We'd like to push things towards considering the role of models
in building knowledge. From the encyclopedia entry, it is clear that
there is an enormous range of different kinds of models. Are these
distinctions subtle and important, or an irrelevance for what we
typically do? As ever, read, digest, and cogitate. Email cogitations to
us please by Tuesday evening.
Levins, strategy of model building in Population biology (pdf)
Stanford encyclopedia on models, Frigg et al., 2006 (as for last week) (pdf)
Polya - how to solve it, 1944 (selections) (pdf)
If you have the time read all of the Polya excerpts, it is a lovely
book. The problem-solving dialogue between a teacher and a student is a
gem If not enought time, focus on:
1. the problem solving check list (p. xvii)
2. part II. How to solve it - a diaglogue (p. 33)
3. the entries on practial problems (p.149), progress and achievement,
(p157), signs of progress, (p178)
David's notes from last class:
- Maybe we should identify what we value in science – what
motivates us? . The truth? The search for the truth?
- Can truth only be defined in simpler systems (or subsystems of
complex systems)? If for the latter, then you can’t really know there
is an absolute, or whether you are close to it, or whether you have
just moved further away from it.
- If you come up with a theory that predicts something suprising
that is later confirmed, shouldn’t that be closer to the truth? If a
theory is of a lower dimension compared with the scale of the problems
is describeds/informs/solves, then should this be a sign you are closer
to the truth?
- Physics is where “truth” originates. Perhaps it isn’t possible to
find truth beyond the microscale?
- Disturbed that we don’t aknowledge/teach that good scientists
have ignore evidence that their idea was wrong – that data contradicts
it. But Sandy points out that data can be wrong --- or misinterpreted.
- Perhaps we should not be after the ‘truth’, but we should be
after ‘useful models’
- Choice of domain of a problem is almost as important as the
question you are asking.
- Science: 1. body of knowledge; 2. process of building
information; 3. culture (honesty; guarding against ego; self critique;
etc) and motivation (understanding).
- Honesty is the root of good science.
Is the following true? Understanding means explaining things which are
complicated or numerous in terms of things which are simpler or fewer.
Any given piece of work can be divided up into the background knowledge
which is assumed and the problem which is tackled. Big progress in
understanding can be judged by the difference between the compexity of
the phenomena and the simplicity of the building blocks of that
explanation. But it must also be measured by the level of confidence in
those building blocks.
From last time: Induction is creative. Deduction is logical. Both are
necessary for moving forward.
Questions that should be asked at every seminar.
- how confident are you of your 'background knowledge'?
- how have you critically evaluated your argument?
- how wrong might your argument be?
- what would form a critical test that would cause you to reject your