Mathematical Travels


What? Is there such a thing? All that mathematicians need is a pencil and paper.  They’re not like geologists or anthropologists who need to go to other places to study the objects of their interest.  In fact mathematics is so easy to do (no big machines, no complex equipment) that you can stay in your garret and do it. 


But this is just the point.  Since it is so easy to do, all the simple things have been done and mathematicians must look around for more and more esoteric problems to challenge them.  This has caused the fragmentation of mathematics into a large number of different sub-areas most of which are incomprehensible to those pursuing other sub-areas.  In any one location with, say, 30 mathematicians, there are 30 different (at least) areas of mathematics being pursued.  Mathematicians, in spite of their reputations, are social animals and like nothing better than to discuss their current pursuits with other pursuers.  Since the only persons who can understand them are often in other parts of the world, they need to travel to get an audience.


This has been the motivation behind much of my own travel.  I usually felt that if I could only travel and talk with X, I could solve the problem that has been bothering me.  Of course it never works out that way.  X usually has his own problems that he’s working on, and although we speak the same mathematical language, we rarely communicate the difficult ideas that each needs to make progress.  So I have frequently taken the opportunity to explore the exotic places that mathematics has called me to with the idea of understanding them rather than the mathematics.


I. Pre-mathematical travels


1. A train adventure.


My first travel adventure occurred before I could really talk very well or even solve differential equations.  This was at the age of 4 in the little town of Ottawa, Illinois.  In our neighborhood, there was a large open field surrounded by the neighborhood houses.  Most of the children in the neighborhood spent most of the day playing in this field.  There was no adult supervision since there was little mischief we could get into. 


That is until the day I convinced my playmates we should go look at the choo-choo train.  I remembered going to the train station with my parents to pick up visitors.  There was always a large steam engine snorting and puffing smoke and steam.  I thought it would be nice to watch it again.  So about a half dozen of my little friends and I walked the 6 blocks to the train station.  We were lucky because just as we got there, a train came in.  It thrilled us with all the noises and sights.  After about ten minutes it left again and so did we.  When we got back to our neighborhood, I remember seeing adults running around from house to house.  It never occurred to me that they were worried about us.   Thus ended my first trip.


2. A Hitchhiking adventure.


My second big trip, about 12 years later, was a bit more adventuresome, though still pre-mathematical.  I had just graduated from high school in a Chicago suburb, where my parents now lived.  A friend and I decided we wanted to see something of the country before we started serious pursuits.  We had both worked in local restaurant after school and had each saved up $50 with seemed like a fortune at the time.  With this money and a pair of sleeping bags, we set off for the west coast by hitch-hiking.  This was 1948 and hitch-hiking was not considered a dangerous activity.  In the second world war, it was a very common way of getting around since gasoline was rationed.  This lasted for a few years after the war until in the 1970’s it was suddenly perceived as being dangerous and in fact had become more so.  In any case in 1948, it was a suitable way to travel and my parents did not make much of a fuss.


Our procedure was to get as many rides as we could during the day and then, in the late afternoon, look for a place to bed down for the night.  Usually it was in some farmer’s field, but once we slept in a sandbox in a park.  For meals we cooked our own, if you can call heating a can of beans over a campfire and burning a hot dog on a stick cooking.  But it was cheap and we wanted our $50  to last a couple of months.  One night when it rained we opted for a tourist cabin for 75 cents a piece and almost ruined our budget.


After 5 days of this we got to Cody, Wyoming.  By this time we were sick of our frugal meals and wanted something more substantial.  It was then our restaurant job experience served us well.  We went to a local restaurant and asked if they wanted any help.  To our surprise, they hired us both on the spot as busboys, and gave us a western stick-to-the-ribs meal. They money they paid was used to rent a tent on a platform, which was much more comfortable than the ground particularly since I was afraid of snakes.


But Cody was not that interesting and after a couple of days we headed for Yellowstone Park.  One of our rides was with a couple staying at a place called Pahaska Teepee, who told us the restaurant at that resort was looking for dishwashers.  So dishwashers we became. It was really an idyllic existence; after a half day of washing dishes, we were free to take advantage of everything the resort had to offer.  This included hiking in the mountains, fishing for trout in the Shoshone river, swimming in the horse pond, riding horses on the back country trails, and best of all, playing games with  the numerous girls who were waitresses in the restaurant.


After a couple of months of this, we felt we had to leave if we were ever going to realize our dream of going to the west coast.  So we reluctantly said good-bye to all of our young (female) friends and started hitchhiking west again. We eventually, after a few days, made it to Oregon and the Pacific ocean.  We then headed south to California where we had couple of new adventures.


We were picked by a car full of Indians in California, who asked us if we wouldn’t buy them some beer, since it was illegal for Indians to buy beer!!  Nonetheless at the liquor store they sold some to me a, minor of 17 who looked younger.  We then went to a hillside overlooking a ravine and drank beer together until we were all plastered.  We then found a convenient flat spot to bed down for the night and woke refreshed (sort of) in the morning.  Our Indian companions had left with all the beer; no great loss since they had paid for it.


We continued to hitch hike down the California coast, but time was running short, so we eventually headed inland toward Redding.  There were a number of hills of mine tailings nearby which seemed wild and secure, since they were overgrown with vegetation.  We chose a wild spot in a little valley and camped for the night..   We had stopped in a city and bought our usual hot dogs and beans which we cooked over a campfire.  However there were some left over which we were saving for breakfast.  But during the middle of the night, some animal, circled our camp growling and making a coughing sound ( a dog with a sore throat?).  We each crawled down in our sleeping bags as far as we could and covered our heads and held our breath and hoped the animal would be content with our hot dogs.  It was.  They were gone in the morning and so we were as fast as possible.


We set out again in the direction of  Nevada where a rancher dropped us off in the middle of nowhere, more precisely in Golconda, which was little more than a water stop for freight trains.  After sitting the hot sun for several hours hoping in vain for a ride, we decided to try to find if we could get a ride on one of the freight trains stopped nearby.  Fortunately there were several other itinerants in a boxcar who told us what to do (stay away from gondolas whose load could easily shift, and get on the front and not the back of a boxcar).  The railroad workers were generally friendly and told us at one point that the car we were riding in was due to be side tracked.  We rode in various freight cars in the course of the next couple of days and crossed the Great Salt Lake in one of them. 


When we got  to Ogden, Utah we were very tired and dirty and looked for a place to refresh ourselves.  We found a nice cool stream nearby and took off our clothes and went for a swim; we also found the railroad police, or  rather, they found us and said they would arrest us if we didn’t leave railroad property. So we did, and walked to bus station and reluctantly parting with some of the money we had made as dishwashers, took a bus back to Chicago, thereby ending our adventure. I went away to school and my friend Chuck moved to Oregon with his parents.  We never saw each other again.


 3. A government trip.


There were a few other pre-mathematical trips, the first of which was sponsored by the US government which shipped me as an army draftee to Fort Leonard Wood and then to Fort Bliss, Texas.  There I learned the usual army skills, namely how to lie, cheat and look busy.  It also gave me a number of recreational opportunities in Juarez, Mexico, and made it possible for me to spend a night as a guest of the Mexican government in the Juarez jail.  But I also learned something about electronics and was able to get out of the army early to study electrical engineering at New Mexico State University.  After a year of study I got my degree in electrical engineering and was subsequently hired by a company in Milwaukee to work on guidance units for ICBM’s.  While this was very challenging work, it bothered me a little to be working on these superbombs which could destroy an entire city instantaneously. This led to another pre-mathematical trip.


4. Finding my roots


My parents had been German immigrants who came to the US in the 1920’s, but I still had lots of relatives in Germany that I had never met.  I had wanted to get to know them so I could get a better understanding of my roots and to try to make sense of  the many contradictions I saw around me. So I took a leave of absence from my job and with another friend, Jim, I set off for Europe. We went by ship, by slow ship.  It took 10 days to get to France which we took advantage of by carousing in the ship’s bar every night and sobering up in the sauna every morning.  We arrived in Le Havre and immediately took a train to Paris where we stayed for about a week. I would like to say we enjoyed the flesh pots of Paris, but they were too expensive and we were too cheap. We saw more bean pots than flesh pots.(In fact, I have never tried a flesh pot).


After tiring of Paris we took a train to Stuttgart and met some of my relatives.  They let me borrow a bicycle to tour the rest of Europe, which we did, visiting Austria, Italy, Spain, and France again.  We then went to Germany again and caught the return boat (I mean ship) back from Hamburg. It took 14 days to get back, a not all together unpleasant time. 


When I got back my boss chewed me out for getting back 3 days late (I hadn’t checked the dates and thought the return trip would only take 10 days as the trip to Europe had). So I quit and went to graduate school in Madison (having already applied and been accepted just in case).  After I finished with my PhD and perhaps not coincidently, fathering 3 children with the help of Edie, my wife (I had gotten married first, it was the fashion those days), I returned to Milwaukee temporarily to teach at the local university.  Two years of this was enough for me, so I looked around for other opportunities.  That laid the foundation for my first mathematical trips.


II. Early Mathematical trips (with Kids)


5. Two quick mathematical trips


I had returned to Milwaukee before I finished my dissertation  and spent the first year there writing it.  My major professor had gone on leave to Stanford University and I had to visit him there in order to put the finishing touches on it. (Actually I had gotten stuck on a proof and needed his help). So I flew out San Francisco and then went on to Palo Alto, where I spent about a week in some cheap hotel, and made daily trips to the Stanford campus. The walk to the campus was the most interesting part for me since it passed through a large grove of eucalyptus trees.  These had a delightful aroma usually associated with mouthwash, and had strangely shaped conical nuts which gave off this characteristic smell.  I gathered some and brought them home to my children whom, I thought, would prefer them to the usual hotel soap bars I brought back from my trips. After a week of 16 hour days, I finished and returned to Milwaukee.


The second quick trip was also to the San Francisco area, to a mathematics conference at Berkeley, where I gave a short talk on my research.  I went there with my fiend Louis, who was a flamboyant Pole.  He went everywhere first class and insisted on renting a car even though, in the Bay area, it was more a nuisance than a convenience. He was also a very erratic driver; once when we stopped at a traffic light on of the steep hills in San Francisco, he could not get it into gear and we started rolling backwards.  Fortunately we ran into the curb before we hit anything worse.  After that I wouldn’t ride in the same car with him unless I was driving. When we left the conference he arranged for a helicopter to pick us and take us to the airport. That remains the only time that I have ever taken a helicopter ride.


6. California here we come.


After spending two years in Milwaukee at my temporary job,  I decided to look for greener pastures.  Fortunately my major professor, Jaap Korevaar, had now moved from Madison to  La Jolla, California, and was able to arrange a visiting position for me at the University of California –San Diego.  So we bought a van, replaced one of the back seats with a mattress, threw our three kids on the mattress, and set off for California.  We also had a tent and other camping equipment and planned to camp on the way out to save the cost of motel rooms. 


Things went smoothly until the second night of our trip.  We had  camped in a state park in Nebraska, and were settling down for the night when we discovered we had pitched our tent on an ant hill.  The ants did not like our intrusion and came into the tent to complain.  This in turn led to complaints from our children. After a few hours, Edie and I calmed them down and we were all able to go to sleep. For about an hour until the thunderstorm started.  Still our tent was fairly waterproof so the rain didn’t get in at first.  But then the water started coming in the entrance. In addition to being on the ant hill, our tent was in a low spot, which soon became a small pond with us in the middle.  Soon everything was soaked; our sleeping  bags, our clothes, our tent, and our spirit. So we dumped everything into the van including our sleeping children and took off again around 3 in the morning.  In the morning  we arrived in Colorado Springs, where Edie had a brother who put us up and helped us dry out.


After a couple of days we left the comfort of the house and  set off for New Mexico to see what new adventures awaited us.  We didn’t have to wait long. A few days later, after camping in the mountains, we stopped at a small lake in New Mexico, where our older son, Pierre, fell and tore open his knee on a rocky outcropping.   We took him to the emergency room at a  hospital in Gallup,  where they treated his knee, but it later got infected anyway. It was  a couple of days later, when we were camping at Grand Canyon, that we noticed he was feverish and in much pain. Fortunately there was a nice little hospital at the canyon where he was admitted and stayed for about 3 days until his knee got better. We then set out on the final leg of our trip and arrived in San Diego (actually Del Mar) in reasonable health.  


We had previously arranged to rent the house of a mathematician who was on leave for a year.  We unpacked the van and tried to settle in. But the previous tenant had had a dog, and the dog had had fleas, and the fleas took it upon themselves to form  a welcoming committee.  We soon all had  little red bumps on our legs that itched furiously. That was before the boils started.  Our son with the knee had been given so many antibiotics that all the good bacteria were killed and made way for bad ones that gave him boils, which he in turn gave to his brother.


But we were finally here in southern California about a block from the beach and only a few miles down the road from the university.


The year we spent there went very rapidly, with the beach, the mountains, the desert, Mexico, the exotic plants and animals all contributing to our enjoyment. It was also very satisfying mathematically as well.  Since the university was new the faculty had not had time to develop the cliques that characterize academic life at most established places. Everyone was willing to share his or knowledge and there were many impromptu seminars.  One such was devoted to constructive analysis led by Errett Bishop, who felt that the use of the law of the excluded middle (i.e., proof by contradiction), was inappropriate to the infinite sets to which it was often applied.  I became a convert after attending his seminar, and decided to change the direction of my research.  But try as I might, I could not do mathematics in this way and I soon returned to my old ways, but as a result have always tried to avoid these indirect arguments.


We left a bit reluctantly in June for our return trip to Milwaukee, again throwing a mattress and our children in the back of the van. No sooner had we left than our older son complained about a tickle in his throat. He leaned forward so Edie could look down his throat.  This was when he vomited. So we spent about an hour in gas station cleaning up the car and changing clothes. Fortunately this cured the tickle in his throat, and we returned to Milwaukee without further incident two weeks later. That is, except for the bear in Yellowstone Park. We were sleeping soundly in our tent when we heard a clatter outside. A bear had picked up our footlocker with our dishes and was rolling it around and shaking it.  I stuck my head out of the tent and yelled at him, which startled him and he ran directly at me, which startled me.  When he was about five feet away, he stopped and ran in another direction, and so did I, to the outhouse.


7. Off to exotic Peru


After returning from California, we settled into our comfortable routine in Milwaukee for two years, after which I again got the urge to travel.  I had found out about a Ford Foundation program to improve science teaching in Peru, and immediately applied for it. There was one problem, and that was that I would have to lecture in Spanish, which I had studied for only one year in high school. But I had applied early enough to give me a semester and the summer to learn the language (sort of).


When I found out that I  had been accepted, I decided to go ahead in spite of my poor Spanish.  Edie and I packed up a bunch of large crates with housekeeping supplies and the whole family took off for Lima, Peru by plane.  The Ford Foundation put us up in the fanciest hotel in town, which delighted our children since there were all sorts of buttons and bells. They had merely push a button and someone appeared at the door. But after two days of this fun, I was expected to start giving lectures in Spanish!!


I had a small class of about a dozen students who dutifully listened to me making a bunch of strange sounds in front of them. I had no idea if they were understanding me or not. They, in turn, made some strange sounds which did not have much resemblance to the Spanish I had studied.  After a couple of weeks of this, I began to recognize some of the things they were saying, but I’m still not sure they followed me.


Our life became a little more normal when we found a house with the help of the Ford Foundation, which paid for it, and gave us a car, and sent our children to the American school. In addition they paid my salary and gave me a 10% hardship bonus each month. The hardship consisted of enduring the Peruvian weather, which was dismal for half the year. In spite of being almost on the equator, the country has a temperature in the 50’s during most of the summer; it is cloudy every day with a mist that seems to permeate everything.  It seems to be on the verge of raining, but never does (except once every 20 years). Since few houses have central heating, one gets used to wearing a jacket inside and out. That is, if we had had jackets, which we had left in Wisconsin.


We live in the San Isidro area of Lima and the university where I taught (Universidad Agraria) was about 12 miles away. Just the right distance for a bike commute, I thought.  So I bought a bicycle, and tried it for awhile. I had some trouble dodging the potholes and the drivers who assumed I was too poor to afford a car, and thus not worthy of sharing the road.  However, the biggest problem was the dogs, which traveled in packs looking for cats, rats, and bicyclists to devour.  I was able to outrun them on my bike but always got to school exhausted. I started driving  the next week.


We gradually settled into life in our new environment, as oligarchs in a feudal society. We had a maid, a gardener, a private school for our children, the use of a new car, a free house; all courtesy of the Ford foundation.  In return, I was supposed to help raise the level of mathematics education at Universidad Agraria.  It needed raising.  Except for my counterpart, Alberto, who had arranged for my visit, the faculty were very poorly prepared and didn’t show much interest in the subject of mathematics.  I arranged a seminar for the faculty and taught a few courses for the advanced students. 


But then it happened: a revolution took place and changed everything.  Or so they thought.  It was actually a palace coup which removed the elected president and replaced him with a military strong man.  Our landlady told us to go the store and stock up on sugar and flour (for sugar cookies?) But other than what I read in the papers, I was unaware of any changes.


However, after a few weeks, the students on campus started demonstrating about something and the military invaded the campus.  This was rather surprising, since the coup was carried out by leftist generals who introduced a number of  progressive changes (land reform, taxation of landowners, formation of cooperative farms).  These demonstrations disrupted our classes which were held only sporadically for a while.


Meanwhile we took advantage of what Peru had to offer; a rich history with many traces of ancient civilizations, a varied landscape with desert, mountains, and jungle all within a couple of hours of Lima. We went on many excursions with my colleague Alberto and his extended family. At first we visited the mountain villages each of which has its own unique character.  The dress differs from one to the other; the music, very strange to my ears,  also identifies to local people the village from which it comes.  There were only two things wrong with these trips. One was that the roads, often cut into the face of cliffs, scared me so much I could barely drive.  The other was the lack of oxygen at the altitude of the mountain passes (15k feet) which made me so dizzy I could barely drive.


I was thankful when the weather became warm enough to start going to the beaches, which we did almost weekend.  And what beaches they were: very wide with phenomenal breakers, which compared to the ones in Hawaii, lots of tide pools with a large variety of sea life, thousands of birds, many rocky islands, and not many people. Peru at that time, and perhaps still today, was the leading fishing country in the world, thanks to the Humbolt current which brought cold water from the south to the coast of Peru. It resulted in an upwelling near the coast which brought nutrient rich waters to the surface which fed the plankton and ultimately the fish and sea birds which abound in the area.


We also took occasional trip with other Americans who were part of the same program.  One notable one was to a large area of ruins north of Lima to look for pots made by the inhabitants who had occupied the city about 500 years ago.  The surface was covered with pot shards, but we didn’t find any complete ones.  However we did find something else.  A piece of cloth was protruding form the ground and we started digging to find out what it was. It turned out to be a large cloth sack attached to a stick. We opened it and at first a withered leg came out. Then the complete body of a mummy in a fetal position and wrapped in cotton. I took a couple of pictures and we quickly buried it again (no curse of the mummy for me.) WE gave up on our search for pots and drove back to Lima with a few shards.


Another scary trip with Alberto and his two nephews was to the fishing port Pucusana south of Lima.  There was a large harbor sheltered by a rocky guano island, which lots of sea birds used as their privy.  Their droppings were a good source of fertilizer and were harvested for that purpose every few years.  Alberto had the interesting idea of  hiring a fishing boat to take us on a cruise around the island, so we got a fisherman to take us out in an open boat with a one cylinder engine that always sounded as though it was about to quit. The harbor had a large variety of fishing boats and was full of interesting activity, but the other side of the island was a completely different scene.  There were huge waves that (so it seemed to me) threatened to swamp our little boat.  These waves crashed against rocks on the island and I kept looking for places to swim to in case the boat sank.  The fisherman and Alberto were good Catholics and were not as concerned.  But then I saw a penguin swimming by and realized it was hopeless anyway since the water was too cold for non-penguins.  The motor, however, did not quit and we got back safely.


The university, in addition to being closed sporadically because of strikes or “paros” was closed for an extended period at the end of the year. We were invited by another colleague from Paraguay to spend Christmas with his family and so decided to take off on an overland trip to Asuncion.


Our trip to Paraguay took us first to Cuzco, the old Inca capital in the mountains.  The altitude of Cuzco is about 12k feet and lowlanders like us often come down with “soroche” or altitude sickness and, in fact, we did.  Two of our children and Edie suffered flu-like symptoms for a couple of days until their bodies became adjusted to the altitude (with the help of a local tea made from coca leaves).  The city is quite interesting in that it has elements of both Inca and Spanish architecture often in the same building.  The lower levels are often closely fitted stones while the upper levels are whitewashed adobe with red tile roofs.  The reason for this, I was told, is that the Spaniards tore down the upper levels of the Inca buildings looking for gold and then rebuilt them in their own style.  While there we took side trips to the usual tourist sites such as Machu Pichu, the lost city of the Incas, which has now been found by hordes of tourists.


Then we started our real journey, by train across the altiplano, accompanied by lots of local people, who, we were surprised to learn, couldn’t speak Spanish any better than we could.  Their  main language was Qechua, the language of the Incas.  Mostly they were coming or going from market towns with their recently purchased wares or goods for sale.  One fellow had a load of fish in a paper bag that he put in the luggage rack over Edie’s head, where it kept dripping on her.  She thought it was just some condensation until the smell became quite strong.  But there were lots of strong smells on that train, so no one much noticed it. 


We got off the train in Puno and caught an overnight steamboat across Lake Titicaca.  We had had the foresight to reserve berths on the ship figuring we could get  a good night’s sleep while traveling. It didn’t turn out that way. The berths were designed for smaller people, very much smaller people.  They were just right for our children who were 6, 7 and 9, but too small for Edie and me.  So we just strolled the deck and tried to catch a few winks on a chair.  That is, until the storm came.  The ship anchored to ride it out, but it still was tossed about, and made sleep impossible for us but not for our children who awoke the next morning refreshed.  From the ship we went to a rail car which took us across the dessert to La Paz, Bolivia.  La Paz is located in a valley and the railroad comes down on it from above. In the morning sunlight it looked like a jewel with a thousand points of light. Later we saw that these points of light were just tin roofs of houses, very poor houses, and the city which looked so lovely form above, was quite depressed up close.


A few days in La Paz were enough to see most of the interesting sights, and we looked around for a way to leave.  We had planned to leave by train, but would have had to wait another week for the next train, and opted to get a flight out.  This turned out to be more difficult than we thought because we didn’t  have the right exit papers, but more probably because we didn’t know whom to bribe and how to do it.  Fortunately our Paraguayan friend was with us and knew the right sort of threats to make so we were eventually able to fly to Buenos Aires.


Buenos Aires was a different world.  Christmas shopping was in full swing which seemed kind of incongruous because the weather was warm and sunny. There were lots of decorations on the streets and in the stores in contrast to La Paz which was rather austere.  The city has a very European feel with lots of wide avenues and outdoor cafes.  Best of all, it had a zoo, which was the most interesting for our children. After a few days there we flew to Asuncion, Paraguay to spend Christmas with our friends.


Asuncion was like something out of the nineteenth century.  There were still donkey carts on the streets and hardly any buildings higher than two stories. The entire city had a decayed look to it probably because most buildings were decayed and in a poor state of repair.  The economy, under the dictator Stroessner, was not doing very well. But the place we stayed, a Mennonite guest house, was another world.  It was clean and neat and well built, and served heavy meals. It turned out that our friend was part of this community and had arranged for us to stay at this house.  They invited us to their Christmas celebration which, however, was not exactly what we had expected. It consisted mainly of a long dull church service. We had our own little celebration later without the church service and with the benefit of some aguardiente.


It was a short bus trip to Iguasu falls at the frontier of Paraguay with Brazil.  It’s bigger than Niagara, but surrounded by jungle. It was overwhelming, but our children were more excited by the huge centipedes they found on the path to the falls and the many large butterflies which seemed everywhere.  We took the bus back to Asuncion and hopped on a plane back to Lima a few days later.


I found the University was still shut down and I was beginning to feel guilty about taking the huge salary without doing much in return.  A friend who was a Fullbright scholar told me that the Marine Institute was looking for someone to teach them about differential equations.  They wanted to apply a logistic differential equation model to the  anchovetta  fish population to help them regulate the catch. So I gave them a series of lectures on existence and uniqueness proofs for solutions of  general differential equations.  I discovered later that, for the most part, they had no idea what I was talking about.   All they wanted to know was how to use this one simple model with their data.  I came back to this problem later and found that finding the solution is the easy part.  Finding the equation is much harder.


The university eventually opened again and I resumed my teaching and tutoring there.  But now the time went faster as I became more fluent in Spanish.  We soon had to leave Peru and return to our middle class existence in the US.  Our friend Alberto saw us off and came to the US to study with me a few years later.  He then returned to his position as assistant professor but soon rose through the ranks.  His last name was Fujimori.



8. Fish and crabs in Wood’s Hole


The stint at the Instituto del Mar in Peru had got me interested in mathematical models of fish populations and I worked with a fish biologist in Milwaukee to study the fish in Lake Michigan.  We put together a multispecies model of the major species in the lake.  This model, in turn, was picked up by some fisheries scientists at the National Marine Fisheries Service in Woods Hole, Massachusetts.  They wanted to fit a multispecies model to the various fish stocks off the coast of New England and so I volunteered to help them. But it was harder than I thought.  Nonetheless, I worked with them for the summer and they arranged for me to get a cottage out in the woods not far away.  We loaded the family and bicycles in and on the car and drove out to Woods Hole. Unfortunately our cottage in the woods had previous occupants, a family of skunks.  This didn’t really cause too much of a problem as long as we were careful not to cross their paths. There was an occasional aroma, but I guess we didn’t smell so good to them either. It was also close to the beach and not far from some good fishing spots so was otherwise ideal.



The next summer we went there again but were unable to get the cottage in the woods.  We had to settle for a place on Waquoit Bay about 20 miles away.  This turned to be even better, since there were several salt water streams nearby. This time, instead of bicycles, we brought our canoe. I discovered a good way to catch crabs by swimming along with a face mask and snorkel while towing the canoe.  When I spotted a crab or whelk in the water I would scoop it up with a net and throw it into the canoe.  In this way we were able to have fresh crab every day until the children rebelled and vowed never to eat them again.  The whelks were tougher, literally. We never did discover a way to make them tender enough to enjoy.


After the second summer I returned sporadically, but lost my enthusiasm after a few years. But these fisheries models led to an interest in mathematical models in biology in general, and laid the foundation for our next trip.


III. Later Mathematical trips (without Kids)


9.Biomath in Costa Rica 


My new found interest in biomathematics was mainly directed to ecosystem models.  These gave me a legitimate excuse to travel apart from trying to work with colleagues, and led to short trips to Texas, California, Canada, Colombia, Italy and, later, China.  Most of these involved going to conferences during which there wasn’t much time to get to explore the place very well.  However the trip to Costa Rica was longer and involved my lecturing at the university for about a month. I had wanted to go there to look at the data and papers from La Selva, a tropical research station.  When a friend told me that the University of Costa Rica was looking for someone to give some lectures on biomath, I jumped at the chance (or rather bounced since the runway at the airport in San Jose was very rough).


Edie and I left the children behind this time since they were too independent to want to go places with us. But we had a number of exciting adventures nonetheless.  This was mainly because of the Costa Rican drivers and one Italian driver. There was also a visiting mathematician at the university from Italy, whose wife, Adriana, was the driver in question. Our host, Jenny, who had invited us, was generous enough to let us use her cars on weekends to take excursions to the coasts. 


The university is located and most of the people in Costa Rica live in the central plateau which is high enough to make the temperature quite comfortable year around. There are extensive and beautiful beaches on both the Pacific and Caribbean  coasts of the country, but one has to drive down winding mountain roads to get to them.  Our first excursion was to the Pacific where we spent a weekend at an upscale resort located on wide, sandy beaches with calm waters.  The temperature was warm but not uncomfortable.  The next weekend we went to the Caribbean coast expecting the same.  This time Adriana came along and drove a jeep at a breakneck speed, which I could not keep up with. Surprisingly she survived the trip to the coast, which was hot and humid, with the countryside covered with banana plantations and jungle. The road, which was initially a highway gradually deteriorated to a dirt path with few cars.  I was sure we were lost when we suddenly arrived at Cahuite, a small town of wooden shacks on a beautiful bay ringed with coral reefs. The hotel had rooms with bare beds with a single light bulb hanging from the ceiling. The lights all went off at 10 o’clock, so we couldn’t do much reading anyway, or anything else.  The bathroom was down a dark corridor but the was a parrot stationed outside the door whose squawks helped us find the way.  We spent the weekend exploring the area but didn’t do much swimming.  The water had many beautiful fish, but it was the jellyfish, which are also beautiful but whose sting is painful, that kept us out of the water.  We returned to San Jose and planned for the next weekend.


It was turn of the Pacific coast again the next weekend.  We drove again at the same high speed with our Italian friends to a different beach. We were not unique in our driving habits.  The Costa Ricans seem to compete with each other to see who can get to the beaches first on every weekend.  There is a mass exodus from the highlands with both lanes of a two lane road crowded with cars going in the same direction.  The new beach was uncrowded, with relatively calm waters and an island about   a mile off shore.  Adriana immediately announced she was going to swim out to the island and waded into the water.  I swam with her for about a hundred yards, but could not keep up her pace and turned back.  A group of us then walked the beach and had a leisurely lunch at a beach restaurant.  After a couple of  hours we started wondering what had happened to Adriana.  She had not come back to our section of the beach and we started searching for her.  Her husband kept calling for her.  Finally in the late afternoon just as  we were becoming frantic, she came out of  the water casually announcing that she had stopped and looked around the island a little before starting back.


We traveled around the country  a little more during the next couple of weeks.  I gave a talk at an Agricultural station (remember this was  biomathematics), and saw cacao beans growing for the first time. They have huge pods which grow directly on the trunk of the tree.  I’m sure they were the model for the pods from outer space in the movie “Invasion of the Body Snatchers”.  I wasn’t able to accomplish my objective of finding data for tropical ecosystems models.  I searched through all the sources I could find, but none had any real numerical data..


10. Queen’s Gate in London


My interest in biomathematics led naturally to problems in statistics since the data  used in fisheries and other biological sources was often full of noise and had to be analyzed by statistical techniques.  We also had hired a new statistician in Milwaukee who challenged me with a mathematical problem arising in statistics. So I decided that my first sabbatical would be spent learning more about statistics.  And what better place to do it than Imperial College in London?


The department at Imperial College gave me some sort of visiting appointment there and arranged for us to get a bed sitting room, i.e., an efficiency apartment on the sixth floor of the rector’s residence. This was a veritable palace located on Queen’s Gate, but the visiting faculty accommodations were in former servant’s quarters and involved climbing five flights of stairs. However, it had its advantages. It was only a block from the Statistics department and only a little farther to the Queen’s Arms, where they served a beverage called bitter that beats any American beer.  Also within a short walking distance were three museums, the Royal Albert Hall, Hyde Park, a shopping street, and the Kensington tube station.


I gave several talks, participated in a seminar, and went to a number of Royal Statistical Society meetings around the city of London, but unfortunately did not speak the local language very well.  In the US, most theoretical statistics is based on rigorous mathematics, but in the UK, the statisticians jump over the details of the theory and base their conclusions on intuition to a greater extent. Try as I might, I could never master their techniques, and try as they might, they could never understand why I went through all those obvious details.


The department observed a tea break every afternoon at which tea and biscuits were served. On special occasions such as a colloquium talk, shepherd’s pie and other pub food was served.  This consisted of meat with congealed fat in a pastry shell and was considered almost inedible even by the English.  In fact, this seems to have been a fairly common food item.  Once, when my sister was visiting us from the US, she decided, as a special treat for us, to buy an expensive large cut of meat in a pastry shell at Harrod’s.  It still tasted like congealed fat covered with soggy dough.


Fortunately there were many Indian restaurants in London which served quite interesting food with some vegetables other than Brussel sprouts.  Generally their food was fairly mild in deference to the English palate, so we made a habit of ordering curry and other Indian dishes extra hot.  We had become accustomed to hot food in Peru and on visits to California.  But the day before we were to fly home, we stopped at an Indian restaurant where, when Edie ordered the extra hot curry, it was indeed extra hot.  So hot she couldn’t eat it.  I had ordered a milder dish which I exchanged for her hot curry and proceeded to eat it all (Clean up your plate, my mother had told me).  Afterwards I thought I was going to burn up. My skin felt hot and even my sweat (as well as other excretions) burned. This lasted the entire trip back to the US, which at its best was uncomfortable, but I eventually recovered.


We took advantage of most of the things London had to offer, such as theater and music and castles.  But we also took advantage of our location to visit other places.  While attending a conference in Sussex, I ran into an old friend, Rashid, from Milwaukee who invited us to come to visit him at Strathclyde University  in Glasgow, Scotland, which we did.  We stayed with him for a few nights in a historical old row house, which of course did not have central heating.  He enjoyed having a drink or two and contended that the Scottish beer was superior to the English and much superior to the American brew.  We sampled a number of different varieties  to test his thesis, which left me some what tipsy.  This seemed not much of a problem since I went to bed right away.  This is where the lack of central became a problem. Our bedroom was heated, but the hallway to the bathroom was not, and I had to make the trip several times.  It reminded me of camping  in the winter.


A Hungarian friend, Lidia, also stopped in for a visit and invited us to come to visit her at the Hungarian Academy in Budapest which we did. In contrast to most other continental cities, Budapest was not heavily damaged in the second world war and retained many of the charming old buildings.  This seemed out of sync with the then communist regime which had constructed the usual rectangular apartment blocks on the outskirts of the city, but left the center alone. We had to register with the police when we got there and were able to observe their phone monitoring  system.  They had a large number of wires  coming from various places connected by hand to listening and recording equipment.  It was so chaotic I’m surprised they could make a telephone call, let alone monitor others.   Another incongruous element was the presence of large banners strung across the street celebrating the arrival of Coca-Cola in the city.  It seemed even more incongruous when one day there was a parade of workers carrying banners celebrating the triumph of their system.  After about a week we returned to London which seemed bland by comparison.


We made one more trip to the continent before we left London. We took a hovercraft across the channel at Christmas time figuring that it would be a faster and smoother ride than the regular ferries. It was faster but not so smooth.  We should have been warned when all the attendants donned smocks and came out with buckets of disinfectant. At least we didn’t get seasick in contrast to most of our fellow passengers.  We went on to visit some of my relatives in the city of Maulbronn in Germany which had an old cloister dating from the 14th century.  They invited us to attend Christmas Eve service there, but didn’t tell us the Chapel was unheated.  Everyone including the preacher and the band wore overcoats.  We were glad to get back to my relatives’ house where they warmed us with homemade kirsch. We returned to London via Paris and then came back to the US, but not to Milwaukee.  Rather we went to Florida on our way to Mexico.


11. Finding a place in Mexico City


Mexico City is located in a valley on a high plateau at an altitude of about 7k feet. Its climate is relatively mild in winter with a usual temperature in the 40’s or 50’s. The valley is surrounded by mountain peaks which keep a lid on the pollution from the many cars in the city.  The smog is sometimes so severe that you can’t see more than a block. But still, it’s warmer than Milwaukee


 I had arranged to visit the statistics section of the Institute of Applied Mathematics and Systems (IMAS) at the national university (UNAM).  The university is located along the southern edge of the city and has less smog than the central part.  They had located an apartment for us close to the university, which was built in typical Mexican style.  That is, with lots of stone and concrete and ceramics, but not much heat.  In fact it was so cold and uncomfortable that we moved out after a week and found an apartment closer to the downtown along Avenida Insurgentes.  This, in turn, lasted about a month before we got sick of the smog and noise, and again looked around for greener pastures or at least pastures without green air. We found them in Cuernavaca, a smog free city just over the mountains from Mexico City.  It was about an hour’s bus ride through the mountains to the edge of the university campus but it was worth it.  The bus drivers seemed to compete with each other to see who could make the trip in the shortest time and not too many went over the edge.  That is until it snowed one day in the mountains.  Fortunately the bus I was on was not one of those that went off the road.


The place we stayed  at in Cuernavaca was called Hotel Paraiso, and at one time it might have been a paradise.  It was a little run down when we got there but the people were warm and friendly and he hotel had a swimming pool which unfortunately had the look of the green pastures we were hoping to find.  I went swimming anyway and didn’t contract any dread diseases from that.  Rather it was the fashionable resort of Acapulco that did me (and my wife and daughter ) in later.


I found the statistics group much more communicative than the group in England and was able extend my knowledge quite a bit. There were weekly seminars together with another university which were preceded with wine and good Mexican cookies instead tea and congealed fat pastries.  Much more civilized.


Since our daughter Natalia had joined us, we made many excursions to the pyramids and other ruins in the surrounding countryside.  They did not quite measure up to Peru, but were bigger in some cases. We also rented a car and drove down to Acapulco one weekend.  This resort has two parts, one with high rise hotels on the beach and the other with smaller, often family run, hotels that were on a different part of the beach.  The former catered to international tourists while the latter was populated chiefly by Mexicans and was much cheaper. We of course chose to stay in the Mexican section.  There were numerous restaurants on or close to the beach which served freshly caught fish and shellfish.  Yummy!  It was later that we learned the waters in the bay were quite badly polluted in spite of looking clean and clear.  Edie and I both came down with hepatitis in Davis, California after we left Mexico.  So did our daughter Natalia except that she had stayed in Mexico. Fortunately some Mexican friends took her in and nursed her for a couple of weeks until she recovered somewhat. Our doctors in the US misdiagnosed our disease but our Mexican friends knew exactly what it was and what to do (lots of rest, no proteins, little exercise).


12.Wine and Hepatitis in Davis, CA


We left Mexico after the end of  the winter quarter and traveled to Davis where our friend  Julius was in charge of the Division of Statistics.  I was still trying to learn more about the subject and was happy to teach a large lecture in elementary statistics.  Edie and I had found an apartment in the student ghetto which was a short bicycle trip from the building where I taught.  Moreover we were close to California wine country and I was looking forward to trying some of the local vintages.  The University of California at Davis is where many of the wine making techniques that made California a producer of  quality wines were invented.  Napa Valley wasn’t far and we planned to take a number of pilgrimages there.  That’s when the hepatitis struck.  First Edie became quite sick and took to bed for a couple of days.  I took her to the doctor and said I suspected hepatitis, but he said it was some form of the flu.  After a week of rest and little food she recovered rapidly.  Then I got it.  I was also acutely sick for a week or two, but recovered very slowly.  I became aware of having a liver for the first time.  There were other alarming symptoms as well; my urine turned black and my mind seemed to leave my body.  This was mostly unpleasant but caused me to have very beautiful dreams.  Unfortunately these occurred when I was nominally awake.  It was several months before I felt very strong, and six months before I could try some of the California wine.  By that time I was back in Milwaukee.


Davis is located in the central valley; the surrounding countryside is very flat and covered mostly with tomato fields.  Because of the flat terrain, it is very easy to get around on bicycle, and most of the students do.  There are lots of dedicated bicycle paths which are often crowded with bicyclists.  Fast bicyclists.  My friend Julius let me use his extra bicycle and I was able to commute to the university with it.  Because of my weakened state I could not go very fast and was almost run down by mobs of racing student bikers.  It reminded me of the weekend dash to the beach in Costa Rica.


There was little to do in the town of Davis, but we took a number of side trips to more exciting places such as Sacramento. Sacramento exciting?  Well, we also went to San Francisco and the Napa Valley, if only for the view.


13. Fish and Tortillas in Yucatan


When we returned to Milwaukee, I pursued my new found interest in statistics for a while and had a chance to teach most of the undergraduate and a few graduate courses in the subject.  But then I got some mail from Mexico inviting me to a fisheries conference.  It seems some researchers in Merida, Yucatan had stumbled across some of my old fisheries papers and were interested.  So I went for a few days and found a very attractive set-up.  It was a branch of the Polytechnic University, CINVESTAV, and had several scientists who were fitting mathematical models to the fisheries of both the Gulf of  Mexico and the Caribbean.  They also were able to communicate with the local fisherman and were thus able to gain good insight into the meaning of their data.  There were also quite a number of graduate students, who, in contrast to their US counterparts in biology, were well versed in mathematics.  The laboratory was a small operation, perhaps less than 100 people.  But the best part was the cafeteria.  It was run by two local women, who cooked up gourmet Yucatecan delights every day.  Some, such as pollo pibil I had never heard of before, others were familiar from my previous trips to Mexico.  But all their dishes were flavored with some local herbs whose names I have forgotten but which gave them a unique and delicious  flavor.


I returned perhaps a half dozen times for conferences or just to work with them for a while.  There were usually excursions to local sights of interest such as the Mayan ruins at Chichen Itza.  But after my third visit I became somewhat jaded and felt I could lead a tour myself.  But I found the Mayan civilization, the temples, the system of writing, and above all the numbering system, fascinating.  Their numbering system was base 20, and used place value notation just as we do with our numerals.  They even had a symbol for zero.  It was fairly easy to read when you got used to it.  Many of the temples and stella had numbers engraved on the sides together with their heiroglyphic writing.  I found I could read the dates, but had no idea what the writing said.


One excursion during a conference was to a cenote.  These are caves filled with water which open to the surface.  Yucatan is covered with limestone through which water easily percolates.  When it rains the water goes right into the ground instead of flowing into rivers of  which there are none.  For our visit we first took a laboratory van to a yucca farm surrounded by extensive fields of yucca which had been planted as a crop.  The fibers from this plant had been used to make binder twine and some fabrics but were superseded in recent years by synthetics.  From the farm house we took a rail car several miles to the cenote.  This rail car consisted of a flat bed wagon on rails pulled by a mule.  Fortunately we had a cooler full of  beer.  The cenote itself looked like a hole in the ground which we entered and went down ladders to the water level.  The owner had rigged lights in the interior which  otherwise would have been completely dark. Surprisingly the water contained small invertebrates which were completely blind.  They apparently survived on the droppings from bats since there was no light and no vegetation in the cenote.


My last visit was for a semester during which they were kind enough to pay me (in cash).  They even arranged for an apartment for Edie and me.  But it again was in the Mexican style (concrete, stone, ceramics) and we opted for an inexpensive hotel instead.  On weekends we would usually rent a car and explore some of the lesser known Mayan ruins, some of which had not been completely excavated yet and had trees and vines covering the pyramids. One weekend we went with our friend Ernesto to his cottage on the gulf.  It again was in the Mexican style (of course), with little furniture except for hammocks.  Then we saw the scorpions and understood the reason for this style. To get to the beach we also had to run a gauntlet of mosquitoes.  This kept sunbathing to a minimum.  We were happy to get back to Merida.


We found the people and the city of Merida very simpatico and left it reluctantly to take another stab at California.  I never went back although my friend Paco from there visited me in Florida a couple of years later and we worked out a paper on multispecies fishery models of the Caribbean.


14. More wine in San Luis Obispo


I had taken a leave from the university for the entire spring semester when I went to Merida, but only spent a couple of months there. I had previously arranged to spend the spring quarter in San Luis Obispo, at California Polytech.  My former student Ahmed had a position there, and he and I planned to work together on problems in generalized functions. As it turned out, during my stay we both got interested in the mathematics of signal processing, and decided to devote ourselves to that area for awhile.


San Luis Obispo is about half way between Los Angeles and San Francisco located in a valley surrounded with hills covered with Live Oak savannas.  Many of these hills had recently been converted from pastures to vineyards.  Some of these vineyards produced very good wine grapes, and a number of wineries had sprung up in the area.  This was very fortunate, because there wasn’t much to do in San Luis Obispo, and every weekend there were wine tastings at one or another of the wineries.  The members of the mathematics department were enthusiastic participants in these affairs, and even went so far as to help one of them crush the grapes and bottle the wine.


There were other things to do besides drinking wine.  Morro Bay was only a few miles away and was full of  all kinds of sea life.  There were large numbers of sea lions at an adjacent state park, and in the bay itself you could always come across a group of sea otters playing with each other (or so it seemed).  There were also extensive wide beaches, but the water was too cold to swim.  Nonetheless we went there frequently to walk the beaches looking for shells and stones and nirvana. 


Since it was almost impossible to function anywhere in the southern half of California without a car, we had bought a cheap one in Los Angeles and drove it to from there to SLO.  Before we left I had checked out the brakes and tires and steering all of which we satisfactory.  But I had neglected to check the engine, and discovered that it was very difficult to start when it was hot.  Or even warm.  This meant that whenever we went somewhere and stayed for less that 24 hours, we had a hard time returning.  After a while I found that I could prime the carburetor with some extra gas and get it started.  This usually worked until one weekend when we went up into an isolated part of the mountains.  I eventually found a telephone and called a tow truck which came and towed us about 30 miles back to SLO.  After that it got progressively worse until the head gasket blew and I gave the car away to a garage mechanic who thought he could fix it. I doubt that he could, but by then I had left.  There was a certain advantage in having an unreliable car. I usually rode with friends to go to wine tastings and was therefore able to drink more and finally make up for my lost semester at Davis.


15. Delaware, a good example?


After a couple of years back in Milwaukee, I again became eligible  for a sabbatical leave.  Since I had started to work on applied mathematics, I decided to spend part of the year at the University of Delaware which had been very successful at establishing a program in applied mathematics.  I had written a colleague, Zuhair, who arranged my visit. This time rather than taking a chance with a cheap car, we decided to drive out to Delaware.  It turned out to be a good thing since the area around the university in Newark is mainly urban sprawl, and we were only able to find a place about 6 miles from there.  The entire area is composed of a bunch of disconnected communities with interspersed shopping malls and commercial strips.  There was very limited bus service and the roads were too scary for bicycling.  So I had to commute every day via car (ugh!).


Mathematically my stay there was very satisfying. I had a large office away form the center of campus, there were several colleagues I could work with, and the department had a very good support staff.  So I was able to get a lot of work done and actually collaborated with Zuhair on a paper.


The advantage of Delaware was that it was close to lots of other things on the east coast.  We took a number of trips, mainly to visit friends, but sometimes just to be tourists.  These usually involved driving along the New Jersey turnpike, which was very pleasant in rural New Jersey, but became populated by increasingly aggressive drivers as we approached New York.  I tried to avoid it whenever possible, but was not familiar with the area and frequently ended up on dead end streets.  We passed the community where some friends lived three times before we were able to find the street to their house.


The weather in Delaware is not much better than Milwaukee, so at the end of the semester we took off on a leisurely trip to Florida.  It was less leisurely than we had hoped since Edie got sick and we had to avoid some side trips.  I had hoped to spend some time at Okefenokee swamp, but was only able to dip my toes in the murky waters.


16. Tampa, Florida, less than a paradise


Before we had left Milwaukee, I had invited myself to visit South Florida University in Tampa.  I don’t think they were too enthusiastic about my coming since they felt I probably only wanted to go somewhere warm in the winter.  They were right.  Still, since I had a sabbatical and wouldn’t cost them anything, they were willing to give me an office as well as library and swimming pool privileges.  I also had a friend, Mourad, there, with whom I tried to work a little, but for the most part, I did my own thing.


We had other friends who spent the winter there and arranged for us to get an apartment in a complex not too far from the university.  As was my custom, I bought a cheap bike and used it for transportation to the campus.  Unfortunately we lived on one side of a busy street which had a large shopping mall on the other side.  There were no provisions for pedestrians and certainly none for bicycles.  In fact motorists seemed very aggressive toward me, as if I had no business being on their road.  Part of this attitude, I’m sure, comes from the fact that the area’s commercial districts are almost all in malls of one kind or another.  So to do anything at all, whether to buy something or go to a bank or a restaurant, you have to get in your car and drive there.  The private housing is very much economically segregated.  Well to do people live primarily in gated communities with no stores or services, which makes it even more imperative to use a car for everything.  The result is extensive traffic jams at all hours.


I thought that since Tampa is on a large body of water, Tampa Bay, we would be able to enjoy the beaches and swimming in the ocean.  No such luck.  It’s about 20 miles to the gulf beaches along roads that are lined with malls and  are often grid locked. It was such an ordeal that we didn’t go there very often. 


In spite of its glamorous location, Tampa is a poor city.  The tourist industry doesn’t pay very much and there is very little other industry.  Social services are not very good, many of the schools are in temporary trailer like buildings and the roads are not very well maintained.  The city itself has large areas of slums, with no central city to speak of.


The countryside around Tampa is more interesting.  There are quite a few cypress swamps sometimes with streams running through them.  The canoeing along these streams was often exciting, not because of the rapids, of which there were only a few, but rather because of the presence of alligators and snakes.  We would sometimes see alligators in the water, but more often resting on the banks waiting to devour reckless swimmers. The snakes would sometimes be in the trees overhanging the water.  Every time we passed through an area of thick vegetation, I had visions of snakes dropping down on us from the trees.  It never happened.


One of my friends from Mexico, Paco,  came to visit me for about a week to finish up a paper we were doing on the Caribbean fisheries.  What better way to entertain a fisheries biologist than to  take him fishing?  So we went out for a day trip on a party boat in the Gulf of Mexico and caught a few dozen fish, mostly porgies.  I thought it was pretty successful, but when I asked him how he liked it, he said, “we throw those little ones back in Mexico.”


In May, Florida started getting a little too warm for us and we decided to head to back to Milwaukee.  On the way we stopped in a place called Wakula Springs in northern Florida.  This was a state park with a huge spring which formed the start of a river.  There was a beach in the park on this river as well as tour boats going down the river.  The tour boats were to let people see the alligators which were abundant and large.  We would sometimes see them on the beach and once climbed up on the diving platform to watch them.  We saw a chase with one larger alligator chasing a smaller one on both land and in the water. They moved very fast on both. I didn’t go swimming there.


17. Giessen, Germany, a perfect setting


After I returned to Milwaukee, I gradually became interested in a new area of mathematics that was becoming popular, the so-called wavelets, which were found to be very useful in engineering.  They made it possible to reduce data requirements for images and signals, but I found them attractive for their structure.  I went to a number of conferences related to them in order to learn more.  Then I had chance to go to Giessen, Germany, where the local university had an exchange program with our department, to give a series of  lectures on wavelets.  I was supposed to give the lectures in German, and was sweating bullets worrying about whether I would mess up the language.  I was saved by the presence of two Russian visitors who were going to attend my lectures.  They didn’t know much German and so I was asked if I could please give my talks in English instead.  Whew!!


Giessen is not a very attractive city since it was destroyed in the second world war and reconstructed rapidly with nondescript buildings.  The surrounding countryside and nearby cities are another matter.  Not far away were towns such as Marburg or Limburg that had their prewar architecture intact or were faithfully reconstructed.  They gave a feel of what the country must have been like a hundred years ago.  That is, except for the cars.  German drivers seem to think that any restriction on their driving speed is unconstitutional.  Consequently they roar through the narrow streets of these medieval with total disregard for pedestrians (like me).  Fortunately most of these towns have a pedestrian only zone in their downtowns.


The real treat in Giessen, however, was the housing that the university supplied us.  They had a guest house for visitors on the edge of town.  As with many German towns, there was an extensive forest adjacent to the town.  In this case it began next to the building we were in.  There was a path through the woods beginning behind our apartment that we decided to explore the first weekend.  The path led up a hill through a variety of woods both conifers and deciduous trees with surprisingly few mosquitoes.  It eventually came out, a couple of miles later, at an old monastery at the top of the hill.  We didn’t discover this until our second hike, when we heard music coming through the trees.  The monastery had been converted to a beer garden and had a concert on weekends.  I couldn’t figure out at first how they got all that beer and food to this beer garden which was quite large.  It took a few more trips before we found the road behind the monastery.


We took advantage of our location to visit many historical local sights.  As usual, we didn’t have a car, but I was able to borrow a bicycle for the commute to the mathematics department which was about three miles away.  To go to other places we used public transportation including buses, trams, trains, and railcars.  In fact we used all of these on one trip to a castle outside of Heidelberg for a wedding, but ended up walking the last mile. 


We intentionally avoided visiting my relatives whom we had seen quite often and instead went to Berlin to visit some of Edie’s distant cousins.  This was shortly after the wall came down and East Germany was still an exotic place.  The change in the countryside in going from west to east was quite striking.  The villages in the eastern part of Germany had a uniform gray color and seemed to blend into the earth, whereas those in the west had brightly painted houses which seemed stuck onto the landscape.  We located the relatives who showed us around Berlin and its extensive nightlife.  Unfortunately we saw it in the  daytime when it was a little less exciting.  They also took us on a tour around the countryside which was very similar to Wisconsin.  There were lots of little lakes and woods, but much less development around the lakes, probably because in the east private property was restricted.  This in spite of the fact that the region is much more densely populated than Wisconsin.  The summer was about over and we returned to Milwaukee to wait for another sabbatical.


18. Hawaii, a real paradise


I resolved to spend my last sabbatical in a place that was pleasant all year long.  What better place than Hawaii, which we had never visited before?  Fortunately I had an old friend, Jake, from San Diego in the mathematics department at the University of Hawaii.    I wrote him and he arranged for me to get the usual office with library and computer access and we were off.  The university also let me have an apartment close to the campus for a nominal price.


I wasn’t sure what to expect and thought that perhaps the whole city of Honolulu would be like a Disney World.  The first surprise was that the countryside around Honolulu was not covered with the lush tropical vegetation I expected, but rather was more like southern California with shrub like chaparral.  In fact a lot of it was exactly the same species of mesquite found all over the American southwest.  The second surprise was that the humidity was quite low, at least on the Honolulu side of Oahu.  This is because the island has a mountain ridge in the center with most of the rain and humidity on the windward side of the mountains and much less on the other side.  The third surprise was that the people of Hawaii, not all of whom were employed by the tourist trade, were very friendly and open, in spite of the fact that we didn’t look like most of them.  In fact, they reminded me of Wisconsinites down to they way they spoke (and ate, with lots of starches).


The apartment we rented had neither heat nor air conditioning.  Neither was necessary since the temperature varied from about 65 to 85 every day with little variation throughout the year.  Also, the trade winds, which blew down from the mountain behind our building, were a good substitute for air conditioning.  If it was too hot we would merely open the door and have a cooling breeze.  Since there were few insects we had no need for screens, but occasionally a cat would wander in.  At first we tried to live without a car, but it was a about a mile walk to the nearest supermarket, so I relented and bought a cheap car from a student.  It looked terrible and always threatened not to start, but it never gave us any real trouble during the year we lived there.


My office at the university was on the fourth floor with a window at the same level as the tops of a pair of coconut palms.  Behind the palms I could see the Manoa valley and the vegetation covered mountains surrounding it.  Frequently rain clouds would appear over the mountains in the afternoon and gradually move down the valley where it would sometimes be raining even though it was dry where we were.  This made for a lot of rainbows without the discomfort of having to experience the rain.


The campus of the university was full of trees and shrubs which I was unfamiliar with.  Many of them had fruit which looked good, but which I was afraid to try, at least until I took a botany course the second semester.  Then I discovered that many of them were indeed edible and good.  They included guavas, strawberry guavas, passion fruit, mangoes, Java plums, and even bananas.  I would pick whatever was in season and bring them back home with me.  Edie made jams out of the strawberry guavas and Java plums, but the mangoes were too good to use for anything except eating raw.  That is, they were until I found out I was allergic to them.  Apparently they are related to poison ivy; the stems have a white latex type sap, which in my case, caused eruptions on my skin.  What a blow!!


There are also many flowering plants on the campus and elsewhere on the island.  Many of these are found everywhere in the tropical world such as poinciana, orchids, shower trees, plumeria, and hibiscus.  But I found the endemic species more interesting.  These are plants that evolved on the islands and are found nowhere else.  The most common are the Koa and the Ohia Lehua, which is found in abundance on the big island, but has been largely cleared from Oahu.  The Koa is a very large tree with flowers that look like dandelion seed heads. The Ohia is not so large, but together with giant ferns, form the principal species in the rain forests on the flanks of the Mauna Loa volcano.  The campus had a large number of kukui trees which are not strictly endemic but are thought to have been introduced by the early Polynesians.  The nuts are supposedly poisonous, but I think this is exaggerated since I tried them and suffered no ill effects (yet).  The larger trees are found mainly in the mountains which have abundant rainfall.  Unfortunately, the native trees are mostly replace by introduced species, such as the Norfolk Island Pine.  There was a forest of these on the hills behind our building.


The trip from the central part of Honolulu, which is on the dry side of the island, to the windward side is one of the most spectacular I have seen anywhere.  The Pali highway takes one up to a pass surrounded by heavily wooded mountains from which one can see the entire windward side.  This part of the island is the crater of an ancient volcano and is surrounded by are steep cliffs going down to a plain containing a few dormant volcanic cones.  The view takes you breath away because of its splendor, much like the grand canyon does (and also because of the strong winds in the pass).  At the bottom of one of the cliffs is a large botanical garden of several hundred acres which contains specimens of most of the native plants as well as plantings of main introduced species from both Asia and the Americas.  I became so enamored of this place that I signed up for a course to become a tour guide.  When I finished the course, I would occasionally lead tour groups around the gardens, but did not tell them I was a mainlander (nor a mathematician).


I did try to be a mathematician too, at least a little.  But I would find myself staring out my office window at the beautiful Manoa valley and forget what I was trying to do.  I did give a few talks on wavelets and sat in on a seminar.  There was also a fisheries laboratory on the edge of campus; I had written them before I came and hoped to get some sort of collaboration going.  I did give one lecture there, but then the Federal government was shut down for a while and further collaboration proved impossible.


We also visited the other Hawaiian Islands, since there are special weekend deals for residents.  It would cost $79 for round trip air fare, a rental car and a hotel room for one night. We took advantage of these to visit Kauai, Maui, Hawaii, and Molokai.  Since we had a number of visitors, we would sometimes take them along on these trips.  We also took them on whale watching cruises in the waters around Oahu.  There weren’t many whales to be seen, but the cruises offered a free ticket if whales weren’t seen.  This is something of a scam, since most tourists couldn’t wait around for another cruise.  On the other hand, we could and did, taking different visitors each time until we were unlucky enough to spot some whales.  However our biggest whale watching thrill was on Molokai, where we had stopped at an overlook when we saw a number of whales about 500 yards from the shore.  They must have known we were there, because they decided to entertain us by slapping the water with their tails, by showing most of their bodies, and finally by jumping completely out of the water and landing on their backs with a huge splash.  We were too dumbfounded to take any pictures.  We saw a lot of other sea life as well.  There were porpoises, many fish of course and green turtles.  On e day when the water was murky, I almost had a head on collision with one.  We were both so frightened we swam away as fast as we could in opposite directions.


I was beginning to feel very much at home there when it became time to return to the mainland.  We returned for a short visit a few years later on our way to Korea, but I hope to return again and use my skill as a guide in the botanical gardens.


19. Sand and heat and smog in Tempe.


After my last sabbatical in Hawaii I began to think of retirement since I would have to wait a long seven years for another sabbatical.  But then the Dean of the college made me an offer I couldn’t refuse.  If I would agree to retire in the next year, he would give me a semester off with pay.  So I readily agreed since I was ready to retire soon anyway and immediately began looking for interesting warm places to spend a semester.  My wife had relatives in Phoenix, Arizona so we decided that would be a good destination since after all, it was noted for its clean desert air, just what someone on the verge of retirement neeeds.  I had also become tired of my research area and wanted to return to some aspect of biomathematics.  Fortunately I had a friend at Arizona State University whom I wrote asking about the possibility of visiting him.  He agreed that it would be OK and we made plans.


This time, instead of looking for an apartment after we got there, we decided to check out the apartments before we left and were able to find one in what we though t was a quiet area about five miles from the University.  The area was quiet except for one thing: the freeway that was next to the apartment complex.  The constant roar of traffic and the resulting smog was something I never got used to.  But it was a nice bicycle ride from the university with no hills or other obstacles on the way.  Unless you count the traffic that raced down the main streets at 60 mph.


This was the first time we lived in a gated community.  This is not exactly the same as a prison but it sure feels like it.  We had cards that would let us in and out of the gates, but our friends didn’t.  They were supposed to be able to dial a code so they could get in, but nobody (except possibility a professional thief) could figure out how it worked.


The clean dry desert air I was anticipating doesn’t exist in Phoenix.  The city is like one huge suburb with urban sprawl extending in every direction for dozens of miles.  The air is smoggy much of the time and the humidity is much higher than one would expect in the desert.  No doubt this is due to the presence of extensive irrigated lawns imported from the Midwest by escapees from colder climates.  The freeway system rivals that of Los Angeles in its extent.  But it still took us an hour to get to Edie’s relatives when the freeways weren’t jammed up.


In order to get around we bought a cheap used car.  This enabled us to explore the desert and mountains around Phoenix.  It is part of the Sonoran desert which has a very rich flora, probably best known for its saguaro cacti which form dense stands in some areas.

We spent many weekends hiking in the desert, which was very quiet without the noise and pollution of the city, but it took a while to get there.  The car gave us no problems until the weather got hot in May.  Then it sometimes wouldn’t start during the day and we would have to wait until night to go out.  But we were ready to leave then anyway.  Rather than try to sell the car, we gave it to our daughter Natalia who lived in El Paso at that time (some gift).  She picked it up after we left and drove it to El Paso, but had a great deal of difficulty when it got hot.  Fate resolved the problem for her since the car was stolen shortly after she got there.


20. Short trips


Most of the previous trips I described were for extended periods of a semester or more.  But every active mathematician takes many more short trips in the pursuit of his (or her) trade.  In my own case these shorter trips sometimes took me to exotic places such as Xian, China and Oshkosh, Wisconsin.  Xian is where those life-sized terra-cotta statues of warriors were found.  Oshkosh is where they used to make overalls, by gosh.


These shorter trips were of two kinds: the first consisted of going to conferences in other cities and countries.  Such conferences took me to Orono, Boston, Philadelphia, Baltimore, Princeton, College Park, Washington, D. C., Atlanta, Orlando, Detroit, Cincinnati, Columbus, Nashville, Memphis, Auburn, Toronto, Chicago, Madison, St. Louis, Biloxi, New Orleans, Minneapolis, Kansas City, Huntsville, College Station, San Antonio, Denver, Phoenix, Edmonton, Seattle, Corvallis, San Francisco, Berkeley, Los Angeles, Santa Barbara, and San Diego. 


In most cases I gave a talk about my research in order to get someone to pickup the travel tab.  These conferences were about 25% mathematics, and 75% social, although there was considerable variation.  The social consisted mainly in seeing old friends and ex-students from around the country and gossiping while having coffee (mathematicians consume a lot of coffee) or other drink and sometimes going to dinner with them. Only rarely was there an opportunity to become familiar with the city or its surroundings. 


In recent year American Mathematical Society conferences have mostly been in large cities with convention centers.  These were the most boring since they differ little from one city to the next, and have entertainment and local activities in the neighborhoods designed to appeal to insurance salesmen.  The big conventions would have a “party” with a cash bar and snacks.  These were usually less than successful because (i) mathematicians are cheap and unwilling to pay for drinks at inflated prices, and (ii) they are not party animals.  Engineering conferences, on the other hand are much better in this respect.  They have a high registration fee, but the booze (at least beer) is usually free and the parties are therefore much livelier.


Some of the cities such as San Francisco have very walkable neighborhoods which I took advantage of when the meetings got too boring.  (This happened more and more in recent years).  There were a few memorable meetings, such as the very first one I went to in Berkeley. After I finished my talk, some heckler asked me why I thought it was interesting.  I didn’t have an answer so I just stood there dumbfounded. Fortunately, he grew impatient and gave me several plausible reasons, one of which I immediately accepted. The next meeting I went to was in Amherst, Mass. And I was worried about another heckler appearing.  My talk was on Fourier series, and I noticed Antoni Zygmund, the world authority on the subject in the audience.  Oh, Oh, I thought, he’s going to say that what I was presenting was trivial or uninteresting.  Fortunately, again, when it came time for questions, there was a commotion in the back of the room where my wife and a friend appeared. They were looking for the cafeteria and were lost. But the commotion took up the time available for questions and I was saved.


One of the more memorable meetings was at College Station, Texas (Texas A&M) in the summer. The temperature was close to 100 every day so I took every opportunity to go swimming in the Olympic sized pool.  Because it was so warm, they had to treat the water with copper sulfate to kill the algae.  This caused my hair to gradually change color from white to green.  I thought at first it was something wrong with my eyesight, but then I noticed a lot of people snickering when they saw me.  And it wouldn’t wash out.  I finally got a short haircut and waited for it to grow out. I also started wearing a baseball cap.


The second kind of short trip was usually more interesting.  It involved going to another university to present the results of my work in what is usually called a “colloquium” in mathematics departments but called a “seminar” in engineering and statistics departments. The format of such visits was always the same.  I (sometimes with my wife) would arrive at the university in the morning, meet the person who invited me, go to lunch with a few of the faculty, talk informally with people in the afternoon, have cookies and coffee around 3:00, give a talk afterwards, and then go to dinner at some local eatery with some faculty.  Sometimes there was a party at someone’s house in the evening, but more often we went out for a few drinks afterwards. These visits usually involved staying over night and the next day, unless I was actively involved with research with my host, I would be free to explore the area with the help of the locals.  This gave me a much better feel for the local place compared to attending a meeting. These places were often small towns instead of large convention cities and had more character. The visits were more productive mathematically because the hosts were usually genuinely interested in my area of research.


Trips of this kind took me to most of the universities in Wisconsin, to several in Illinois, Ohio and Michigan, as well as a number of other states. Both types of trips took me overseas as well.  In fact I was able to visit Canada, Mexico, Costa Rica, and Colombia on such short trips.  I never felt very uncomfortable in these third world countries, but my wife had her wallet stolen twice in Mexico and her earrings stolen off her ears in Cali, Colombia.


We also went to Europe frequently. I attended conferences in Norway, Sweden, England, Ireland, Holland, France, Portugal, Spain, Italy, and Yugoslavia. I was also able to visit Germany, Poland, Hungary and Scotland to give talks.


Some of the more notable short trips were:


20.1) Norway.  The visit to Norway was for a conference on sampling.  It took place at a hotel on a fjord in a small town named Loen.  The town didn’t appear on any map I could find, but the organizers gave us directions so we eventually found it.  To get there we took a train from Oslo to some other little town named Otta, which fortunately was on the map.  There we caught a bus that went over the continental divide (at least the Norway version) and down through a spectacular valley to the fjord.  The town was perhaps a few dozen buildings, but the hotel was large with lots of amenities.  I don’t know how they got all their supplies; but since most of the meals consisted of various kinds of seafood, they probably got it by ship. There was access from the fjord to the ocean and we took an excursion one day to another fjord and a glacier which seemed out of place since we were approximately at sea level.


When the conference was over, we retraced our steps and again caught the bus and train to Oslo where we arrived in the early evening.  We went to the usual tourist information desk to try to find a hotel, but were informed that the entire town was booked up solid for a fashion convention.  But, they said, there is a ski resort that you can get to by tram.  Since the alternative was sleeping in the train station we took it.  The resort was almost at the end of the line and when we got off, we found ourselves in the dark in the countryside with no sign of the resort.  But then we noticed a small sign nailed on a tree pointing up a wooded hill.  After about a half hour walk we found a clearing at the top of the hill and there it was: a very modern building with a sod roof overlooking Oslo.  It was worth the trip and we decided to spend several days there with day trips into the city to see the sights.


Instead of going right back we traveled around Europe a little.  We took a train and a ferry (at night unfortunately) across the Baltic and thence to Berlin.  From there we went to visit friends in Dresden for a few days and then to Stuttgart to visit relatives.  We planned to return the US from Amsterdam and got there in the evening to find that history was repeating itself.  There were no hotel rooms available, we were told.  But if you don’t mind a long tram ride, there is one a little far out.  Again we took it and weren’t disappointed.  It turned out to be only a few blocks from the Concertgebau and in fact we were able to get tickets for a concert the next night. It was also close to the Van Gogh museum which we took advantage of.  Most of the night life was in the city center; but we didn’t miss it since I’ve grown to prefer beer to marijuana, and since my wife was with me, had little interest in the other activities for which Amsterdam is famous.


20.2) Spain, Italy and Yugoslavia. 


Our daughter Natalia was spending a year in Spain teaching English so we decided to take advantage of her presence to visit Spain.  There was also a conference later that summer in Dubrovnik, Yugoslavia which I wanted to attend.  As luck would have it, Yugoslav airlines had the cheapest flights to Europe that year and also allowed us to fly to Madrid and return from Zagreb.  In order to help justify the trip I had also arranged to go to a statistics conference in Spain during the course of our stay there.


After the usual confusion of lost luggage and lost directions, we found our way to Natalia’s apartment.  We spent a few days visiting the usual tourist sights in the city and trying to do as Madridleños did, namely, strolling along the principal boulevard until midnight and stopping occasionally in tapas bars to sample the food (and drink).  Dinner came later.  I don’t know when they sleep; perhaps before they go out on the town in the evening.  We also took some excursions to Sevilla and Granada both of which have remnants of Moorish architecture but which seem to be mainly populated by European tourists.

Natalia then came with us on the train to Alicante on the Mediterranean  coast.  While on the train I heard a couple of people behind me talking about mathematics.  Since I had worked on some of the things they were talking about, I introduced myself and joined the discussion.  It turned that they were going to the same conference in the little fishing village of Altea.  That is, it once was a little fishing village, but now was home (temporarily) to a large number of Germans.  In fact after arriving there , I decided to go out for a beer at a local pub and asked for a “cerveza”.  The bartender looked at me dumbfounded and then informed me (in German) that he couldn’t speak Spanish.


The conference was in a resort hotel at the edge of town on the beach.  It was nice enough with the usual amenities including a large swimming pool overlooking the ocean.  Overlooking the swimming pool in turn were a number of young ladies who were in the usual European swimming attire, and overlooking them were a number of North Americans who weren’t used to seeing bare breasts.


I don’t remember much about the conference (on Bayesian statistics) except for the fellow I met on the train.  We became fairly well acquainted and I visited him at his university when we returned to Madrid.  I showed him some of my work and we eventually wrote a paper together.


The second part of our trip was to take us to Yugoslavia (this was before the breakup of the country). To get there, we went by train from Madrid over to Italy and down the length of the country to Bari, where we caught a ferry across the Adriatic.  On the way we stopped in Rome for a couple of days to pay our respects to the ancient city.  We stayed in an ancient hotel which also had ancient toilet facilities.  Edie had a little adventure in one when the door stuck and she couldn’t get out.  Eventually they broke the door and released her from what she thought was going to be an extended imprisonment.


I had thought the ferry would be like a romantic, but cheap, cruise on the Mediterranean.  But the ship left just as it was getting dark, and we were assigned berths in separate rooms below the water level which we couldn’t leave after the ship got under way.  All night long we had to listen the groaning of the ship and the pounding of the waves.  In the morning things were better.  We got to go up on deck and watch the approach of  he beautiful Dalmation coast.  The shore is very rocky with lots of small islands and coves covered with a smattering of evergreens. 


Dubrovnik itself is an old Roman city built on a peninsula sticking out into the sea.  The buildings are all made of stone which makes the entire city appear to be a single unit.  The conference I went to was not in the city itself, but rather in a more modern building on the mainland. 


There were many opportunities for sight seeing around Dubrovnik in addition to the old buildings and rocky coves.  One such was an island off the coast that was a sanctuary for nature lovers, that is, there was a nude beach.  I went there with a few of my colleagues from Eastern Europe.  They wore their suits while we explored the island but I deferred to the local customs and went swimming au naturel.  I had looked forward to engaging in a little voyeurism with visions of a young Brigitte Bardot dancing through my head.  Unfortunately most of the nude women (and men) looked like they enjoyed dumplings and beer more than cavorting in bed.  My colleagues had a better time discussing mathematics.


After the conference we decided to take a short jaunt to Belgrade to see more of Yugoslavia.  My impression is that it was a poor town with lots of sullen looking men hanging around.  It did have a tourist office of sorts and we picked up a map and started exploring the town.  We immediately got lost.  Our map was printed with the Latin alphabet but all the street signs were in Cyrillic.  Since I had studied a little Russian (very little) I was able to sound out the street names and then sometimes figure out what they might be in the Latin alphabet.  One long one turned out to “George Washington Street”. 

We left Belgrade the next day and flew to Zagreb again and thence to home.





20.3) China.


When we (Edie and I) went to China, it was still the old, that is to say, the communist China.  But our son Pierre had been there a couple of years studying Chinese and teaching English.  So, when I learned about a biomathematics conference in Xian, we decided to go.  Unfortunately, by the time the conference came up, Pierre had left and gone to Taiwan to study Chinese and teach English and get paid in a convertible currency.  So we planned our trip to stop in Taiwan first and then go on to the mainland.


I had also contacted a friend in Taipei and arranged to give a talk at the Chinese Academy (Taiwan version).  My talk was on sampling theory and I think most people thought it was on a subject in statistics.  Since the talk was sponsored by the mathematics department, very few people showed up.  In fact, apart from my friend and a couple of his colleagues, there was only one person who sat in the back of the room.  After the talk I asked if he was interested in sampling theory too, and he replied that he was just waiting for the room to clear so he could sweep the floor.


During the next week we explored Taipei and a few other spots in Taiwan with the help of our son.  I remember the city as being dirty and noisy and full of smoke spewing motor scooters.  I was glad to get out of there after a few days and visit the country-side which is quite scenic with mountains and sub-tropical vegetation. At the end of the week we returned to Taipei to leave Taiwan and our son and go on to Xian in a roundabout way.


To get there, we first had to go to Hong Kong to get tickets for travel within China from a travel agent that was authorized to sell them.  Our son had recommended a good, inexpensive hotel in the Kowloon section of Hong Kong.  It was quite inexpensive but not quite good, but we stayed there anyway since we were only going to spend the night. It was a highrise building in which each floor was a separate hotel usually catering to a particular nationality.  One elevator with a capacity of five people served the entire building.  The stairwells were impassable since they were occupied by people camping out and cooking their meals on charcoal grills.  Getting in and out was an ordeal and almost kept us from getting our China tickets. 


We found out that the travel agent was in the central part of Hong Kong on the other side of the bay and called him to get directions.  But he was closing at 5 and it was then 4:30.  Fortunately the city has a good subway system which ran under the bay.  So we dashed down to the subway station, tried to guess at which stop we should get out, and made it to central Hong Kong with five minutes to spare.  But we had guessed wrong; the travel agent was still a mile further down the road. The rush hour traffic on the streets was at a standstill, so we ran the mile to the travel agent.  When we got there it was closed. But there was a happy ending; somebody had waited in the office for us and gave us the needed tickets.  The next morning we left for Guangzhou where we could catch a domestic flight to Xian. 


The airport terminal in Guangzhou was mostly a large room crowded with people waiting for flights.  It was noisy, hot and confusing.  There was no indication where we could go to catch our flight.  Fortunately there was a gate agent who spoke some English and who took our tickets and passports and then disappeared.  When she finally came back after an hour, she informed us that our flight had been delayed for six hours.  We killed the time by taking a taxi to a new hotel that had air conditioning and sitting in the bar until it was time for our flight.  When we got back to the airport we found our flight had been delayed an additional four hours.  By then it was cooler and getting dark, so we stayed there until the flight was ready.  We got to Xian about midnight to find a dark deserted airport.  But someone from the conference was expecting us and had waited all day for us to show.


Xian was the ancient capital of China , was the terminus of the “silk road”, and was the place where the life-sized terra-cotta warrior statues were found.  There were still many traces of its ancient splendor and, at the time we were there, not much in the way of modern development.  A large park with a lagoon was near the university where we were staying.  We took advantage of it by frequently strolling around the lagoon and attracting much attention from the Chinese who were not used to seeing many westerners.  In fact they would sometimes approach us and try to speak English with us (I think).


The organizers of the conference had arranged for post conference tours of parts of China.  We opted for the southern tour which took us to Chengdu, and to Guilin on the Li River.  The tours were led by graduate students and by party cadre.  I don’t remember much about Chengdu except for a couple of our son‘s students that we met.  They spoke impeccable English in spite of never having left China.  There were also the phenomenal bicycle traffic jams.  Thousands of bicyclists would peddle down the streets moving very fast in unison with hardly a foot between bicycles.  The Tour de France has never looked so impressive.


Guilin, on the other hand was a place I had always wanted to see.  It’s the place where those steep karst hills surrounded by mist that one often sees in Chinese paintings are found.  We took a cruise along the Li River into the midst of these formations.  You half expect to see dragons coming out of some of the caves.  But all we saw were souvenir salesmen at the entrance of one cave we visited.


From Guilin, we went to Guangzhou and thence to Hong Kong.  We arrived there after midnight with no local money, no hotel reservation, and no way to get from the train station to the downtown.  Fortunately, a couple of Spanish women were on the tour with us and had one of those miraculous ATM cards.  We borrowed some cash from them, took a taxi downtown, found a hotel, and the next morning headed home again.


20.4) Down the Nile to Abu Simbal.


The only place in Africa I have ever visited was Egypt for a conference at the University of Cairo.  To get there, we had to first fly to Athens and then get an Egyptian Air flight to Cairo because of some government restriction.  This gave us an opportunity for a superficial visit to some of the ancient ruins such as the Parthenon in Athens.  I didn’t have a chance to check if its dimensions really satisfied the “golden mean”. 


In Cairo we stayed in a hotel on the banks of the Nile from which it was a walk of about a mile to the university.  The walk was made more interesting by the fact that I had to pass the Israeli consulate surrounded by machine gun emplacements manned by troops in battle uniform.  The more dangerous part of the walk, however, was crossing the street.  The avenue parallel to the Nile had very few traffic lights and a continuous stream of cars.  I watched Egyptians crossing this street safely and marveled at how they did it.  I finally hit on the device of following one of them, but it was still frightening.


The most memorable of the trip was a cruise down the Nile taken with some other people from the conference to visit some of the archeological sites.  A short time before we took this tour there had been a terrorist attack on a tourist bus; as a result tourism was down considerably.  The cruise boat sailed up the river stopping at important sites such as the valley of the kings where we would get out and walk around.  I was struck by the extent of the ruins and by the size of some of the statues.  In Abu Simbal, the statue of Ramses is about 60 feet tall (I’m guessing).  Also, the symbols and the hieroglyphics seemed to be the same everywhere.  This is in contrast to Mexico where they are not.  The Nile’s banks are crowded with very dense green vegetation which stops abruptly at the edge of the irrigated land and becomes complete desert.  The waters are quite brown looking and probably polluted.  The boat we were on had a small swimming pool so I wasn’t tempted to jump into the river to keep cool, but I came down with a flu-like sickness anyway.  As on most cruise boats, there was considerable partying which I had to forgo.


20.5)        Other little adventures


There were many other interesting places that mathematics brought me to.  In Ireland I got used to eating kippered herring for breakfast (better than oatmeal).  In Poland I got lost when I couldn’t recognize the apartment complex near where we staying.  In Portugal I told everyone the fisherman were looking for some sort of powder, but then discovered that pulpo in Spanish translates into polvo in Portugese.  In Istanbul I enjoyed eating those little sardine like fish until I saw where they were catching them.  In Korea I forced myself to eat huge meals every night to avoid insulting my hosts.  Each of these places probably deserves a separate chapter, but wil have to await the next edition.