Hashigui-iwa

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 failed to mention this in the original post, but Meiji-jingû is also a high point of sumo culture. Newly promoted yokozuna, the highest rank in the sport, perform their first ring entry dance there, before their first tournament at that level. This would be their first appearance with the "horizontal rope" (that's what yokozuna means), in the shimenawa style, around their waist.

That's just happened, with the 74th yokozuna making his debut.

NHK WORLD

Hoshoryu performs first ring-entering ceremony as yokozuna | NHK WORLD-JAPAN News

About 3,500 people gathered at Meiji Jingu shrine in Tokyo on Friday to see sumo yokozuna grand champion Hoshoryu perform his first ring-ent

The New Year shrine visit: Meiji-jingû

A common New Year ritual in Japan is to go to a shrine, possibly a large one, a visit known as 初詣, hatsumôde. NHK reported that Meiji-jingû in particular was very busy. Of course, I would avoid that, so here we are with a more tranquil time, closer to the Autumn festival.

Meiji-jingû was, as its name suggests, founded to enshrine the spirit of Emperor Meiji after his death. The first Emperor of the post-Edo period presided over sweeping societal reforms, such as the abolishment of classes like the samurai, as Japan re-opened to the rest of the world and sought to catch up. The Imperial attachment is symbolised by the Chrysanthemum crests on the torii.

One of the things that can be wished for at Meiji-jingû is a happy marriage and family life, particularly at this dedicated spot with two camphor trees planted in 1920, linked with sacred rope - these are called "married trees", 夫婦楠 Meoto Kusu.

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 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!

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.

For Vectron!

Produced since 2010 by Siemens, the Vectron is a modular locomotive platform with various engine options - AC electric, quad-voltage for use across Europe, "last-mile Diesel" option for parking, Diesel motors, dual mode/hybrid... It hauls both freight and passenger trains. But the main reason I've wanted to mention the Vectron is...

this Mitchell and Webb sketch!

This is from series 3 of That Mitchell and Webb Look, which was aired in 2009. The Siemens Vectron was officially launched in 2010, so it's fair to say that the name appearing in both is a coincidence. However, when I see a Vectron, it reminds me of this sketch, so it's harder for me to take this train seriously!

But it is serious business, as it is one of the most common locos in continental Europe. Only Iberia (due to using a different gauge) and France (because if it ain't Alstom, they'll oust 'em) don't see much of them. The examples shown here are from Germany, Switzerland and Slovakia, and were all pictured in the same area of Germany. The quad-voltage version in particular allows companies to carry freight all over Europe, they're virtually borderless.

Yet here I am, still snickering at the name, by Vectron's beard!

"Stick an aircraft engine in it" part 1 - Boeing Jetfoil

In the late 60s and early 70s, all branches of transport were hoping for an increase in performance similar to what the jet airliner brought to aviation, and the solution was invariably to use similar gas turbine technology, with invariably identical career trajectories when the oil crises hit, as, apart from in aviation, far more economical engine options were available. So I was very surprised to see this still active in Japan last summer:

This is a hydrofoil which uses gas turbines to power a pump-jet. Once it is going fast enough, it takes off and runs on foils, greatly reducing water resistance and achieving speeds up to 45 knots, over 80 km/h (which, on water, is very fast). I remember seeing exactly this type of vessel in ferry brochures when I was a child; Oostende Lines operated some between England and Belgium. The advent of the SeaCat, a class of huge Diesel-powered car-carrying catamarans, got the better of the hydrofoils and the hovercraft, which was incidentally another case of "stick an aircraft engine in it".

This specific class of hydrofoil takes the mantra to another level, as it was designed by Boeing, which named it the 929 Jetfoil. Production was licensed to Kawasaki Heavy Industries in Japan, which made boats for the domestic market. The Rainbow Jet is one of these, running between Sakaiminato on the San'in coast and the Oki Islands. I saw more of them at Atami in Eastern Shizuoka, providing transport to the Izu Islands. So, despite the astronomical 2150 L/h consumption (though to be fair, I can't find consumption numbers for equivalent foot passenger-only catamarans), Japan still runs them...

A few details from Singen Stadtpark

This bridge is not particularly big or special, but it cost YES Marks in the early 1920s, as post-WWI Germany went through a phase of hyperinflation.

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.

Now that @fredomotophoto is back from Alsace and Germany, I can do a piece on Black Forest clocks without spoiling his trip! The area has a lot of clock-making history, and to this day, typical tourist shops like the one above - TriBär, a play on the town of Triberg and the word Bär which... you can guess, a.k.a the House of 1000 Clocks - are full of cuckoo clocks ticking and going off all the time. It probably gets quite weird working in one of those places...

Triberg is host to the most extreme cuckoo clocks. The world's smallest are housed in the Schwarzwaldmuseum in the town centre. Wall camera on the right for scale.

Further up into the hills, on the edge of Schonach, is the opposite: this is world's first largest cuckoo clock, referenced in this previous post. As it was closed on the day I visited, I don't know much about the history of this clock, but it's housed in a building the size of a small house (gate on the right for scale)... and it isn't the biggest one any more.

The current biggest one is on the other side of Triberg, and located at the base of a big climb on the Schwarzwald Railway Adventure Trail. Gate on the right for scale. The whole building doesn't count as the clock itself (that would be too easy), only the mechanism does, and it is 4.5 m wide, with an 8 m pendulum. It took 5 years to build and its cost is estimated in the millions of euros, so you know what you're in for if you want to beat it. For a small fee, it is possible to visit the interior, but I was a bit pressed for time as I didn't want to miss the next train at the next viewpoint. I just took a break in the shop and caught the 5 o'clock cuckoo before moving on.

Bonus clock from the museum: