Fascinating Look at the Mathematics Behind Cities versus Corporations

This is a TED talk I personally am fascinated by, which looks at the math behind cities and corporations. The idea is to see if, through data, there is a theory or math model one can use to predict what will happen to a city and/or corporation. Geoffrey West, a physicist who works on network theory and complex systems, and his colleagues have done this, to see what the behaviors are of human-built entities such as cities and corporations, and how they compare to living systems. There are clear trends, which is a characteristic of a network, and he shows these trends clearly and convincingly. Check it out!

Spread of Epidemics

Thanks to Matthew:

A Talk on One Way to Look at Complex Networks

Thanks to Anja:

Often when I am faced with a difficult problem, I find the best way to go about approaching it is to break down the complexity of it by highlighting each simple aspect. This is a really interesting video because it explains how the mind can make sense of complicated pieces of information. The best way to simplify something that appears harder than it is would be to start with what you already know. This video does a great job of explaining and applying this method.

Some Advice - To Embrace Complex Networks to Find Simple Solutions

Scientist Eric Berlow shows a few examples of how one can think about complex systems and networks in order to find simpler structures and solutions. In networks where there are hubs (i.e. agents of the network which have many connections compared to most agents), one can look and focus on the first few orders of connectivity to begin looking at the key components and eliminate 'noise.' Rather than be freaked by a complex problem, step back and look at the overall picture to pick out the key pieces of the problem. Sound familiar? This is the approach we take for something like those systems with tension. We only look at the forces that may affect the motion and don't worry about the others. So we continuously try to simplify the complexity into simpler pieces. Or in circuit analysis, we isolate smaller networks of resistors, and simplify those to single resistors, until a complex circuit is redrawn as a series circuit. This is the idea Berlow is promoting. Check it out, and let me know what you think!

Do keep in mind, though, that this is not foolproof. Some times this approach makes a problem more manageable and it can lead to some sort of solution, or at least some sort of approximation, but other problems have so many intricacies that this approach leads to nowhere. It is a strategy you may try to see where it takes you.