A visit to Escher's world

Today we had breakfast and headed to the Escher in Het Paleis (Escher in the Palace) museum. We stopped at a little book store that we passed yesterday. They had some interesting used books. We also walked on many pedestrian streets with little boutique shops. The weather today was sunny and 60-ish. It was very pleasant and enjoyable to be out and walking. The streets are very nice and many wider streets have grassy areas or flower beds. It is wonderful to see all the daffodils, tulips, and grape hyacinths in bloom. The trees are starting to bud and everything says spring.

The museum opened at 11, but we got there about 30 minutes early. The area where the museum is located is near many embassies, including the US embassy. There was a group of about 50 people protesting in the plaza area about closing the Iranian embassy because of the recent crackdown of civil liberties in Iran. We pondered how a government shutdown might influence our trip. Will the US embassy will close? Will TSA workers not work? Will air traffic controllers not get paid? Will customs agents not check our bags?

The Escher museum is located in the former palace of the queen until around 1948. It was not huge, but 3 floors that were filled with Escher's works and information about Escher. There was also an area dedicated to optical illusions, a theme of several Escher's works. The first floor had early prints and pictures of Escher. Many of the pictures in the museum were copies of the pictures from Escher's photo albums that we saw yesterday at the Gemeentemuseum. There were also some examples of Escher's printmaking instruments and some matrices containing interesting patterns.

The second floor contained many of the print's that are classic Escher. Many contain impossible ideas, such as Reptiles, Convex and Concave, Drawing Hands, Belvedere, Ascending and Descending, and Relativity. Others contain mathematical figures, such as Stars, Moebius Strip II, and Knots. It was quite fascinating to see originals of nearly ever Escher print ever made. The detail and tonalities on the prints is quite amazing.


Another amazing thing to see was all the planning and details required by Escher to carry out a final design. He had notebooks or different was of dividing the plane into identical blocks. While not a mathematician, he created his own notation for these patterns. He created multiple examples of each of these patterns. For example, the pattern shown above (design from April 1959) is characterized by a gyration point of order 3 (near the fins) and a point containing 3 fold kaleidoscope point (heads and tails). This kaleidoscope point is a point where 3 lines having mirror symmetry meet. This is a fourth type of symmetry pattern possible in the plane. Escher's code for this pattern is IIA2 Type 1*; crystallographers classically denote this pattern p31m and a newer mathematical orbifold notation for this pattern is 3*3.

On the top floor of the museum, there were many display associated with optical illusions. There was a physical Penrose triangle model, which is the basis for Escher's Waterfall. There was also an Ames room, which makes objects of the same size seem much different in size. I had fun menacing poor little Amy.


After several hours at the Escher museum, we had a nice lunch at a nearby outdoor cafe. We sat in the sun and watched the bikes and trams go by. Service in Europe is quite different than in the US. Waitstaff generally ignore you until you demand attention. The drink sizes are also tiny. I seem to be dehydrated most of the time. I ordered a diet coke, which is typically 25 cl, or about 8.5 ounces. Luckily the food was good and we had a nice rest for the next museum.


After lunch we went to the Mauritshuis, a former mansion that is now the royal picture gallery. It is in the Binnehof area shown above. The main artists whose work was on display include Vermeer, Rembrandt, and Jan Steen. In one gallery the conservator was working on the restoration of a Jan Steen painting. I was surprised to see so many of the paintings were made on wood panels. Many had amazingly vivid colors. Amy had a great time looking at these 400 year old paintings.

We then went to the Hague's historical museum. It had some interesting displays about the Hague and its growth over time. We learned that the Nazi's destroyed 8000 homes to create a tank barrier during WWII. After the war, a new large road was built along the tank line. Not much lemonade from a sour time in history.

We had a simple dinner and are just hanging out in the hotel tonight. We are catching up on email, blogging, and we had a chance to skype with Hannah. I think tomorrow we are headed to Amsterdam.

Enjoying the trip, day and night

I spent the day at the Gemeentemuseum library looking at materials from the archives. They say they have the world's largest collection of Escher's papers. I was able to see many very interesting items and took hundred of photos. There were many small patterns Escher produced using repeated rotated and reflected copies of simply decorated square tiles. I looked at details of Escher's trip to southern Spain, including pictures from the Alhambra in Granada and the Alcazar in Seville. While there were no photos from Cordoba, but there was a large charcoal drawing of the column forest in the Mezquita. There were interesting details from work Escher was commissioned to do. I saw several colored drawings Escher made of tiles in the Alhambra. I read letters to Escher from many people including H.M.S. Coxeter, Martin Gardner, and Donald Knuth. There are more items in their archives and also some in private collections. Overall a very productive and amazing day. All the staff were very helpful, particularly Vivian and Herbert.

Escher, Day and Night, 1938

Escher produced some amazing works. He was the first person to explore using uniform tessellations and use these as a design element in his works. For example, in Escher's Day and Night, the black and white birds face opposite directions. There are no gyration points, but translations in the horizontal direction for each colors, however one requires both a reflection and a translation to move a white bird to an adjacent black bird. This combination of a translation and reflection is called a glide reflection. This is yet another type of symmetry pattern.

After leaving the archives, we went to a small local market for some cold beverages and chocolate. We stopped at our hotel and then went local yarn shop. Amy enjoys going to new knitting shops where ever we travel. Amy purchased some interesting new yarn that she said was possibly going to be a gift for someone. We did a little window shopping and gift shopping. We then went to dinner at a pub and have some typical pub food and libations. We then walked back to our hotel, past quite a few coffee shops, and are planning for tomorrow. Interestingly, the police stopped to talk to a young man about jaywalking just as we were approaching the crossing. At least Amy and I know better than that!

Archives Work

Alright, I told Dave I was NOT working on this trip . . . but we are in an archive and my curiosity has gotten the better of me. I explained to Herbert, guardian of the Gementeemuseum reading room,  that I was an archivist.  He invited me to see the electronic catalog.  When I inquired about a painting in one of the current exhibitions, a Charles Leickert, (more on that later), he looked in the catalog for info, saw that there were two books about Leickert in their collection, and invited me to help retrieve  them.  From the shelves in the storage areas.  Down one level through a key-access elevator and through the security doors.  Very exciting, to say the least.  He gave me a thorough tour of the storage area and of the physical layout and intellectual control of the collections.  So, I'm NOT working, but it is terribly interesting. My archives pals will all agree, seeing someone else's mess is as exciting as showing off your own, even if it bores most regular people to death.

A note about Charles Leickert, he was a Dutch artist, born in Den Haag in the early 1800s.  The Brueckner Museum at Starr Commonwealth owns a painting by Mr. Leickert and there is one currently on display at the Gemeentemuseum.  I looked at the two books here on Leickert - he was an orphan in his later youth and was shuttled around institutions and homes. He had learned how to draw and paint and earned his living by being a prolific painter of Dutch scenes, with over 700 paintings to his credit.

Dave is having a great time photographing MC Escher's notebooks and looking through the personal family photo albums.  There are photos of his trip to Spain and also of his children - George, Arthur and Jan.  The are funny photos of George and Arthur in bunny costumes, sitting on the training pot, dressed up as bandits and sticking out their tongues in family portraits.

Weather here is 58F and sunny/partly cloudy. The trees are in bloom as well as the daffodils. We passed a flower shop and they had bouquets of 50 tulips for 4.95 Euros - about $6.00 American. I'm sure they are not going to be that cheap for Betsy's wedding next year!

I am sure we will post more later.

Off and Running

Dave in the Gemeentemuseum library

My research is off and running, just like the characters in the Escher print Cycle from 1938. As Amy mentioned, we spent several hours in the Gemeentemuseum library (open only by appointment) looking at books about Escher. Some I had seen, others were in Dutch, some were small catalogs, and others I had never seen. I was able to get some additional information from them and would like to get our library to purchase a few more books on Escher. I am really looking forward to our visit with the archivist tomorrow.

M.C. Escher, Cycle, 1938

After a quick bite to eat, we visited some of the Gemeentemuseum collections. There were a number of interesting artworks on display. My favorites were 3 Escher prints tucked away in a corner; one was Cycle (shown above), where Escher morphs a landscape into a set of interlocking figures. If you look carefully, you can find three different places where three figures (black, white, and gray) pivot around a point. Specifically, the heel, the forehead, and the knee. These are a gyration points of order three because at each point there are three possible positions for the person without changing the underlying overall pattern. These three gyration points are a characteristic that defines this type of pattern. Note this pattern is significantly different from the pattern found in 8 Heads. I was very excited to see these prints up close and in person. It is amazing to see the level of detail and tonality Escher achieved in theses works.

We left the museum and returned to our hotel to finally check into our room. It is about a 20 minute walk. Spring has arrive in The Hague. The grass is green and the daffodils, forsythia, and magnolias are blooming. Our hotel is small, but very nice. We have free wifi in our room which makes blogging and email much easier. We power-napped for about an hour and then went to a little Italian place for dinner. We are both ready for a good night of sound sleeping!

DTW-AMS

Hi Folks!  We have made it to the Netherlands, although not without its challenges.  After taking the Michigan Flyer from Jackson to the Detroit airport, we stood in line to check our bags and check-in for the flight.  We were originally on a 1:30 flight to Philadelphia, connecting at 6:50 to Amsterdam.  We were in line around 10:30, because of the timing of the shuttle.  The US Airways clerk asked if we wanted to get on a earlier flight to Philly, because there were thunderstorm/weather delays, and we might want to get there as early as possible.  Agreeing, he issued us new boarding passes for an 11:45 flight and off we went to security.  We got to experience the full-body scanners, which seemed pretty painless.  And no one asked to rifle through our bags for anything unidentifiable, so that was also a plus.

We headed to the gate to check the flight boarding, because it should have been soon, only to find out that the NEW flight we had been booked on had been cancelled!  There was a flight at the gate that should have left for Philly at 10:25, that was in the process of boarding.  We stood in line to ask questions and the clerk was nice enough to get us on THAT flight, as it was boarding.  She called the bag room to have our suitcases transfered to the new flight.  Luckily, they were easily located due to the neon green duct tape strips Dave put on the top and bottom of each bag. We boarded, the plane pushed back from the gate and we then proceeded to sit on the tarmac for another 1/2 hour because of traffic and weather.  Finally, we made it to Philly about 1:30 pm. This gave us plenty of time to stretch our legs, get something to eat, and hang out until the evening flight to Amsterdam.

The fight to AMS was not full, so we were able to sit reasonably comfortably, as comfortably as you can on long flights like this.  Flight time was about 8 hours landing around 8:15 local time this morning.  The Schipol airport is set up a little differently than Detroit, and you have to walk through a large part of the airport to get to the customs desks and then baggage claim.  Dave was interested in knowing where the MC Escher mural that was supposed to be in the airport was located, so first thing we did was stop and ask at the information desk.  We had passed it, so we went back to locate it, and discovered it was in an area under renovation.  not to be undone by this type of triviality, there was luckily a staircase nearby at the top of which we could see the mural from above and photograph it.  In the US, you are definitely NOT allowed to photograph in airports, but no one seemed to mind.

We got through customs pretty quickly, collected our bags and headed for the train connection area in the airport.  We ended up buying tickets from the ticket window, and not the automated kiosks that are available.  After asking the difference between first and second class seats on Dutch trains, and being informed that the difference was the price, we purchased the second class tickets, which were 14 euros instead of the 1st class 25 euro tickets, we headed for the platform.  Note - many Dutch residents speak A LOT of English. There are 2 stations in Den Haag, our pit stop for this leg of the race, and we definitely wanted one over the other.  After discussing which train might be going there, a friendly man on the platform assured us that the train in front of us was going where we wanted to go.   Alas, we sadly found out he was mistaken.  We ended up at THE OTHER station, on the other side of town from our hotel.  Luckily there are information booths for travelers pretty frequently sprinkled about transit stops.

We now bought tickets for the tram, which supposedly would take us where we wanted to go.  Trams are like buses, having regular routes and stops, but not always going in the same direction.  Sometimes the 17 tram is going north and sometimes it is going south. We ask the ticket takers which tram we want, but they decide as we are getting on the 11 tram, that we do in fact want the 17, which boards across the street and around the corner.  We head to the shelter and look at the map, trying to figure out which stop we want and how we can relay this to the driver.  The next #17 comes along and in our hesitation on deciding how to ask the driver, the doors close and the tram leaves. The next one comes along 10 minutes later.  Lets pause now to think about the fact that we have taken a transatlantic flight and been traveling for quite a few hours on very little sleep, and even littler coffee. The driver of the next tram punches our tickets, affirms that we are going the right way and makes sure we know where to get off the tram. We don't find seats with our luggage, but stand until one opens up.  I rise a few stops later to give my seat to an older woman who looks like she desperately needs a seat, proceeding to almost knock her over and elbow the woman across the aisle in the head in the process. I retake my seat as she has a companion farther back in the bus waving her back.

We find the hotel with no problem. check in isn't until 3:00, but they are glad to store our bags and give us a map to go somewhere else until the room is ready.  We are now in the Gemeentemuseum, repository for much of the archival Escher materials Dave wants to see.  We did not have an appointment, but they were slightly aware we were coming, as Dave had sent email last week.  Dave is looking at books on Escher and had a talk with the archivist who will be pulling Escher's personal photo albums, among other things, for us to look at tomorrow at 10:00 am.  We are going to head over to the museum cafe for a break and to plan the rest of our day.

The M.C. Escher Odyssey begins!

M.C. Escher: Eight Heads, 1922

As you likely know, this semester I am on sabbatical. For those of you who are not part of academia, sabbaticals are granted to allow faculty to have a time away from normal teaching to pursue new research, teaching ideas, and engage in creative endeavors. In the past few years I have become very interested in mathematical tilings (essentially how we can subdivide the plane) and writing software to allow anyone to explore tilings. During my sabbatical, I am gaining expertise in this area to help my research. I am also developing a new course on mathematics, computing, and the arts.

One of the people who created very unique tilings was the dutch graphic artist M.C. Escher. I have enjoyed Escher's artwork for many years. You can see some of his works in the gallery at www.mcescher.com. Escher was a pioneer in creating tessellations of interlocking repeated animal shapes. He was not a mathematician, but many of his artworks contain mathematical themes. If you are interested, you can read a recent article by Escher expert and mathematician Doris Schattschneider at www.ams.org/notices/201006/rtx100600706p.pdf. She also wrote a very comprehensive book about Escher about 20 years ago.

The woodcut Eight Heads (above) was one of Escher's first explorations into tiling and he did not return to do any significant work in this area until 1936, after visiting southern Spain. During his trip, Escher toured Moorish ruins with elaborate tilings in Granada, Seville, and Cordoba. While not readily apparent, copies of the Eight Heads block shown above can be used to tile the plane! In fact, this is an example the simplest of all tessellations where copies of an underlying block or tile are simply translated left, right, up, and down. A snippet of the tessellation is shown below. Did you find all eight different heads?


What about the odyssey? I am traveling to the Netherlands to visit the Escher Museum, the library and archives of the Gemeentemuseum, and several places where there are public Escher works on display. I then travel in Escher's footsteps to Spain to see the Alhambra in Granada, the Alcazar in Seville, and the Mezquita in Cordoba.

I am very lucky that my trusty assistant and wife, who has vast knowledge of art history and significant archives experience, is able to come along! Amy will be of great help as I explore the works of M.C. Escher and see the Moorish sites that inspired his work on tessellations.

As with our trip last summer, we have hotel reservations and plane tickets, but we still need train and bus tickets. We also need to get tickets to museums. I have most major details planned and we are looking forward to an awesome trip! Today we fly from Detroit to Philadelphia and then on to Amsterdam. The weather in Amsterdam is likely to be cool, but southern Spain is likely to be sunny and 80.

Merry Christmas!

Hi Everyone,

Christmas has been very nice this year. We went to 11 pm Christmas Eve service last night. It was very nice with the senior choir singing and other special music. There were empty seats in the pews, but enough voices to make the hymns very lively. We got up around 7 am and opened presents. We then had a traditional breakfast of kielbasa from Stanley's in Toledo, eggs, and Polish coffeecake that Amy made. We then went to Whitehouse to visit Amy's parents and family. We had a nice dinner and opened presents. We got back home at 7:30. Elizabeth and Shane are out and about visiting with more of his family. The rest of us are just relaxing. Here are some pictures from yesterday.


Merry Christmas to everyone!