p.ix Have you ever built a model? ...You would not be able to think
if you were incapable of building models. What you might not have done yet is build a model explicitly so
that other people can understand it and perhaps use it... An explicit model is a laboratory for the imagination. You
can tweak a model to see how it responds... You can explore its strengths and limitations. You can even guardedly
make predictions and then argue how good (or poor) those predictions might be.
p.x We have written this book to demonstrate that there indeed is a subject called "modeling" which can
be learned and needs to be learned. We believe that it is an important subject, not only because models are becoming so pervasive,
but also because the skills of modeling are so closely related to the more general skills of problem solving. Learning
to model is bound up with learning to solve problems and to think imaginatively and purposefully.
p.1 modeling is an integral part of problem solving in any discipline.
p.19 Whenever you build a model you have to be selective. You have
to identify those aspects of the real world that are relevant and ignore the rest. You have to create a stripped-down
model world which enables you to focus, single-mindedly, on the problems you are trying to solve.
p.21 The point we want to make is that thinking consciously and explicitly about
models is a crucial part of problem solving in general.
p.28 Struggling is a precursor of learning and being temporarily perplexed is a natural phase in problem
solving.
p.45-46 As we have seen, searching for simplified versions of the problem,
or for upper and lower bounds, can also lead to the solution, albeit in two stages. The first stage is to find a simple model
or a bound. The second stage is to ask how we can refine that model or bound... Powerful heuristics generate
useful ways of thinking... We solve problems by thinking. It seems as though people need stimuli to provoke
thought or to make their cognitive leaps. [problem solving] Heuristics are powerful stimuli... Asking how we recognize
that a heuristic is pointing in a useful direction or how we know that we are using heuristics intelligently are both much
more difficult questions. There are no easy answers and there are certainly no short answers. If we could answer these questions
in a paragraph or two, there would be no need for this book.
p.60 [equation for modeling the temperature of a warm beer cooling in a refrigerator]
T n+1 = Tn - K dt (Tn - F)
p.152 If you think you know what you are doing, ask yourself a question
or set yourself a task to convince yourself that you know what you are doing!
p.160-164 What information do we have? ...What assumptions can we make?
...What, in particular, would we like to know? ...We do not know the answers to these questions, but can we make any
reasonable assumptions? ...Is there a simpler version of the problem that we could think about?
...Have we thought how the element of chance affects our problem? ...How can we express the likely outcome of
following one strategy rather than the other? ...What kind of model could we build? How would we use it?
