The Reality Checkpoint

Heading towards Tokyo, two high-speed Shinkansen lines join up roughly 8 km North of Ômiya. I am riding an E7 train from Nagano, and at the junction, a red E6 coming down from Akita on the other line appears, coupled to a bright green E5 which has come all the way from the Northern island of Hokkaido. Another E5 shoots in the other direction, having just left Ômiya.

My train is overtaking, and I exchange amused waves with the passengers who have just seen an E7 appear out of nowhere in their window, but the long nose of the E5 just gives it the win at Ômiya station.

There could be clearer pictures of these impressive trains in the future, but for now, that's the story behind the blog's banner picture!

Location of the first photo (link to OpenStreetMap)

Here we are: Miminashi-yama

When I visited Kashihara, looking to explore some deep Japanese history in the former province of Yamato, I expected to move around a bit, but there was actually enough in Kashihara itself to make for a busy day.

First up was this curious green round space in the middle of a residential area on the town map I'd picked up. It just seemed conspicuous to me, I decided to check it out.

This is Miminashi-yama, one of the Yamato Sanzan, or Three Main Mountains of Yamato. Though it stood out on the map and it does stand out in the plain around it, it's not huge, and it's a short climb to the top where a shrine awaited.

In that shrine, a sangaku geometry tablet is displayed. By chance, based on a whim, I had found one! Nearly six years on, I've finally solved it - it's not very difficult mathematically, it's just taken me this long to get on with it, having said that, even today I'm still figuring out extra things on it! - and will be presenting it at a conference tomorrow. I wouldn't have thought it at the time... I guess curiosity didn't kill the cat that day!

It's been a wild couple of weeks in France, so when it got to a point when I had to go outside, I couldn't set my mind to find somewhere interesting. So I settled on nowhere special, just somewhere across the border with a train station and countryside not too far.

Lahr/Schwarzwald. Perfect.

Actually, there was a slight purpose to the trip given the time of day. I was hoping to see what was running on the Frankfurt-Milan "EuroCity Express". I'd seen an Italian train run it before, and this time it was a RABe 501 Giruno, the most recent Swiss high-speed train. I'd seen it before, but not caught a decent shot of it, so here it is!

The busy Karlsruhe-Basel main line sees a lot of traffic: higher speed like the ICE 4 at the very top and the ECE (I say higher because they can't travel at proper high speed because of everything else), regional trains, international freight... Among the inter-city trains out that morning was this Flixtrain, the same Flix who run buses across continental Europe. They have a few lines in Germany, using some old Inter-Regio carriages.

For an outing where I was just expecting to watch trains go by like a cow in a field, I dare say got more than I was banking for that morning, as a Baureihe 708.3 track inspector (Doktor Gelb?) and a brand new Mireo Smart regional set with no livery, either undergoing testing or out for delivery, made some surprise appearances.

Running around Koblenz station the other evening, I couldn't resist the cute message on this local train. Instead of a deadpan "depot" or "not taking passengers", this train is "going to bed"!

The train to Kushimoto: a JR West 283-series Kuroshio express. The sets are getting on a bit, they were introduced in 1996 and the livery could do with a refresh, but the "dolphin nose" is distinctive, and I, for one, really like it. They're also quite rare, only 4 sets exist.

The Kisei Main Line is essentially the coastal route from Nagoya to Wakayama. The full trip around the Kii peninsula takes 8 hours by express train, with a change required at Shingû or Katsuura, but it's definitely scenic as it gets very close to the sea (photo between Kii-Tahara and Koza).

Izumo Taisha's rabbits

@shoku-and-awe made a great post on the rabbit statues at Izumo Taisha and why they're there, so I'll only add that they are all over the shrine's grounds, and as far as East as the Ancient Izumo History Museum.

In the gardens, the rabbits are depicted doing all kinds of things: reading a book, taking pictures, birdwatching... Yes, all that!

And of course, there are a lot of rabbits facing the shrine buildings and praying.

The plaque behind these two recognises Senge Takamasa and Kunimaro, father and son, current and presumed future chief priest of Izumo Taisha. Tracing their origins back to the rulers of the Izumo province way back in the Nara period (Takamasa is the 84th head of the clan), the aristocratic-priestly Senge family has very much stayed in high society to this day, from being involved in politics and governor of Tokyo around 1900 (the shrine had been taken out of their control following the Meiji revolution and the abolition of the nobility), to Kunimaro marrying an Imperial princess (who no longer holds the title as per the rules) in 2014.

The tri-national S-Bahn of Basel

Due to its location, Basel attracts people from three countries, and the rail network reflects that. On top of lines within Switzerland, one line arrives from France at Basel Central station, and several arrive from Germany at the Badischer Bahnhof on the North side of the Rhine. My trip to Augst via Basel and Wyhlen was a chance to ride on this suburban network of three companies in three countries.

Starting after lunch with the Hochrheinbahn which runs from Basel Bad., along the Northern side of the Rhine in Germany. This is the only line out of Basel that isn't electrified, so Baureihe 641 Diesel railcars run the route. We have this type of railcar in France too, it was designed as a response to a joint French-German tender for regional trains. Designed by De Dietrich and Linke-Hofmann-Busch, which were both bought by Alstom shortly after, it is the first example of what would become the Coradia platform.

On the Swiss side, the S-Bahn sees RABe 521 commuter trains run between Basel Central and Frick. This type of train is made by the Swiss company Stadler and is marketed as... the FLIRT. Stadler does this a lot, they also have the KISS and SMILE platforms, and each is the result of a convoluted acronym in German, though this one translated very nicely into English: Fast Light Intercity and Regional Train.

Finally, the French line of the S-Bahn goes out as far as Mulhouse, and is currently operated by electric AGC (Automotrice Grande Capacité - high-capacity unit) regional trains built by Bombardier (also since bought out by Alstom). 200 km/h express trains from Strasbourg also reach Basel Central, with the push-pull sets we already presented. The line from Mulhouse to Basel Central is electrified with French voltage (25 kV 50 Hz AC), which is different to the rest of the Swiss network (15 kV 16.7 Hz AC), hence the SNCF can run their trains into Basel with few adaptations (mainly comms).

And that's it for my tri-national tri-trip over the April-May break! Back to some older material next, it's time to look at Japan again.

On the JR Nara line

Uji city and the the building on the 10-yen coin can be accessed by train from Kyôto by going roughly a third of the way to Nara. Other famous sites near the line are Fushimi Inari Taisha (Inari stop), and the studios of Kyoto Animation, famous for the music and sports anime K-On and Free! (Kohata stop).

The most recent type on the route is the 221 Series, and it's already getting on a bit, introduced in 1989. It won one of the Japan Railfan Club's two main new train design awards, the Laurel Prize, the following year. The 221 is used on the fastest Miyakokji Rapid services, which do the Kyôto to Nara run in under 45 minutes.

Green 103 Series sets can also be seen. This is the oldest type still in active JR service (if not, it's close), as it was introduced in 1963. In 2016, when I first visited Japan, I was living near Paris, and some Métro and suburban lines were running trains of a similar age, if not older, and these were atrocious in hot weather - no air conditioning, and ventilation only provided by opening windows! The RATP MP 59 used on Métro line 11 was stinky to boot; it was withdrawn just before the Games, no wonder! Point is, the 103 doesn't have air con either, but is at least trying...

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).

Views from Ôwakudani

As the volcano's activity isn't explosive, and there's a whole hot spring business around it, humans have been trying to tame Mount Hakone, as evidenced by the many consolidation structures seen at Ôwakudani.

These continue down the valley to contain landslides which could happen if things get more intense. Nonetheless, occasionally, a gas vent juts out, placing a distinctly natural form amongst the organised, man-made network of walls.

The yellow deposits are typically sulphur from a very pungent gas. Depending on the direction of the wind, the smell in some locations on the summit can be quite literally breathtaking.

The views, meanwhile, are figuratively breathtaking, from the striking contrasts in vegetation in the foreground to Lake Ashi and the outer mountain range of the Hakone caldera in the background.

And, of course, it is possible to see Mount Fuji from Ôwakudani. Terms and conditions apply, as always, but what little I could see on that morning gives a sense of scale to the great mountain. However, later that day, we would be treated to a much clearer view of Fuji-san.