I just returned yesterday from the Joint Mathematics Meetings in San Diego, where I gave my talk commemorating Fr. Magnus Wenninger. Last week, I posted several excerpts from my correspondence with Magnus which I included in that talk. Today, I’ll continue that discussion, again adding commentary as appropriate.
I included this quote because of Magnus’ translation of Kepler: “Beyond doubt there exists in the mind of God the eternal form of all these shapes, which we call its truth.” Magnus had a very philosophical approach to mathematics, and always considered that his work was some manifestation of the Divine.
Is mathematics invented or discovered? This age-old and unresolved question has sparked much debate over the centuries. But for Magnus, the answer is clear: mathematics is discovered. The polyhedra he created all existed in the mind of God long before he reimagined them with a few pieces of paper and a little glue.
So Magnus’ vocation as a Benedictine monk strongly influenced how he thought about his life’s work. Having personally held and studied some of Magnus’ models, it is not a stretch to say that perhaps they were in fact touched by the Divine….
This excerpt again shows how very active Magnus was during the 1990s. But this particular letter is part of a thread in our correspondence where I was planning my first visit to see Magnus.
What made the trip a little more challenging is that I also wanted to visit Peter Messer in Wisconsin as well. Magnus introduced me to Peter as someone very interested in studying stellations of polyhedra, both from concrete and abstract viewpoints. (I also have a folder of correspondence from Peter, but that for another time!) Also, Peter was using Mathematica, which I was quite familiar with. So it seemed appropriate that we should meet.
Peter just recently retired, but was a dermatologist at the time, and hence had a busy professional schedule. So I was trying to juggle three schedules to arrange a series of visits — all through written correspondence! Now we would consider this approach somewhat anachronistic, but at the time, it was perfectly reasonable.
The title of my talk at the Joint Mathematics Meetings was Working with Magnus Wenninger. So in addition to excerpts which documented our getting to know each other, I also included excerpts which illustrated various aspects of our collaboration.
If you look back at the very first excerpt from last week’s post, you’ll notice the second paragraph begins “I’m in no hurry to get information about barycentric coordinates.” In my introductory letter to Magnus, I mentioned that I had begun work on finding coordinates of polyhedra using a barycentric coordinate system.
But over the next several months, I did send Magnus notes on barycentric coordinates, and he did study them. Now is not the time to go into a detailed discussion of barycentric coordinates — the point is that Magnus occasionally included diagrams in his correspondence to present his perspective on different aspects of our collaboration.
The first figure shows barycentric coordinates relative to a six-frequency triangle. The second figure shows how he would use this abstract idea to create a template which he would use to make what would be called a six-frequency geodesic icosahedron. Again, now is not the time to go into details, but I did want to include a brief description for those who are a little more familiar with polyhedra and geodesic structures.
Although, as I mentioned just a few moments ago, I began arranging my first visit with Magnus through letters, I must have finalized arrangements with him and Peter over the telephone. This excerpt from 10 June 1994 was the first letter since February which mentioned my visit; I must have realized that calling both Magnus and Peter was ultimately more efficient than writing them. I should mention that Magnus had difficulty hearing over the phone, and so we never had any substantial conversations on the telephone; our chats were confined to arranging logistics of visits or other such details.
I always enjoyed my visits with Magnus. I would stay in a guest room in the Abbey at St. John’s University in Collegeville, Minnesota — this was a spartan room with a simple bed, a small desk and chair, and I think maybe another chair to sit in…it’s been too many years to remember the exact details.
I’ll recall a typical day during one of our visits — although the individual visits tend to blur together. I’d say I made a half-dozen visits while I lived in the Midwest, including a time when Magnus visited me and I drove him to a conference at the University of Illinois Urbana-Champaign.
In any case, there was a common room for guests in the abbey for breakfast. Nothing too elaborate, but enough to get you going. I’d be on my own in the morning — working on polyhedral pursuits, or perhaps just walking around the beautiful campus. My visits were usually during the summer, so I was spared the cold of Minnesota winters.
Magnus would then find me around lunchtime. He had permission for me to have lunch and dinner with the other monks — a real treat, since this was not the usual protocol. But Magnus and I often had philosophical and theological discussions as well as conversations about polyhedra, and so I was welcome at meals. I can’t remember details, but the conversations were always quite stimulating. The Benedictines at St. John’s were rather liberal.
In the afternoon, we’d meet to discuss various aspects of polyhedra or perhaps work on some models. Often Magnus would be building while we talked.
Then I’d be on my own for a bit. Often I would go to one of the Offices in the Abbey church before dinner, and I’d meet Magnus after the service (the monks sat in their own section) and we’d walk down to dinner and more interesting conversation.
Our evening sessions were a bit more informal, and our discussions would often be more philosophical rather than polyhedral in nature. Magnus would have his nightly brandy — or perhaps a little Grand Marnier, since I would usually bring him a bottle when I visited.
Then it was early to bed for Magnus, although I was up a little later. I am not sure when the first Office was in the morning, but I am fairly certain I was always in bed at the time….
We must have made arrangements for future visits either by phone or email, since this is the only correspondence I have which includes any details of visits with Magnus. But they were wonderful times which I shall always remember fondly.
I’ll continue with excerpts from my correspondence with Magnus next week…so stay tuned!
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