Fr. Magnus Wenninger, O.S.B., III

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.

Excerpt from 3 February 1994.

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….

Excerpt from 27 February 1994.

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.

Excerpt from 3 March 1994.
Excerpt from 16 May 1994.

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.

Excerpt from 10 June 1994.

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!

Fr. Magnus Wenninger, O.S.B., II

In this next installment of my commemoration of Fr. Magnus Wenninger, I’ll excerpt various snippets from our correspondence together which illustrate Magnus’ unique perspective as well as highlight our collaboration together.

This is by no means meant to be a complete biography of Magnus’ life; rather, I hope you get to know Magnus a little through our particular correspondence.  Of course everyone who knew Magnus had a slightly different experience.

I have about 65 letters in my folder of correspondence, which includes both letters from Magnus and my replies.  I had to be selective in preparing my talk for the Joint Mathematics Meetings, and what follows are the excerpts I chose (in chronological order), along with some personal commentary.

Excerpt dated 24 August 1993.

I chose this excerpt for a few reasons.  First, Tom Banchoff will also be giving a talk at the JMM in our session commemorating Magnus.  But I also wanted to highlight the fact that Magnus, although already in his early seventies, was still very active.  He was routinely invited to give talks and presentations, and also published papers occasionally.

And, as he indicated, when not otherwise occupied, he was always building models of one sort or another.  And I really do mean always — even at conferences, he would often have a table set up where he would build models and discuss polyhedra with anyone interested enough to stop by and see what he was up to.  Which was usually very many people….

Excerpt dated 30 August 1993.

This excerpt is from a letter dated 30 August 1993.  It would take too long to set the stage for what this letter discusses, but I want to draw attention to the words “eye-balling” and “guessing” here.

Magnus’ focus was on building models, not on studying their precise mathematical properties.  So if he didn’t actually know exact coordinates for a model, he would approximate, and build what he called a variation of the abstract mathematical model.

But here, Magnus is being somewhat humble — for his eye-balling and guessing is scaffolded on decades of model-building experience.  It’s like giving a chef who graduated from Le Cordon Bleu a bowl of soup, say, and asking him or her to “guess” what spices were used.  You’d get a lot more than just a guess….

This intuition about three-dimensional geometry was absolutely key to Magnus’ model-building success.  If a spike on a model was too “pointy,” Magnus would simply design a variation with the features he wanted.  And somehow, almost magically, they always turned out wonderfully.

Excerpt dated 13 September 1993.

This next excerpt is dated 13 September 1993.  The important quote here is the last complete sentence.  As I mentioned last week, Magnus is best known for his trio of books Polyhedron Models, Spherical Models, and Dual Models.

Magnus is not the first to have enumerated all the uniform polyhedra; this had been done by a few others earlier — Coxeter (et al.) published a complete enumeration in 1954, Sopov proved completeness of the list in 1970, and Magnus’ Polyhedron Models was published in 1971.

And even though Polyhedron Models was always the most popular of the three books, Magnus’ felt that Dual Models was more significant since it was the first time all the duals of the uniform polyhedra were published.

I also note his use of words:  “more significant.”  I don’t think Magnus would never had said “I am more proud of Dual Models.”  He was not a prideful man, always giving credit to his God for his insights and abilities.

But I think significance here is all relative.  In terms of popularizing polyhedra and model building, Polyhedron Models was certainly the most significant of the three books. But in terms of a contribution to the mathematics of polyhedral geometry, I would agree with Magnus that Dual Models was the most significant of the three.

Of course Spherical Models is quite wonderful, too….  But in this book, Magnus indicated how to build (or approximately build) a wide variety of spherical models.  However, moving in this direction is much more difficult mathematically and in some sense broader than just considering the uniform polyhedra or their duals, since there are many ways to build a spherical model based on a given polyhedron.  So there would be little hope of being so comprehensive when discussing spherical models.

Excerpt dated 4 October 1993.

I include this next excerpt since it is one of the few times Magnus has mentioned his own abilities in his letters — it also echoes the excerpt from 30 August 1993.  So there is little more to say here, except to note that he mentions his intuitive abilities are derived from building over a thousand models, not to any inherent ability.  Again, an instance of his humility.

Excerpt from 6 November 1993.

In this excerpt, I point to the phrase, “…holding a real model in my hands is still my greatest thrill.”  Those of us who knew Magnus absolutely knew he felt this way about model building.

Because of his extensive polyhedral network, he had connections with mathematicians who helped him with precise, computer-generated diagrams to help him make models for his books.  But he was less interested in the details of how the diagrams were made than he was in diving right into building the models themselves.

He was also well aware that computer graphics were an excellent tool which could be used to discover new and wonderful polyhedra — changing a parameter here or there would result in a different polyhedron, and it is easy to look at parameterized series of polyhedra with a computer.

But, this was all in aid of model building, not an end in itself for Magnus.  There are plenty of others who focus on the computer graphics — as it should be, since any polyhedral enthusiast will have their own particular areas of interest and expertise.

Only five excerpts, and it’s time to finish!  I didn’t realize I had so much to say about these snippets of correspondence.  But I hope you are beginning to have some insight into who Magnus was and what he accomplished.  I’ll have still more to say as in the next installment of excerpts from my correspondence with Magnus.