Tuesday, 26 October 2010


Stefania Ugolini - senzafissadimora (2010)

Nonostante la base da cui una persona parte la sua vita sarà incentrata
sul movimento, trovandosi a volte in posti sconosciuti o non scelti,
destinata a percorrere strade e spazi che la porteranno a volte lontano,
a volte vicino a quella "casa" che resterà comunque il suo rifugio per sempre.

Così anche l'opera, apparentemente stabile, è destinata a viaggiare
trasformandosi da porta (casa) a "portale".

L'inutilità nell'opera sta proprio nella sua capacità di muoversi
senza essere spostata materialmente.

Può essere vista e conservata anche senza essere acquistata,
tramite il QR Code può essere scaricata in uno smartphone
e condivisa con un numero imprecisato di persone.

Tuesday, 19 October 2010

Collapsing New Buildings

La Musica Futurista (the Music of Futurism) began with Francesco Balilla Pratella's publication of Futurist Musician's Manifesto (Manifesto dei Musicisti Futuristi) in 1910. Pratella, and other futurists wrote music that promoted disharmony and free rhythm in a deliberate attempt to overthrow the established composers of the time such as Puccini and Umberto Giordano.

In 1913, Pratella's new composition, "Inno all Vita" (Hymn of Life), had its Baptism of fire at the Costanzi theatre in Rome. The performance was met with such hostility that it sparked off riotous rampages.

A leap forward in the development of Musica Futurista occurred with the arrival of the painter and musician, Luigi Russolo.

Russolo's La Musica (1911)

Russolo introduced new sounds with the intent of brushing aside all before him from Beethoven to Wagner. Instead of using traditional instruments, with their pure sounds, Russolo applied sounds from the new, mechanized world the Futurists so revered: moving trams, the internal combustion engine, wild screaming, etc. Russolo, however did not reproduce the actual noises of the industrialized world, instead he invented a series of machines that could reproduce analogues of those sounds.

Large boxes (called Intonarumori) were constructed, each containing a device that produced a specific sound, by rotating a handle or pushing a plunger. A megaphone was attached to each box to project the sound. So was born the experimental, heavy industrial soundscape that has paved the way for a wide spectrum of musicians ever since from Stockhausen to NIN (Nine Inch Nails).

Russolo's intonarumori composition was performed at the theatre dal Verme in Milan in 1914. The performance was ruined by constant interruptions from the audience. The entire episode eventually erupted into a fist fight which was followed by legal action and court proceedings.

The intonarumori later found a better reception in London and Paris. Unfortunately, all were destroyed in World War II during the bombings on Paris.

Recently I discovered this utterly brilliant video by the Berlin-based avant-garde group Einsturzende Neubauten. The perfect epilogue to Russolo and his intonarumori.

"Futurismo, L'avantguarda delle avantguardie", Claudia Slaris - Giunti press.
Jana Haŝková: Thanks for the YouTube link to the Einsturzende Neubauten video.

Monday, 18 October 2010

i = imaginary

Mathematics began when humans needed a system to count objects. We could use our fingers to count 1,2,3,4,... apples, for example. Our numbering system is based on multiples of ten, most likely because we humans have ten fingers (including thumbs). We call these numbers the set of natural numbers. It was the ancient Egyptians who developed a set of distinct hieroglyphic symbols that could be used to represent natural numbers (up to one million).

This was great but we also needed to do things like divide two apples among three people. Thus fractions were invented and we could calculate how give each person ⅔ of an apple.

This set of numbers was satisfying to ancient Greek philosophers and mathematicians. They argued that all measurable quantities could be expressed as a fraction. Pythagoras showed this was wrong when he proved that the length of the diagonal across a square with unit lengths was equal to the square root of 2.

The square root of 2 cannot be described as any fraction of integers. In fact, using fractions, we can only write down an approximation of √2 such as 1.4142, the actual value simply cannot be written. Hippasus of Metapontum, proved that this was true.

Unfortunately, the Pythagoreans could not accept that any measurable number should be so irrational and thus, according to one legend, they sentenced Hippasus to death by drowning.

Negative numbers began to appear at around 100 BC in China, and much later in the West (around 300 AD in Greece). Negative numbers were also fiercely resisted, although they eventually proved useful to numerically represent things such as quantities of debt.

Taken together, we call this the set of Real numbers. They are real in the sense that each of them can be physically plotted on a horizontal line (above) with zero in the middle, negative real numbers extending to the left and positive numbers to the right.

These numbers give us a powerful tool for performing many calculations, and can represent any measurable, or countable quantity. But there was more trouble on the horizon.

i = impossible

In the 1530's Italian mathematician, Girolamo Cardano, had figured out a formula for solving quadratic equations. In certain cases, however, his formula gave answers with components that were impossible to calculate because they included such values as the square root of -1.

It had long been established that two equal numbers, when multiplied together, always produce a positive number. Thus only positive numbers have a square root. How then could √-1 be considered a number if it is not real. Cardano simply reasoned that his formulas did not always work properly and rejected the cases where the answer included √-1.

i = imaginary

Cardano's contemporary, Rafael Bombelli of Bologna, realized that if you just ignored the fact that √-1 is impossible and represent it with a symbol (say i), then you could work your way through Cardano's rejected formulas, because each instance of i was matched by an instance of -i. By matching them up you can cancel them out (i.e. i - i = 0), and you are left with an answer that is both rational and correct.

Bombelli went on to develop the theory of complex numbers, the set of all numbers that could be represented by adding a Real number, and some Imaginary number (a multiple of √-1). These are now written using the formula a + bi, where a and b are real numbers and i = √-1.

In the centuries following Bombelli, mathematicians gradually came to accept imaginary numbers (kicking and screaming in some cases, but at least not drowning anybody) as a serious and useful mathematical tool.

In the beginning of the 19th century, three mathematicians, Carl Friedrich Gauss, Jean-Robert Argand, and Caspar Wessel came up with a clever way to physically represent complex numbers, the Argand Diagram.

Since imaginary numbers do not belong on the horizontal line representing Real numbers, these three independently came up with the idea of plotting imaginary numbers on a vertical line that intersects the real number line at 0.

Now, instead of representing numbers on a one dimensional line, we had a new set of numbers that could be plotted on a 2-dimensional grid. This geometric representation of complex numbers proved to be both insightful and useful. Simply manipulating the geometry of numbers represented in this plane is the analogue of performing arithmetic operations on those numbers.

For example, if you want to multiply a number on this diagram by i, you simply rotate the number on the diagram by 90º.

Above is a geometric representation for the multiplication 
of two complex numbers (A x B) = X.

Einstein and the 4th Dimension

Among other things, complex numbers are useful in General and Special Relativity (I'm walking on thin ice here by the way). The 4-dimensional field equations used by Einstein to represent gravitational bodies in space-time can be represented and manipulated using complex number algebra where the 4th dimension, time, is represented by the imaginary component.

Moving right along from mathematics, to contemporary architecture: In the three dimensional world we live in, how might we represent the geometry of, say, a 4-dimensional cube?

One approach is to use the same idea of projection that we use to draw a 3-dimensional cube on a 2-dimensional sheet of paper. This beautiful animation (below) demonstrates a rotating 4-dimensional cube projected onto 3-dimensions.

The Danish architect, Johann Otto von Spreckelsen, understood this when he designed the wonderful La Grande Arche de la Défense building in Paris in 1985.

While considering these projections, their connection to complex number theory and Argand diagrams, I decided to design a 4-dimensional projection where the inner cube is rotated by 90º along the vertical axis. The resulting shape is shown below.

Taking this a step further, I added a square to the center of the inner cube and rotated that a further 90º. This modified cube is shown below.

That is interesting, but I want to develop some practical Cubist forms that I can use for such things as a supporting column. The blue shape shown below uses the same geometry as the cube above, but it makes a solid of that shape's hollow core, I then cut away the exterior edges...

That's a pretty cool shape whose geometry has meaning, historically, philosophically and mathematically. I think it has a lot of potential and so I plan to be using this in some future projects. As John of Salisbury wrote in 1159, "we are like dwarfs on the shoulders of giants".

Saturday, 9 October 2010

Sofa #1

The concept behind the design for Sofa #1 is to project clean, minimalist lines while also to giving the impression and feeling of strength. The frame which carries the base is over-engineered to the point where it would support the weight of a medium-sized truck, yet it can easily be carried by two people.

I struggled for quite some time with the design for the back and arm rests. In the end, I realized that if it was minimalism I wanted, then I should go all the way. There are no arm rests. Instead, a stiff padded cushion sits at each end. These serve as arm rests but can also be moved or removed completely. The back is formed by three straight lines that are neither connected with the base nor each other. Instead they bolt directly to the wall aligned at the correct angle to provide a comfortable recline.

Sofa #1 fits into the overall theme for the furnishings of the apartment where it is installed. That is the theme of 'suspended objects' and the use of strong colors against a plain background.

Music to enjoy while seated...