To Build Or Not To Rebuild? The Case Of Heijô-kyô

Grand Geroldseck castle - only a cat of different coat

Close to impressive Haut-Barr castle, a one-hour hike from Saverne, sit two more ruins. All of these castles were built around the same time, late 10th to early 11th century, but despite being so close, they weren't owned by the same people.

While Haut-Barr was under the control of the Bishop of Strasbourg, the two Geroldseck castles, the Petit and the Grand, were built by the Geroldseck family, in charge of protecting the lands of the Abbey of Marmoutier. At the time, Alsace was part of the Holy Roman Empire and divided into many largely independent pieces, so these castles facing each other were on a border of sorts. However, the male Geroldseck line went extinct at the end of the 12th century, and the land was co-owned by so many people that no-one was maintaining the castle. The last stand came in 1471, when a group of disgruntled knights used it as their base. The Imperial bailiff laid siege, won and the castle was left as a ruin after that.

While Haut-Barr castle gets a lot of visitors, owing to the possibility of driving there, the Grand Geroldseck is worth the extra walk and brief climb from its neighbour. As well as the dungeon, lots of walls and rooms are still present, making it an interesting place to explore. The remaining walls continue to receive restoration work - there seem to be a few differences between my first visit with @teamroquette and my second this summer, for example, I don't remember seeing the little garden a few years ago.

All that's left to say is: "OI YOU!... YES, YOU! Have a good time."

Schauinsland

Since it's been mentioned in the comments on the previous post, we might as well have a look at the Schauinsland, a 1284 m peak on the outskirts of Freiburg im Breisgau. Only 7 km from the Schwabentor, the base is accessible by bus, before boarding a 3.6 km gondola lift ot the summit.

Opened in 1930, the Schauinslandbahn was the first gondola lift built for continuous operation, with the cabins running through each end station at slow speed to turn around while letting passengers off and on. The cable car takes the riders up the hill, offering panoramic views of the Black Forest. And then there's the view from the tower at the summit... I visited in summer, but it must be fantastic in winter too.

The cable car is not the only transport infrastructure to be found on the mountain, as mines operated there until the mid-20th century, so some mining railways with preserved vehicles can be found. Some of the tunnels can be visited (though writing this post reminds me, I haven't been inside yet).

Where I grew up (initially): Great Chesterford

Going back to Great Chesterford with my current eyes was quite interesting. I hadn't realised (as no 6-year-old would) how pretty the village centre was, with many charming houses and thatched cottages. The nearest town, Saffron Walden, is even better, but I'd need to go back and visit properly. This time, we just passed through there to go to the shops - and pick up a bunch of biscuits and sweets I remember from my childhood!

Said sweets and biscuits are very nice, of course, but also a tad underwhelming. I remember feeling disappointed by the size of Party Rings the last time I bought some, and I had a similar sense of underwhelming when passing near the school. The wall along the street was much higher in my memory, as was the hill at the back of the playground - in my mind, it was a proper hill! But take into account the fact that I was so much smaller back then, and it all checks out, really!

The old school building itself was apparently built by a single person between 1845 and 1849. Chesterford has a very rich history, dating back to Roman times (and if nothing else on the topic, I remember dressing up as a Roman at school once), and the church dates back to the 13th century. The village's biggest claim to fame is probably having been the home of Germaine Greer, a feminist author from the 1970s, for a few decades.

Freiburg's Schwabentor

The Germany city of Freiburg im Breisgau, on the transition between the Rhine valley plains and the hills of the Black Forest, was part of the Duchy of Swabia until it dissolved in the 13th century due to the ducal line going extinct. It was around this time that its "Swabian Gate" was built at the Eastern edge of the town, facing the Swabian heartland.

Like Schaffhausen's Schwabentor, it has undergone upgrades and downgrades, taken damage and been restored over time. The current illustrations on the tower include St George slaying the dragon (1903) on the outside, and a merchant with a cart (first painted in 1572) on the inside, just visible in the picture below.

Freiburg's Altstadt has many gorgeous, colourful houses decorated with trompe-l'oeil facades. An effort has also been made to preserve the little rivers in the streets, known as Bächle. Local superstition says that anyone who accidentally steps in a Bächle will marry a local - unusual to see a place that values clumsiness!

For Vectron!

Produced since 2010 by Siemens, the Vectron is a modular locomotive platform with various engine options - AC electric, quad-voltage for use across Europe, "last-mile Diesel" option for parking, Diesel motors, dual mode/hybrid... It hauls both freight and passenger trains. But the main reason I've wanted to mention the Vectron is...

this Mitchell and Webb sketch!

This is from series 3 of That Mitchell and Webb Look, which was aired in 2009. The Siemens Vectron was officially launched in 2010, so it's fair to say that the name appearing in both is a coincidence. However, when I see a Vectron, it reminds me of this sketch, so it's harder for me to take this train seriously!

But it is serious business, as it is one of the most common locos in continental Europe. Only Iberia (due to using a different gauge) and France (because if it ain't Alstom, they'll oust 'em) don't see much of them. The examples shown here are from Germany, Switzerland and Slovakia, and were all pictured in the same area of Germany. The quad-voltage version in particular allows companies to carry freight all over Europe, they're virtually borderless.

Yet here I am, still snickering at the name, by Vectron's beard!

A couple of quick-fire photos from the boat on a recent ride on the Canal de la Marne au Rhin. Picture sharpness isn't always fantastic when it's a rather fast reaction situation, but I still like this duck!

A Belgian Série 13 loco with freight, crossing a viaduct in North-Eastern France. The 13s are very flexible but do not support 15 kV, so the loco will be changed at the German or Swiss border if its cargo continues on.

First time in the Channel Tunnel!

Hard to believe, given that I have family on both sides of the Channel, that this month was the first time I used the Tunnel! For a long time, I've lived on the Western side of France and travelled in a car, so going to Calais to catch the shortest ferry links or LeShuttle never made sense compared to a relaxing six-hour crossing from a port in Normandy. Now I live in Eastern France and don't use a car, so the train is a no-brainer, and finally, I took the Eurostar from Lille to London.

On paper, the trip is amazing: just 90 minutes, roughly 30 on the French high-speed line, 30 in the tunnel, and 30 on High Speed 1 in England. Buuuuut... you need to get to the departure station around 60 minutes early for security and border checks, there's not a lot to do in the densely populated waiting area, and once on the train, I found it quite hard to relax in the hard, narrow seats under rather harsh lighting. While the ride was quick and operations felt reliable, the comfort of some regional trains has won me over more swiftly. That said, I've also been underwhelmed by the German ICE 3 (BR 407), which is the same Siemens Velaro D model as the Eurostar e320.

The Channel Tunnel turned 30 this year, with the French high-speed line connected to it upon opening and TGV-derived stock at the ready (now called the Eurostar e300, left), while the UK finished their high-speed line to London in 2007 (plaque at St. Pancras, right). Since then, it's been possible to go from London to Paris or Brussels in under two and a half hours (not counting security before boarding).

And there I was, starting to think I'd be riding the Seikan Tunnel before the Channel Tunnel!

Arrived here a year ago today: Nagoya station. I did little more than settle in at the guest house and wander back to the station for food before getting a good night's rest.

At each end of the station concourse, there's a distinctive clock - one called the Silver Clock, and the other the Gold Clock, which make good meeting points.

At basement level, there's a good row of restaurants, and I settled on one that serves miso katsu, pork cutlet fried with a hatchô miso sauce. It turns out I'd hit the jackpot, because that's a local dish, and because I loved it! I went back for more another evening with fellow guests, and once again when I made a stop-over at Nagoya on the way from Western Japan to Tokyo. I'm definitely eating there again if I get the chance!

Sangaku Saturday #14 - the grand finale!

We are only a few steps of algebra away from solving the "three circles in a triangle" problem we set in episode 7. This method will also yield general formulas for the solutions (first with height 1 and base b; for any height h and half-base k, set b=k/h and multiply the results by h).

Before we do that, it's worth noting what the sangaku tablet says. Now I don't read classical Japanese (the tablet dates back to 1854 according to wasan.jp), but I can read numbers, and fishing for these in the text at least allows me to understand the result. The authors of the sangaku consider an equilateral triangle whose sides measure 60: boxed text on the right: 三角面六尺, sankaku-men roku shaku (probably rosshaku), in which 尺, shaku, is the ten marker. In their writing of numbers, each level has its own marker: 尺 shaku for ten, 寸 sun for units, 分 fun for tenths and 厘 rin for hundredths (毛 mô for thousandths also appear, which I will ignore for brevity). Their results are as follows:

甲径三尺八寸八分六厘: diameter of the top (甲 kou) circle 38.86

乙径一尺六寸四分二厘: diameter of the side (乙 otsu) circle 16.42

反径一尺二寸四分二厘: diameter of the bottom (反 han) circle 12.42

I repeat that I don't know classical Japanese (or much modern Japanese for that matter), so my readings may be off, not to mention that these are the only parts of the tablet that I understand, but the results seem clear enough. Let's see how they hold up to our final proof.

1: to prove the equality

simply expand the expression on the right, taking into account that

(s+b)(s-b) = s²-b² = 1+b²-b² = 1.

2: the equation 2x²-(s-b)x-1 = 0 can be solved via the discriminant

As this is positive (which isn't obvious as s>b, but it can be proved), the solutions of the equation are

x+ is clearly positive, while it can be proved the x- is negative. Given that x is defined as the square root of 2p in the set-up of the equation, x- is discarded. This yields the formulas for the solution of the geometry problem we've been looking for:

3: in the equilateral triangle, s=2b. Moreover, the height is fixed at 1, so b can be determined exactly: by Pythagoras's theorem in SON,

Replacing b with this value in the formulas for p, q and r, we get

Now we can compare our results with the tablet, all we need to do is multiply these by the height of the equilateral triangle whose sides measure 60. The height is obtained with the same Pythagoras's theorem as above, this time knowing SN = 60 and ON = 30, and we get h = SO = 30*sqrt(3). Bearing in mind that p, q and r are radii, while the tablet gives the diameters, here are our results:

diameter of the top circle: 2hp = 45*sqrt(3)/2 = 38.97 approx.

diameter of the side circle: 2hr = 10*sqrt(3) = 17.32 approx.

diameter of the bottom circle: 2hq = 15*sqrt(3)/2 = 12.99 approx.

We notice that the sangaku is off by up to nearly a whole unit. Whether they used the same geometric reasoning as us isn't clear (I can't read the rest of the tablet and I don't know if the method is even described), but if they did, the difference could be explained by some approximations they may have used, such as the square root of 3. Bear in mind they didn't have calculators in Edo period Japan.

With that, thank you very much for following the Sangaku Weekends series, hoping that you found at least some of it interesting.

"Stick an aircraft engine in it" part 1 - Boeing Jetfoil

In the late 60s and early 70s, all branches of transport were hoping for an increase in performance similar to what the jet airliner brought to aviation, and the solution was invariably to use similar gas turbine technology, with invariably identical career trajectories when the oil crises hit, as, apart from in aviation, far more economical engine options were available. So I was very surprised to see this still active in Japan last summer:

This is a hydrofoil which uses gas turbines to power a pump-jet. Once it is going fast enough, it takes off and runs on foils, greatly reducing water resistance and achieving speeds up to 45 knots, over 80 km/h (which, on water, is very fast). I remember seeing exactly this type of vessel in ferry brochures when I was a child; Oostende Lines operated some between England and Belgium. The advent of the SeaCat, a class of huge Diesel-powered car-carrying catamarans, got the better of the hydrofoils and the hovercraft, which was incidentally another case of "stick an aircraft engine in it".

This specific class of hydrofoil takes the mantra to another level, as it was designed by Boeing, which named it the 929 Jetfoil. Production was licensed to Kawasaki Heavy Industries in Japan, which made boats for the domestic market. The Rainbow Jet is one of these, running between Sakaiminato on the San'in coast and the Oki Islands. I saw more of them at Atami in Eastern Shizuoka, providing transport to the Izu Islands. So, despite the astronomical 2150 L/h consumption (though to be fair, I can't find consumption numbers for equivalent foot passenger-only catamarans), Japan still runs them...