathematics as a means for helping justice-involved people achieve self-rehabilitation by connecting them to a community and culture that exist around their passions for higher education.
Q: What are you working on currently? Could you explain your research in slightly layman terms?
CH: Oh, I’ve got about six research projects in the process! But how about we build on our previous question? Remember the Zopf number $z = [1, 2, 3, \dots]$? Since we are dealing with a continued fraction, we have a sequence of rational approximations, called convergents, where $p_{n}/q_{n} = [1, 2, 3, ... , n]$ for $n > 0$. Now let's just imagine what would happen if we experimented with a sequence of greatest common divisors of the numbers $q_{n-1}, p_{n-1}-q_{n-2}$ and $p_{n-2}$. Then we have the beautiful sequence $$gcd(q_{n-1}, p_{n-1}-q_{n-2}, p_{n-2})_{n>1} = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7,\,\dots\,.$$ Whaaaaaaaaat? :D So here is the problem... Let $\mathcal{G}_{n}(z) := \gcd(q_{n-1}, p_{n-1}-q_{n-2}, p_{n-2})$. Prove that $\mathcal{G}_{n}(z) = 1$ for all odd $n$.
Basically, we are asking you to prove that —starting at the first— every other number in the sequence is equal to 1, no hiccups and no funny business. We call this the "GCD Conjecture.”
Just FYI, this phenomenon of the natural numbers 1, 2, 3, ... twisting around the number 1 is part of the reason why the name Zopf is so fitting! Just recall the translation of Zopf from German to English. This is only one research project, and I am inviting any of you to try solving this problem. My research partner and I have presented this problem in our first textbook on continued fractions (to be published very soon). Here’s the catch... If you make progress or if you solve it, we would like to collaborate and add some related results. These GCD sequences are beautiful and they are an incredible area for exploration.
Clemency was never my goal. I started making changes, and it felt so right and beautiful that I surrendered to that maelstrom of change that was churning inside of me. I worked on myself for years, and I continue working on myself to this day.
Q: I hope many of our readers do take up the challenge! Now, moving on to a very salient event coming up. What is clemency? What does it mean to you?
CH: Clemency is, for an incarcerated person, an appeal at the State level to have one's sentence reduced according to the interest of justice and extraordinary circumstances based on the incarcerated person's actions while serving out their sentence. What clemency means to me is a chance to use what I've built on the inside to give back to the world in ways that I've never been able to. I use mathematics as a means for helping justice-involved people achieve self-rehabilitation by connecting them to a community and culture that exist around their passions for higher education.
If I were out, I could focus on these efforts. I would share my experiences and my story by speaking at functions that would help to inspire further growth in the intersection of Justice, the humanities and mathematics. My role at the PMP would become full-time, and I could then work together with our Executive Director, Ben Jeffers, to help the organization reach new heights, and therefore help more people to not make some of the mistakes I made in my own life.
On top of that, I'd be able to research math with technology. Woohoo!! But closest to my heart is that I will be able to be the pillar my family deserves. My fiancée and I are ready to advocate on behalf of people who have Ehlers-Danlos syndrome, which is a disorder that affects the connective tissues in our bodies. The sad truth is that they don't get the care that they need, and so many people who suffer from this live for the rest of their lives in pain and suffering. I will project my voice in this area, just as I do in mathematics.
Q: How did you begin the process of petitioning clemency? What do you wish people knew about this journey?
CH: I began the process of petitioning for clemency by hiring a lawyer and having them submit my story to the Washington State clemency board. However, people often request legal assistance through the Seattle Clemency Project. Sometimes they even file pro se and act on their own behalf.
I think it's important for people to know that you should never be good for the purpose of achieving clemency. If you haven't changed your life around, fixed the behaviors that led you to making the mistakes of your past, then you can use more time to heal from the traumas we've endured and the ones we've inflicted. Clemency was never my goal. I started making changes, and it felt so right and beautiful that I surrendered to that maelstrom of change that was churning inside of me. I worked on myself for years, and I continue working on myself to this day.
But while I was rebuilding myself, there was never a single thought of getting out early. So, I say this... If you have experienced a profound transformation and healed those traumas inside, and if you understand that Justice is more important than your early release, then perhaps you might consider it.
Q: On the prospect of getting out, what is it like to imagine oneself outside prison while you are inside? How do you deal with managing hope and expectation before the hearing?
CH: It's like trying to convince myself that the surreal landscape in a sci-fi film is real, and that I'm about to visit it. I'm not easily convinced that something of this nature will really happen, but the reality is that I must now prepare for this. The world is so different. But if I try to think of all the changes that have occurred, I might get overstimulated trying to keep up.
Instead, I'm thinking of this as if I'm just moving to a foreign place where everybody just happens to speak my native language. I do imagine myself doing most of my work from a computer, virtually, and that way I can focus on the things I love, like the Prison Math Project and mathematics, while being able to be fully present for my fiancée and my family.
Managing hope and expectations before the hearing is hard because I have an inner need to be with my loved ones. And they need me to be out as well. But so long as I do all that I possibly can, I just try to remain optimistic yet prepared for any eventuality. There's not much else I can do.
Q: What is your routine like nowadays? How would a sentence commutation impact your ability to work?
CH: Well, it's nothing glamorous... I wake up at about 7:00 am and do groundskeeping, which is nice therapy. Up until about 1:30 pm, I get to be connected to nature. I usually have meetings at about 2:00 pm with my research partner in Hannover. My fiancée and I connect throughout the day, but from about 3:00 pm until about 10:00 pm, I hop back and forth from research in number theory, UCLA research or my work with PMP.
Commutation would impact my work by allowing me to continue working for UCLA as a Staff Research Associate on a part-time basis, but my role at PMP would shift to full-time. This new freedom would allow me to incorporate technology into the current work I do, turning everything up a few notches.
I also have a dream of solving a very specific problem out there, one that involves helping people with Ehlers-Danlos syndrome. On the inside, it will be incredibly hard to achieve what I have in mind... But if my sentence were commuted, I would like to breathe life into a support network which offers life changing resources for them.
Q: If you are granted clemency, what are your more long-term plans? Would you start a PhD?
CH: If I'm granted clemency, I'll begin working in a full-time capacity for PMP, which is really something that I've wanted for a long time. My position at UCLA will last about another year, and as my schedule frees up a little from getting into a rhythm, I'll work on some of my bigger picture projects.
I will be continuing all my research projects, except with the added benefit of technology. I have several problems that can be simplified using programming... and then MORE questions occur, which is just one of the aspects of beauty in research. I do want to pursue a PhD, but I also want to make sure the timing is right so that I can set up strong financial security. My fiancée and I are starting a new life together, and so I want to make sure that I'm in a mindset of our future instead of just mine. So, the PhD will happen when I can approach it responsibly. I do actually have a mathematical side project in mind, which I will wait until I am out to pursue.
It has been a dream of mine to write a book on continued fractions for high school students. Carsten Elsner and I just authored a textbook through Birkhauser-Springer together, but it was written for mathematicians... and it is beautiful!! But now I want to make this beautiful topic accessible to the younger mathematical minds. My vision is to write something approachable and fun, like the Art of Problem Solving series, but a little more lengthy. Tons of problems, tons of examples, with historical and cultural anecdotes, taught as if the student has had zero exposure to the topic. That's the goal!
We, unconventional math learners, have a unique gift that makes us different from conventional math learners. Where they might have extensive foundations that come from years of schooling, we have the chance to cultivate something incredibly valuable. Our style of learning is often through exploring the books on our own and then exploring until it all starts to settle into our minds in a way that fits us.
Q: That sounds amazing! Your story opens a new world for many people and highlights the powerful role education can play in nourishing positive self-identity for incarcerated people and in paving a path of desistance from crime. When did you begin to see yourself differently?
CH: Hmm... There is no hard line for the precise time this happened, but there were a couple pivotal moments relating to the role of mathematics in self-identity. Ultimately, these are what led to desistance, so let me try to explain a little.
When I was a kid, I thought of cryptographers and mathematicians as the wizards of the modern era. They slang symbols and the world would change around their pen strokes. These were my heroes. Of course, that was all they would be. All of these sorcerers having minds that were so brilliant that they could make new math and solve real-world problems using nothing but intellectual thought made real through chalk on a blackboard!
When I first began studying mathematics, I was in the hole (the prison inside of prison) and it muted the world around me. I remember how miserable and horrible it was in the hole when I was immersed in that life. But after I started studying math, everything went quiet, and all I can remember are the dreams of numbers and my relationship to this new source of fulfillment in my life. There were changes occurring inside me, and it was the strangest feeling.
I remember standing in my little concrete room, and I felt as if I were standing next to myself, watching these changes happen. It's a real memory, but my mind created a scene where there I was... standing next to a version of myself that was kneeling on the floor, and I could see the growth happening to me in real-time. It was a profound moment, because I realized that nothing had ever had such a transformative effect in my life. It humbled me.
Not long afterward, I was standing in my cell, looking at the concrete wall. This wall was bare concrete, painted grey... the security that kept me inside. Only, I was looking at it for the first time as a blank space… Like a blackboard, which represented the rest of my life, just covered in mathematics. I realized that I had 25 years, and with that gift of time, I could become one of those wizards I idolized from my childhood. So, I decided to spend this time of my incarceration learning math, with the goal of making some new math of my own.
I had decided that I wanted to become a mathematician and that I wanted to cultivate the growth I was experiencing. The disappointment that was Chris was being left behind, and I would spend the last half of my life in a pursuit of forward growth. Symbolically, I began using the name Christopher.
Q: What is your advice to unconventional math learners? Have you encountered many cases of people who didn’t have affinity for math but changed through their self-studies or mentorship?
I have encountered several people who hated math and suffered from THE WORST cases of math anxiety from their past experiences or preconceived notions of what math really is. One person I know, Marshall Byers, absolutely hated math to the point of getting angry at the thought of it. He could not stand it!!
But I made a social mathematics experiment and included him in it... I built a program called the Social Mathematics Experiment that included staff and inmates coming together to learn math through human connection as a central focus. Everyone loved it, and it wasn't long before Marshall was taking a math class in prison, for which he found he was pretty good at! Marshall then became a PMP participant and did excellent with some mentorship and exposure to different flavors of math, which he never even knew existed.
Today, Marshall is out of prison, living a life of desistance from crime. And I hope, one for which numbers no longer cause him to break out into hives!
So... my advice to unconventional math learners is this: We unconventional math learners have a unique gift that makes us different from conventional math learners. Where they might have extensive foundations that come from years of schooling, we have the chance to cultivate something incredibly valuable. Our style of learning is often through exploring the books on our own and then exploring until it all starts to settle into our minds in a way that fits us. So, use that, because it helps us to cultivate mathematical creativity.
Also, play. Play with the numbers and see what happens. Explore. If you can't figure out the answer to your own questions, then research the topic and go down the rabbit hole! That is exactly how I stumbled onto my first new theorem. As unconventional math learners, we have the opportunity to hone our ability, to be creative and play through research and exploration... and THAT is where so much of the beauty is at.
Teach with a little flexibility. Take the time as a teacher to learn the way students learn, and then teach in a way that allows people to see the same ideas in more than one way.
Q: When did you first think of something like the Prison Math Project? Has it been difficult to bring it to fruition?
I first thought of starting a math program in 2013, during my first mentorship with Luisella Caire, of Turin, Italy. Luisella and I had decided to build a plan for a math program, complete with a library of math books. Then in 2014, I moved to the Monroe Correctional Complex where I started working with the admin to make that happen. It took until 2015 for our ideas to finally become finalized, and it was funny because in our meticulous planning, we never thought of a name for the program!
On the day the program would be finalized, I sat in an office of one of the prison’s administrators, and he said, "What are you going to name it?” Good question... I asked him, "Do I have to give you a name right now?" He was quite literally finalizing the process, typing an email to the staff in charge of the scheduling, so he said, "Yes... Right now." I was on the spot, and until that moment, I hadn't even put a single thought into a name, and so I spoke the first words that came to my mind... "The Prison Mathematics Project!". He grunted and nodded in approval, and I knew instantly that the name was perfect.
Over the next years, PMP became a thriving community behind the razor wire. But when Covid hit, all education inside of prison came to a screeching halt. PMP stopped running. It wasn't until my first research project was published in 2020, when my story became widely circulated, and Walker Blackwell reached out to me to collaborate that we launched the PMP as a national non-profit organization. We decided to transcend the limitations of prison as Covid ran its course, by recreating the conditions that helped me in my own rehabilitation.
In this new PMP, we would give people what Luisella Caire gave me... We would provide mentorship with real members of the math community and connect them to a community and culture that exist around their passions for higher education. Our aim was to inspire desistance through the study and exploration of mathematics... and that was how PMP began. Difficult? Yes. But thanks to our core team, it has been a growing entity which has evolved into what you see today. All the best things are usually very difficult.
Q: What is it like to get people engaged in math while incarcerated? How do you connect with people who might have very different experiences and challenges from yours?
Good question! Well. It's like this: Take any classroom of students. How many of them just don't understand or fail to connect? It should be obvious that every teacher has their own style of teaching, and perhaps they're incredibly good at it! But the same goes for students. Each and every student has their own "learning style", and so I connect with people having different experiences and challenges by taking a few minutes to learn how they learn.
I have this belief that everyone can learn math and can actually be good at it, at least at a basic level, but if we expect everyone in our classroom, with all of their different styles of learning, to really connect with one specific teaching style, then that expectation is unrealistic. Teach with a little flexibility. Take the time as a teacher to learn the way students learn, and then teach in a way that allows people to see the same ideas in more than one way.
People in prison have incredibly diverse levels of mathematical maturity, so I teach in ways that reach many people. I do this by learning everyone's style of learning. I stay flexible and accept when I need to try a different approach of showing them something. And it's also helpful to have people with more mathematical maturity learning by teaching the ones that are struggling. For those that struggle, I start the day by speaking to their needs. I then identify who is ahead of the class, and I pair each of them with the ones who struggle the most. From there, I continue from the previous day. Even then, I ask everyone whether the ideas are clear and if they want alternate explanations. Almost always, they do. So, we explore as the lessons progress. By the way, it helps when you explain history and culture around the topics. It seems to really interest the people who are learning.
