These are exercepts from Bill Thurston's notes for the seminar Topics in Topology which started on August 29, 2011 (used by permission from the author).
Here is one downside of the flocking behavior: a great part of the propogation of mathematical understanding is by face-to-face discussions and oral tradition, because mathematical papers are often much more technical, tedious, and denatured compared to how people really think about the ideas when they are actively working on them and developing them, Participants in a flock read each other's papers, but often this is made much easier and more natural because fo their shared background. It is much harder for someone not already versed in the basics of a topic to understand from a technical paper what it is all about. Different flocks use different language to discuss similar mathematical phenomena; people have a big decoding problem when they jump to papers written in a different tradition.
We take in things geometrically bu do not really have adequate ways of communicating these things in the same way.
At the time, I didn't think the side topics led anywhere special, but over the course of my career, again and again, the mathematical side-branches that I pursued enough to gain some insight have connected, often in significant ways, to other more mainstream branches of mathematics that I was interested in. I've seen enough occasions where I or others developed surprising interconnections that I think potential connections are quite common.
A major difficulty in the development of connections is not only that there is limited intermingling between different flocks of mathematicians, but also flocks, like individuals, have a limited life-span: topics and points of view often disappear from sight as flocks of mathematicians dissipate and move on to fresher feeding rounds, and solitary mathematicians also move on or go out of circulation.
Crocheting Adventures with the Hyperbolic Planes - it is possible to read it by clicking Look Inside!
W. Thurston On Proof and Progress in Mathematics
About photos: first one is in Stewart Park, Ithaca, NY, the others are from my recent trip to Canada.
Tuesday, August 30, 2011
Wednesday, August 10, 2011
The outdoor kitchen and "dining room" our family was using then is still the same, just by now two cabins at both ends of it are added.
This swimming pool which is used by all community members is also essential in early history of crocheted hyperbolic planes - in summer 1997 I spent many hours at the pool side while my two daughters were learning to swim and improving their English. We arrived in United States just before Christmas in 1996 and they did not know any English. When in fall of 1997 they returned to school, they had no more problems with American English and were correcting me who was taught to speak a proper British.