Curating GRASP exhibition at EXPO 2020: COMPLEX NETWORKS

When I was a student some fifty years ago, one of the subjects was “Graph Theory”. It was about the mathematics of networks constituted of nodes and the connections between them. We learned to calculate the complexity of such graph structures when they were used, for example, for representing spatial objects in the form of wireframe models. I came across another one of these models years later when I was living in Bilbao, in the form of a draft rendering of the Guggenheim Museum. I was working at the European Software Institute there in Bilbao at the timeand had been challenged to communicate a feeling for the complexity of software systems. I deliberately referred to graph models, which I thought could visualize the structure of computer programs. Alas, such models could only represent the static structure of program code. The true complexity of software comes when it is executed, i.e. when the structure is animated by its dynamic execution.

In the further course of my professional life I learned about so-called “Petri Nets”, named after its inventor Carl Adam Petri, whom I also had the opportunity to meet in person after I had left the university. (There is a legend that Petri invented “his” nets in August 1939 at the age of 13 for the purpose of describing chemical processes).

A Petri Net is also known as a place/transition (PT) net. As described in Wikipedia, “it is one of several mathematical modelling languages for the description of distributed systems. It is a class of discrete event dynamic system. In essence, a Petri Net is a directed bi-partite graph, in which the nodes represent transitions - i.e. events that may occur - and ‘places’, i.e. conditions ‘firing’ a transition. In the visual representation directed arcs describe which places are pre- and/or postconditions for which transitions (signified by arrows)”.

(In contrast to other “flow net standards” in use by the software industry today to represent dynamic systems, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for the analysis of processes represented by such nets).

So much for the theory of modelling of nets. In practice, real nets are much too complex to be described in a mathematically consistent and complete way. The most impressive example is the internet which, as a net, would need to be represented by trillions of nodes and quadrillions if not quintillions of “firings” (executions) per second – all this happening in the invisible space of information processing which we as individuals would not be able to decipher for decades – if ever.

The idea of a living, vibrant network in nature brings us to the model of the functioning of a brain as the center of the nervous system – for example, the nervous system of human beings. In a human, the brain contains between 70 and 100 billion neurons (“nodes” in graph terms). Each neuron is connected by synapses to several thousand other neurons. The neurons communicate with one another by means of so called “protoplasmic fibers” called axons, which carry trains of signal pulses called action potentials even to distant parts of the brain or, in extension of the brain, to the body by targeting, i.e. activating specific recipient cells. The sheer number of potential configurations of “conditions” and “firings” makes it impossible to realistically model the processes in a human brain. Although science is doing its best, understanding the functioning of the brain will remain a Book with Seven Seals for the next few decades at the very least. We are condemned to look with astonishment upon the huge fireworks display of signals taking place in every nanosecond in our body, especially at brain level where we think and conceive.

The next World Exposition EXPO will be held in 2020 and 2021 in Dubai. GRASP is currently engaged in preparations for a potential exhibition there, most likely to be hosted in the Austrian pavilion. The key challenge in curating a contribution for its exhibition fitting into a given architectural framework was to identify a “philosophical superstructure”, which we believe to have found in representing “unGRASPable” situations such as software influencing future working and living conditions by modelling them with nets. Since we are exploring such situations in an environment strongly influenced by Austrian science and knowledge history, we committed to refer to the known schools of constructivism, prominently represented by Austrian philosophers such as Ernst von Glasersfeld or Heinz von Förster or Paul Watzlawik, to name just a few.

In aligning our superstructure concept with the philosophy of constructivism, we committed to make reference also to the Latin-American scientists Humberto Maturana and Francisco Varela, both biologists and authors of the oeuvre “The Tree of Knowledge” in which they elaborate on the self referentiality of living systems. The term they invented for this phenomenon is autopoiesis. The most fascinating living organism they investigated for gaining insights on the nature of biological life was the mycelium, which is the vegetative part of a fungus or a fungus-like bacterial colony. A mycelium doesn’t merely constitute a local living environment for a fungus, but also connects colonies of fungi even over large distances, e.g. as extensive as in the case of the fungus Armillaria Ostoyae. Its mycelium has been discovered in Eastern Oregon in the United States as probably the largest organism in the world, spreading over an unbelievable 970 hectares connecting fungi colonies over hundreds of kilometres. (This may serve as a symbol for EXPO’s slogan “Connecting Minds”).

Thus, the concept for the participation of GRASP in the World Exhibition which the curators developed is to span a space between a mycelium represented by an animated pathway on the floor and, in the other dimension, a sky-high animation of a neural network projected at the cathedral like ceilings of the Austrian exhibition pavilion.

And what is this whole arrangement made by the two networks all about? It is an attempt to induce the visitors of the exhibition who will walk between the two networks – the mycelium on the bottom and the neural network on the ceiling – to become part of them, to experience and to ponder what usually happens in the invisible spaces “behind” the curtains of information technology user interfaces.