In the book "Applications of Mathematics in Models, Artificial Neural Networks and Arts (Mathematics and Society)" theres a simple model applying quantum thermodynamics to the phenomena of culture. It tries to explain culture tends to homogeneity in some cases and heterogeneity in others based on simple rules that each individual follows. The concept of identity is introduce as a list of binary categories (like or dislike), the identity of each individual is transformed as it interacts with the rest through the thermodynamic equation. The conceptual framework is that of social psychology (imitation). In the end this model follows the same rules as a Hopfield neural network, therefore, stating that culture is capable of remembering its pattern(s), explaining why there is a certain order.
This model, however, is very simple and I plan to extended it through agent-based simulation. If there is anybody interested, let me know.
Its fair to worry Rossella, reductionism is a constant fear in science. However, your reference to determinism and reductionism when talking about these models seem to suggest that you are not familiar with theories of complexity. I'll try to answer the best I can in this short space. This was more like an invitation for those doing similar research, but then again, I thank you for taking your time to read it.
1. The fact that a model includes math and logic doesn't make it "reductionist"; reductionism depends on how you give the explanation of the phenomena: you reduce the explanation to the behavior of the systems individual components or you admit that its an emergent phenomena. Many social theory are infact quite reductionist in their form of explanation. In this model culture is seen as emergent.
2. Identity is taken a "collection" (vector) of categories. Since each category could be any discrete concept and you can have as many categories as you wish, it doesn't limit the possibilities of identity into close concept such as sexual or gender identity. Sexual identity for example could be represented using a 2 dimensional vector (S = [M F]), where you state the individuals attraction (like or dislike) for each sex. If you wish to represent the fact that a person might like both but tend more to one, you could use a fuzzy set.
3. What you say about the effect of age on the transformation of identity is true. It could be modeled by introducing a change in plasticity, in terms of resistance to change or deformation, and making that resistance variable with time. The model already takes the rate of change into account, this would just mean making it variable. However, since that is not my main concern I don't wish to introduce it into my model, simplicity is best for a start.
4. Identity is also seen as a structure, meaning there are relations between categories. This structure could have "incoherences", for example liking two categories that oppose. It could even represent a double moral or a split personality depending how you model the interactions between categories; a double moral should not be to complicated to simulate given some social conditions.
Ohhh, I by sexual identity I meant "how much attraction do you feel for each sex?". In this kind of models gender wouldn't be a category, it would be a structure of categories, (mostly dealing with visual appearance, attitudes, conducts) that are relate to a gender category (masculine, feminine, androgen...), so its in fact quite complicated.
I think I made a little mistake in explaining reductionism, I said that its when "you reduce the explanation to the behavior of the systems individual components", but in fact it is "that the explanation of the system is reduce to the explanation of an individual, even isolated, component. Lets say that you found a way to predict exactly how an individual takes a decision by itself, a reductionist approach would be to extrapolate that result and try to predict how a group of 100 people together would take a decision, as if it were a huge "single person". The best example is a school of fish, when each fish is studied isolated, biologist find out that it follows certain rules, but the school of fish doesn't behave like "a big fish", each fish follows simple rules that have to do with the direction and position of the fish in its visual field, the result is an emergent phenomena: the school of fish's behavior.
Every theory is a reduction of reality, the more you reduce the more precision you can obtain but it become less realist, but if you are to realist you might not be able to understand the phenomena you are observing. So its about trying to get the best in between possible. Math and logic are just languages, but the models they form are logically consistent, meaning that they will respond accordingly to any condition that you insert, avoiding the voids that verbal models can produce, so that is why I prefer them. But any language could just be as valuable.
Again, thanks for the feedback.
Cristian, Did you ever follow-up and try to build this model? I'm curious how it turned out or if your idea produced a paper.
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