Design Challenge 7

Visualizing Hierarchies of Complex Systems :
posted by Neil Theise

Summary

Levels of scale are central in determining how a complex system appears: as a population of interacting units on a lower lever or, higher up, as a single unified entity with characteristics defined by the emergent self organization of the population. So, for example, bodies may be conceived of as a thing, or may instead be seen as the phenomena arising from the interactions of cells, comprising the agents of a complex system. Likewise, in turn, cells can be considered as entities or, instead, as the emergent phenomena of interacting bio-molecules. 

This concept of a laddered hierarchy of complex systems, variously appearing as unitary things on a higher level of scale or as interacting agents on a lower level of scale may be important in many ways.  For example, the rising debate in the United States over whether a "theory of intelligent design" is required to explain the appearance of design unexplained by evolution, could be answered by showing that the appearance of design can be a result of self-organization through the entire range of biological entities, from single cell organisms upward. 

Similarly, extending such hierarchies downward further, through cells, to biomolecules, to interacting atoms, subatomic particles and, ultimately, strings or some other smallest entity, yields descriptions of reality which appear identical to those reached by mystics and contemplatives from diverse traditions.

Exploring these issues would be greatly aided by a display which could give an easy sense to a non-mathematician/scientist/programmer how such hierarchies result in various appearances depending on level of scale, much in the way computer visualizations can move one up and down levels of scale through a fractal display.  Unlike such a fractal display, however, the levels of scale would involve dynamically interacting agents at every level of scale, rather than static images.

Can such a dynamic hierarchy of complex systems be created that would be aesthetically intriguing for a layperson unfamiliar with mathematics?

What sort of computational power would be required to create such a display, as it logarithmically increases in the number of agents to be modeled as one descends through levels of scale?

How many levels could be contained within a single display?

Might such a display be useful as part of educational practices in places where "intelligent design" must now be included as part of a curriculum in American publicly funded schools?