The picture above is a simple multiplex network for a network of co-authorship and the respectively handled content (taken from¹). The multiple layer of data contain information about covered topics of publications and the frequency of co-authoring to the topics of each author. The visualization with NTM (NodeTrix-Multiplex¹) can reveal community relationships within the complex multilayer network (multiplex). The concept and system of Multiplex.One is however more conceptual. It associates and processes not only semantic and data associations between multiple layers but temporal logic, multilinks and dynamic interdependency-relations. Current Multiplex research centers on real world examples and analyzes them within multiplex frameworks. We approach the subject from the multiplex side, searching for surface complexity reduction into semantics (concepts). Why should one care about complex networks?
Cascades in multiplex systems such as the atmosphere are not well understood. But we can be sure that they are taking place right now, threatening future generations not in decades but in years and months.³ We look at a culture for which chaos and the butterfly effect are felt as relicts or novelties, while the relevance of everyones indvidual contribution to the global problems is more obvious then ever. A community change requires individual change and the difficuties we face take place on interconnected multilayer networks. Not only on the geophysical but also on the cultural and economic domains. In order to face the climate emergency efficiently, the systems and dynamics of global object- (goods) and currency- management (as well as automation, work- and performance-quantification) and specific distribution (towards globally unconditional minimum living conditions and human rights) must be re-designed and re-thought entirely. The production and industry chains are not globally optimized and the loss is enormeous. We want to operate on short-term time-scales with ambitious goals and actualizing as well as self-referencing strategies and systems. We think the year 2050 will not help the issue in the present and we cannot aim for the lobby-accepted strategy as it will destroy live due to insecurity and economic barriers. We must aim for the shortest shared lifetime. We need those who are 5 years away from retirement. We need those who are 5 years into their job. It is not a decade-based thinking we need but a versatile, rapid and interconnected approach.
We need time scales with missions which are actualizing and challenging. Agendas which are actively engaging civilians as well as experts. We must approach near-impossible goal spaces with a clear and ambitious intention and strategy. We must assemble talent, hope and the readiness and ability to cope with failure. That is why we want to build a next generation digital eco-system, the Multiplex.One. It is a system optimized for a multi-domain strategy which centers on establishment of participatory inclusive complexity management. We want a system which allows collective decentral government of theoretically up to 8 billion humans. The climate change is only one symptom of an underlying systemic ‘system disease’, caused by unprepared and asymmetric globalization. Now we face further asymmetric exponential growth which will set apart human rights from luxury and prosperity once more. Monomodal currencies are at their end. We need a network thinking as our foundational design approach.
Our project aims to mirror real world system-activity and interreactions in a meta-model environment. In this we can then implement specific assumptions and parameter variations to identify global complex system designs. The digital world models would be based on network dynamics from the bottom up. For new kinds of Ecosystem Model-Engines we intend to use a multi-domain theory which allows native multiplex architectures as complex real-world ecosystem-control instances, postulating multiplexing operations and their design as necessary aspects of global government capability. Multiplex.One would process classical data as well as semantics and associative networks. Dynamicity arises as layer interact through multiple channels (polyparametricity) while individual parameters can be of multi-valent or irregular logic which allows qualitative and smooth data processing.
The sketch above is not a classical 3D graphic. The axis are not entirely linear related but induce a tensor field in the space. The depicted arrangement is a static frame of ongoing temporal interconnections. For example the inverse proportionality of economics and ecology depicted in the top and bottom fields. More cooperative intensity with low connectionality increases economic impact. When the ability of things to interconnect is fostered by active design of social ecosystems and their partitions to be interconnectable (increasing their ‘interconnectionality‘), the relationship between ecology, health and the negative impacts of economics can become more aware. As such, high cooperative intensity with high connectionality can decrease economics relevance for the ske of ecologic responsibility. We are reaching the transitional exchange between these fundamental system-aspects, which require new forms of cooperative structures and organizing.
This multi-domain ecosystem model is very simplified and parameter free, however the relationship between nature and industry can be visualized clearly. Economy and ecology undergo interdependent relationship. The more cooperation (-intensity) is achieved, the bigger the role of ecology gets (left to right) for infrastructure regulation. As such, a natural economy can be achieved. The complex interconnection-networks are reduced in a complex transition plane as local common goal space for civilizatory development.
Example of a simple tensor field and its physical background (taken from wikipedia).
Higher order networks require computational processing of (economic) regulatory functions and matter distribution planning (pre-logistics and deployment). While the individual can reach the informationally active layer, the Conceptual space, the collective and cultural awareness is depending on the identity distributions. A collective awareness requires a high number of continually aware individuals in the distribution. Intersectionality is a significant issue in contemporary network systems. As there are no parametric (nor conceptual) gauges, the lack of information exchange dampens the entire multiplex. Forming an architecture for this kind of complex shifts between local and global optimization requires a polyparametric trace system (undergoing participatory control).
For multidimensional tensors and interacting layer the intersection-nodes can be understood as topological indices of graphs to express their evolution as complex tensor products².
¹NodeTrix-Multiplex: Visual Analytics of Multiplex Small World Networks
(Shivam Agarwal, Amit Tomar and Jaya Sreevalsan-Nair)
²On some topological indices of the tensor products of graphs
(K. Pattabiraman, P. Paulraja)