Response from Prof. B.

Touche on the comma comment. I do try to pack a lot in sometimes.

It is interesting to read responses that come in after a number of other classmates have expressed their opinions, in class or in their writing. That, it seems to me, is an important aspect of education in a classroom setting. The questions of others are not merely tolerated, they add to the total experience, or they can anyway.

It seems that the notion of configuration space show be illustrated better so that a definition emerges somewhat more clearly early in the chapter. Tim Faulkner has suggested in his week 11 response that the order of chapters 7 and 8 should be inverted so that coordinatization can be brought in at an earlier stage. That would make for an easier handle on the crucial notion of the dimension of a configuration space, where that dimension is the number of controls necessary to specify a configuration, as opposed to the dimension of the coordinate space in which the configuration is sitting. There is a subtlety here that I am beginning to appreciate more, although I am still not certain of the best mix of the synthetic-wordy approach and the analytic-formal alternative.

It isn't just time anymore. I'm glad you (and your friends?) agree on that.

The catastrophe theory is really a more subtle topic that I couldn't express in a way suitable for inclusion in the Scientific American Library volume even though the best exposition of that subject appeared in a Christopher Zeeman article in the Scientific American journal. I'll try to find that reference in case you are interested further. In did find a reference on the web, to a guest lecture given by E. C. Zeeman at Trinity College. Here it is. http://www.math.utsa.edu/~gokhman/ecz Unfortunatiely I haven't been able to get it to come up on my machine, but maybe you will be luckier?