GEOG 01 San Jose State University Networks Discussion

Nearly everything of significance that has been happening lately seems to be related to the existence of networks in both the natural human worlds. A great many scientific and mathematical insights have been gained about networks in general, and many of these could be used beneficially, if we knew more about them. Unfortunately, most of us are taught very little in a formal sense about networks, unless we take a specialized course on the topic as part of a computer science, math, or engineering curriculum. Even the, there is usually not sufficient exploration of how networks work in the real world. There’s also a great deal of superficial nonsense out there. The Systems Innovation channel, which you watched earlier, provides a set of introductory videos on networks, a few of which you need to watch. We will soon see how relevant this topic will be as we examine pandemics for example or the effects of a coronal mass injection from the Sun on communications networks worldwide. Following are the first two and the last two videos in the Systems Innovation playlist for networks. There are many others in between, and for a more complete picture you can watch them as well.

Watch: Network Paradigm [Systems Innovation]

Watch: Network Theory Overview [Systems Innovation]

Watch: Network Diffusion & Contagion [Systems Innovation]

Watch: Network Robustness & Resilience [Systems Innovation]

The following lecture provides a glimpse into what current network research is like.

Recommended: How Networks Can Change Everything [Computational Social Science ETH]

Topic 2: Deterministic chaos

The last topic of a general nature I think you should keep in mind involves chaotic dynamics. The popular use of the word ‘chaos’ is not what we are talking about, so for many of you an accurate understanding of this topic may require you to differentiate between its popular and formal definition. The science of chaos is actually far more interesting and engaging than our common use of the term would imply.

Watch: Nonlinear Dynamics & Chaos [Systems Innovation]

While this video does a good job of explaining the fundamentals, it seems to imply that deterministic chaos occurs primarily in simple systems. They do not discuss actual chaos in nature or in complex systems or networks. All of these are in fact real, common, and of particular importance for this course.

For example, consider one of the most famous examples: the Lorentz attractor. This is the shape described by the trajectory of a point in three-dimensional ‘space’ of three variables, as described by a set of simple equations. Notice that through much of the trajectory, the path of the point is fairly predictable. Although the pathways never repeat perfectly, they are aligned like the rings of Saturn. But in certain regions, the paths can diverge wildly from nearly the same coordinate, moving in this example between the two distinct lobes (looking conveniently like the wings of a butterfly: just a coincidence). Check out the other attractors that the author programed with the same sorts of qualities. One thing to keep in mind about deterministic chaos: it is often fairly predictably, and it stays within certain bounds (the attractor), but it is also magnificently unpredictable at other points, and certainly unpredictable over the long term. That is fundamentally why weather prediction is limited.

Watch: Are there other Chaotic Attractors? [Orfeas Liossatos]

Homework 3:

  1. What is a paradigm? What are some of the key features of the network paradigm?
  1. Describe at least two examples of diffusion and contagion acting on natural or human-created networks (from the third video above).
  1. What are network robustness and resilience? Describe some of the characteristics or practices that are more likely to result in resilient networks?
  1. Can a system that is fully deterministic, also be chaotic? What does this imply about the limits of prediction?