Circle and square

John and Michael, the twins whose case is described by the neurologist Oliver Sacks, didn’t know how to add, divide or perform the most basic mathematical procedures, for example, answering what is 3 times 7. However, they could memorize huge numbers just by listening to them once, recognize the prime numbers in figures of more than six digits and state without mistake, what day of the week would be any date that would be requested to them in a range of 40,000 years ahead and 40,000 years back. The scene with the matches is classic, and Oliver Sacks' narrative is astonishing:

A box of matches on their table fell, and discharged its contents on the floor: '111,' they both cried simultaneously; and then, in a murmur, John said '37'. Michael repeated this, John said it a third time and stopped. I counted the matches - it took me some time - and there were 111.

From:
March 10, 2021
To:
May 1, 2021

Christian Abusaid, Olga de Amaral, Carlos Cruz-Diez, Francisco Fernández, Ramón Laserna, Andrés Moreno Hoffmann, Edgar Negret, John Mario Ortíz, Eduardo Ramírez Villamizar, Martha Rivero, Fanny Sanín, Yorely Valero and Andrés Valles.

John and Michael, the twins whose case is described by the neurologist Oliver Sacks, didn’t know how to add, divide or perform the most basic mathematical procedures, for example, answering what is 3 times 7. However, they could memorize huge numbers just by listening to them once, recognize the prime numbers in figures of more than six digits and state without mistake, what day of the week would be any date that would be requested to them in a range of 40,000 years ahead and 40,000 years back. The scene with the matches is classic, and Oliver Sacks' narrative is astonishing:

A box of matches on their table fell, and discharged its contents on the floor: '111,' they both cried simultaneously; and then, in a murmur, John said '37'. Michael repeated this, John said it a third time and stopped. I counted the matches - it took me some time - and there were 111.

'How could you count the matches so quickly?' I asked. 'We didn't count,' they said. 'We saw the 111.' (...) 'And why did you murmur '37', and repeat it three times?' I asked the twins. They said in unison, '37, 37, 37, 111'.

And this, if possible, I found even more puzzling. That they should see 111 - '111-ness' - in a flash was extraordinary, but perhaps no more extraordinary than Oakley's 'G sharp' - a sort of 'absolute pitch', so to speak, for numbers. But they had then gone on to 'factor' the number 111 - without having any method, without even 'knowing' (in the ordinary way) what factors meant. (...) 'How did you work that out?' I said, rather hotly. They indicated, as best they could, in poor, insufficient terms - but perhaps there are no words to correspond to such things - that they did not 'work it out', but just 'saw' it, in a flash.

The twins, diagnosed as autistic, psychotic, or severely retarded, joined the lineaments of the "wise idiots," while analysts were concluding that they had an unconscious mental algorithm —an unconscious mental algorithm?!—which allowed them to calculate a series of useless but curious topics. However, no one, only Sacks, seemed to notice what they claimed: the possibility of seeing the quantities, not of counting them, not of calculating them. I persist: an ability to see the 111 displayed in space, at a glance, and not in the sequential time of the operation itself.

The numbers were specific for them, spatial and tangile, without the slightest glimpse of abstract. Although the numbers serve to count, before that, they have a being as entities, a quality of their own. If you will, a personality. Who does not keep his favorite number as a hidden treasure since their childhood?

Despite so many years of school, each one of us persisted deeply suspecting that numbers were not just quantities, but entities that we could recognize in other ways besides calculation. School mathematics turns out incomprehensible, precisely because it focuses on the abstract part of numbers, without ever exploring its concrete, sensible and phenomenological nature. What greater pleasure there is than finding the pie number through a rope that measures the circumference in diameters?

Visiting artists’ workshops to organize this exhibition, numbers, geometry, chance and probability appeared everywhere. On a table there was a dice and a pencil, the relationship between them was more than evident. On another, a series of photos of the numbers of wagons of Mexicos’ City subway revealed a particular interest in knowing how many times one could have traveled in the same wagon in a certain time. I cannot imagine this artists’ joy when getting on the wagon 757 for the third time in a month, not an impossible but quite unlikely issue. On another, mathematical progressions were extended across fabrics, while patiently removing pieces of thread drawing some geometric and monochromatic figures. In each of these cases, numbers wanted to be seen, not counted, with what arose before my eyes, the forgotten character of the digits. By this, I do not refer to a numerological exploration or to a magical research, but to a series or rational experimentations that far from being abstract were spatial and concrete.

In other workshops, city traces appeared and as the excessive love for the square, and, of course, for his friend the rectangle (and a rectangle is nothing more but an addition of squares). In paintings and installations our world appeared, divided by lines: the division of land into blocks, the division of blocks into lots, the division of lots into cubes, the division of cubes into regular and uniform rooms. A few days ago I asked my students: How many squares and rectangles do you see in your surroundings?: Start by the window, the table, the screen and the keyboard, and keep going… Some begged me for mercy: Julia, we can’t count them, I am at 17 and still not finished. How many circles? 3, at most 7.

In sum, the numbers as concrete figures and the traces of the chaos ruled by mathematics laws, appear through all the exhibition, or rather, along its contemporary artists, not the modern ones. The modern artists, —and modernity is already a word that expresses past, just like the term “future”— they worked geometry in a very different way. The moderns, Ramírez-Villamizar or Jesús Rafael Soto, do not trace a geometry full of tangible foodprints, of the city, of its chaos, but a geometry that opens like a window to an immaculate forecast. For the moderns, geometric art is full of future, for the contemporaries, geometric art is full of past, full of other paths distinct to utopie, to abstract mathematics and empty numbers.

Finally, Circle and square, the title of this exhibition is a quote from the movement founded by Torres-García in the 1930s. The proposed dichotomy is accurate, it's about the only two geometric figures that exist, in fact, there only exists one circle and one square, which we see from far or near. Nevertheless, its opposition is clear, the circle, the 1, it was already invented when we arrived in the world—the falling drops into the lake are in charge of declaring it—, while the square, the number 4, is our only contribution to the universe, that is why our life whirls in its tribute, it just takes to see the floor where your feet are and the canvases that spread through the living room.

Curator: Julia Buenaventura Ph.D. in Architecture and Urbanism.