#2018-04

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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.

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The Tower of the Sun

With another World Expo underway at Osaka this year, a massive park to the North of the city (actually in the neighbouring city of Suita) sits on the site of the first Japanese World Expo in 1970. There's usually some form of centrepiece: in 1889 it was the Eiffel Tower, and at Osaka Expo '70, it was the Tower of the Sun.

It is a massive sculpture by Taro Okamoto, which it was possible to climb into to view another work called the Tree of Life. As it was going to have people inside, it needed a lightning rod - that's what the top face (officially a mask, but I tend to call it the "bird face" - whose eyes light up at night apparently) is sporting. The three faces on the back, front and top represent humanity's past, present and future respectively, though some art critics and historians have a more bleak interpretation due to Okamoto's larger body of work and stance against technological progress, something the Expo would put emphasis on.

Similarly to the Eiffel Tower, the Tower of the Sun was supposed to be a relatively ephemeral structure, and nearly all the Expo pavilions around it have been demolished. Like the Eiffel Tower, it was avant-garde and no doubt not everyone liked it. But this building is one of the few to be preserved, and requires regular attention - again, like the Eiffel Tower which needs periodic repainting. In any case, the Tower of the Sun is one of Osaka's most iconic landmarks.

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Shinobazu-no-ike

It's cherry blossom time! OK, this variety doesn't bloom until April, but it is my favourite, seen in Ueno in 2018. It's roughly the same variety as we have at the Citadelle, with lovely pink pompoms. I haven't visited Japan in peak sakura season, but I did have a picnic with Japanese people today under a light snow of petals.

The exact location of this tree is in Ueno, by Shinobazu-no-ike. Benten-dô temple stands on the island in the centre of the pond, and there was a decent amount of wildlife on hand that day, of the feathered and of the... er, plastic kind.

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The Osaka Monorail

The final post in this mini-series on the Osaka Expo 70 Commemoration Park is the obvious: how does one get there? Considering the Expo was all about bringing together the world's shared (or non-shared) visions of the future, the Monorail seems perfect! Except this line wasn't launched in time for the Expo - it was a later project, opened in 1990.

The straddle-beam monorail links Osaka Airport to Kadoma, and is due to be extended by the end of the decade. A short branch line pops out just to the East of the Expo 70 Park station, so a visit to the park is also a chance to see some mighty impressive sets of monorail points either side of the station, as the West side (above) also connects to the depot.

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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).

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Expo 70 Japanese Garden

While most of the pavilions of the 1970 World Expo at Osaka were demolished, a very large exhibit was preserved: the Japanese garden. Located in the North of the enormous Commemoration Park, it's designed as a stroll through the ages, with four sections inspired by different periods, Ancient, Medieval, Modern (Edo period) and Contemporary - kind of like the zones from The Crystal Maze, just without the puzzles and Richard O'Brien.

From rock gardens to ponds and rolling hills, from a bamboo grove to wisteria and maple trees, it hits the notes you'd expect from a summary of Japanese landscape styling, but allows one plenty of room to contemplate each tableau - I'm emphasised how big the overall park is, but the Japanese garden alone covers 26 hectares.

One of the few gripes I have with Koishikawa Kôrakuen, my favourite garden in Tokyo, is that some buildings are close and large enough to appear in the background. With the Expo pavilions gone however, most views in this park don't have that problem. Only the Tower of the Sun and the Osaka Wheel are able to rise above the park in this view towards the South.

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

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Arashio-beya

The quickest way to witness some sumo wrestling is probably to watch a morning practice session in a stable (though we'd probably use the word "club" in Europe). Arashio-beya in Tôkyô is one such stable, with the nearly-daily practice watchable from the street.

On some days, wrestlers may come out to meet the spectators and pose for some photos. This happened on the day I was there.

While researching for this post, it appeared that these two wrestlers may be among the stable's most successful. Arashio-beya was founded in 2002, and has had four wrestlers reach the top division as sekitori. Their first one is retired and now manages the stable, and their second was Wakatakakage, who won their first major tournament in March 2022 - and who probably is pictured left (I'm confident it is him based on other photos, but I'm couching it slightly just in case I'm wrong). Wakatakakage is the youngest of three brothers who all wrestle for Arashio-beya, and one of his brothers is the third sekitori from the stable. The fourth and most recent is Kôtokuzan, probably pictured right.

For someone who knows absolutely nothing about sumo, looking back at that morning, it's neat to think I was in the presence of people who would fulfill their ambitions.