Response from Prof. B.

I agree that doing some more exercises regularly would have been another way to penetrate more deeply into mathematical ways of thinking, and the next time I do the course I most likely will be more forceful about encouraging students to hand things in regularly. At one or two points I threw some problems out but there was not much enthusiasm, partially, I believe, because they do not easily lend themselves to solution online. Also it is a bit hard, but not impossible, to come up with problems that work for everyone, especially since people come to this course with very different backgrounds and expectations. Nonetheless I do hope to have in future versions of this course a range of problems that will challenge each person at his or her own level. We already have accumulated some, and the hypertext capabilities of the software should enable readers to find things that are possible without being unproductively frustrating on one hand or too easy on the other. But it is true that there is a price to pay by insisting on problem-solving as an essential part of the course and I chose to go along with the response patterns of the most active members of the class for the most part.

As I mentioned in class today, technical support for html in particular will be a given in future versions of this course. Also we should arrange for better access to scanners, and better software to avoid the problems you had getting things to fit on the page. I am glad that you devoted the effort to getting the project to work well, although I would have liked to see some of your own writing in the final project since I have enjoyed reading your comments in the weekly responses. By the way, did your society ever get a response from Madeleine L'Engle?

Course Grade: Satisfactory.

Comments on the Literature Group

Geometric poetry has fascinated any number of writers over the years, and the topic can be explored from several different viewpoints. The classical work of writers like George Herbert (1593-1633) is related to, but not identical to, the more modern examples. There should always be bibliographical references for such figures, especially those who have entries in standard reference works. As it happens a search of the net brings up a number of things, like a chat group arguing over the significance of shape in "Easter Wings" and an interesting tangent in the mention of George Herbert Walker Bush. For the modern writers, it is important to give references so that their work is placed in context. With respect to dimensional poetry, see the example of Dan Margalit in the Cosmology Project.

In the section on children's literature, it is again important to give biographical references to the various authors cited, and links to some particular passages that contain overt dimensional content. Otherwise the page seems rather sketchy. The substance has to be made accessible to anyone who wants to get beyond the introduction.

The short story on Flatland Genocide would be more effective with some links that go into some additional levels of detail concerning the Huygens principle that forms the basis of the plot. One of the virtues of the interactive hypertext is that it permits this sort of explication in a non-intrusive way, to allow the reader to decide on the degree of pedagogy or pedantry, following personal taste. This aspect of the technology is related to the idea of sidebars, as Dewdney's "The Planiverse".

The series of five short essays gives a nice range of approaches to the general topice of dimensionality. The linkage to various sites connected with authors is effective, as is the linking to other parts of the final project. I was happy to learn about Jean Rhys for example, and to see her picture and the first page of her novel. The Joyce page, on the other hand, is a bit hard to navigate. A specific link to "Ulysses" might be more useful. It would be possible to move from the overviews in these paragraphs to more substantial commentary, for example on the implied higher dimensionality of the multiple-narrator fiction of William Faulkner. (Professor Weinstein has something to say about this in his courses and he has given guest lectures in Math 8 in the past.) The idea of presenting plays from different viewpoints suggests other geometric questions. I gave a talk on this topic earlier this semester in a course at RISD on experimental theatre and it would have been good to bring that topic up for our class as well--how does the staging of a play bring out the relationships? The classic example of a story told from many perspectives is the Japanese film "Rashomon", for which there are good web links available. (I just saw it again Sunday night--I recommend it.)