Wednesday, 7 August 2019


Most people are probably aware that the ancient Greeks identified four ‘elements’—earth, fire, water and air—although these are not elements in the modern sense. The ancients will have been aware of the existence of gold, silver, iron, copper, tin and lead, but there is no evidence that they recognized them as fundamental. Of course, the Greek conception of elements is purely metaphysical, but it is preserved in English phrases such as ‘braving the elements’, which translates roughly as stepping outside in bad weather.

However, the Greeks had a problem. How many elements should there be? Plato had discovered that there are precisely five regular solids—tetrahedron, cube, octahedron, dodecahedron, icosahedron—and the prevailing wisdom was that by analogy, there must also be five elements. This is a false analogy, but it is the origin of the word quintessence (literally, ‘fifth essence’).

It is less well known that the ancient Chinese recognized a similar system of elements, one that is still in use today, especially in astrology and fung shui. They also identified five elements, although, unlike the Greeks, this was not by analogy with the five Platonic solids. The theoretical basis for Chinese astrology and fung shui is the lo shu square, two examples of which I present here:

The lo shu square is what Western mathematicians describe as a ‘magic square’, the fundamental property of which is that every row, column and diagonal adds up to the same total. This ‘magic square’ has other properties, the most obvious of which is that 5 must always go in the centre cell, and the four even numbers must occupy the four corners. In fact, once the starting condition has been defined, constructing a lo shu square becomes a forced process. And there are only two possible solutions, one of which is a mirror image of the other (see above).

The necessary presence of 5 in the centre cell seems to be why the Chinese decided that there must be five elements, each of which corresponds to one of the four corner cells or the central cell of the square.

So what did the Chinese decide were the five elements? Three—earth, fire and water—are the same as in the Greek classification, but the other two seem to me to be not even remotely elemental. Wood is a hybrid of earth and water, while metal is a hybrid of earth and fire. In this classification of elements, there is no way to explain the force exerted on the sails of a ship or a windmill, which is particularly mystifying given that the Chinese were the first to develop fore-and-aft sails, so they must have been aware of the force. Why did they fail to recognize air as a separate element?

Sound is another phenomenon that requires air for its explanation. It is a pressure wave that propagates through air, or another gaseous medium, and it is directional. It can also be transmitted through solids and liquids, but it does not exist in a vacuum. The earthquake-detection machine built by the Chinese more than 2,000 years ago could only have been designed by someone who understood that the shock waves from an earthquake are also directional, so why did they not make the connection? To be fair, there is no evidence that the ancient Greeks understood sound either, but at least they did have the means to explain it. Nothing in Chinese cosmology explains sound.

And there is another way to look at the Greek interpretation. You could argue that earth, water and air correspond to the three phases of matter: solid, liquid, gas. And there is a fourth phase! Plasma. The temperature at the heart of the Sun is so high that atoms no longer exist. Plasma is simply a fizzing soup of protons, electrons and other subatomic particles. That sounds like fire to me. And one hell of an insight for more than 2,000 years ago.

Meanwhile, perceiving some kind of esoteric magic in a lo shu square seems to me to be like believing in the healing power of crystals, the shapes of which are also the result of a forced process, one that depends solely on the relative size of their constituent atoms.

Wednesday, 24 July 2019

housey! housey!

I was walking from Tai Wai station towards Che Kung Temple, one of the best-known such edifices in Hong Kong, in February when I passed a school. I couldn’t help but notice the names posted on one wall:

All six names are well known, although apart from their being the names of the school’s six houses—and the original bearers being famous—it would be difficult to identify a hard connection between them. There are three scientists, a moral campaigner, an explorer and an artist.

The junior school that I attended between 1953 and 1957 had four houses, all named after local mountains: Blencathra (blue); Crossfell (red); Helvellyn (green); and Skiddaw (yellow). The local grammar school, which I attended from 1957 to 1964, had just three, two of which—Lowther (yellow) and Blencowe (green)—were the names of local village grammar schools that were amalgamated with the town’s school at some point in their history. The third house—Tudor (red)—is a nod to the royal dynasty in power when the school was founded.

When I worked at the Eskdale Outward Bound Mountain School from 1971 to 1972, each group of twelve students, known as a ‘patrol’, was named after a famous explorer. I can’t remember all the names used, but both Scott and Shackleton were represented. The following year, at the Moray Outward Bound Sea School, I found that the ‘watches’ were named after famous seafarers such as Drake and Nelson.

It’s obvious that these names were intended to be inspirational, so it was something of a surprise to discover that the watches at the Hong Kong Outward Bound School were merely named after local mountains (Tai Lam Koi, Nam Tse Tsim, Tai Mun Shan and Ma On Shan) that the students would climb during a course. There was no inspirational component whatsoever.

However, the men—there are no women in the group—after whom the six houses that are named in the above photograph must have been chosen specifically to inspire their members. After all, William Wilberforce’s main claim to fame is that he was the leading campaigner against slavery in the British Empire. Fridtjof Nansen was a recipient of the Nobel Peace Prize for his work helping displaced persons in the aftermath of the First World War, although he is probably better known for his exploration of the Arctic and his contributions to the science of oceanography.

On the other hand, I would consider Alexander Fleming and Ernest Rutherford to be relatively obscure personalities. Yes, Fleming did discover penicillin, the first antibiotic, and Rutherford was identified in the popular press as the man who ‘split the atom’, thus proving that despite the original Greek meaning of the word, atoms are not indivisible. I would have been more inclined to choose Isaac Newton and Charles Darwin if asked to nominate two British scientists, but perhaps these two are just too well known.

Nobody is likely to quibble over the inclusion of Albert Einstein, undoubtedly the most famous scientist of the twentieth century, but Leonardo da Vinci does seem to be a fish out of water here. He was a very clever man who dabbled extensively in futuristic thinking, although he is probably best known for paintings such as Mona Lisa and The Last Supper. His inclusion would seem to reflect the breadth of the school’s curriculum and the fact that the arts are important.

However, if I’d been the one choosing six inspirational house names, I would not have included any of the six I’ve been discussing here. In addition to Newton and Darwin, I would have nominated Isambard Kingdom Brunel, William Shakespeare, Michael Faraday and Joseph Mallord Turner (or Galileo Galilei to replace Turner if I’m not required to restrict my list to British nominees). I imagine that most readers will have their own nominees.

Sunday, 30 June 2019


I first cycled along Ma Tso Lung Road several years ago, shortly after the closed-area status of the frontier road was rescinded. I cycled the full length of the road as far as its junction with Ho Sheung Heung Road, where I turned left onto the latter on my way to the village of Ho Sheung Heung. There was a very obvious problem.

Both roads carry a lot of industrial traffic to and from premises on each road, and I did not like having to mix it with big trucks, even though their average speeds are not high. However, it didn’t take me long to find a suitable alternative. The northern part of Ma Tso Lung Road has few industrial premises, and where these sites begin to proliferate, I found an unnamed road that led to Ho Sheung Heung Road beyond the point where one might encounter trucks and other industrial traffic on the latter road.

However, on one occasion last year, this road was blocked by a large truck unloading something or other. I had no idea how long I might have to wait, so I wondered whether I could find an alternative. I could. I discovered the alleyway that I originally described in Serendipity #1. Although I started my original exploration from Ma Tso Lung Road, we now tackle this section starting from Ho Sheung Heung Road (this starting point is directly opposite the exit from heart of darkness).

There are a number of paths branching off #1, not least serendipity #3, which we rarely did simply because it meant missing out the best part of #1 (the hill), but shortly before returning to the UK earlier this month, I worked out a way to do both, together with a few other variations. I set out to shoot a video of this reworked route through the alleys, and what follows is a series of video stills of the route. I haven’t uploaded the video to YouTube though, for reasons that I will explain when I come to it.

The start of #1 is straightforward:

The next two images show a path that branches off to the right and is followed later in the sequence:

Straight ahead appears to be the better option here, but it’s a dead end:

The next image shows the start of the hill, with the start of #3 to the left:

A short distance up the hill, a path comes in from the right and is accessed via the path that I referred to above:

There is another path at the top of the hill:

It actually leads all the way back down to Ho Sheung Heung Road, which would be fairly pointless, but as you will see, there are other options. I decided to assign #4 to this alley.

The path starts by passing a row of squatter houses. The second image shows that one occupant has decorated the outside of their house with crude but colourful artwork:

The left-hand option in the next image leads to the grave with bas-relief panels that I described in Photographic Highlights: 2018–19, so turning right is the way to go:

It leads to a steep and narrow path:

Turning left here leads eventually to Ho Sheung Heung Road, while turning right takes one back to the start of #1:

There are quite a few twists and turns:

…before rejoining #1:

The next image shows exactly why the video didn’t come out as planned:

I would eventually reach #1 again, but I knew that I would do so before the cyclist in the wide-brimmed hat, and I would therefore have to stop to allow him to pass.

This next sequence shows what the new path looks like:

The turn shown in the last picture leads to quite a rough section:

Having been forced to stop, Paula was slow to restart, so the following sequence of #3 shows me as a mere speck in the distance:

Serendipity #3 emerges onto Ma Tso Lung Road directly opposite the start of #2 (not shown in this final image):

I don’t think there are any more options hereabouts to explore, but shooting a video of the combined serendipity alleyways (sequence: #1, #4, #3, #2) is a high priority for the coming winter.

Thursday, 13 June 2019

ignoble hill

Although I’m currently in the UK and won’t return to Hong Kong until October, I’ve been thinking about cycling projects to work on next winter. Probably the project with the greatest potential is the one I shall be calling ‘ignoble hill’.

Noble Hill is an upmarket housing estate on the northern side of Ma Sik Road, which marks the northern boundary of Fanling:

You can tell that it’s an upmarket estate by the height of the blocks—and by the grand entrance to the estate.

The other side of the road is considerably less salubrious. There is an extensive squatter area with several alleyways up and down the hill and other alleys that run horizontally across the hillside. The aim, as always with this kind of development, is to construct a circuit that takes in as many of these alleyways as possible. What follows is an account of the progress to date. I’d cycled through the area several years ago, turning off the dedicated cycle track that runs alongside the south side of Ma Sik Road to see what I could find.

I didn’t follow up this initial exploration because I had many other areas to explore, and ignoble hill isn’t on the way to anywhere else. However, at the beginning of April, the day before I was due to go to Nethersole Hospital for an operation, I was returning from the final frontier and decided that I wanted to extend the ride, which I did by following the cycle track that runs alongside Jockey Club Road.

On this occasion, I then followed a rough road that starts next to the temple on the corner of Ma Sik Road and Jockey Club Road. Where that road bends around to the right, I found an alleyway that leads back down the hill, and I couldn’t help but notice the admittedly primitive artwork painted on a couple of squatter houses:

I was unable to do any cycling for several weeks, so I decided to take a look around the area on foot. This is where any route that I establish through the area will start and finish:

The right turn is the way to go. It leads up a hill that is not especially arduous:

Although I’ve described this area as a squatter area, this does not imply that the houses here are slums, only that there are specific legal restrictions on buying and selling them. Not only do all the houses have piped water and mains electricity; each house also has its own postbox, which is in a central location:

I also followed the road that I described above as bending around to the right for a short distance. This road to the left looked to be worth checking out:

In fact, it’s a dead end for motor vehicles:

…although there is an alleyway starting in the corner next to the wrought iron gate:

By following this, I found myself on the path that eventually returns to the start/finish point in the photo above. However, before reaching this point, I came to the junction with a path that leads back into the built-up area:

I wanted to see whether this would be a better option:

And I did find what I was looking for:

I dare say that I could continue around the corner to the left, and the turn to the right does look to be quite tricky. But that’s the point of the exercise! Whatever ride through the area I eventually come up with, the more technically difficult twists and turns the better.