Châteaubriant: A Regional Rail Hard Border

The Montech water slope

At around the same time as the "Inclined Plane" of Saint-Louis-Arzviller, other types of boat lifts were being engineered in other places. One of these was the Montech water slope, situated in Southern France on the Canal Parallel to the Garonne (Canal Latéral à la Garonne), the canal from Toulouse to Bordeaux which most people would probably refer to as the Canal du Midi - a better-known term though strictly speaking, the Canal du Midi is only the section from Toulouse to the Mediterranean.

From what I can garner, the two-headed vehicle used on this slope is a conjoining of two Diesel railcars built by Soulé in the early 70s, running on tyres and featuring a daunting-looking shield. This shield would be lowered behind a boat, and the machine would travel up and down the slope, carrying along the boat and the water it bathed in!

However, the performance of this system is less impressive than the Inclined Plane. It bypasses 5 locks, and saves 45 minutes of travel time. That's not nothing, but if you arrived at an end and just missed the train, then going straight to the locks wasn't going to be much longer than waiting for the next one. Also, far more power is required to make this work (I'm reading 1000 hp motors, versus 125 hp for the Inclined Plane), and it's Diesel.

These photos were taken in late 2017, 8 years after the water slope closed. It was only serving leisure boats by then, and, as I've insinuated, it wasn't very economical to run. As far as I can tell, the 5 locks beside it never closed, and are in use today.

The slope and its tractor have since been renovated, and the site's current state can be seen in a Tim Traveller video published in 2021.

Karlsruhe Palace

Thought I'd pop up to Karlsruhe today; it's not very far and I'd never been. It was... well, OK for a light outing. There's a lot of construction work going on in town, and it wasn't very animated being late January. Still, the weather was good enough for a pleasant walk around the centrepiece, the Palace, which houses the history museum of the State of Baden.

Karlsruhe is a relatively young town, by European history standards, as it was founded in 1715 as a new seat of power for the Margrave of Baden. A symmetric living building with a rear wing mounted by a tower was surrounded by vast gardens, and streets radiated out from the palace - a rather original urban arrangement, I don't remember seeing it in other places. Following French invasion in the late 18th century, Emperor Napoleon granted Baden the status of Grand Duchy: the ruler gained access to more riches and symbols such as a crown, a throne...

The Grand Duchy was briefly overthrown in a revolution in 1849, and abolished entirely following the fall of the German Empire in 1918. The region of Baden, stretching from Mannheim and Karlsruhe in the North, along the East side of the Rhine down to Freiburg and Konstanz, became a Republic within the Weimar Republic, and merged with neighbouring Württemberg, the area around Stuttgart, into the Land of Baden-Württemberg we have today in 1952. Baden was the smaller of the two former Grand Duchies, and was more reticent to the merger, as this poster in the museum shows.

"This is what the merger will be like!"

Ultimately, the merger wasn't as bad a deal as feared: when a Baden-only referendum was held in 1970, a return to a split was emphatically rejected. Still, it is not rare to see the yellow and red flag of Baden in the South-West corner of Germany - I've seen it outside a drinks hut near Oberkirch (bottom left picture) and on several castle ruins. It naturally flies atop the Karlsruhe Palace tower.

The things people write on clocks...

Craignez la dernière - Eglise Notre-Dame de Croaz-Batz, Roscoff

Literally, this means "fear the last". OK, but the last what? Well, you're looking at the sundial for the time, which here, in French, would be "12 heures", so the full saying is inferred to be "craignez la dernière heure" - "fear thy final hour". Reminding people of their own mortality was an important part of medieval-Renaissance Christian discourse, as we saw with the ages of Man passing before Death among the automatons on the Astronomical Clock in Strasbourg Cathedral, built around the same time as this church in Roscoff.

Die Zeit eilt, Die Zeit heilt - Rathaus St. Johann, Saarbrücken

I've only got a close-up of one, but the tower of the historic town hall in Saarbrücken has at least two clocks, each with a message. The meaning of "die Zeit eilt" is similar to "time flies", and could be linked to what we saw above: be aware of what time you may have left. The second clock cleverly adds one letter to that to make "die Zeit heilt": "time heals".

"How to use this sundial" - Piazza della Borsa, Trieste

In the ground in front of the Chamber of Commerce in Trieste is a sundial, but conspicuously, the hand is missing. That is because you are the hand! Taking astronomy into account, one should stand in a slightly different place depending on the season, and apply corrections to the minutes to get official time. It was cloudy when I saw this, so I'm afraid I don't have a nice picture of the sundial in action. The instructions are in Italian on the left side of the base.

Toba Castle ruins

After Hikone Sawayama and Numazu Nagahama, a final entry in my mini-series of castles that are outside the Top 100 and Next 100 lists - until I get to see more! - is Toba Castle, located on the glorious Shima coast, and of which little beyond a few walls and foundations are left.

Now a park, the top level offers some good views of the coastline, only a short climb up some stairs from Toba's attractions sea level. Admittedly, the best views require a longer hike, and when I visited, Shiroyama Park was at the end of quite a long day's walk!

Sounds like a train, but isn't: the Saig to Titisee Rodelbahn

In fact, it's just a footpath. OpenStreetMap puts it at 1.2 km in length, and it's all downhill from Saig. A 165 m drop to be precise, which means an average gradient of nearly 14% - that is steeeep with four Es. In the winter, it should be covered in snow, and, with its four turns, you'd figure it would be a really cool route for tobogganing...

Well, that's what a Rodelbahn is, it's a sled/luge/toboggan track! If you look up the term, you'll come across summer Rodelbahns which are rides on rails (little roller coasters, I've seen one next to the Arzviller boat lift that I'll probably talk about one day, and the Bobbahn is a cracking bobsleigh-style ride at Europa-Park), but this is a natural Rodelbahn. Which runs on a hiking trail, so a few rules need to be laid out, such as pedestrians should hug the inside of the corners.

Most of the trail is in the forest, but once (if!) you reach the final stretch, the ride into Titisee with this view of the lake must feel incredible.

Notice on the left that the base of a pole has got some padding around it... That's not (just) for visibility in the snow! If you can zoom in that far, you might notice that the walls of the bridge at the bottom are padded too.

You'll probably be thinking "again!" once you've reached Titisee, but, as we joked with my sister, that "again!" won't come soon - you've got a long, steep climb back up to Saig first! Those numbers, 1.2 km and 14% gradient, aren't so amusing when starting from the bottom... And the train from Titisee to Schluchsee mentioned yesterday doesn't stop at Saig! XD

Sangaku Sunday #6

We are about to solve our first sangaku problem, as seen on the tablet shown above from Miminashi-yamaguchi-jinja in Kashihara.

First, we should conclude our discussion: what are sangaku for? There's the religious function, as an offering, and this offering was put on display for all to see, though not all fully understood the problems and their solutions. But a few people would understand, and these would have been the mathematicians of the time. When they visited a new town, they would typically stop at a temple or shrine for some prayers, and they would see the sangaku, a sample of what the local mathematicians were capable of. Whether the problems were solved or open, the visitor could take up the challenges and find the authors to discuss.

And this is where everything lined up: the local school of mathematics would have someone new to talk to, possibly to impress or be impressed by, and maybe even recruit. With the Japanese-style mathematics of the time, called wasan, being considered something of an art form, there would be masters and apprentices, and the sangaku was therefore a means to perpetuate the art.

Now, what about that configuration of circles, second from right on the tablet?

Recall that we had a formula for the radii of three circles which are pairwise tangent and all tangent to the same line. Calling the radii p, q, r, s and t for the circles of centres A, B, C, D and E respectively, we have

for the circles with centres A, B and C (our previous problem), and adapting this formula to two other systems of three circles, we get

for the circles with centres A, C and D, and

for the circles with centres B, C and E. Add these together, and use the first relation on the right-hand side, we get a rather elegant relation between all five radii:

Of course, we can get formulas for s and t,

r having been calculated previously using just p and q, which were our starting radii.

For example, setting p=4 and q=3, we get, approximately, r=0.86, s=0.4 and t=0.37 (this is the configuration shown in the figure, not necessarily the one on the tablet - I will be able to make remarks about that on another example).

The abandoned Arzviller station

The old canal we followed yesterday is flanked by the Zorn river and the Strasbourg to Sarrebourg railway. Trains call at Lutzelbourg and/or Réding, while, half-way in between and opposite lock n°6, sits Arzviller station - actually located on the territory of Saint-Louis - closed. Shockingly, I can't find when it was closed (one source suggests the 1980s, though in my mind it was more recent).

Going from the canal to the station requires dropping down to the level of the Zorn river, crossing it, and going under the railway and road. There is a very dark underpass, but if you look closely and sport the light switch... Club Vosgien, the association which manages hiking trails in the Vosges mountains, literally shines through with this installation!

Given that Arzviller station is closed, and not wanting to tread the same ground twice, I decided to walk from one station to the next, Réding to Lutzelbourg, and I can't recommend the part from Réding to Arzviller: not signposted for hikers, really requiring a map if you're trying to avoid roads... and the only real highlight is the chance to glimpse the twin canal & railway tunnels: boats and trains enter and exit together at the West end (no boats on the day I visited though).

Space Port Kii (from a distance)

Japanese company Space One has been in the news recently for their second attempt at launching their rocket, Kairos - for Kii-based Advanced & Instant ROcket System; as far as acronyms go, I'd give it a 5/10, it's rather long-winded but has some good ideas at the right moments. The rocket, designed to be a cheaper option for lighter satellites, unfortunately didn't make it into orbit, losing control after 95 seconds.

The launch site is located on the North-East edge of Kushimoto, Honshû's southernmost city, its entrance building visible from the railway line. The action area is further into the woods, by the coast. I didn't visit the site obviously, but the entrance and some support posters in Kushimoto town were hints of the project's presence. They have a neat little mascot too, a space puppy!

Up the Monumental Stairs at Auch

Some 75 km West of Toulouse, the city of Auch is far away enough for red brick to be far less prevalent in buildings. It developed along the Gers river, with the higher-ups living... well, higher up.

The Monumental Stairs were built in the 1850s when, following a rebellion against Napoleon III's coup installing the Second French Empire, the prefect decided to give the townsfolk something to do (per the city council, "créer des chantiers afin de donner de l'ouvrage à ceux qui en manquent"), rather than just repress. The results were a water and gas distribution network, and the Monumental Stairs, creating a comfortable link between the upper town and the riverside 35 metres below. Later, a statue of d'Artagnan, a musketeer made famous by Alexandre Dumas novels, was added.

Behind d'Artagnan here, rises the Tour d'Armagnac, a 14th-century prison. Unfortunately, it is privately owned and cannot be visited, unlike the neighbouring cathedral, built between 1489 and 1680.

While the back of the cathedral, visible in the top photo, is clearly gothic, which fits the start of construction, the front facade is in a later, classical style. This would fit the timeline, as cathedral building usually started with the crypt and the altar, working outwards, and finishing with the massive entrance and towers. Walking away, further West, we encounter one more figure of the town: Intendant Mégret d'Étigny, who administrated the Auch-Pau area under King Louis XV, and is credited with infrastructure improvements in the region at the time.

Fort National, Saint Malo

Work is starting to pile up on my end, so I have to make this a quick one.

This is Fort National, a building we saw in the post on MV Bretagne. It was built in the late 17th century by Vauban - one of many, many, many projects he designed for Louis XIV's grand plan to fortify the French border. It was called Fort Royal, a name which would stick for little more than a century, before the Revolution banished any mention of royalty. It became Fort Républicain, then Fort Impérial under Napoleon, and finally Fort National after Napoleon III's Empire was defeated by Prussia in 1870. This regular name changing was derided by a local nickname, "Fort Caméléon", but it also give a glimpse into France's political history.

The rock on which the fort sits, known as Îlette (the small island), has quite a sorry history. Before Vauban, it was apparently used as an execution ground by local lords, and during World War II, the occupying Nazis used it as a prison during Allied bombings - fully expecting the fort to be bombed.

Today, the fort is privately owned, but visits are allowed on occasions.