Thank you for the reflections, which bring up a few issues that have to be considered when designing this sort of course for non-concentrators. Like many students in the class, you have a busy schedule with a variety of demands on your time. It may be difficult to keep up with weekly assignments in an S/NC course of tangential interest. Yet the course, especially in its electronic form, depends to a greater degree than most non-seminar courses on up-to-date responses so that students can establish patterns of interaction using the internet. When someone falls behind, then it is easy to end up "on the margin" (to use a term from Business Economics?) The complication of finding available machines is another drawback, but I think that that is temporary insofar as there should be more and more machines on campus capable of handling the level of interaction appropriate for this course, and I look forward to the day when it won't be very inconvenient for people to keep up the pace.

The pacing became important from the instructor's side too, since it was easier to make responses to a group of entries all of which came in roughly at the same time, just before a couple of days of class discussion. It just wasn't as easy to respond to late submissions.

As I mention below in the general comments, there are some things that would make the presentations better, and part of that has to do with linkages. I was curious when you mentioned W. Flinders Petrie, and I used the search capabilities of Netscape to check on my conjecture--he was not only a world-famous Egyptologist, but also he had an indirect connection with the fourth dimenison! I quote from one of my favorite math books, "Regular Polytopes" by H. S. M. Coxeter, whom I have mentioned often in class:

"John Flinders Petrie, who first realized the importance of the skew polygon that now bears his name, was the only son of Sir W. M. Flinders Petrie, the great Egyptologist. He was born in 1907 and as a schoolboy showed remarkable promise of mathematical ability. In periods of intense concentration he could answer questions about complicated four-dimensional objects by 'visualizing' them. . . He worked for many years as a schoolmaster. In 1972, after a few months of retirement, he was killed by a car while attempting to cross a motorway near his home in Surrey." Interesting.

Does dimensionality figure in water polo? I wish I had known the golf connection since I have a geometric computer golf game that I would like analyzed. Good luck with continued contact with mathematical ideas.

Course Grade: Satisfactory

Commentary to the Maze Group

Although your work has furthered the study of mazes and labyrinths beyond the preliminary investigation that some of you carried on in the book report exercise earlier in the semester, it does not seem that there has been that much progress in understanding the mathematical principles involved, in particular the function of dimension in the subject. It may be that there just isn't that much there, and the subject is too easily exhausted.

Let me comment on several aspects of your website. The overall structure is certainly fine, inviting the reader to explore the concept in literature, history, art, recreations, and algorithms, but there could have been more of an attempt to coordinate the form of the various sections. All of the pages seem quite wordy, unrelieved by illustrations, even though there were links to visual material.

It would have helped in the literary portion to include links to biographical information on the various authors, especially George Eliot with her Victorian connections. The Borges link is a nice one, although itself a bit rough and unscholarly in its writing. The background texture on the Auden poem makes it difficult to read, and it would have been better to analyze it somewhat, since it is a fairly good poem and it does bring up a number of interlinked images that can be related to other aspects of the topic. In particular it is one of the most "dimensional" of the literary examples in that it explores the concept of an overview. This overview notion shows up in at least one of the computer games, where a player can navigate a series of rooms without looking at the floor plan, or choose to see the plan of the maze "from above". That would have been a nice way to establish some linkages within the final project, to get away from the impression that the parts are separate somewhat unrelated entities.

The history section would have done well to link to some of the artistic representations of the Minotaur legend (there is an nice on in the "Mazes and Mathematics" link in the Recreations and Games subsection) as well as to some more serious sources of information of the encyclopedia variety. It should not be necessary to highlight the words each time they appear in the page, a very distracting feature. The link to Borges is not particularly historical, and the "Greece" link only goes to a very general source on mythology, with no further information on how to follow that thread. "Crete" appears to go to a travel folder, and "Nile" to a field trip, neither of which adds much to the narrative or gives any information that might be useful to labyrinths, mathematical or otherwise. There must be more legitimate sources out there. The material on Egypt was intriguing since mazes are not so commonly associated wht that culture. It would have been good to give the reader some more idea of places where additional material could be found to follow up this introduction.

In the art presentation, although the choice of images includes some that are quite striking, there is not enough elaboration to show how the mathematical concepts are suggested. The link to Escher for example does not lead to anything specifically related to mazes and there is little assistance provided in the text. There has to be some further biographical information provided about the unfamiliar artists, like "der Hundertwasser". The notion of a maze inside one's head is something that could be developed even further, in that the two-dimensional slice of a brain, in CAT Scan or MRI form, resembles a maze structure, which only can be navigated by moving into the third dimension, into the full range of convolutions of the brain. It is not clear to what extent the mandalas represent mazes at all. A link to the history section of the paper, with reference to the classical themes, would have held the sections together better. Hedge mazes as forms of artistic expression could receive more attention too.

The maze references in the World Wide Web could have been annotated more helpfully. Some of them are quite mathematical while others have little to add to the discussion. Singling out some of them for special consideration would have made the section more useful, especially if some of the games could have been linked to other sections of the final project.

The algorithm section, curiously enough, seemed less interactive than the earlier trio demonstrations that used hypercard stacks. Some visual illustration in the code sections would have been much more helpful in showing how to pair a simple maze up with a tree, and how to use the queues and stacks to make the various analyses. The in-class presentation made the comparison clearer, but it never had the force of the earlier demonstration. Some illustrations of weighted graphs could have motivated the Dijkstra method, and tied in better with the applications of maze algorithms to practical problems, as mentioned in the introduction.