TWO TO THE SIXTY-FOURTH MINUS ONE
by Raffaele Gavarro
Clear as a star in heaven the truth she set,
And, as she ceased her words, each coronet
Shot forth innumerable lights, as shoot
Sparks from the bubbling iron; and every one
Danced in its circle at its circle's speed,
Numerous to any mortal count defy,
As we the chessboard's squares may multiply.
Dante Alighieri, The Divine Comedy, from canto XXVIII, Paradiso
(translation by S. Fowler Wright)
Fantastic magic of numbers. I say that as one not initiated and thus, perhaps, more easily impressed. The legend of the Indian philosopher Sissa who teaches the Persian king the game of chess, and in response to the latter’s reckless generosity proposes that he be granted, in exchange for the invention of this admirable pastime, just one kernel of grain for the first square, two for the second, four for the third and so on, doubling the quantity all the way to the 64th, and thereby laying claim to the entire planetary harvest for a period of about 10 years, is proof of the danger of underestimating the practical and imaginative possibilities of numbers. It seems incredible that in the finite banality of the grid of the chessboard a number can be generated so overwhelming as to evoke the notion of infinity. It’s almost dizzying, and this is precisely why Dante turns to the chess story on the subject of angels in the canto of the “ninth heaven” or “primo mobile”, borrowing a metaphor previously utilized by St. Thomas.
Recently, stimulated by the 80.000 of Pierluigi Calignano, I’ve been investigating numbers. I have gotten a better idea of what is meant by prime numbers, or those divisible only by themselves and by one. For example: 1, 3, 7, 11, 13.
Then I discovered that there are perfect numbers, or those equal to the sum of their divisors. An example: 6, whose divisors are 1, 2 and 3. Add them up: 1+2+3 and you get 6. Simple, isn’t it? 28 is another perfect number, because 1+2+4+7+14 equals 28. After 6 and 28, the third perfect number is 496, the fourth 8128, the fifth 33,550,336.
Apart from the prime numbers and the perfect numbers, there are also numbers known as amicable, because they are paired in friendly couples like 220 and 284, where each is equal to the sum of the divisors of the other. Things are beginning to get more complicated. A simpler amusement is that of the numbers called triangular, obtained from the sums of the series 1+2+3+4+5+etc. Therefore the triangular numbers are 1, 3 (1+2), 6 (1+2+3), 10 (1+2+3+4) and so on. But there are also the square numbers, those obtained by adding only the odd integers. For example, after 1, we have 4 (1+3), 9 (1+3+5), 16 (1+3+5+7), 25 (1+3+5+7+9) and so on. As you have undoubtedly noticed, the square numbers are the result of the sum of the triangular numbers. Both take their names from the figures of their graphic representation. We have to admit that art and mathematics are more closely linked than is commonly believed. Apart from the use of the golden section, there is the perspective of Brunelleschi and Piero della Francesca, a direct ancestor of descriptive geometry, or the anamorphoses of Leonardo Da Vinci, which approximately one century later led to the development of projective geometry. Of course we cannot leave out Dürer, or Paolo Uccello, who was evened accused by Vasari of being more a mathematician than an artist, maker of that ingenious polyhedric mosaic - the star dodecahedron - on the floor of St. Mark’s Basilica in Venice.
Albrecht Dürer and Paolo Uccello are also, and not coincidentally, directly evoked by Calignano through the three-dimensional reworking and partial alteration of the rhinoceros of the former and the famous Chalice of the latter, which is composed of segments that subdivide the surface into rectangular geometric forms, very similar to the polygons of today’s wireframe computer images. In Calignano’s construction they become 1040 quadrangular modules in cardboard, to be precise.
The 20th century also offers interesting relations between visual arts and mathematics. Wassily Kandinsky, for example, theorized the replacement of the imagination of the artist with a mathematical conception, and Piet Mondrian compared his painting to mathematical abstraction. Even artists like Salvador Dalí could not escape the influence of numbers and geometries, while others like Escher should probably not even be considered artists. In our period in Italy we find Merz with his Fibonacci series, the geometries of Paolini, and above all Alighiero Boetti, with the genius capable of making this union harmonious and even necessary. Perfection? When the famous e between name and surname, apart from indicating the coexistence of the double in the one and vice versa, established the perfect squaring in 16 letters of that random association of signs that forms the representation of his identity. It is probable that Boetti never made a work without a mathematical dimension. Just as it appears that the world, or the universe, always reflects a condition of fractal complexity.
This intuition sets Calignano the builder into motion, the fantastic assembler of cardboard, scrap objects and materials, which undergo an unpredictable process of distancing from their everyday status. This is not simply because of the persistent sense of surreal alienation still found in most of the recent works. Instead it is the placement of these materials in highly finished, precise structures that accomplishes the effect, of exemplary aesthetic machines, just as certain powerful equations may appear to those with eyes to see their beauty. Like such equations, every construction has its own internal logic and reason for existing, so much so that they appear as systems endowed with closure, a sort of set of references and aptness, new accesses to meaning that overlap, each time with a different method. Observe 80.000, where side by side you will see not only the above-mentioned rhinoceros with a sharkfin and the chalice, but also strange mechanical arms in wood and metal that can be worn and put into action, and a little gorilla (gorillotto), a petrified and shackled stuffed toy, arms chained like some absurd Prometheus. The continuity amongst these works is based only on the mode of formation of the objects, free of any belonging to a single genre of content or style. Even if we trace back, from the submarine decorator with colored plungers to the village of dwellings on piles, we find no precise symptom of coherence. The fact of the matter is that in the work of Calignano each thing is true in and of itself. In the sense that each object incessantly fills the ever-changing present. And just as every present is charged with the past and the possibilities of the future, so these works, in an utterly similar way, accept the dense tangling and interweaving of fragments of individual and collective memory, of historically documented forms with those only imagined and suddenly raised to the plane of the fantastic, or lost in the impalpable realm of dreams. Randomness taken to the level of a system, trained to a mathematical model, or the idea of one, demonstrates that this aftertrace of the 20th century is an extremely complex reality, undoubtedly rendered all the more so by the nearly infinite filiation of imagery produced by the media. The name 80,000 has precisely this meaning. It is a finite number that describes the infinite quantity of things that characterize our everyday world. In this multitude of events, actions, reactions, information, realities and hypotheses, the construction of a chalice made of 1040 pieces with a steel vegetable colander at the center demonstrates, in a directly visual way, the continuous and random clashing and fusing of objects and thoughts from different places and times, in what I would define as a present “caught in the act”. In like manner, the finned rhino is simply the intrusion of the fantasy dimension in our increasingly mutable historical memory. While the present assails us to the point that the future seems like a parody of itself, as shown by the two mechanical arms. But the true point of contact and equilibrium of all the images of 80.000 is the little gorilla. A sort of silent witness condemned to listen and see, without the possibility of expressing assent or dissent about unfolding events. The toy in chains takes on a heroic, mythic tone. But it also makes us smile. This playful irony is one of the constants in the work of Calignano, but over the years it has evolved, in a process of refinement and fusion, in particular, with that imaginative-fantastic side that is another recurring characteristic of his activity.
From the little robots and the first constructions to the palafitte villages, the question has taken on less unified tones, both in terms of iconography and in terms of meaning. What we perceive as ironic shading is the result of the activation of the different dimensions that form the work, i.e. it is the effect of the interlocking of the different cultural inputs that compose our present. The images of Dürer and those of comics are forced to interpenetrate, favoring the tendency toward mimesis and contamination of today’s imagery. Just as the suggestions of the Fictions of Borges or the Invisible Cities of Calvino mingle with the labyrinthine experience of everyday life or the ancient disorientation of the voyage, glimpsed today only in the dimension of dreams. This continuous wavering between micro and macro undoubtedly has an ironic aspect, but this too is the result of the mere exaggeration of conditions already found in our normal everyday world. When a peanut becomes a geometric suggestion and formal model, the process is precisely the same as what happens with the chalice of Paolo Uccello. Calignano keeps the two on the same plane, and this too makes us smile, while prompting us to ponder the fact that it is a shared horizontal plane that contains, without any divisions, everything we draw on from the past, along with everything we continue to produce. A plane that is, of course, also its own dumping ground, and which we continue to call the postmodern.