Alien aesthetics

By many professional measures Gaudi was an unsuccessful architect. His best-loved works are the few public projects he undertook. His designs for houses had few takers. Why did his modernism not have a market? In the decades when he was designing modernist projects which failed, elsewhere in Europe Art Nouveau and Jugendstil were spawning commercial success. We went to one of Gaudi’s few successful building projects to find out what it was like inside. This is Casa Mila, located just off Barcelona’s famous shopping avenue of Passeig de Gracia.

Casa Mila: atrium

The atrium was full of light. The floor was covered in trencadis mosaic, the iron gates were in typical Art Nouveau style, and the bottom of a staircase was covered with a mural in delicate pastel colours (which is not original). One architectural innovation which can be seen here are the pillars. They largely carry the load of the six storeys high building. In 1906, when the construction began, it was supposed to be a radical innovation, allowing interior walls to be free of load.

Casa Mila: interior passage

As a result of being built around an atrium, the interiors of flats are full of light. The doors and windows are made with the flowing curved lines which reflect the aesthetics built into the walls. It is said that Gaudi paid as much attention to the handles on doors as in the architectural design.

Casa Mila: bedroom

The furniture was also specially designed. The flat which is on show has reproductions of the furniture that was made for the original flats. These are typical Art Nouveau pieces. I wouldn’t mind some in my flat. As you can see from the photo above, there is no lack of light in the rooms. The main problem that customers faced was the lack of straight lines in the walls. As a result every piece of furniture had to be specially made for the building. When you see the kitchen or the bathrooms you are immediately struck by this realization.

Casa Mila: bedroom ceiling

I looked up at the ceiling and was amazed at the detail there. I’m not sure that I can sleep in such ornate rooms, but the aesthetics of that time could have been different. Apparently owners began to change the furniture and colours inside the flats as soon as they could. By the time the house was declared an UNESCO heritage structure, internal and external changes were so many that it was hard to restore the original colours. As a result, I’m not sure whether this ceiling, for one, now looks as Gaudi wanted it to look.

Casa Mila: facade

The facade of the building is very distinctive. The rough and unfinished look gives it the local nickname, La Pedrera, meaning the quarry. The intricate iron-work grilles on the balconies are remarkable. But the most remarkable part of the building is probably the roof, with its fantastically shaped chimneys and flues. The alien in the featured photo is one of these.

Trencadis in the Park

Breaking up ceramic tiles into pieces and using them in a mosaic is called trencadis. You can see this in many parts of Barcelona, but my favourite collection of trencadis is Gaudi’s work inside the Park Guell. All the photos here come from this place. Gaudi assembled the pieces from discarded tiles and broken pottery. You can see that Gaudi’s style of architecture with its dearth of straight lines was unable to use the usual rectangular tiles, and so was forced in this interesting direction.

Park Guell: Trencadis covered spire

We’d reached Barcelona late in the morning, and decided to go off to Park Guell after lunch. Not a great decision on a burning hot day, since there is a bit of a climb from the nearest metro station. For the last four years one needs tickets to get into this municipal park! Unless you have thought ahead to buying them, you could be in for a surprise. On this hot afternoon tickets were sold out five hours in advance. The ticket allows you in to all the parts of the park which have Gaudi’s work, including his wonderful tiles.

Parc Guell: Tencadis on the main terrace
Parc Guell: detail of trencadis

Apart from the buildings at the entrance, and his famous lizard-dragon (vandalized in 2007 and restored quickly after), the main trencadis work is on the main terrace. You can see this in the photo above. One of the interesting things about this style is that the component tiles are used only as tesserae in a mosaic, and the original design on the tiles has nothing to do with the pattern that emerges. A closer look at the details (see photo alongside) will tell you how that happens. Work of this kind requires an artist. That’s one of the reasons that the modernist art movements of the early twentieth century never took over the world. The machines of the time could not build this. It also turned out that the buildings which Gaudi designed were not a big draw for the paying public: now you can see about three of them in Barcelona, and one was the house where he himself lived.

A Magic Square

I wandered through the Sagrada Familia in a daze until I came to the western facade and its Magic Square (see the grid of numbers in the featured photo). The facade is called the Passion Facade because it depicts the crucifixion and resurrection of Christ: the events are called the Passion of Christ in Christian dogma.

Work on this facade began in 1954, after Gaudi’s death, but followed his plans. The sculptures were made by Josep Maria Subirachs starting in 1984. I thought that the sculptures looked unlike the rest of the church, and found later that there is indeed a bit of controversy related to the look of the facade. When Subirachs took the commission, he insisted that he should be allowed artistic freedom, and not be forced to follow Gaudi’s designs slavishly. So, I wonder whether the magic square behind the sculpture of the Kiss of Judas is Subirachs’ or Gaudi’s.

A magic square is a square filled with numbers such that each row, each column, and the two diagonals all sum to the same number. In this square the sum is 33, which is the age that Christ was supposed to be during the events portrayed in this facade.

A magic square may (or may not) have other characteristics. One that people often insist on is that the numbers used be consecutive, starting from 1, and that no number be used more than once. This convention is clearly violated by the Passion Square, since 12 and 16 are missing and 10 and 14 are repeated.

This magic square has other magical properties. The square can be divided into four 2×2 squares, by a horizontal and a vertical line bisecting each side (the upper-left square has the numbers 1, 14, 11, and 7). The sum of the four numbers in each of these squares is also 33.

The 2×2 square at the center contains the numbers 7, 6, 10, and 10. These also add up to 33. If you take the two numbers above this central square and the two below it, then they also sum to 33. The two numbers to the left of the central square and the two below it also give the same sum.

There is an easier way to think of these two disjoint blocks of numbers. Imagine a large floor tiled with copies of the Passion Square. I’ve tried to show this in the image here: the thin black line marks each copy of the magic square. Mark out on the floor all copies of the central square with the numbers 7, 6, 10, and 10 (I’ve coloured them red in the image on the left). Then you will see that the two numbers above and below the central square also become a 2×2 square, repeated on the tiling (I’ve left them white). Similarly, the disjoint set of 2 pairs of numbers, two to the left and two to the right of the central square also become a single 2×2 square (also white).

When you think in terms of the tiling, then you discover that the corner squares become a single 2×2 square on the tile (the blocks of blue tiles). And, of course, the numbers on the corners of the Passion Square also sum to 33!

The diagonals join blue and red squares. The four numbers along the forward diagonal sum up to 33, as do the backward diagonals. On the tiled floor you discover other diagonals. Of these, only the diagonals removed from the circled ones by two spaces are associated with the same arithmetic magic, ie, they sum to 33. So there is a set of magic diagonals in the coloured squares, and another in the white squares. This is easier to see if you bleach the colours, as I’ve done in the image below. In the resulting chessboard pattern, there is a set of diagonals on coloured squares, and another in the white squares. Both kinds of diagonals are magic. Interestingly, magic squares of this kind are called pandiagonal squares, or, more interestingly, diabolical magic squares.

Finally, the first two numbers in the second row and the first two in the third row also sum to 33, as do the last two numbers in these rows. Shifting down by one row, the first two numbers in the second and fourth rows also add up to 33, as do the last two in these rows. If you try the same thing column-wise, the magic goes away.

Of course I could not have been the first person to discover these marvellous tilings hidden in plain sight. A quick search led me to a paper by two mathematicians from the University of Las Palmas, Jose Pacheco and Isabel Fernandez, who examined these symmetries some time ago. They also refer back to the first (paywalled) description of this square in the mathematical literature in 2001 by Pieter Maritz of the University of Stellenbosch. The symmetries of magic squares was first discussed in the early 20th century.

The beautiful hidden symmetries of the Passion Square open up through the tiling into a beautiful doubled lattice. This can be represented in many ways, and I show one in the image above. This harks back to the Mudejar style of the Spanish churches of the middle ages. Is this Subirachs’ hidden contribution to the Sagrada Familia?

Modern comfort

After spending a morning with Gaudi’s idiosyncratic architecture in the church of Sagrada Familia and then in the apartment building called the Casa Mila or La Pedreda, The Family and I went off to a nearby restaurant for one of Barcelona’s famous three course lunches. Gaudi’s architecture is mesmerizing, and both of us were a little stunned by the decorativeness of his style. During lunch The Family asked who the other famous architects in Barcelona are. Now Barcelona has works by so many brilliant architects, that I fumbled for an answer. When I blurted out “Mies van der Rohe”, it was my subconscious speaking.

My first acquaintance with the work of one of the makers of modernist architecture was through photos of the Barcelona chair, which (I later found) were designed to go with his German Pavilion in the Barcelona World Fair of 1929. One of the iconic structures designed by him was this pavilion. I was under the impression that it was dismantled within a year of being set up, but was surprised to find, just a few months ago, that it had been reconstructed.

So we found the simplest connection through the subway to take us there, finished our coffee, and set off into the hot afternoon. The clean lines of the pavilion are a refreshing sight after a morning of Gaudy excess. There is a small fee for entry, which we gladly paid, as we walked past the glass curtain “into” the structure. The interesting thing about this pavilion is that there is really no inside and no outside. The walls do not partition the structure; rather they offer a continuous path through the structure. Immediately behind the glass curtain is this wall of red-gold onyx (photo above).

When you go round this wall another curtain of glass appears (photo above), and you must decide whether to pass in front of it, or behind. The slab of the roof floats lightly above this, providing welcome shade. There were a very small number of people taking photos, very considerately moving out of the field of view of each others’ cameras. On the far side of the view above was the rectangular pool which is called the large basin.

Behind me was the small basin (photo above) with a statue called Alba by George Kolbe. The U-shaped wall behind it is made with green marble, and creates the main enclosed space in the pavilion. Interestingly, there is no roof above it, so that in another dimension it is open.

I found one place from which you could see all the different kinds of material used in this structure (photo above). This was the wall where a few of the Barcelona chairs had been placed (featured photo). The Family sat down on one of the chairs and declared that it was indeed comfortable. Was it the most comfortable chair ever designed, as advertisements used to claim once? She was not sure, but she said she could sleep in it. I’d always thought of the Barcelona chair as black, but it turns out that the first edition, which was placed here in 1929, was white.

We sat there together and contemplated the vision which has now conquered the world. If the Barcelona Pavilion seems to be so ordinary, it is because every modern atrium looks faintly like this: the mixture of exotic polished stone and steel and glass curtains, soaring above you. Even the little pool with Kolbe’s architecture has been copied and transmuted. This is why Casa Mila stands out as extraordinary: it is not the way the world is. I’m happy that the world followed Mies van der Rohe’s vision and not Gaudi’s.

Rushing through Sagrada Familia church

All those who have some interest in Barcelona probably know two names for sure: Lionel Messi and Antoni Gaudi. Messi plays for Barcelona Football Club and Gaudi designed the church of Sagrada Familia. Barcelona FC cannot be seen in action every day, but the Sagrada Familia is open on all days. You need to get a ticket, and then come in the exact 15 minutes that your ticket says you have to enter. After that it is a mad rush through this church. Can you help it?