Modeling Ecosystems

Full Title

Modeling of a system that is under constant change creates challenges that not not well understood.

Introduction

Call it Induction, Correlation, Simulation or Modeling, the basic rule is to start with a system at Equilibrium or Homeostasis so that the math is not too difficult. But real systems are never at Equilibrium, those are all figments of the physicist's imagination. If a system is at Equilibrium, it is not able to change, and so is of limited interest to anybody. Even when an Equilibrium can be achieved in a laboratory, the question is still present. What exactly are we comparing reality to? Or, in other words, are we discussing auto-correlation or cross-correlation? Is the system self-similar or a model of other other physical variable that might be nothing like. For example physicists equate black-holes with information theory or gas particles. But philosophers think the physicists might be all wrong about that. Even philosophers can't egree with the Platonists telling us that the ideal form comes first and the reality is just a poor copy of the ideal and the empiricists telling us that first we build a chair and then we create an abstract idea of "chair". But in reality the chair is nothing by an anthropomorphic attempt to minimize energy consumption so a human, who is just the creation of random acts of evolution, can put their attention to some details of a social system that is itself an accidental organization of thousands of years of human attempts to avoid killing each other. Not only the the chair a complete accident, but so is the human a complete accident of evolution.

Dynamic Systems

Without induction, the human species, or any other mammalian species, would not have survived long enough to procreate. They need induction to understand where to find food, and how to avoid becoming food. The philosophical argument about whether induction can lead to truth pales in comparison to where we would be without it. So too with the discussion about mathematical models of reality. Reality exists without the models. The models do not exist without reality.

All Models are Wrong

The professor of statistics George Box noted that "All models are wrong; but some models are useful." In physics there as been sufficient modeling since Newton to narrow the discrepancy of reality and the model to a very small percentage. But that does not imply that they are correct, just useful. Box also noted:

Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so over-elaboration and over-parameterization is often the mark of mediocrity.

Artificial Intelligence (AI) has been an experimental science only since 1960 and so has not produced models of intelligence that are particularly close to the real thing. Brian Christian described "the Alignment Problem" as the difficulty that AI has with aligning the results of providing an AI with the results obtained. It is worse than you might imagine. When Machine Learning is introduced into society before it has been fully vetted, we must expect that the results will not align with human values. By 2016 the US already had an AI deployed for predicting the future of criminals what was blatantly racist But since the AI was trained on real-word data, it was just doing the same thing any any human would do given the same inputs since society as a whole was also racist. The point here is that both the racist profiler and the physics standard model are doing the same thing. it just that one system is more regular than the other.

Scaling

Some abstract models, like fractals, work well at all scales. But when we are looking for verisimilitude in the models of individuals, like leaves, or hair, they become unimaginable computationally expensive. Tim Sweeney of Epic Games put it this way:

When you're standing on a mountaintop, looking out into the distance you're seeing the effect of trillions of leaves of trees. In the aggregate they don't behave as ordinary solid objects. At a certain distance, trees become sort of transparent. When you look at the real world and see all the areas where computer graphics are falling short of the real world, you tend to realize we have a lot of work yet do do."

See the wiki page on Phase Transitions for how aggregates can model, for example, the flight of starlings.