p.2 We tend to get very attached to our models, and think that they are the only right way to describe
the real world. We easily forget that we are dealing only with simplifications that are never perfect
p.3 Note that the models we build are defined by the purposes that they serve... The best model,
indeed, should strike a balance between realism and simplicity... The model is made simple, but no simpler than we
need.
p.5 When dealing with something complex, we tend to study it step by step, looking at parts of the whole
and ignoring some details to get the bigger picture... models are essential to understand the world around
us. If we understand how something works, it becomes easier to predict its behavior under
changing conditions... Models can be used to find the most sensitive components of the real-life system
p.6 The model can represent only a certain part of the system that is studied. The art of building
a useful model consists mainly of the choice of the right level of simplification in order to match the goals of the study.
p.8 We may look at a system as a whole and focus on the behavior of elements in their interconnectivity
within the system. This approach is called holism. In this case it is the behavior of the whole that is important,
and this behavior is to be studied within the framework of the whole system - not the elements that make it. On the contrary,
reductionism is the theory that assumes that we can understand system behavior by studying the elements and their interaction.
p.9 the relationships between elements are essential to describe a system.
p.12 The elements of a system and their interactions define the system structure. The more
elements we distinguish in a system and the more interactions between them we present, the more complex is the system structure.
p.17-18 What are the elements and processes in our system? ...Which are the limiting ones, where
are the gaps in our knowledge? What are the interactions between the elements? ...By answering the basic questions about space,
time and structure, we describe the conceptual model of the system... Building the right conceptual model leads us
halfway to success.
p.20 Creating a conceptual model... very much resembles that of perception, which is individual to every
person.
p.25 In more recent years, people have really started to appreciate the importance of the systems
approach and systems analysis. We are now talking about a whole new mindset and worldview based on this understanding
of systems and the interconnectedness between components and processes. With systems we can look at connections between
elements, at new properties that emerge from these connections and feedbacks, and at the relationships between the whole and
the part. This worldview is referred to as "systems thinking".
p.29,30 There is really a lot of art in building a good model... It is the model-building process itself
that is most valuable for a better understanding of a system, for exploring the interactions between system components, and
for identifying the possible effects of various forcing functions upon the system... In most cases, the modeling process
starts with a conceptual model. A conceptual model is a qualitative description of the system, and a good conceptual model
is half the modeling effort. To create a conceptual model, we need to study the system and collect as much
information as possible both about the system itself and about similar systems studied elsewhere. When creating a conceptual
model, we start with the goal of the study and then try to explain the system that we have in terms that would match the goal...
we decide what temporal, spatial and structural resolutions and ranges are needed for our study to reach the goal.
p.42 the goal of any modeling exercise is to simplify the system, to seek the most important drivers
and processes. If the model becomes too complex to grasp and to study, its utility drops. There is little advantage
in substituting one complex system that we do not understand with another complex system that we also do not understand.
p.48 Conceptual diagrams are powerful modeling tools that help design models and communicate them to stakeholders...
In most cases, building a conceptual diagram is the first and very important step in the modeling process.
p.48 "A maxim for the mathematical modeler: start simply and use to the fullest resources of theory."
Berlinsky
p.48 the goal of any modeling exercise is to simplify the system and to seek the most important
drivers and processes... It is better to start with a simplified version, even if you know it is
unrealistic, and then add components to it. It helps a lot when you have a model that always runs and the performance of which
you understand... Complex models are hard to handle, they tend to go out of control
p.49 The more you know about the system, the better the model. However, that does not mean
that all the available data and information from previous or similar studies have to end up as part of the model.
p.108 Let us consider some of the main types of equations and formulas that you can encounter in dynamic
models (Figure 3.9). If you have a good feel for how they work, you can put together quite sophisticated models using these
simple formalizations as building blocks.
p.114 Sensitivity analysis explores the parameter space and can help us identify
some of the critical parameter values
p.135 modeling should always be iterative. All the time during the modeling process we
need to check our balances. Is the level of complexity justified? Are we maintaining control over the model, or is
it becoming too complex in itself to be useful? Does the model complexity match the goals of the study? Do
we really need all that?
p.135 Rykiel (1996) defines model credibility as "a sufficient degree of belief in the validity of a model
to justify its use for research and decision-making."... there is no use talking about some overall universal model validity;
the model is valid only with respect to the goals that it is pursuing, and only the users of the
model can define whether it suits their needs or not.
p.335 The better the model you build, the more reasonable behavior you will find in it.
p.342 Generally, when mathematicians end up with a problem that they cannot solve they start simplifying
it by making certain additional assumptions about the system.
p.355-356 The gist of modeling is to simplify the reality to improve the understanding of real-world
processes. But we do it for a purpose: we want to find solutions for the real world problems and to make better decisions
to improve life and avoid disaster. Otherwise, why bother modeling?
p.362 models do not tell us the "truth" about the system. They should be rather
viewed as a process of striving towards the truth. The best model is a process in which we learn about the system
and understand how best to manipulate and manage it... We can succeed only if the model is viewed as a process that
is designed to accommodate these changes and adapt to them. A good model should evolve with the system; it should
be able to change both quantitatively and qualitatively as the system changes and as our understanding about the system improves.
p.363-364 as you go through all the essential steps of model building you get a really good understanding
of all the processes and interactions involved and develop a certain intimacy with the system, learning what is more
important and what can be approximated, getting a handle on the inputs and understanding how they may affect the outputs.
You also learn to appreciate the uncertainties embedded in the system, and realize that even with these uncertainties
there is certain level of confidence, or a comfort zone, that may be large enough to make a decision.
p.401 Our ignorance is not so vast as our failure to use what we know. - M. King Hubbert
p.406 Models are an important part of... understanding. They are building blocks of our worldview...
for models to be good they need to be based on a culture of modeling - on good modeling practice... The modeling process can
work as our shared fact-finding and understanding experience that leads us toward a shared vision of the past, present and
future.
