Tricotomania and more

In case you thought that it was all tourism and teaching around here, I have some knitting to show you. When last we spoke of knitting, I was experimenting with fair-isle. I have now completed three hats.

The first, I am not so pleased with. I tried to do too much. I was using multiple colours for both the background and the pattern and without any clear bands this ended up muddy in places. There is also a spot where a little bit of red contrasts too much and it appears that there are some very grumpy faces marching around the hat. I suspect they are displeased with the overall effect.

All is not lost. This was primarily a learning exercise and I learned much. Not only did I learn that I need to move more slowly in my experimentation with colour, but also that when knitting in the round using magic loop, my tension can get tighter when there are fewer stitches. Although some of the difficulties came out in the wash, I was more attentive to this potential problem in later incarnations.

I decided to take a break from that pattern, though, and try the other. This hat was more successful. I will admit that I have a difficulty with any design that could be considered representational. I don’t often knit leaf lace patterns, for example, because I dislike green and it seems weird to knit leaf lace in a colour that leaves are not. So the trees at the top of this hat constricted my colour choices.

The banded patterns were helpful, though, in that they provided more constrained sections in which to experiment and clear divisions between one and the next. I am not as happy with the bottom pirie band as with the rest of the hat. Perhaps that green is too dark? And the contrast between the white and the beige and light purple is greater than I might have liked. But overall, it works well. One of the darker purples has so much green in it that it appears green when knit with the whites and purples. So I used this, instead of the dark green, for the trees at the top.

Strengthened by this success, I returned to the first pattern and colour palette, though I left out the green. I did start by incorporating the beige from the other hat but it did not distinguish itself at all from the other beige (despite looking different in the ball) so I abandoned it. I stuck to one colour (red) for the pattern and varied the background in bands of different widths. I also sketched out how I might incorporate the decreases into the pattern, and decided to go with the double decrease every 3rd row, as in the 2nd hat, as I liked the shape better.

I am much happier with this hat, though it doesn’t really capture that autumn leaves colour palette that inspired me. I think that I really need some other colours of wool. That other red (which has now come in, but in a place where I am not) will help, though now I’m out of this red. I will also have to examine the sample card for a wider range of greens (and maybe oranges).

As for technique, I am quite comfortable knitting these and rectified the tension problem immediately. I should get some 3 mm dpns as these would make it easier to do the crown but working with a long 3 mm Addi using magic loop is fine. I carry both colours in my right hand (I knit English style) and have developed a rhythm for knitting 2 colours in that way. I have also mastered minimizing or eliminating twisting of the two colours. On the last hat, I also managed to incorporate most of my ends as I went along.

As this is primarily a learning exercise for me, I welcome all comments and suggestions about the colour choices and how they work together. What areas do you think work well? Can you articulate what exactly is not working with the sections that are not working as well? Do you have any suggestions for the kinds of colours that I might incorporate? In particular, I am not that good at identifying that one less obvious colour that would really bring some zing to the mix if used in small quantities. So suggestions of possibilities for this would be particularly welcome.

We are on the move again on Saturday* with a long (but beautiful) train journey down the Rhine to Switzerland. I have packed socks, which I can do without looking fort the most part. I’m on the second of a pair for Tigger out of the yarn we bought in Trier. There should be enough left over to do some small child’s socks, too. And I’ve wound the Koigu I brought with me into balls so that I can start a pair for myself.

*It is hard to write about time when I am writing these in Word with no idea when I will actually be able to upload them. But we head to Switzerland on October 27. Actually we are going to be met at the Geneva station by Mat’s parents and will be staying with them in Annecy, just over the border in France for about 10 days.

P.S. I am not reading blogs right now. We don’t have internet access where we are staying and have been paying for time in a T-Mobile hotspot. Now that we are in France we have found free wi-fi but I’m in a place with no electric connection and the battery on this machine is not great so no time for that. When we get to Paris (Nov 10-18) we’ll have wi-fi in the flat and I might spend some time catching up. I have been reading the comments, though, and trust you are okay.)

Our visit to the Arithmeum got me thinking. Sometimes we are so used to the number system that we use all the time that we forget how new it is. And our education system (both as a set of institutions called schools, and as a set of practices for helping people learn things) is so focused on memorizing math facts and being able to use them in calculations that we lose sight of the fact that the algorithms we use for calculations are merely short cuts for what can be accomplished with a number line.

In fact, although we sometimes begin teaching about addition and subtraction with a number line, it is often seen as a sign of weakness to continue to use one. This is one of the beliefs that those with right-brain-dominant children have to learn to overcome. And hanging out with some of these folks online has given me new insights into how we can do math. I typed up the multiplication tables for Tigger and printed them on a 5” x 8” index card that I let her refer to when she works on her math problems. It seems to me that the concepts and the strategies for accomplishing multiple digit multiplication and division are much more important than the memorization of the multiplication facts. (And by using them, she remembers more and more.)

To return to the Arithmeum and what it got me thinking about, I started to think about how we came to have a base-10 system and what that meant. When we learned about bases in school, I never quite got it, but all of a sudden it came to me. All “base-10” means is that we have 10 symbols in our system of numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). And it is easy to forget that they are only symbols. Some of the historic number systems discussed at the Arithmeum included one which had 64 symbols and another with 16. I can’t even begin to imagine how you calculate in a base 64 system. (Actually, before the geeks chime in, I can begin to imagine, because 64 is a multiple of 2.)

So the other day, Tigger and I sat down and we talked about bases. Instead of focusing on converting things from other bases into base 10 (which is what I recall about how I learned them), we talked about how a number system with a different base would work. I began by pointing out that base 10 merely meant that we had 10 symbols. I also reminded her of the importance of a concept of 0 and a system of place value for doing calculations on paper, as we had learned at the museum. We then went on to experiment with other bases.

I started with base-5 (a number I chose randomly) and I made up a number line — 0, ∆, , ◊, ♥. We counted and filled in our number line up to a few 3-digit numbers. We made sure we had a zero because we had learned how important that was. Then we did some addition by jumping along the number line (just like you do when first teaching children to add). Once we could do simple addition like that, I created a few multi-digit problems and Tigger used her normal strategies for adding multi-digit numbers (with redistribution) to solve them. She was fascinated. Knowing the math facts is absolutely not an issue here, and she was amazed by the fact that as long as you have a concept of zero, you can make up your own number system and do all the things we do with our base-10 system.

My purpose in using completely different symbols was to circumvent confusion with the numbers that she knows. When you are looking at a 10 it is hard to think that it might mean what we normally think of as 6 objects (as it does in base-5). My strategy worked and once she had grasped the concept, it was possible to use the same symbols that we normally use without confusion. We moved on to a base-16 (using A, B, C, D, E, F to extend the number of symbols). And then I showed her binary (base-2).

She had a great time. I think that playing with number systems like this can be engaging for kids, whether right-brain-dominant or not. The concepts behind the arithmetic become clearer as you work out how to use a number line to perform calculations. And the concept of place value can be learned through manipulation rather than accepted at face value and memorized. This conceptual learning can then be transferred back to the base-10 system we normally work in, giving children conceptual tools that they can use even when they forget the math facts and algorithms. For right-brain-dominant kids (and I’m not convinced Tigger fits that description though many strategies I’ve learned from those whose kids are much more right-brained work well with her), this could be really exciting, playing to their strengths in conceptual and visual thinking and not really requiring the memorization of math facts that they often struggle with.

After playing with bases in this way, I noticed that one of the chapters in Zaccharo’s Becoming a Problem Solving Genius was about bases. We had a look the following day. Although it started with the idea that Mrs. Mouse was writing a science fiction book in which the people of her fictional world worked in base 7, the explanations then went quickly into converting between base 7 and base 10 (something it seems to me those fictional people would only need to do to communicate with us). We worked through some of the explanation and I watched Tigger get less and less excited about something that had made her quite happy the day before. We stopped.

And then we talked a bit about the different ways of presenting the concept of bases. And we played with base 7, which had been introduced in Zaccharo, but in the way we had played with other bases the day before. We made a number line. We did some multi-digit addition and subtraction. Then we constructed a multiplication table together. And did some multiplication. She texted* her uncle: “26 x 21 = 606?” (He’s a mathematician, but he got off on the wrong track and they went back and forth a bit. Finally she told him that it was base-7. He called her a cheat but was also impressed. Then he told her she should learn more about base-16 and base-2 which he uses all the time in his work.)

That evening, after a day walking along the Rhine and hanging out in Starbucks (which is where we go online) she sat down and worked out base-6 while her dad cooked dinner. As if it was just a fun puzzle to play with. And that is how math ought to be. I’m sure we’ll get to conversion between different bases at some point. But it seems much more fun to just play around with making up number systems and doing calculations in them as if we live on some fictional planet where they count in 7s. She’s 10. There is plenty of time for useful later.

(And then this morning, she just decided to make times tables for the bases she had. We’re in the middle of base-16.)

*Do North American’s say that? Or do they say “SMSed”? Leaving aside the whole question of whether text/SMS messaging is the downfall of literate society, of course.

We are staying in an apartment in the suburbs of Bonn. We are right on the edge, though. As these photos, taken from the living room window, demonstrate.

The first two are the same view at different times of day. You are looking east. And it is often quite misty in the mornings. If you look closely you can see a white and black church steeple just to the right of centre. The third photo is just around to the left of the first but taken from the same window. Those white blotches are cows. There are brown ones, too. Their pasture comes right up to the street just past the house next door. (as always, click for bigger photos)

The Constantine exhibits were very well done. There were three, one focused on the military and political aspects of his reign, one on the religious aspects, and one focusing on “tradition and myth”, examining the legend of St. Sylvester, the Constantine donation, the “true cross”, and cults of Constantine (I’m not sure if that is the right word in English. I am translating, probably badly, from the French.).

The signage for all three exhibitions was odd. In each room, the main explanation of the room was in German and French but the signs on the individual artefacts displayed were only in German. There was an excellent audioguide (available in German, French, English and Dutch, with a special children’s guide available only in German) that explained specific artefacts and gave some wider context to them.

We visited the “tradition and myth” exhibition first, largely because it was right next to the tourist information office. I found some of this interesting but it seemed to assume knowledge of the traditions and myths that I didn’t have. It was quite busy and we visited after our (unnecessarily) long train journey so Tigger tired quickly. I did learn a bit about the legend of Sylvester, which seems important to the role of the bishop of Rome in the church; and about the donation of Constantine (again, I’m not sure if that is what it is called in English), which secured secular power for the pope in the Middle Ages and seems to have been important to the Reformation though I need to read a bit more church history to sort this out. The bit about the true cross had some interesting commentary on the development of Christian iconography.

On Friday we began with the exhibition in the Ecclesiastical museum. I had had my doubts about how interesting this would be but Tigger and I agree that, of the three, this was our favourite. The exhibition was well organized with excellent commentary in the audio-guide. We got some of the basics of church history, especially as they relate to the role of Constantine in the recognition of Christianity as a religion and then in the building of churches (including the Church of the Nativity in Bethlehem and the Church of the Holy Sepulchre in Jerusalem, models of which were shown and explained). Much of this exhibition also had architectural artefacts that could be appreciated without understanding the labels. The exhibition wasn’t very crowded, which also helped.

There was good information about how artefacts such as coins have been used by historians to work out what was going on in this period. For example, initially Constantine and Licincius (co-emperors) provide freedom of religion in the Edict of Milan (sorry, dates don’t seem to have stuck but this is early on, maybe 306?). This applies to all religions and the main difference it makes for Christians is that their refusal to make sacrifices to the Roman gods (and the emperor) is no longer considered traitorous. Christians (and presumably others, including Jews, who are not mentioned but presumably also refused to make sacrifices to Roman gods) are now required to pray to their own gods for the well being of the emperor as a sign of loyalty.

But in this early period, Constantine himself is not Christian. The coins are important evidence of shifts in his own beliefs because at some point (and again, I forget the dates), coins start to have the Christogram on them. Later still, there is evidence in the burial practices of Constantine’s family that suggest a stronger commitment to Christianity. Constantine is not baptised until 337, quite late in his reign.

The freedom of religion granted by the Edict of Milan enable Christianity to grow more quickly in the years that follow. This growth is then aided by the church building program undertaken by Constantine. It seems that this is related to a longer tradition of emperors building monuments that are seen as gifts to the people. So although there is evidence that Constantine does become Christian, it is not because of his own beliefs that he builds these important churches. Nevertheless, the church building program is an important contributor to the growth of Christianity.

The end of the exhibition had some interesting commentary on the evolution of imagery on Christian sarcophagi (stone coffins). Apparently Christians were slow to put any religious images on their sarcophagi due to the commandment against worshipping idols. Early in the 4th century, they begin to have carvings, mainly of Old Testament images of salvation (the one on display was of Noah). Then they began to have images from the New Testament but these were primarily of Jesus as miracle worker. There was a sarcophagus on display that showed a whole series of miracles – the blind man, the bleeding woman, the feeding of the 5000, the water into wine, the lame man, etc. Later in the century (and I can’t recall if this entire shift took something like 50 years or more like 100 years, but either way it seems quite fast), the imagery changes yet again to show Jesus as a central figure giving the law (shown as a scroll) to Peter with images of the miracles at the sides.

Also included in this exhibition was the importance of the meeting at Nicea in 324 (I have forgotten what it is called, which is bad because it was really important). The important debate was whether Jesus was of the same matter as God or only of similar matter (they decided the former). They also decided the dates of Christmas and Easter and to honour Sunday as a day of rest.

On Saturday we went to the third of the exhibitions. Saving it for Saturday might have been a mistake because our experience was marred by the size of the crowd. This was also the largest exhibition. We did learn about the structure of imperial government around the time of Constantine (in particular the tetrarchy established by Diocletian) and the form of succession. The difficulties of ruling such a large territory were much in evidence and there was a lot of information about the Gallic secession and various disputes over succession. Between the difficulties of the crowd, and the lack of English (or French) signage I didn’t quite grasp how we moved from this to Constantine’s evident ability to rule over the whole mess later.

There was a lot of information here about Trier itself, which was an imperial residence at the time. Lots of old mosaic floors and things in evidence and a great model of the Roman city. We skimmed a lot of this exhibition even when the crowds seemed to thin in the later rooms (how does that happen?). The commentary on Constantinople was interesting. I suspect we might have got more out of this had we come on another day.

One thing that was discussed in this exhibition was the relationship between the size of statues of rulers and their power. They had reproduced parts of the Colossus of Constantine, a 12 metre high statue, using 3-D computer modelling to build a replica. The foot was reproduced several times and situated in various parts of the city. We kept coming across feet as we went and they were interesting even before we know what they were. In the exhibition there was a reproduction of the arm and hand and another of the head (itself 3 metres high).

On Thursday morning Tigger and I set off for Trier. We made the mistake of taking the first train to Koblenz that arrived. It was a slow train, stopping in every little place along the way and arriving about 1 minute after a train for Trier departed Koblenz station. Had we waited 10 minutes on the Bonn platform, a quicker train would have arrived. But we were not in a hurry, really. We had a bite to eat at Koblenz and then caught a train to Trier.

The train journey down the Mosel is indeed beautiful. The valley is quite deep and the train runs along the edge of the river with steep hills rising right next to the track. The river is winding so you often get lovely views of ahead or behind. Houses are built in the valley, with vineyards planted in the steep hills (often terraced). At Bullay, the rail line leaves the river and the scenery changes to rolling hills with pastures of cattle and sheep, and orchards. No less beautiful but quite different.

Trier itself is quite large though the main station is near the old city, where most places of interest are located. Despite the season there were a lot of tourists around, mostly people past the years of child-rearing and thus able to travel during the school year. I’m not sure whether the numbers were affected by the fact that the Constantine exhibits are closing in a few weeks. In any case, we had a little difficulty with hotel rooms because the Friday night was pretty booked up. Clearly weekends are still very busy at this time of year.

The town is very pretty with a lot of old buildings of various periods. It was first founded in the 2nd century and was an imperial residence in the Roman empire. I think many of the older buildings are restored, as Trier was bombed late in WWII. The centre of the old town is now clearly the major shopping district. It is busy with a thriving market in the old market square.

We bought a combi-ticket for the 3 Constantine exhibits and went to one each day of our visit. To keep this post from getting way to long, I’ve discussed them in a separate post. On Friday, we walked around some of the city taking in the Konstantin Basilika (originally Constantine’s throne room in the Trier residence and a protestant church since the mid-19th century), the palace gardens, and the Kaiserthermen.

Of course none of the museums open before 10 a.m. but there was an amazing toy shop near our hotel that Tigger was keen to explore. Germans are well known for good toy shops, and rightly so. We spent a lot of time looking at the display of dolls and doll-house trappings. In encouraged her to consider not buying things we could get at home but there were some little things we don’t see often. So we bought shoes for some of her dolls. These came in an impressive range of sizes and we correctly guessed the right sizes for her two smallest dolls. It is amazingly difficult to find clothing for these dolls at home, given the dominance of the market by a few brands and sizes of doll so this was a great find.

The Basilica is an amazing piece of architecture given its age, a very large single room structure with a semi-circular apse at one end. It was bombed in 1944 and the restoration worked mainly to the original Roman style. There was a series of plaques (with English commentary) explaining the history. The heads of a series of statues from the 19th century church are displayed along the sides showing the contrasting aesthetic of the 19th and 20th centuries. The font is particularly beautiful with a mosaic floor (not a roman reproduction but a modern mosaic). There is also a series of 3 modern mosaics on the pulpit and an interesting cross on the altar.

The basilica forms one side of a courtyard of the Prince Elector’s residence. The contrast in styles is quite striking, as the later is pink and frilly. There are beautiful formal gardens outside with a lot of statues of what we assume are Greek or Roman gods and goddesses. Greek mythology is on the list of things to do when we return. You can’t go in the building (or I don’t think you can) but it is nice to walk by.

A little ways off, the Kaisertherman is a very large Roman bath complex which was never completed nor used as such. This was one of Constantine’s big building projects but the later emperors didn’t have the money to complete it. At some point the structure was included in the city walls, something that is still evident. It has recently been restored (well, it is a ruin but a restored ruin) with a new entrance building and a look-out tower. You can walk through some of the tunnels underground. It is quite an impressive structure though I would have appreciated a bit more explanation of the heating system and whatnot that must have been either constructed or planned. Knowing what those tunnels were for would have been handy.

Our last stop on Friday, after tea and cake, was a toy museum. Tigger loved this. And it was quite a display. Old dolls, trains, cars, etc. Fascinating.

On the way back to the hotel, we stopped in a wool shop and bought a bit of sock yarn. Tigger also chose a cross-stitch kit to make a bookmark. On Saturday morning, while waiting for the museum to open, we went to a fabric shop we had passed and bought some very pretty corduroy (flowery). It was a nice shop and I again had to explain about buying things we don’t see often at home. The corduroy is for skirts for Tigger so we got a half metre of each of two patterns.

Our first museum visit in Bonn was to the Arithmeum, housed in the department of mathematics at the university. It is an easy walk from the main station (through a park which has a play structure on the other side). The museum is in the atrium and stairwell of the building, a very light and open space.

I had expected a museum about mathematics in some of its higher forms, which lend themselves to artistic and other representations. And there was a bit of this in an exhibition of paintings on the walls. We noticed these but didn’t really focus on them.

The main exhibition is about arithmetic (duh, given the name), particularly the development of aids and machines to perform calculations. We ran out of steam before the development of electronic machines (the pun was not intended but is apt) but the museum does go right up to the development of computers with some interesting looking displays of the innards of some of them and explanations of how they work.

Historically, you start on the top floor and work your way down. The larger exhibition space is on the main floor. But the historical stuff is really interesting. While I have often remarked at the relatively short period of time that we have moved from computers the size of houses to computers you can fit in your pocket, I hadn’t realized that it is only about 900 years since Europeans have even had a system of written numbers that allow us to do calculations on paper.

This provides an interesting twist on the debate about whether children should be using calculators for calculations. The ability to calculate on paper is, historically, not very significant and seems to come between older forms of reckoning (using objects to count with, and more complicated arrangements of objects such as the abacus) and mechanical and electronic machines to perform calculations. In fact, it seems that the development of machines to speed up calculation is crucial to the development of higher mathematics as it enables more time and energy to be spent on the concepts.

The ability to calculate requires a system of written numbers that includes a concept of zero not only as the null set, but also as a place-holder in a system of numbers. Roman numerals do not have this. This is first develop in India, then adopted by the Arabs who bring it to Europe (through Spain) in the 12th century (I think, I may be remembering the dates badly). All that stuff about place value is actually a major advance in mathematical thought.

We also learned that the word “calculate” probably derives from the Greek word for stones (calculi – I assume calciferous stones, and the examples shown were white). These were used early on for reckoning (long before the development of a system of numbers). There were also several types of abacus, and reckoning boards. So, for a considerable time, calculation was done primarily by counting things (knots on cords, stones, beads, coins, etc).

The ability to calculate on paper, which we now consider normal, seems to quickly create a problem of speed. In order to work on more complicated mathematical concepts, complicated calculations are required. Mathematicians would rather work out the mathematics than perform calculations and a demand arises for aids and machines (the latter are distinguished by an automatic tens-carry mechanism) to make the calculations faster.

Because the early demand is from mathematicians, early developments aim to develop something that could do all 4 operations. Interestingly, as the technology developed, this became less important. When we get to the period of mass produced machines, they mostly just add (and perform multiplication as repeated addition). This is largely because the market is business people who need to do invoicing and so on. It isn’t until the development of electronic calculators that the ability to perform all four arithmetic functions returns.

Of the aids to calculation developed in the earlier period, we were particularly taken with Napier’s rods. These then form the basis of several calculating machines. Tigger even took out her notebook and made some notes. I think we might try to make some, as they are quite interesting. And I think they might be useful for those of you teaching multi-digit multiplication to your kids.

I would definitely recommend this museum. Some of the old machines (or reproductions of them) can be tried. And many have mirrors strategically placed so that you can see how they work. It would be even more interesting for those folks interested in how things work as there was a lot of detail about the kinds of gears needed to make a tens-carry mechanism work and so on. We found this interesting but only have a limited interest in such details.

Travelling through countries where a language is spoken that I am not very familiar with has reminded me that reading is absolutely not about turning marks on a page into sounds. Reading is about deciphering meaning from marks on a page.  Looking at signs, descriptions, newspaper headlines,  menus, or whatever in a foreign language one begins to recognize the multiple strategies we have for doing this work.

Sometimes we use pictures, and many of those who produce what we read helpfully provide us with pictures to help us out, especially on road signs and in train stations.

Sometimes we compare a word to one we know. I suspect many of our children could quickly work out that König and King are related  or biblioteket (in Swedish) and bibliothèque (for those who don’t speak French, this is a library).

In both cases, we also make use of the context. So when we see a sign at the corner of a road with something Strasse, we might assume that it means “street”. Or we look at the name of a shop and then look in the window to see what is sold inside. In thismanner we learn that “cheese” in Sweden is “ost”.

On the homeschooling creatively yahoo group, one of the most common topics of discussion is how to help right brain dominant kids learn to read. Phonics don’t work for these kids, typically, and they often learn to read late. So we talk about other methods that have worked, including frequent discussions of great comic books and other highly visual resources .

In these discussions, it seems that many parents have to overcome ingrained ideas about what it means to learn to read. And those ingrained ideas seem to focus mainly on the ability to turn printed words into speech.  And yet most of us rarely read aloud (certainly until we have children to read to). As my examples show, the strategies we learn for turning printed words into speech are not all that important to the task of deciphering meaning from words.

Perhaps we should put Dr. Seuss and nonsense poetry at the centre of our young children’s lives – resources that might teach them the important lesson that meaning, even of made up words, is at the centre of this thing we call reading. And that we have multiple resources to hand for working out what that meaning might be.

(Of course, there are many situations in which we need to make connections between the written and spoken language. These are important but do not change the fact that meaning, and the communication of meaning, is at the centre of the enterprise.)

Julie  at Bravewriter has a great post up about unschooling. Anyone who has struggled with the word despite some attractions of the practice would find it helpful, I think.

As for me, I think that the epitome of “child led learning” might just be buying tickets to the opera because your kid seems to like it. Tonight we are going to see La Bohème at the Bonn Opera house. It is in Italian with German surtitles. But, like the puppet theatre, I think the language is probably not crucial to the enjoyment. There is the music, the costumes, the melodrama…

We took the night ferry from Sweden to Germany.  Although  I didn’t sleep as well  as other nights, I slept well enough to make it worthwhile.

We arrived in Travemunde at 7:30 a.m. but by the time we got the shuttle from the boat to the ferry building and then the bus into Lübeck it was about 9 a.m.  Oh, and it seemed more difficult than it should have been to find the left luggage lockers at the train station. Our plan (which worked out in the end) was to leave the big bags on the station and just have day packs with overnight things in them while we wandered about. So by about 9 a.m. we found somewhere to have a cup of coffee and make a plan for the day.

Our first stop after coffee was the Holstentor, the medieval gate to the city, recently restored. It houses a city museum much of which we fascinating. Although Lübeck seems to be a thriving small city, its heyday is long since past. From the 12th to 17th centuries it was really a power centre in the Baltic trade. With the decline in the importance of the Baltic and the rise of the Dutch and the English powers, Lübeck declined.

The first room of the museum is interestingly laid out to illustrate the importance of trade to the medieval city. A map of the Baltic region is on the floor so that you can see what was going where, with information about different types of goods located at appropriate places on the map. Despite the fact that the majority of the information was in German, we learned a lot. Interestingly, at dinner our last night in Lund, Johannes and I had been talking about how Stockholm was historically important because it is a Baltic port but that it the real industrial and commercial centre of modern Sweden is the Skane region (that a should have a ° over it but I can’t work out how to do that).  Shipping routes are still very important, it seems (and the ferry was disproportionately trucks and truck drivers).

After the Holstentor  we walked up to the market place, had a look at a bit of the old medieval architecture that remains, and then found somewhere to eat lunch. On the way we happened upon a shop selling antique dolls and toys. Tigger was fascinated and the owner was very kind, showing a doll in good condition he was preparing for sale and even fetching a couple from the back that he was restoring.

After lunch we went to the puppet theatre for a production of The Princess and the Pea. Again, very enjoyable even without understanding the language (for Tigger at all, and for us missing lots). There were some chickens that had a role I don’t remember from the H.C. Andreson version, for example. The puppetry was good. And the kids loved it. There was also a display of puppets, sketches and other wooden sculptures by a Czech puppet designer in the lobby. These were beautiful.

Next door to the puppet theatre, is a puppet museum housing an amazing collection of puppets from around the world. The range of styles of puppets is quite interesting.  We all enjoyed it.

Well after all of that, I was ready for a nap. We had found a hotel room right after lunch so we went back there and I had a nap. We then went out for dinner and returned to the hotel for an early night. After a walk along the river and through the town in the morning, we headed back to the train station to pick up our bags and head for Bonn. It turned out to be a good day to spend hours on a train as Tigger had picked up some sort of bug and was running a mild fever and feeling nauseous. She slept on the train and it seems to have gone.

The Swedes seem to be very keen on turrets. I offer you a selection as seen in and around the university here in Lund.