Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Sunday, July 6, 2014

Some notes on network and hierarchy in complex systems

Well, now, this is an interesting point of view.

But it is a false dichotomy. It is like titling an article "Men vs women--which will win?" when in fact life goes better when both are present.

I offer a little perspective from the natural world. Networks and hierarchies are both present in complex natural systems. In fact, the two appear to be inseparable. There is presently considerable debate as to what exactly the role of each is in complex systems which are both robust and adaptable.

Natural complex systems show a complex hierarchical structure, which can be partially extracted using some of the techniques described on this blog here and here, and presented here and here. The technique represents an extension of the method of reconstructing state spaces from observations of a single variable--the more recent work (including much in progress) suggests that a hierarchy of processes from large-scale tectonic evolution to shorter sea-level variations to shorter-still climatic cycles driven by variations in the earth orbital parameters can be extracted from a 20 million-year long "record" of atmospheric CO2 (reconstructed from isotopic records from sediments).

The figures below show multiple regions of stability for atmospheric CO2 at different points in time (ka means thousands of years ago). Although the amount of global CO2 has varied widely over the last 20 Ma, there is always stability in the system, which is due to the network architecture of global climate (whether we would be happy at radically different levels of atmospheric CO2 has not been established).

We are able to indirectly perceive the hierarchical structure of the earth system, but cannot deduce the detailed structure of the hierarchical levels. To interpret these we look at what we do understand about the earth system. It appears that each level in the hierarchy is composed of interlocking networks. The network architecture is largely responsible for the stability of the system, by way of interacting feedbacks, both positive and negative.

Although this aspect of the science is young, there is much to suggest that the hierarchical structure is responsible for the interesting behaviour of complex systems. Hofstadter argued that improperly nested hierarchical structure may lead to evolution in the behaviour of complex systems (his argument related to the origination of conscious thought within natural and artifical brains).

The hierarchical structure lends itself to adaptibility--although the networking is a necessary part of this. High-level hierarchical changes lead to stunning reorganizations of complex systems--which the network architecture allows to happen without the system dissolving into chaos.

An unfettered economic system will naturally develop both networks and hierarchy--both of which are key to its healthy operations. Think of what Ford Motor Co. was like 60 years ago--or what Google was like (before we knew it was telling everything it knew about us to the bad guys).

The conflict today is not hierarchy vs. networks--the conflict is between an artificial hierarchy that has been superimposed on the economy by agents with political power--which is siphoning wealth and power from the system--and the natural hierarchical agents that have arisen through natural organizing processes.


  1. Black or white, them or us, one or the other - these are much easier to communicate than complex reality. ZH deals only in the simplistic.

    I would argue that the artificial hierarchy imposed by political power is just part of human nature, and the response will be a "stunning reorganization", lets just hope there is a sufficient network in existence to stop "the system dissolving into chaos"

    1. I agree with you about the reorganization. As a cautionary note, I would add that we are unable to project what the results of such a reorganization will be.