Thank you for your reflections. If you and Dave Stanke were in an unofficial competition on background colors, I think that your "red shift" has reached an unsurpassable level. I guess I will have to get used to high contrast writing as we continue to explore this medium.
Your comment about the in-class lectures is well taken, but there is not an easy answer to the problem it represents. One of my aims in the course is to expose the class to some mathematical concepts that they ordinarily would not have met in elementary courses but that can be appreciated at some level and illustrate important breakthroughs in mathematical thought. One such was the fact that there are uncountable as well as countable infinities, and another is the fact that it is not possible to build any surface containing a Moebius band in three-space without having some self-intersections. Each of these topics would require several lectures even to set them up with any completeness, but that would have left behind a good many members of the class, who had hopefully grasped some of the flavor of the arguments but who would not get that much more out of examining the details. Of course one has to pick and choose among these examples, and I have used different ones over the years, some more successful than others. It will be interesting to see if the use of the internet will make certain topics more accessible than others.
Your group was quite successful, I'd say. Below are some general comments on the presentation on Monday. By the way, your course grade is Satisfactory.
Comments on the Cosmology Group
Your group certainly did a thorough job with your substantial web pages and your presentation. I'm glad that we allotted a full class period to it since it covered so much ground.
The Field of Cosmological Dreams was a very creative and successful way of presenting numerous interrelated theories connected with the nature of the universe, especially in relation to geometric ideas. There was effective use of visual materials and historical links, a nice final presentation component which was both engaging and historically accurate (even if the spelling and pronunciation of the names was somewhat inconsistent).
Possible shapes for the cosmos covered a great many topics, some combined in ways that were not included in any of the references. It might have been better to decrease the number of topics and to try to find some new ways of presenting concepts already introduced in class or in the readings. As it was, it definitely invited the audience to look at the references for further elaboration.
The Haikube was a very imaginatively presented illustration of a slicing operation, although the edge-first slices are still hard to understand and corner-first is quite mysterious. It might have been good to start with a more conventional Haiku, to illustrate the literary form and to serve as a basis of an expansion into another space. Following along the space-time analogy, you might consider a poem where three slices in one direction describe the same scene or phenomenon at different times, past, present, and future. Then slicing perpendicular to a different direction could reveal some other aspect of the poem? The relativity of rotation of a person or of space-time itself was nicely illustrated by the plastic card demo (and I would like to have that model, or a copy of it, for the collection.) These examples were a nice counterpoint to the physics concepts.
The Relativity section made some good links to other sections of the presentation and within the topic itself, although it might have been more helpful to include some suggestions for linking at the bottom of the page. It is a bit disconcerting to come to a dead end with no good idea of the way to continue. The asides were effective uses of the hypertext. There seemed to be some duplication in the pictures of spheres on a quilt and the finger pushing against a grid, so some additional links might have coordinated Flatland analogies better, ultimately among the various final projects themselves.
The Expansion section also uses links well to explore a subject that was only alluded to in general terms in "Sphereland" for example. The Hawking speech might have been connected to other parts of the presentation, along with some of the philosophical comments. The sphereland analogy could have been tied in better with the shape section in this presentation. The overall design of the presentation is effective, and the reader is drawn to consider further reading. A suggested bibliography would have been nice, for the whole presentation, not just for individual parts.
All in all it is an impressive presentation, showing a lot of effort. Good work.