More Faces On Dôtonbori

Châteaubriant: a regional rail hard border

Rennes and Nantes, the largest cities in the Western tip of France, could have three direct rail routes connecting them. The one via Redon has always been used in this role; a second, via Laval and Angers, was ridiculously long until the high-speed line to Laval opened and 200 km/h-capable units were adapted for use on it; and a third... has been cut off at Châteaubriant.

The irony is, the Châteaubriant route would be the shortest in distance, at just over 120 km in length, in a fairly simple North-South direction. The trouble is, the line wasn't built with the traffic between the two cities in mind, is mainly single track, and has some steep inclines (1.5% is steep for a train). As such, it has always seen modest levels of traffic, and since the 1980s, it had been falling into disrepair in parts, and become abandoned in others.

The Nantes side saw a resurrection in the early 2010s: the line was electrified and, in 2014, tram-trains began operating. We've seen a tram-train on this blog before, but this service is only technically a tram-train, as it only uses a tram line parallel to the urban tram for a few kilometres inside Nantes, and only making one stop on that stretch. The Alstom Citadis Dualis (SNCF class U 53500) units are effectively regional trains in tram clothing, and are the only tram-trains in France to have onboard toilets.

But in France, local trains are managed by the administrative regions, and Nantes to Châteaubriant is under the authority of Pays de la Loire, so the electric wires, renovated stations and new trains went no higher. Worse, the line has been cut in half by a platform link, as shown above - and a photo on this webpage seems to indicate they used to be joined. So the Rennes side, managed by Bretagne region, has remained without electric power. I remember the stark contrast between the two sides of the regional border when I visited in early 2020: to Nantes, modern infrastructure and trains; to Rennes... nothing, and tracks that were starting to be overgrown!

It turns out the line was indeed closed for repair works at the time, and in 2021, Rennes to Châteaubriant reopened, with first-generation bi-mode Bombardier AGC (B 82500) sets, which only use Diesel power on this route, operating a peak-only service.

In conclusion, the Rennes-Châteaubriant-Nantes route has always been in the shadow of the slightly longer route via Redon, as the latter provided good connections to other major towns on the South Brittany coast: Vannes, Lorient and Quimper. The Châteaubriant route was never double-tracked, and today is a striking illustration of regionalisation, with different levels of investment on either side of the border, and through service now impossible.

Plan Incliné de Saint-Louis-Arzviller

This is going to be a rather long post as there is a lot to say about this thing! But the short version is: this is a boat lift.

Built in the 1960s, this "inclined plane" was designed to carry barges as part of the fluvial coal transportation industry. However, that trade declined pretty much during the edifice's construction, and today, it almost exclusively serves leisure boats. But if you're going to do a canal cruise, this thing gives it quite the difference!

Its function is that of a lock, taking boats from the lower water level to the higher level, or vice-versa, but it does this by technically being a lift or elevator. A caisson carries the boats and the water up and down, using counterweights to ease the travel.

In fact, the caisson will take on more or less water in order to be heavier or lighter than the counterweights. Though the total mass of the caisson and counterweights is enormous, the difference in mass between them isn't, so very little power is needed to get the system moving, and gravity does most of the work. Two relatively modest electric motors (centre of photo below, steps to the right for scale) start the movement and control the speed.

As such, the system uses comparatively little power, for impressive results. The boat lift was built to bypass a "ladder" of 17 locks which required a whole day to go through, while the travel time of the lift is just 4 minutes. The ride is seamless and very comfortable, effortless even, for reasons mentioned above but also because the effort is distributed across 5 times as many cables as physically required to hold everything together!

Water-tightness is also extremely important, not just for the caisson obviously, but also for the other doors, particularly the top door, which is holding back a whole length of canal. A serious incident in 2013 has led to further reinforcement of redundancies and the construction of an emergency dam closer to the lift in the event of major leaks.

With a lot of freight traffic in mind, the structure was actually designed for two caissons, side-by-side, as evidenced by a second gate hole visible at the top of the ramp (4th picture), and extra space at the bottom, visible in the final picture below. Doubling the caissons would have meant doubling the counterweights, and a second set of rails were laid for that scenario and are visible in the 4th picture. As mentioned earlier, demand dwindled as the lift was being built, so it never operated with two caissons.

For a long time, this place was a childhood memory, visited during a school trip. In my hiking spree after the 2020 and 2021 lockdowns, I sought this place out again and was glad to see it was still working. And just this week, I returned with my parents and rode the lift! It's without doubt one of my favourite pieces of engineering.

To build or not to rebuild? The case of Heijô-kyô

In 710, the Imperial court moved from Kashihara to Nara. Just over 80 years later, the capital once again changed location, settling in Kyôto where it would stay for a millennium. The palace in Nara was abandoned, and in the 1000 years that followed, the grounds were used for menial things. However, a few structures have been rebuilt in recent years, such as the main audience hall in the background, which was completed in time for Heijô-kyô's 1300th anniversary.

Besides a museum housing artefacts from its 8th-century heyday, the palace is seen here hosting some art exhibits, and a play is underway, just visible in the above photo. Of course, I didn't understand a word of it...

This view of the Suzaku South gate shows how recently interest was given to the site: by the time excavations had begun, a railway was already running through it! This is the Kintetsu line, opened in 1914. As such, trains between Ôsaka and Nara pass directly through this historic site.

Sangaku Saturday #12

Having mentioned previously how mathematical schools were organised during the Edo period in Japan, we can briefly talk about how mathematicians of the time worked. This was a time of near-perfect isolation, but some information from the outside did reach Japanese scholars via the Dutch outpost near Nagasaki. In fact, a whole field of work became known as "Dutch studies" or rangaku.

One such example was Fujioka Yûichi (藤岡雄市, a.k.a. Arisada), a surveyor from Matsue. I have only been able to find extra information on him on Kotobank: lived 1820-1850, described first as a wasanka (practitioner of Japanese mathematics), who also worked in astronomy, geography and "Dutch studies". The Matsue City History Museum displays some of the tools he would have used in his day: ruler, compass and chain, and counting sticks to perform calculations on the fly.

No doubt that those who had access to European knowledge would have seen the calculus revolution that was going on at the time. Some instances of differential and integral calculus can be found in Japan, but the theory was never formalised, owing to the secretive and clannish culture of the day.

That said, let's have a look at where our "three circles in a triangle" problem stands.

The crucial step is to solve this equation,

and I suggested that we start with a test case, setting the sizes of the triangle SON as SO = h = 4 and ON = k = 3. Therefore, simply, the square root of h is 2, and h²+k² = 16+9 = 25 = 5², and our equation is

x = 1 is an obvious solution, because 32+64 = 96 = 48+48. This means we can deduce a solution to our problem:

Hooray! We did it!

What do you mean, "six"? The triangle is 4x3, that last radius makes the third circle way larger...

Okay, looking back at how the problem was formulated, one has to admit that this is a solution: the third circle is tangent to the first two, and to two sides of the triangle SNN' - you just need to extend the side NN' to see it.

But evidently, we're not done.

The New Year shrine visit: Meiji-jingû

A common New Year ritual in Japan is to go to a shrine, possibly a large one, a visit known as 初詣, hatsumôde. NHK reported that Meiji-jingû in particular was very busy. Of course, I would avoid that, so here we are with a more tranquil time, closer to the Autumn festival.

Meiji-jingû was, as its name suggests, founded to enshrine the spirit of Emperor Meiji after his death. The first Emperor of the post-Edo period presided over sweeping societal reforms, such as the abolishment of classes like the samurai, as Japan re-opened to the rest of the world and sought to catch up. The Imperial attachment is symbolised by the Chrysanthemum crests on the torii.

One of the things that can be wished for at Meiji-jingû is a happy marriage and family life, particularly at this dedicated spot with two camphor trees planted in 1920, linked with sacred rope - these are called "married trees", 夫婦楠 Meoto Kusu.

Neuviller-la-Roche

Quick post today - just a few views of climbing out of the village of Neuviller-la-Roche in late March 2022.

C'est avec grand plaisir que je présenterai le mardi 16 avril à la Maison Universitaire France-Japon de Strasbourg une conférence sur la géométrie pendant la période d'Edo, avec en support le sangaku de Kashihara. Entre grande Histoire et petits calculs. Lien vers les détails 4月16日(火)、ストラスブール市の日仏大学会館に江戸時代の算額についてコンファレンスをします。楽しみにしています！ Looking forward to giving a conference on Edo-period geometry on 16 April at Strasbourg's French-Japanese Institute. Expect a few posts about Kashihara around then. Has it really been 6 years?...

Engelbourg: the castle with the hole!

A less glamorous variation of the 10 yen coin photo, but I did say back in March that this place made me crave Polo mints!

More seriously, I returned to Thann this weekend with two Japanese people working in France this year. The timing was impeccable, as there had been some snowfall in the previous days, giving us some spectacular views from the summit.

Also, just in time for the start of the Christmas market! Getting into the festive mood early this year... and no need for fake snow! At least, that was the case yesterday. Today, the weather got much warmer and it's probably all gone.

I can't remember riding a steam train before, though deep inside, I feel I probably had. Anyway, now I'm sure! This is the Chemin de Fer Touristique du Rhin, a short line near Colmar which runs steam engines and a set of old Austrian carriages, of which I'll say more in another post. Meanwhile, it's been a busy time for me recently, so this is just a few photos from the ride while I wind down.

Been a busy bee today, so here are some animals from the Expo 70 Commemoration Park.