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.
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….
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.
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.
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.
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.