I Can't Remember Riding A Steam Train Before, Though Deep Inside, I Feel I Probably Had. Anyway, Now

After that news post, back to Thann, for this view of the Thur valley and the Vosges mountains. On the day of my visit, I climbed here first, before continuing along a ridge to the Grumbach summit and down to the Grumbach pass, before circling back down to Engelbourg Castle which I posted about first. A nice hike, not too difficult - most of the climbing is done when you've reached the Roche Albert viewpoint. There's something to be said about why it's called "Albert's Rock", but I'll save that for another time.

Coot chicks in Schaffhausen and herons in flight at Konstanz. That is all for today.

Meoto Iwa - the married rocks of Futami

We noted the presence of "married camphor trees" at Meiji-jingû last time, so I guess we can talk about other sacred things linked by rope.

One of the most famous of these is the couple of "married rocks" on the coast of Mie, on the premises of Okitama-jinja at Futami, near Ise. The Meoto Iwa represent the founding couple of Japan according to Shinto, Izanagi and Izanami.

The shimenawa ropes are more heavy-duty than what we saw on the camphor trees: 5 strands, 40 kg each. Still, as they are exposed to the seawater spray from crashing waves, they need to be changed several times a year, which involves quite a few people as you'd expect, as shown on the poster below. Ceremonies occur in May, September and December.

The ropes certainly look heavy on the smaller rock in particular, they look like they could slip off, but instead they cling on rather gracefully.

Dotted around the shrine are statues of the messengers of the gods: frogs.

While Futami's Meoto Iwa is the most important example of "paired rocks" in Japan, owing to how far the tradition dates back and its proximity to Ise Grand Shrine, there are quite a few others across the country. Below is another Meoto Iwa in Mihonoseki, Shimane.

Contrasted sunset on Shinji-ko

On the south side of Matsue, there is a famous sunset-viewing spot, overseeing the "great lake" mentioned by Kitty-chan on the train, which would be Shinji-ko, and a small island inhabited only by a torii, called Yomegajima.

It's so famous, that there's a sign to tell you where to stand to get the Sun over the island depending on the season!

While the sunset was gorgeous on the evening I was there (last year to the day), there was also something ominous. To the left in the top photo, one can make out some rain hiding the horizon... and to the South, a thunderstorm was active in the hills.

Still, the showers were kind enough to hold back for us to see the Sun set between the cloud layer and the mountains. But they soon caught up - as soon as I stepped off the bus at Matsue station, it chucked it down!

Port du Crouesty

We start the new year where we left off in the last, on Presqu'île de Rhuys, but one year later. Or should that be two? The previous post was from the stormy 2013-2014 New Year celebrations, whereas this covers the calmer 2014-2015 change with most of the same friends, and our walk around the tip of the peninsula and Port du Crouesty.

These aren't the best photos given the relatively low light, but also this was before my current camera. Still, point it towards the sunset and the result isn't too bad.

The Mulhouse-Thann tram-train

Combining a suburban train service with the ability to navigate city streets sounds amazing. People can live nearer to the countryside, get frequent service into town, and, if everything lines up, commute straight into work without changes and avoiding the main station. The complementarity and opportunity to revitalise a branch line all sounds appealing... but a real challenge to implement. In France, only Mulhouse has truly achieved it.

Tram-trains aren't exactly rare in France: there are several lines around Paris, Nantes and Lyon have them (and many more had tram-train projects at some point). But, while the vehicles are capable of running in both modes, they are mostly used as a cheaper way to operate a line. The Nantes-Clisson and Nantes-Châteaubriant tram-trains, for example, which I have ridden, are just regional trains, running on heavy rail nearly all the way, and only stopping where the trains always used to.

Mulhouse is the only place in France to have true tram-train operations as described in the introduction: the tram-trains add traffic to line 3 between Mulhouse central station and Lutterbach, before switching to train mode and continuing on the branch line to Kruth as far as Thann.

The vehicles themselves are remarkable, as they need to be equipped for both streetcar and heavy rail operations, and each has its own requirements: lighting, horns, power supply, safety features... Mulhouse's vehicles are Siemens Avanto S70s, built in 2009-2010, and operated by SNCF as class U 25500. Similar units were introduced near Paris as early as 2005.

July 1830: the Revolution I forgot

This is Bastille square in Paris. As anyone who's had history classes in France will know, this is Bastille as in Bastille day, 14 July 1789, when Parisians raided the Bastille prison to get weapons for their revolt against the king - the flashpoint of the French Revolution.

It's also rather well known in France that the Bastille prison was demolished shortly after, as Paris rid itself of symbols of the Old Regime. So it would make sense that this monument commemorates that, right? It's super famous, after all.

Wrong. This column commemorates the events of July 1830, some forty years later, the significance of which, I'll admit, I had forgotten.

So here's how it goes. Since 1789, France had oscillated between fragile compromises of constitutional monarchy, revolutionary fanaticism and the iron fist of Napoleon. Following the defeat of 1815, Paris entered a period of calm acceptance under King Louis XVIII, but his successor, Charles X, wanted to go back to the old ways.

So, in July 1830, Paris revolted again. Disposing of the king was a surprisingly quick affair, as in just three days, Charles X was gone. He was replaced by his cousin, Louis Philippe, who seemed more willing to placate the bourgeoisie. A new constitution was drawn up, known as the Monarchie de Juillet, or July Monarchy.

In this context, a monument to the victory of 1830 was commissioned, and this is it: the Colonne de Juillet (July Column), a 47 metre-tall column adorned with the names of the fallen revolutionaries, a mausoleum at the base and the Spirit of Freedom on the top - and is that camera surveilling the street below?

Louis Philippe had ascended to the throne after a revolution, but he would also descend from the throne after the next. In February 1848, Paris revolted for a third time, swiftly ending the July Monarchy and establishing the Second Republic... which, within just 4 years, would become the second Bonaparte dictatorship.

The best timepiece in the world (IMO): Strasbourg Cathedral's Astronomical Clock

I could go on about this thing for ages. There's so much history, so many symbols to spot, and so much information on display... This is going to be a long one.

I guess I'll start with the artistic aspect on which I have the least to say because it's the least up my alley. There's loads of mythology and Christian symbolism going on on this 18-metre tall monument, and these are the main draw for the general public, because they move around.

Like cuckoo clocks in neighbouring Schwarzwald, this astronomical clock has automatons. Every quarter hour, the lower level of the photo above sees a change of "age": a child, a young man, an adult and an old man take turns to be in the presence of Death, whose bells toll on the hour. At high noon, the upper level also moves, with the 12 disciples passing before Christ, and the rooster at the very top crows.

Moving on to what really makes me tick: the amount of information on this clock is incredible. The time, obviously, but actually two times are on display on the clock at the bottom of the picture above: solar time and official time. Given Strasbourg's position in the time zone, there is a 30-minute discrepancy between the two. Then there's all the astronomical stuff, like the phase of the Moon (just visible at the top), the position of the planets relative to the Sun (middle of the picture), a celestial globe at the base (pictures below, on the right)...

The main feature behind the celestial globe is another clock displaying solar time, with the position of the Sun and Moon (with phases) relative to the Earth, sunrise and sunset times, surrounded by a yearly calendar dial. These have remarkable features, such as the Moon hand that extends and retracts, making eclipses noticeable, and the calendar has a small dial that automatically turns to place the date of Easter at the start of each year. This sounds easy, but look up the definition of Easter and note that this clock is mechanical, no electronic calculating power involved! Either side of the base, the "Ecclesiastic Computer" and the "Solar and Lunar Equations" modules work the gears behind these features.

The accuracy of this clock and its ambition for durability are truly remarkable. Relative to modern atomic time, it would only need adjusting by 1 second every 160 years, and it correctly manages leap years (which is not as simple as "every 4 years"). It just needs winding up once a week.

Finally, the history. The monumental clock was built in the 16th century, and used the calendar dial above, now an exhibit in Strasbourg's city history museum. It slowly degraded until the mid-19th century, when Jean-Baptiste Schwilgué restored the base and upgraded the mechanisms. The "dartboard" on the old dial contained information like the date of Easter, whether it is a leap year, which day of the week the 1st January is... - all of which had to be calculated by hand before the dial was installed! - and was replaced by the Ecclesiastic Computer, which freed up the centre space for the big 24-hour clock, complete with Solar and Lunar Equations.

As you may have gathered, I am a massive fan of this clock. Of course, nowadays, all the imagery and information would easily fit into a smart watch, but a smart watch isn't 18 metres tall and powered by gravity and gears!

200 km/h push-pull trains

While Germany has recent double-deck train carriages, the Dostos shown previously being built in the 2000s, and updated versions still being produced, France made its last carriages in the 1980s, including Corail cars for inter-city services. But their use was curtailed by the development of the high-speed network.

Some sets were given push-pull ability, with a driving cab at one end that can control the locomotive at the other - the lead car above being a renovated B5uxh: second-class seating, 5 compartments, air-conditioned, driving cab, disabled access. These have found a new lease of life in regional transport, especially in the East, as the straight and flat Alsace line from Strasbourg to Basel allows these 200 km/h-capable carriages to stretch their legs. The "TER 200" puts Strasbourg only 80 minutes from Switzerland (wink-wink-nudge-nudge for a future trip).

The usual motors for these sets are BB 26000 "Sybic" locomotives built in the 1990s, powerful enough to get them to their top speed. While not at top speed in this setting, probably running at 100 km/h on the slower line to the Lorraine region, they still feel like very big trains when they go by.

Other push-pull trains exist in Alsace, with smaller locos and carriages rejoining the fleet for the planned Réseau Express Métropolitain Européen. However, most passengers trains everywhere in France now are covered by multiple units, especially since bi-mode units like the Régiolis shown below, have appeared. These are capable of running on electric power or with a Diesel engine, making them as flexible as can be.

Sangaku Saturday #4

In the previous info post, we went over the debate on the religious aspect of sangaku, and the fact that the absence of prayers on these tablets was more puzzling to some than the mathematics. As such, the tablets are not ema prayer tablets, but donations, which usually don't feature prayers on them. Case in point, some consecrated sake and French wine seen at Meiji-jingû in 2016.

Beyond wishing for good fortune and health, such donations serve two very worldly purposes: to contribute to the life and prestige of the shrine or temple (having a famous contributor makes the shrine famous by association), and to advertise the donor in return, as their name is on display. See this large torii at Fushimi Inari Taisha paid for by TV Asahi (テレビ朝日).

With that in mind, Meijizen's cynical comment from 1673 that sangaku aim "to celebrate the mathematical genius of their authors" may not far from the truth. The authors of sangaku are looking to gain notoriety through the publicity that the shrine or temple provides. But was the bemused Meijizen the target audience?

More on that in a couple of weeks. Below the cut is the solution to last week's problem.

The solution to the first problem (below the cut in this post) is the key. Name K, L and M the intersections of the three circles with the horizontal line. Then, by using that previous result,

Indeed, as in that problem, we can construct three right triangles, ABH, ACI and BCJ and apply Pythagoras's theorem in each.

Now, it suffices to note that KL = KM + LM, so

or, dividing by 2*squareroot(pqr), we get the desired result:

Inverting and squaring this yields the formula for r:

This gives us the means to construct this figure on paper using a compass and a marked ruler. Having chosen two radii p and q and constructed the two large circles (remember that AB=p+q) and a line tangent to both, placing M and C is done after calculating the lengths IK=CM=r and IC=KM=2*sqrt(pr).