How fast does the space of possibilities expand? (replicating Tria, et al 2014)

How fast does the space of possibilities expand?  This question is explored in the following paper (free download):

• Tria, F., Loreto, V., Servedio, V. D. P., & Strogatz, S. H. (2014). The dynamics of correlated novelties. Nature Science Preport, 4. (http://dx.doi.org/10.1038/srep05890)

From the abstract:

Novelties are a familiar part of daily life. They are also fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called “expanding the adjacent possible”. The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose a simple mathematical model that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs. The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (Heaps' law) and for the probability distribution on the space explored (Zipf's law), as well as signatures of the process by which one novelty sets the stage for another.

I've written a NetLogo program to replicate their model, available here.  The code for the model is quite simple.  A majority of my code is for a "pretty layout", which is a schematic version of a "top-down view" of the urn.  Here's a video of a single run

Full screen with controls. (click to enlarge)

The charts on the top and center right show the frequency distribution by ball type (a.k.a. "color").  These are log-log plots, so a straight line (declining) is signature of a power law distribution, while a gradually curving (concave) is signature of lognormal or similar distribution with somewhat thinner tail.  Sharply declining curve is signature of a thin tailed distribution such as Gaussian.

So what?

This model will be useful in my dissertation because I need mechanisms to endogenously add novelty -- i.e. expand the possibility space based on the actions of agents in the simulated world, and not simply as external "shocks".

This is essential for modeling cyber security because some people claim that quantitative risk management is impossible in principle because of intelligent adversaries who can generate and exploit novel strategies and capabilities.

Institutional Innovation in Contested Territory: Quantified Cyber Security and Risk

Say you are an entrepreneurial sort of person who wants to really change the world of cyber security. Problem: nobody seems to know where the game-changing innovation is going to come from.  Is it technology?  Is it economics?  Is it law and policy? Is it sociology? Maybe combination, but what? And in what sequence?

If you aim for institutional innovation, then at some point you are going to need to take sides in the great "Quant vs. Non-quant" debate:

• Can cyber security and risk be quantified? 
• If "yes", how can quantitative information be used to realize security to significantly improve outcomes?

Whether you choose Quant or Non-quant, you will need some tools and methods to advance the state of the art.  But how do you know if you are choosing the right tools, and using them well?  (Think about the difference between Numerology and Calculus as they might be applied to physics of motion.)

Whoever makes sufficient progress toward workable solutions will "win", in the sense of getting wide-spread adoption, even if the other is "better" in some objective sense (i.e. "in the long run").

I examine this innovation race in a book chapter (draft). The book will probably come out in 2016.

Abstract:

"The focus of this chapter is on how the thoughts and actions of actors coevolve when they are actively engaged in institutional innovation. Specifically: How do innovators take meaningful action when they are relatively ‘blind’ regarding most feasible or desirable paths of innovation? Our thesis is that innovators use knowledge artifacts – e.g. dictionaries, taxonomies, conceptual frameworks, formal procedures, digital information systems, tools, instruments, etc. – as cognitive and social scaffolding to support iterative refinement and development of partially developed ideas. We will use the case of institutional innovation in cyber security as a way to explore these questions in some detail, including a computational model of innovation."

Your feedback, comments, and questions would be most welcome.

The computational model used is called "Percolation Models of Innovation".  Here is the NetLogo code of the model used in the book chapter.   Below are some figures from the book chapter.

Innovation as percolation. Progress moves from bottom to top. Each column is a "technology",
and neighboring columns are closely related.  This version (S&V 2005) only models
rate of progress and distribution of "sizes", not anything about the technology or
trajectory of innovation.

A screen shot of the user interface.  Three different models can be selected (upper left).

Dissertation proposal: "Shaping Possibility Space"

At long last, I have submitted my dissertation proposal:

• "Shaping Possibility Space: Coevolution of Thinking and Doing In Organizational and Institutional Innovation"

Fair warning: it is long -- 72 pages not including Glossary and Bibliography.  Being academic work, it will not be 'light reading' for many readers.  I have done my best to be clear and direct, but the subject matter is complicated.

Spoiler alert: I don't propose to solve the Cyber Security Problem(tm) in my research.  Instead, I'm studying the process of innovation that might, eventually, lead to new solutions, especially institutional innovations.  Some readers might find this boring, irrelevant, or 'ivory tower'.

Feedback is most welcome.  If you don't have my email address, ping me on Twitter.

The defense meeting is in mid-October.

Lecture: Exploring Possibility Space of Ideological Change

Here's a nice academic lecture at University of Waterloo Institute for Complexity and Innovation (WICI) by Matto Mildenburger, PhD Candidate at the School of Forestry and Environmental Studies, Yale University.


Exploring the Possibility Space of Ideological Change from Waterloo Institute for Complexit on Vimeo.

His use of the term "possibility space" is similar to my view, meaning a space of possible states of a system along with dimensions or topological relations that give shape to the space.  At 27:04 he discusses the nature of dimensions and their validity in studying the space of ideologies.  At 1:02:19 he answers a question about process of change in ideologies and how change is interpreted spatially.