Introduction:

Aristotle (1924) has one of the earliest descriptions of what we now call emergent systems:

things which have several parts and in which the totality is not, as it were, a mere heap, but the whole is something beside the parts.

This is now commonly phrased as the whole is more than the sum of its parts, yet this formulation misses the essence of the original (or, at least, its translation): “something beside the parts”. That is, the whole is qualitatively different from its parts, rather than having a mere quantitative difference. The whole is other than the sum of its parts. Anderson (1972) pithily captures this essence in the title of his solid-state physics paper “More Is Different”. He goes on to say:

the behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each new level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other. (p. 393)

The whole is not a “mere heap”, because its parts have organisation, relationships, form patterns and exist in a context. For a more detailed discussion, see Stepney et al. (2006). Here we explore this view that emergence is the result of a quantitative change becoming a qualitative one in the digital, computational domain. In this domain, what is it that is “more”, and what constitutes a “difference”?

In classical computing, that of abstract Turing machines and von Neumann hardware architectures (such as are mostly realised by everyday PCs, tablets and smartphones), there are essentially only two things we can have more of: space (memory) and time (number of operations).

Computational power, complexity and capability come from these two parameters. First we investigate how space can contribute to emergence, through a range of concepts: the amount of memory and how that memory can be chunked into higher-level concepts, from simple data structures to entire virtual machine layers. Some properties and functionality of the resulting computation can be readily reduced to the underlying structures; others are more truly emergent, in that they are global properties of the entire system. Next, we investigate the effect of time on emergence, through the effect of iteration: repeating the same process over and over from a different starting point at each step. This can give rise to a whole zoo of emergence, linked to communication between components of the overall system.

  @inproceedings(Stepney-ch26-2019,
  author = "Susan Stepney",
  title = "Digital Emergence",
  chapter = 26,
  pages = "329-338",          
  crossref = "Gibb-2019"
)

  @proceedings(Gibb-2019,
  editor = "Sophie Gibb and Robin Findlay Hendry and Tom Lancaster",
  title = "Routledge Handbook of Emergence",
  booktitle = "Routledge Handbook of Emergence",
  publisher = "Routledge",
  year = 2019
)