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Japan's biggest shimenawa: Izumo Taisha Kagura-den

We've seen larger and larger sacred ropes in our previous posts, and here's the largest of all: the shimenawa adorning the Kagura-den at Izumo Taisha. It is 13.5 m long and weighs 5 tons!

Shimenawa ropes are made with hemp or rice straw. This shot shows just how densely packed Izumo Taisha's shimenawa is - it's almost like a tree trunk, truly an impressive and imposing feature.

Here and in previous examples, we can see folded paper shide streamers, another symbol of sacred items in Shinto, on the first picture. Knots also appear, particularly on the ropes on the Meoto Iwa at Futami, as paper would not fare well by the sea... These ropes and streamers indicate a demarcation line between our world and the realm of kami spirits.

The Kagura-den is a hall just outside the main compound of Izumo Taisha, to the West. It was built to house kagura rituals, traditional dances which retell the stories of the early gods. As Izumo, formerly in Iwami province, is one of the most ancient shrines in Japan, Iwami Kagura is one of the major forms of the dance.

As a bonus, here's a train decorated with characters of Iwami Kagura.

How early is too early?

Christmas markets have been a staple of the month of December in Alsace and Germany, and the concept of local specialities and gifts being sold in chalets has spread far and wide. Most are open for around a month, ending on Christmas Eve, maybe pushing a couple of days more.

Japan also has a few markets, and, considering how differently the date is celebrated (New Year is the family holiday), you'd think a Christmas market would be a little something to bring some cosy European atmos to wandering couples in the week or two running up to it.

Holy cow, the 5th of November! That is by a long way the earliest Christmas market I've ever seen! This was the one in Ebisu in 2016, just outside the Skywalk from the station (nowhere near as spectacular as the Mishima Skywalk), opposite a big mall. It was very calm, much less busy than the big shops nearby, which were also already decorated.

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.

French and German cross-border railcars

Just on the French side of the border, Wissembourg station sees French TERs arriving from Haguenau and Strasbourg, meeting German Regionalbahn from Landau and Neustadt. When a French service doesn't cross the border itself, SNCF and DB services are often synced up, giving us the chance to see both companies' cross-border efforts side by side.

The B 85500 is a brand-new bi-mode (electric and Diesel) multiple unit from the Alstom Régiolis family. While not the first international Régiolis - a tri-voltage electric version runs between Évian and Geneva -, the B 85500 adds autonomous Diesel power. With 30 units on order, it aims to revive and/or intensify cross-border routes into Germany. I was under the impression there was a bit of a gathering at the front end of the train, maybe local politicians marking the type's first visit to Wissembourg?

On the German side meanwhile, we have a standard railcar for what DB regard as a relatively low-density non-electrified regional route, which was closed to passengers for over 20 years between 1975 and 1997. The BR 628/928 (628: power car, 928: trailer car) is a 1980s design. Besides the lack of low floor, there's not a lot wrong with them, and they have comfortable, current DB Regio interiors. More recent types have been used, and if a plan to electrify Landau and Winden stations to allow charging of battery-EMUs goes ahead, there could soon be the latest trains on the German side of Wissembourg station too.

Which brings us to our "I beg your pardon" of the week:

While some wait for cherry blossoms as a sign of spring (and this includes me), another sign of the season in Alsace is the stork. Saw my first one in the sky this week - but this photo is from a previous year.

The Reality Checkpoint

In the middle of Parker's Piece (no relation to the Thunderbirds character) in Cambridge, stands a lamppost. The only lamppost on the common, a beacon and a reference for anyone walking there at night. A bit like the lamppost in Narnia. A lot like the lamppost in Narnia in fact, as it serves as a boundary marker between the university and the town, two worlds with distinct notions of reality. That's one theory behind the name, the Reality Checkpoint.

Another theory suggests one should use the checkpoint to assess their clarity when going back from the pub, and this view certainly calls reality into question... Not to worry, the Ferris Wheel is just being dismantled.

This ornate lamppost has been restored in recent years, and improved with a Dinky Door. Well, I say "improved", but the note on the door says "on holiday, please check reality yourself"!

I promised more impressive views from the hills above Toba, and here they are. They're not very hard to reach: the Hiyoriyama circuit is only a couple of kilometres long around the station and involves climbing around 50 m. Hinoyama is further away, further South and a little higher.

The views of the coastline at Toba were good enough for Hiroshige to use in his Famous Views from the Sixty-Odd Provinces to illustrate Shima province (though there wasn't much else, I presume, Shima province was tiny, it was just Toba and the neighbouring town of Shima - also Shima is 志摩 and not 島 "island").

Beyond the islands near Toba, lies the mainland again, the Southern part of Aichi prefecture across the Ise Bay (Minamichita and Tahara), which the car ferry in the above picture traverses.

To keep or not to keep? The case of the Kyoto Imperial Palace

Completing the set of former Imperial palaces that I've visited, the question regarding Kyoto was a different one, when, after the Meiji Revolution, the throne of Japan was moved to Tokyo, ending Kyoto's 1000-year tenure as Imperial capital. The answer came swiftly: keep it. After all, it had only been rebuilt in 1855, fires having destroyed the palace multiple times in the Edo period alone.

The Shishinden throne hall, with its courtyard and traditional tachibana orange and sakura cherry trees either side of its grand staircase, was used for the coronations of Emperors Taishô and Shôwa (Hirohito) in 1915 and 1928, but since the accession of Emperor Akihito in 1989, coronations have been held at the active Imperial Palace in Tokyo.

Today, the palace is preserved and can be visited for free, albeit on a fixed tour route. Only the exterior of the buildings can be accessed, still allowing good views of the Shishinden and the gardens to the East of the palace.

Eckwersheim rail accident memorial

On the northern edge of the Strasbourg Metropolitan Area, the high-speed railway line crosses the Marne-to-Rhine Canal (of which I've said quite a lot recently) and curves to the South to join the trunk line into Strasbourg. It was here, on 14 November 2015, in the months prior to this section opening, that a test train derailed catastrophically, killing 11 and injuring 42.

The immediate cause of the derailment was over-speed: the crew had failed to brake in advance of the curve and headed into it 90 km/h faster than they should have. The reasons for this failure are a point of contention; as far as I have understood, the accident report hasn't managed to clearly identify them as there was no voice recorder in the driver's cab. The accident has been in the news recently as the trial of the driving crew and the companies involved has just taken place, with the verdict due to be returned in October.

I have been travelling on the accident tracks for years, and possibly since the first time I took the TGV to Strasbourg in 2017, I have made a note of this particular curve, recognising the red bridges from those terrible pictures from the news, not out of anxiety, but out of awareness of what had taken place. Knowing that a memorial garden sits there, and with the court case wrapping up, I decided to go out and see it in person.

Quite isolated from outside noise by the two elevated train tracks either side, and with the canal and paths ahead, the atmosphere there is indeed very peaceful. A large plaque recalls the event, while 11 stones are scattered around the site for the deceased.

"En hommage aux victimes et aux personnes profondément touchées par l'accident de la rame d'essais du 14 novembre 2015, à celles et ceux qui nous ont quittés"

Nagahama Castle Ruins

Like Hikone Sawayama, Nagahama Castle is not on the list of Japan's 100 Famous Castles, nor on the list of Japan's Next 100 Famous Castles. Like Hikone Sawayama, it was a pre-Edo period fort which was owned by clans which at some point landed on the wrong side of the unifiers of Japan. Little is left, and short posts mark where buildings would have been. It's a short climb from the base, and the view of Uchiura from this location is pretty good.

This part of Numazu, and the island in the middle of this shot, Awashima, is most famous for being featured in the anime Love Live! Sunshine!!, which I know nothing about but saw some hints of (train for another day). It's possible to see Mount Fuji from here on a good day. And... well, I could see some it...

It's a considerable distance from a train station, though there appears to be a bus stop at the base, but I was driven there by a friend so I don't know how frequent the buses are. We were also lucky to get on a quick boat tour out to Awashima and back, with the chance to see the castle from a the sea, against the hilly backdrop of Izu Peninsula.