This interview took place between Sharenda Barlar and Danilo Diedrichs while they walked trails in and around Wheaton, Illinois. This is the fifth part of a series of interviews that will take place with faculty from Wheaton College as part of Susan Dunn-Hensley and Barlar's 2020 virtual pilgrimage program.
Hereafter, each individual will be referred to with their initials: SB and DD respectively. This interview has been edited for clarity and length.
SB: What is the history you're writing about, the history of mathematics? Would you want to share how history has repeated itself, especially since we're in the context of the pandemic that we're in?
DD: I was just thinking about the two books on the new [Wheaton] logo. Galileo said God wrote two books, the Scriptures, which are to be interpreted through the language of theology, and the book of nature, which he wrote in the language of mathematics. By saying that, he was pretty much elevating the book of nature and mathematics to the same status to Scripture, which was very controversial in those days, because mathematics was considered very much a lower, less important field than theology, which was considered Queen of Sciences, so he got in big trouble for saying that. But it was kind of the sign of the times, where little by little mathematics became elevated to the point of almost overtaking theology.
When you're writing about the history of mathematics, which is an extremely long and rich history, mathematics has been around since the beginning of civilization. Pretty much the first thing that people wrote down were numbers, before they started writing letters and words, so recordkeeping and doing basic math was at the beginning of civilization. So when you're writing about the history of mathematics, you're spanning millennia, and looking at how the ideas we have today are shaped through very, very long periods of time. So when you're working on those long time scales, you see a lot of cycles repeating themselves. Things like plagues, pandemics, they're commonly mentioned as commonplace throughout the millennia.
There are different dates that stick out in your mind—"that was the date that there was a plague,” like 1348, 1666. Specifically in the development of mathematics, there are things that are generated by the fact that there is a plague, or that there is an epidemic going on. So one of the things I was talking about with you a few days ago was the plague of 1666 in England, where basically the whole country was shut down for two full years. Isaac Newton was a professor at Cambridge, and he was shut down for two full years, and so he quarantined himself at his country home and for two years, that's when he produced some of his biggest works. That's when he invented calculus, that's where he came up with the law of gravitation, his whole theory on optics. So he had an extremely fruitful time in quarantine.
Mathematics is this field where you can do very much with very little, unlike other sciences where you need a whole experimental setup and you need lab equipment. Mathematics, you don't need anything. You need paper and a pencil. Even that, you could do it within your own mind. It's not required to be connected to the physical world. So you don't need any of your five senses, you don't need to be embedded in any kind of a perceivable world to do it, it's all in your mind. Some people like Newton benefit from the quarantine, to be able to focus in that way.
SB: Let's hope this happens this year with faculty and students, where they are just inundated with all kinds of discoveries.
DD: Exactly. Well, it does create a structure to step back from a busy life, I think. That's my personality, I'm always looking for structure in my life, so compared to my previous career where I was working in corporate business and my life was very structured, I could be at the same office at the same time every single morning, I could eat my lunch at the same time, and every day was pretty much the same, for me it was great because I'm a creature of habit, and I want that kind of pacing to my life.
SB: How do you create those habits at Wheaton, since you don't have that structure most of the time? DD: Wheaton is completely unstructured, every season is different, every day of the week is different. That's why the summertime becomes an opportunity for me to recreate that kind of structure. One of the questions indicated that summer was a time for unstructured--for me it’s the opposite. Summer is the time that I recover structure, summertime I get up at the same time every morning, I have all my meals at the same time every day, I get into a kind of a routine I do not have during the school year.
SB: Many would argue that walking a pilgrimage provides that structure, and that's what people crave, much like what you were saying, because you don't have to think. You know you are going to get up, you know you have to walk a certain amount before you stop, you know the routine and it becomes rote and that's a comforting thing. What I'm hearing you say too, is that you find comfort in that structure.
DD: Very much so. I feel much more at peace when I don't have to think about the question, “what do I have to do today?” On a pilgrimage, you get up and you just know that your primary role for that day is getting from point A to point B, and that's it. Everything else revolves around that primary goal. That's comforting to me. That's my summer lifestyle.
SB: You've mentioned before that one of the reasons that you like figure skating and ice skating is that you are unable to think about anything but what you are doing at that moment. Could you talk about that a little bit? DD: I do write about that in my book also, about the fact that mathematics is an unusual field of knowledge in which the insights come very slowly, they have to cook through your mind for days, weeks, months, years sometimes and so mathematicians always have one or more unsolved problems in their minds that they're constantly ruminating, thinking about, obsessing about, for some of them it can be really obsessive. As a mathematician, I have to find ways to press the reset button on the problems that are running in my mind, and so an activity like figure skating is perfect for that because it’s an activity that really demands your complete attention, so after an hour of skating I feel like I have completely reset my mind, in ways that other sports do not. When I go biking or running or other kinds of sports, it doesn't require enough of my mind to be able to disconnect from the mathematics running in the background.
I talk about it in the book because it's a little bit of a new discovery for students who are getting into upper level mathematics who realize that they are stepping into a field where their mind is going to be permanently steeped in some unsolved mathematical problem.
SB: What kind of advice do you give them, when you know that they are going to need moments of rest and ways to decompress? What suggestions do you offer? DD: I always tell the students that because the understanding of these abstract, complex concepts takes time, there's very little you can do to accelerate the understanding or the grasping of them. It's understandably not useful to spend the whole night staring at a textbook, or spend hours and hours trying to cram material into your head because that does not work at all in mathematics. So you just have to do a little bit, do one hour, for example, go out for a walk, go for a bike ride, do other things. Subconsciously your mind is still working on the problem, you don't realize it, but then when you sit down to do another hour the next day, progress will have been made.
There are a lot of historical examples as well of mathematicians and scientists who have these big insights in the middle of these non-mathematic activities. Archimedes who was taking a bath and came up with the Archimedes principle while he was taking a bath. Hamilton came up with the foundational formula for the quaternions while he was taking a walk with his wife in a park. He was not specifically doing mathematics, but the insight came to him naturally. He didn't want to lose that insight while he was in the middle of his walk. He needed to write it down, but he didn't have anything to write it down with—he only had a pocketknife in his pocket. He ran to the column of this nearby little bridge that was going over the river and carved the mathematics with his knife so that he wouldn't forget it. It’s still there, it's kind of a mathematic pilgrimage location now in England. That bridge pillar now has a plaque and a frame, and you can still see the carvings there, what the original formula was. It's a very important formula in mathematics, it spurred massive amounts of extensions.
The other thing is that I was thinking about the more abstract side of mathematics that you explore. Mathematics is this unusual field. Mathematics has these different aspects to it, and the one that's most visible especially to people in the common public is the scientific side of mathematics. I like to call mathematics a toolbox for science, a lot of people view mathematics as a collection of tools that scientists use to solve the problem, which is definitely an important part of mathematics because science uses mathematics as its common language. But like I said earlier, mathematics is not constrained to be tied to science or to the visible world. You can do mathematics completely disconnected from objective reality and there are a lot of mathematics that have been done in that fashion. A large portion of mathematics that's done nowadays is not at all connected to science. What kind of mathematics is that?
Mathematics is not only a tool for science, but also a tool for discerning truth from falsehood. In this sense, mathematics uses the axiomatic method to describe patterns of logical deduction that relate the truth of a statement to the assumed truth of a set of axioms. In mathematics you do it using this other method, which is based on proof-writing, which is a progression from Point A to Point B. Point A being a set of axioms, Point B being the theorem that you're trying to prove, and the path being the chain of logical deduction statements that are based one upon the other, stacked upon each other in order to complete a deductive chain of reasoning.
In order to do that successfully, you can prove that a theorem is true, relative to a set of axioms. That's what you do primarily in upper-level mathematics. It's proof-writing, so you step away from this concept of solving problems of science to proving theorems. The whole exercise consists in finding the path that goes from the axioms to the theorem, and so that could be a long and convoluted path, or that could be a simple path, and oftentimes there's more than one path that goes from Point A to Point B, and a lot of what we do in upper level mathematics is just sitting around discussing the different paths that constitute the proof of a theorem. Some of them are more elegant than others, some of them are more beautiful, some of them are ugly, even though all may be correct.
SB: That's a beautiful metaphor.
DD: It's very interesting to compare the different proof paths.
SB: But they all lead to the same conclusion.
DD: They all lead to the exact same conclusion, and they all start from the exact same point also. When I teach linear algebra, the first day of class I give to students the list of axioms, which is this list of things that we are going to assume in this course for the rest of the semester to be true, without having to prove them. Throughout the semester. we look at increasingly complex statements that are all true, that are not as obvious as the axioms. They can be proved as being true by creating a chain of logical reasoning that ties them back to the axioms. There are many ways of doing that, and everyone has a personal way of doing it. Everybody is pretty much on their personal pilgrimage trail.
SB: Really it comes down to what direction they take, not so much the final answer, although that's important--you want to see the path. That is so interesting, how that relates to pilgrimage.
DD: The destination is given, that's what everyone starts out with, destination and a beginning, and everything revolves around the path between them. Where did people take the wrong turn? Where did people climb over this really tall mountain when there was this really nice shortcut that they missed?
There are some approaches that are called the brute force approach that some students like where you basically plow through in a straight line, even if there are obstacles in between, you keep your eye on the destination, don't divert from the straight line. Usually, it gets you there but sometimes it can be a very difficult path, and then there's other people who like to be creative and explore roundabout ways, and sometimes you stumble on really nice shortcuts. Sometimes you get lost in the wilderness and that's unfortunate. The whole goal is to prove a theorem. In mathematics a theorem is a statement that is true relative to the axioms. True statements proved in this way are unlike truths derived by scientific methods, which are constantly subject to revision. Axiomatically derived proofs are pretty much absolute and eternal. That's why this axiomatic method that we use in mathematics is very similar to what's used in other fields of study that try to derive proof in the absence of empirical data, like in philosophy or theology. In that sense, mathematics, philosophy and theology are three sister sciences that use that same method, separate from those methods used in empirical science.
SB: I would think that some people could argue that if they haven't studied science, especially with someone like you or at Wheaton, where is God in science? How does science or math reflect God? It's not like literature. For those of us who are literary scholars, we can talk about the different connections a little bit easier.
DD: Science is basically the study of the visible world, the world that we live in, that you can apprehend through your senses, as opposed to the spiritual world, or the world of ideas. Science really has to do with the material world. When you're doing science, you are studying the patterns that govern the way the world behaves. The fact that we're able to study it means that there is something to study, the world actually behaves in very regular ways, there are patterns that you can predict, in space and time.
The more you look into different natural systems, you realize that even in systems that appear to be completely random and chaotic, there are patterns that are sometimes very complex and very beautiful embedded within the apparent chaos. That’s one place where you can see the evidence for God— in the fact that the creation that he has made, first of all, is governed by order and by a certain amount of patterns that are regular, and the fact that they can be apprehended by human beings. In many cases, the patterns are hidden enough that it requires study and effort to perceive them. You need to be able to solve the differential equation to be able to see the pattern. So it’s not completely in your face, you have to engage in some conscious search for that kind of pattern in order to be able to see it, but if you put in the effort, if you basically search for it, it is possible to find it. That's the same as God's own nature, where he's always hidden, so he's not in your face. If you're not searching for him, you may not come to know him, but if you put the effort in to search for him, he will reveal himself to you. It is possible to actually behold him to those who search for him.
SB: That brings me to your faith journey, because you came to Christ as an adult. For someone with an analytical mind, how did coming to faith work for you? Did you have to wrestle with those things, or did it just make sense. God is a God of order, there's no confusion with God. Did that resonate with you, or is it something that you had to grapple with as a new Christian?
DD: That's a good question, because I was already completely a scientist before I even became a Christian, but even as a scientist I had a lot of wonder about the complexity of nature. It is complex, but we human beings are able to use things like mathematics. So then when I stumbled upon Christianity as an ideology, it really made sense that that's one of the ways in which God tries to reach out to us, through the patterns of the world. That's what led me to the sacramental aspects of my faith, specifically that God delights in using the material world to reveal himself. That's what I do in my field of mathematical modeling. I use the mathematical tools to reveal how God is continually present in his creation.
SB: Based on your background, you were raised in Switzerland. Although I guess you could say it is Protestant historically, most people are non-practicing Christians.
DD: Switzerland is very secular now. However, it has deep historical ties to Christianity. In fact, it was considered one of the centers of Christianity during the Reformation. But that was such a long time ago that everybody has fallen away. SB: There are all of these theories about secularism, and you were raised in Europe. With Switzerland being the hub of Protestantism, why have so many fallen away? Was it the age of Enlightenment, where science took over thinking? I know you're not a historian, but just living there—do you think it was a combination of things? DD: I think there are a lot of different influences--in my book, I talk a lot about the age of Enlightenment and the profound way that shapes not just science and mathematics but all aspects of study, as the locus of truth shifted from the Scriptures to science.
During the age of enlightenment, the pendulum swung to the other side, where science and mathematics were commonplace for anyone who was educated, who was conversant, in the latest mathematical discoveries. That was still 250 years ago. I think we've progressed even further now in the past few decades, where everyone has adopted their own autonomous personal locus of truth. You don't appeal to any exterior source anymore. I think that's more pronounced in Europe than in America. I have a lot of friends in Europe who are on a personal faith pilgrimage, not at all in the Christian sense. Everybody's on a road to discover some form of spiritual truth. It's very personal, it's a big mixture of all different kinds of religions and spiritual beliefs. When I tell my friends that I'm a Christian, they say, "Oh yes, I was a Christian too for about 5 years, but that was about 15 years ago, but I progressed...we're still on our road to discover the truth.” It's become a fashionable thing to be on a permanent trip and basically never arrive at the destination. Nobody claims to have found a source of objective truth.
SB: You'll meet a lot of people from Europe walking the Camino and they'll be very up front and say, I'm not Catholic, I'm not religious, but I'm spiritual. They'll admit that just the act of walking, they feel something, and they encounter something. A lot of them like to call that the Camino spirit--the spirit, the essence of the Camino. People are in general more open to talking about life issues, even theological issues, on the Camino.
DD: I really have had wonderful discussions with people in Europe, they're all very open. I've found a lot more hostility in America. America is very polarizing. Either people are completely on the same page with you, they're Christians, they believe in the same things that you do, they have a vibrant spiritual life, or they are downright hostile to any talk of Christianity or spirituality. In Europe, it's more tolerant.
SB: The attitude of, "I don’t agree with you, but we can still be friends." I see that as well.
DD: People in Europe are generally very tolerant of me as a Christian. That's kind of the name they gave me, The Christian. They love to bounce ideas off of me to get my Christian perspective, but I've rarely ever been able to convince them of the deeper truth of Christianity. They think I have interesting points of view.
SB: I think too, when you shared with me earlier about your faith journey, it didn't really come from evangelism. With you, it grew out of relationships, where it was much more organic. We're even seeing that in Spain, in places like the Pilgrim House, which is a welcoming center in Santiago, run by Wheaton College alumni. They are a welcoming center, they have all kinds of hospitable amenities where pilgrims can get their clothes washed, they can rest, they can store their bags. The Pilgrim House is not blatantly saying, "We're Christians," they're just there to offer a space for however long you want, in Santiago, when you finish the Camino. A lot of people want to process. The Pilgrim House staff have used that space as a way to open doors, because people are more open to talking once they've been through a big experience like this. In that space, they'll share, they'll pray with you, and they've had several people, especially Europeans, say, "Hey, I'm reading the Bible, I'm looking at, who is this Jesus?"
DD: I think my coming to faith was about two years long. It was a slow process. I came to faith through the campus ministry of the St. Egidio community at the University of Lausanne. It was a very small Christian group, but they're very hands off in terms of evangelism. It's all about doing life together. The reason why it’s called a community is because basically if you participate, there is something to do every single day of the week. Monday night, Tuesday night, Wednesday night, Thursday night, every night, dinner together.
We're all college students, we're all busy people, but there's always either a bible study, or a prayer group, and a lot of it is service to the poor, service to the refugees, service to the elderly people, service to the low income families, service to the homeless. The people in the community are always looking for volunteers for service projects. They don't ask about your faith or the motivation behind it. There are people who volunteer for years and never really asked about the spiritual dimension of this community. For me, I was just a volunteer for over a year, before I started asking questions about why are we doing this, what is the motivation to do this together, and to serve the poor the way we do?
I was very gradually, over the course of many months, incorporated into the spiritual dimension. It was very slow, but I think if it went in faster, I would have been figuring it out and rejected the whole thing, and I would have never become a Christian. Coming from a scientific perspective, I needed a lot of time to process through the spiritual elements. The people in this community were extremely respectful of that. They sometimes waited 4 months before challenging me with something else. That's the time that I needed.
SB: That was a lot of discernment on their part too.
DD: Yeah, a lot of them were on their own discovery path, and so we were all doing life together.
SB: Do you keep in touch with them?
DD: Every time I go back to Switzerland, I keep in touch with those people, and it's amazing that they continue to meet regularly several times a week. They're all married, they have kids, they have families, they have jobs, they're busy, but at least once a week, every Saturday night, they all gather together as a group. They have a little worship service, they have dinner together, but during the week, they'll engage in some other form of community activity.
SB: That is very biblical, because when you think about the Acts of the Apostles, it says that Christians continued, in the Apostle's doctrine, at the temple and at home, breaking bread together. That is the church community. Or that's how it should be, right?
DD: It's been twenty five years since I was a college student there, and we were all completely young and made this lifestyle a priority, and then I moved away and they're still there and they continue to make it a priority despite everything else that has happened in their lives. It's always a very sweet time of re-entering into that communal life when I go back to Switzerland, so, that was one of the highlights of going back for my sabbatical, was being able to meet with them several times.
SB: I think that's something that Americans struggle with. COVID has been interesting because we're not really allowed to get together, but even before that, it felt like our lives were so busy, it was really difficult. I don't know if you've had this experience. I know you're very intentional about forming communities with different groups. It has to be intentional, doesn't it. It's very difficult to do with the fast pace of jobs and life.
DD: As an unmarried person who lives by himself, I really have to be extremely intentional about creating relationships because I don't have a built-in community at home, like people who have a family. A lot of churches basically don't really cater to unmarried people, so it's very easy to fall through the cracks of any community, not just churches, but any type of social setting. Anyways, I've had to be very intentional about creating that community. It's been very interesting that a lot of my friends are married friends who have large families, with a lot of after school activities with the kids, and so I would have to plan, a month ahead of time sometimes, to have a coffee date. But the pandemic was wonderful because I could just call them one day before and everybody's available!
SB: I know! Well, when I text you, “What are you doing tomorrow?” “Nothing!”
DD: I've actually had a lot more spontaneous community which is what I like, being able to call someone and be like, “Do you want to meet in an hour for a walk?” and people say “Yeah, sure, I'm not doing anything.” That's been a blessing in disguise.
And then the technology that we have also. One of the questions was talking about disconnecting with technology, but for me, this has been a season of connecting with technology, I don't think I'm a very technological person in regular times. I have a phone that I leave in my car during the day because I'm just not into checking it very often, because I'm busy, with all kinds of stuff going on, but now my phone has become my friend, because it's my source of contact with the outside world. So I've become much more technologically engaged through the summer, through the pandemic, than otherwise.
SB: Yes, because you had to leave your sabbatical early, your family doesn't live nearby, so technology has really kept you connected with others.
DD: From March to June, I didn't interact with any other human being other than through a screen. I had three months of 100% isolation from human life. And if this technology did not exist, that would have been extremely difficult, but I was able to have all kinds of community through the technology. For three months I didn't use my car at all. There was nowhere to go, and so I would go on walks every day, and I met all my neighbors. Now, I've invited my neighbors to my backyard after years of living there, and I've never had them over. It feels from another era, it feels very medieval, to walk around your neighborhood and know everybody, and know everybody's routine, their schedule, their habits, their work.
The focus of Dr. Diedrichs' research is mathematical modeling; he specializes in nonlinear dynamical systems, bifurcation theory and catastrophe theory. His modeling approaches are used in the analysis, control and design of complex interacting networks in cell biology, biochemistry, ecology, epidemiology and supply chain logistics. As a civil engineer, Dr. Diedrichs has done research in structural engineering at the Swiss Federal Institute of Technology, where he developed a mathematical model for the composite resistance of multi-span wood-concrete beams.
Raised and educated in Switzerland, Dr. Diedrichs is fluent in five languages, he holds a U.S. customs broker's license and private pilot's license. He has extensive professional experience in engineering and intermodal (sea/rail/road) international supply chain logistics gathered throughout his ten-year-long career prior to coming to Wheaton College. Dr. Diedrichs' other interests include playing the piano and remaining active outdoors. In the summer, he enjoys hiking, biking and swimming, and in the winter, skiing and ice skating. He is an amateur ice dancer and competes in freestyle figure skating at the USFSA adult gold level.
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