The ultimate aim of scientific research is to understand the natural world. In order to achieve this goal, Western science has relied on different cognitive strategies, including simplification, both in terms of analysis and explanation. As the British natural philosopher Sir Isaac Newton (1643–1727) put it, “Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things.” In a way, examples of simplification include using idealized models, such as a ‘perfect sphere rolling down a smooth plane in a vacuum’; conducting experiments in a strictly controlled environment such as the laboratory; analysing complex systems by reducing them to their individual parts; and generally by using a linear and deterministic concept of how the world, including life, works.
The emergence of a new simplicity
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.
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.
One function of simulation is as configurations generator. By generating configurations this way we are not just getting configurations. We are also getting information about the process to get the configurations. Correlating the configurations from the simulations to the configurations in real world, we then use the knowledge about the process obtained from the simulation to explain the process in real world.
The aim of a research is basically to find an explanation. For all practical purpose, that simply means searching for a new idea. So, how does one go about finding a new idea? Just by thinking about it, and write it down? That’s part of it. But it is much more than that. New ideas often emerges from the already existing ideas. As such, reading and reviewing what other people have done is an important part of the research. Also, how do you know that your ideas are new without knowing the already existing ideas?