Monthly Archives: August 2016


Why do we need a model? And how do we create and use it?

A model is not the same as the reality that it represents. Particles on two dimensional lattice obviously are totally different from a group of people. But, then, the model has been proven to be quite useful. How can that be? A group of people is much more complex than a group of particles.

People are using equations (often called “models”) to explain collective behaviors in a complex system without taking into account the underlying mechanisms that generate the collective behavior. While the equations are quite useful and powerful they may fail to explain the microscopical mechanisms behind them.

The collective behavior are changing from time to time. The equations that work for some collective behaviors may not work for some other collective behaviors. If a collective behavior persists for a significant period of time, the equations that describe the collective behavior will be very useful to predict the future behavior of the system. However, the equations themselves do not predict the change in collective behavior that have to be explained by different equations. The situation can get worse when the collective behavior has a stochastic element in it.

In this study we propose a method to connect the microscopic dynamics of a system with its collective behavior. While the reality is much more complex than the model system that we use, our model is useful to high-light the dominant microscopical features that would lead to the collective behavior. The purpose of the simulation is, therefore, to explain the collective behavior in term of its underlying microscopic behavior. We employ a simple lattice-gas model where it is simple enough to measure the collective behavior on one hand and to describe the microscopical behavior on other hands, and to make a direct connection between the two.

Lattice-gas model has been used extensively in statistical physics, surface physics, and electrochemistry. Here we propose to apply it to complex economical systems.

In this is study we examine the dynamics of distributions of particles ad-sorbed on a surface. The dynamics of particle distributions can be viewed as the change of configurations with time. The configurations are created by adsorption, desorption, or diffusion. This kind of study is not only important for surface-science studies, but it is also very useful in the study of complex system in general. The average properties of the lattice-gas surface as a function of time are used to model the collective behavior of complex economical systems. We measure the average properties such as coverage and correlation length to represent the collective behavior. The microscopic configurations are representated by snapshots that includes the histogram of size distributions and configuration snapshots, coupled with diversity measurements.

In our modeling of an economic system, a particle is a representative of an agent. When a particle occupies a site, it is basically representing a contribution to economic growth. When a particle leave a site, it is representing a contribution to economic shrinkage. The total growth is proportional to the change of coverage, and the rate would depend on whether the particles are interacting with each other or not. And if they are interacting with each other, how exactly the interactions manifest themselves. The interaction (or non-interaction) creates the dynamics of surface morphology, which later can be shown by diversity and size distribution dynamics. By measuring this morphological dynamics and correlates it with the average properties of the system as a function of time, we effectively connect the microscopical dynamics to the collective behavior.

In the simplest approach, the particles are not mutually interacting. The only limitation is that each lattice site can be occupied by at most one particle at a time. In this case, the way to adsorb, desorp, or diffuse particles on the surface is through random adsorption, desorption, or diffusion. Any application of additional rules for the particle distribution requires interactions.

In a complex economical system, the interaction between the agents are very important. The difference between classical and modern economical model is basically the difference between incorporating or not-incorporating this interaction. In our lattice-gas model, particles are being adsorbed or desorbed with a certain probability. The interactions, therefore, are manifested through these probabilities.

In conclusion, the model is indeed different from reality. But SOME important behavior of the real system have the same manifestation as that of the model. This manifestations in the model can be explained well thus explaining the corresponding phenomena in the real system.


What is Econophysics?

How do we define a subject? Traditionally (as written in Wikipedia for instance) a subject matter is defined according to its objects. Traditionally, physics is defined according to its objects which are “matter and energy” (for example). That also applies to other subject as well. The objects of biology is living beings, and the object of psychology is psyche, and so on and so forth.

However, the objects of Econophysics are economic systems which are not subsets of matter and energy, yet we still call it “physics”. The same is true for biological physics or mathematical sociology, for examples. These are examples where the subjects are not defined according to their object, but rather according to their methods.

Now let me stop you for a minute and let us think about the meaning of physics. Is it true that “physics” can be totally defined by its method, and not by its material objects? Let’s look at a specific examples. Suppose we are going to model an economic system using a lattice-gas model. The model itself works on physical objects (“particles”) which are doing their things on “a lattice” (which is also a physical object). We call it “gas” because the particles are able to move and interact as a gas. We call it “lattice” because the setting is a lattice where each cell an only be occupied by a single particle. Now, this system could represent an economic system because the collective behavior of an economic system can be represented by mathematical models which can be generated by the collective behavior of a lattice-gas model.

Here you may disagree with the necessity of using physics to model an economic systems. If the goal is to obtain a set of mathematical equations that are able to model the behavior of an economic systems, then we don’t need physics for that. This opinion arises, I think, when all that we are looking for is a set of equations that may represent the collective behavior of a system. If that is all there is to it, then ALL problems in economics are basically a combination between economics behavioral science and mathematics. Economics behavior science build a theory that explain the economics human behavior in qualitative manner, while mathematics build a set of mathematical equations that will connect that to empirical data hence completing the whole thing by making it quantitative. Don’t forget also the statistical tools to test whether the mathematical models can explain the data in a significant way. Again, no physics is needed.

In my opinion, physics is not really needed when what you are trying to get is a set of empirical equations. As long as you have the empirical data and a qualitative theory in your hand, all you need is a good mathematical procedure to complete the circle.

Physics is needed when you are having troubles building qualitative theories that can be quantified immediately in response to all possible empirical facts that we are having at that moment. In the past, this need has not been arisen since – apparently – the economics systems are evidently quite simple. The economics behavior during those simple days are quite obvious and can easily be explained by some simple qualitative concepts, which in turn can easily be quantified by some simple mathematical operations to be correlated to the empirical data. Because, obviously, the empirical data itself is quite simple. As the systems themselves are getting more and more complex, we need a new method to explain the reality, qualitatively as well as quantitatively. Here, physics is a method by which we build a qualitative theory which can be quantified and used to explain the empirical data.

Some people say that physics can be used for any economical situation, simple or complex. That may be true. But is it really necessary? If the standard economics is able to do the job, why would we need physics for that? Physics, I think, is needed when all other attempts are failed.

The behavior of complex systems is one example where physics can be quite useful. The simulations using a lattice-gas model directly explained -quantitatively- how the interactions between economic agent generates many different collective behaviors. If the only thing that the simulation is capable of doing is to produce some collective behavior that can be quantified, then it won’t be quite useful. Its ability to show HOW those collective behaviors emerge which can be verified quantitatively is what makes it useful.


How to do a research.

In my opinion, research is a process to find explanations. Some people believe that the purpose of research is the ability to predict. I think the ability to predict is only one evidence among many that the explanations are correct. The ability to predict is certainly a useful thing. But it is not the final goal of a research. An intermediate goal perhaps, but not the final goal.

Now what do I mean when I say “explanation”? Some people would say that as long as you have some equations that describe the empirical data quite well (plus it has the ability to predict) then you already achieved your goal. Well, I do agree with the notion that a set of equations which can explain the empirical data quite well is very important. But having that set of equations is NOT enough.

How about qualitative explanations? Here, I also agree that having a set of qualitative explanations is very important. But again, it is NOT enough. The final goal – I think – is to have a complete integrated explanations which contain a set of deep explanations as well as how to validate them, and the results of the validation.

I have proposed a phrase “deep explanations” as opposed to “explanations”. Also I proposed that this deep explanations must be accompanied by a method to validate them, AND the results of the validation which is a proof that the explanations are correct.

In effect, I have maintained that the purpose of a research is to obtained a correct deep explanations. Not just an explanation, but it has to be a deep explanation. And not just a deep explanation, but it has to be a correct deep explanation. That is why you have to accompany your explanations with a method to validate them, and the results of the validations that would prove that the explanations are correct.

I know that people have said that the purpose of a research is to answer a question. But what kind of question? Not just any question. First of all, it has to be an important question. Secondly, it has to be a question that asked about the explanation of some significant and important phenomena. Thirdly, it has to be a question that has a certain depth in it. And last, but not least, it has to be a question that requires the proof on the answer. In other words, any answer without the proof is not acceptable. Or to put it in other way, a question that doesn’t require proof alongside the answer is not a good research question.

I have seen many researches that simply ask whether there is a correlation between one phenomena to the other. I think these are legitimate researches. Finding a correlation is a good thing to do as long as it can be transformed into explanations (and of course they have to be accompanied by a method to validate them and the results of the validation). The problem is, we have to ask if the correlation that we find would bring us to deep enough explanations or is it only lead to the surface of the phenomena.

The depth of the question, therefore, is an important problem. There is a “minimum depth” of a research in order to be acceptable as a legitimate enough research. But of course, we can go deeper. This suggest layers of explanations. The deepest explanation would be an explanation about the most fundamental of things.

At this point, I have to stress that deeper researches are not always more complex. Often the deepest questions can be answered by the simplest of ideas. However, the simplest idea often require a genius to find it. In other words, the more complex may not be more difficult, and the simpler idea may actually be more difficult to find. Of course, there are instances where complexities are tantamount to difficulties. Here I just want to say that complexities are not identical with difficulties.

The “not so deep” researches are usually more technically challenging, while deeper researches are usually more philosophically challenging. The “not so deep” researches have to deal with technical complexities while the deeper researches have to deal with ideas.

At this point, I have to repeat that all explanations no matter how deep, have to be validated. Just because you are thinking at the deepest level, that doesn’t mean that you don’t have to prove it. Without proof nothing is matter.