Encefalus

First of all, I’m sorry for not having written for so long, but I am really busy. Anyway, this time was not wasted, since I have passed a large part of my free time dealing with new ideas.

These ideas revolve around computation and a possible formal framework of methodology in social sciences.

In this article I want to discuss some thoughts that came to me after reading A New Kind of Science.

In this book, what Wolfram is essentialy proposing, is that simple programs like cellular automata can be the answer to all our prayers He believes that they could replace mathematics, or work alongside with them.

This is an interesting approach (even though its claims have been criticised as overly too extravagant) . What I want to discuss here is if this could be possible in social sciences.

Stephen Wolfram

The main idea behind A New Kind of Science is what is called the Principle of Computational Equivalence. This means that all systems that are not obviously simple (therefore hold some complexity), have been produced by a set of rules that are simple.The additional complexity is due to the additional computation that has taken place, not to more complex rules. More complex rules, as Wolfram says, as he presents many examples (but no formal proof), do not lead to greater complexity.

This means for example, that the evolutionary process that has given birth to millions of species is not governed by zillions of factors as one might have imagined, but rather, by a simple set of rules that have been simply interacting with the environment.

Furthermore, Wolfram, through the study of complex systems with simple rules, is lead to some more conclusions. For example, the reverse engineering (reducibility) of complex systems belongs to the NP-complete class of problems, which means is practically impossible. This means that one might have thought that we can just create an algorithm to analyze a system and discover its rules, Wolfram says that this is higly improbable.

Rule 110 one dimensional cellular automaton belongs to Class 4 rules (complex ones)

According to Wolfram, most systems in nature are complex and irreducible, but we haven’t realized it until now, because mathematics have been used only in occasions where we knew they would be successful beforehand. According to Wolfram, even systems in mathematics belong to this classification.

For example, the solutions of polynomial equations of higher degrees in algebra are complex systems, according to Wolfram, and therefore there can never be a solution for them. The only thing we can do, is to run the program and witness its evolution.

The Principle of Computational Equivalence creates more problems than solves. And this, because, it poses strict limits on what we can learn and what we cannot. However, on the other hand, Wolfram, through the study of simple rules and complex systems, tries to create a new kind of research. While, like we said above, complex systems are irreducible, Wolfram proposes that we should do pure NKS (New Kind of Science). That is, to study computational programs as they are, without any direct reference to something, pretty much like we study mathematical equations and functions, without any direct reference to a system.

The book leaves many questions unanswered, since Wolfram doesn’t clearly explain how this would exactly help us to create better models of reality. So, let’s be a little more specific in this article, by providing some thoughts on this framework.

Let’s take the case of agent based models. It is obvious that these are computation models. However, all agent based models are based on parameters that can become even more complex as the models advance. What if, as Wolfram proposes, these systems are governed only by a set of simple rules and the interaction with the environment. These rules, if Wolfram is right, will be simple than the zillions of rules computer scientists tend to use in complex simulations.

Agent based modelling

This would essentialy mean that we could create a new kind of social science, where we are not based on any human notion, but rather on simple rules. Additionaly, what Wolfram proposes, these rules could be abstract representations, like mathematics. A function can be used in econometry, but it can also be used in physics. If programs, like the ones Wolfram proposes, are indeed ubiquitous, then we could use them to analyse, and predict, social procedures, without caring about specific notions.

So thing for example, of an artifical community, where it advances via simple cellular automaton rules on a grid that represents a certain geographical region. If what Wolfram proposes is correct, maybe we could create a simulation of the core of evolution of this society, just based on a few simple rules.

I don’t know if this idea holds any truth, but it is certainly interesting. It actually proposes that we can formalize the study of social systems with computational programs that hold no inherent meaning. If this is true, then it could mean a revolution in social sciences, which, probably, hold the greatest envy towards physics, than any other sciences, because of the complete lack of any formal framework of research or methodology.

However, what really concerns me is the degree of accuracy between abstract computational models and real life. So, for example, while simple rules can generate complexity, we can’t be sure if a certain set of rules is enough to create some specific kind of complexity.

When modelling car traffic for example, we don’t simply care about finding a bunch of simple rules that create complex behavior, but, rather, we want to find rules that create complex behavior that is like the one we observe in real life traffic.

It is actually a question between general complexity and specific complexity. If general complexity is just the fact of a system being complex, specific complexity represents the fact that this system can provide an abstract, but accurate representation, of a specific process.

Let’s consider, for example, every system as a computational one, just like Wolfram proposes. We can think that are brains are performing computations or the weather performing computations, as they represent systems that interact with their environment based on a certain set of rules.

Then, we can say that the system of car traffic holds general complexity and is specifically complex to the system of car traffic. This means that it represents itself and is tautologous, pretty much like proofs in logic and mathematics.

However, rule 184 has often been used to represent traffic. It is generally complex, but it is not specifically complex to any specific traffic of any specific city.

Therefore, the question of whether we can implement A New Kind of Science in social sciences, is how specific our generally complex models can be.

Further Reading:

A New Kind of Science Online

What is a cellular automaton: http://mathworld.wolfram.com/CellularAutomaton.html

The NKS Blog: http://thenksblog.wordpress.com/

This entry was posted on Tuesday, March 10th, 2009 at 5:38 pm and is filed under Computation, Philosophical. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.