4, 5 and 6.

These refer to the impressive time change on taking this journey in one swoop. We had to 'fake' night, by closing windows, even though the sky was bright... I had never experienced this before.

7.

The honking of horns was amazing in Shanghai. We could hear it from our room until 4am, and it started again at 6am. The horn is honked as a way of saying "Here I am!" and is used every time one vehicle passes another. So the variety and frequency is enormous. On one bus trip, we think our driver honked his horn almost the whole way on a 100 mile trip. It is a friendly gesture, not one of annoyance, and we found it endearing, and humorous. We even miss it sometimes!

8.

It was very hot in Shanghai during our visit and we walked miles each day, exploring. Tsing Tao beer, was there in our room refrigerator when we returned. It was refreshing... and inspiring, in the true Chinese tradition.

9.

The words 'Famous Street' were written on a flashing neon sign we could see from our hotel window. It was the familiar name of Hua Shan Road, the main boulevard outside the University gates.

Henry Brant is our longtime friend and composer, who won the Pulitzer Prize for music in 2002. He calls his music 'spacial music' and his work is usually written for a specific performance space, sometimes outdoors, commissioned for orchestral halls and even city spaces, wordwide.

12.

We actually saw, on a sidewalk not too far from the Shanghai Public Library, that wet cement had been immpressed by many, many footsteps. Nineteen million is the population of Shanghai.

13.

This charming motto was repeated on huge billboards around Shanghai; we noticed it especially on 'Famous Street'. It referred to the proudly anticipated WorldExpo 2010, to be held in Shanghai, China.

14.

The zig-zag, a symbol of good luck, is a common tile pattern on many Shanghai streets. It is mirrored in architectural forms in various ways, including the famous 'Zig-Zag bridge' in the old section of Shanghai, near the antique market. Although to barge straight ahead through the wild maze of traffic on a Shanghai street is often recommended, we found the zig-zag a lucky way to cross...

16.

There are lots of dumplings on one's mind in Shanghai, of course, and this reference to the TV tower is explained by its shape. (See note to 28.)

21.

My husband Rick Wilson, Professor of Mathematics at the California Institute of Technology began his lecture, 'Properties of incidence matrices of t-subsets and k-subsets, and applications' by saying: 'I want to tell you about some of my favorite matrices.'

22.

'Perfect nestedness' is a term coined by Richard Brualdi, Professor of Mathematics at University of Wisconsin. He used it in his talk on 'The Combinatorial classes of matrices' where he used ecology of mountaintop pigeon species behaviour as an illustration. My understanding of mathematics is mostly poetic. I found it particularly effective.

28.

The modern 468 meter high 'Oriental Pearl Radio and TV Tower' at the mouth of the Lujiazui River, is the highest tower in Asia. Eleven spherical structures of various sizes are strung like pearls rising into the sky. One of them (at 267 meters) is the highest rotating restaurant in Asia. (Note that this tower has already been referred to in 16.) We were impressed that many of the newest buildings in Shanghai (part of an immense construction project) are being built to resemble natural forms. Another looked like a huge stalk of bamboo.

30.

Often, on late night bus and taxi rides, returning to our room at the faculty club at the University, we were impressed to see large construction crews with helmets and lights working after midnight. One especially memorable night, we realized they were creating a large neighborhood garden park.

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