lecture 5 Flashcards
what is a model
a model is something that represents something that we want to investigate in a relevant way for the problem at hand
Everything is similar to everything else in at least some regards, so any similarity wont necessarily result in a good model
A good model balances abstraction and idealization to ask a question/ make a point (hear texample)
too realistic – just right – too abstract
The abstraction for me is the idea of getting rid of everything thats not essential to making a point
Looking at a concrete model (baymodel)
Pictures of the S. frnacisco bay model
What do you see
Scale of the model
Materials of the model
4 dimensions: time is one of them
Target: the bay
Abstraction: some features of the real bay are left out
Idealization: new features are introduced that are not in the bay but are useful for the model (e.g. a tidal cycle happens faster in the model)
Why the model and not an experiment (bay model)
There was no way to “experiment” the reber plan in the bay without implementing it; the model allowed to perform just that
Also consider:
Complexity of investigating a situation with so many unknowns
Ethics of potentially destroying entire ecosystems and the existing human way of life around the bay (including businesses)
Ethics + complexity: the animal model
Remember: Different targets; Different aims; Different levels of relevant similarity
Why do different groups tend to live in different neighbourhoods
One hypothesis: segregation can emere without racism
How to evaluate this hypothesis
Thomas schellings model of segregation
Assumptions:
Two sorts of agents
Agents live in a two dimensional grid
Agents initially randomly distributed on the grid
Agents have a preference for their neighbourhood: agents are satisfied only if surrounded by at least t% (e.g. 30%) of agents like its self
Agents interact accordingly to a behavioural rule: when an agent is not satisfied, the agent mmoves to any vacant location in the grid
drawing observations from stimulating schellings model as an agent based compupter program
Small preference for like neighbours result in massive segregation –> housing segregation can emerge without strong racist attitudes
Problem with schelings model
schellings model does not represent chicago, or any other city, realistically and comprehensively
Schellings model involves idealizations
Chicago is not a perfect grid
Not all people share same preference for like neighbours, and not all people know all other people living in their neighbourhood
When people move house, they do not usually move randomly, and they do not usually move at any time they are unsatisfied
Economiics and ecological factors (e.g. how much you earn, cost of housing in different areas, level of pollution) do matter
When can we use a model
If the model is similar enough, in relevant respects, to its target system, then it can allow us to learn about the target
How do you know which similarities and idealizations matter for learning about a target
Robustness analysis
Build slightly different models of same target
Manipulate the models in comparable ways
Compare models results
What is the point of robustness
Assess sensitivity of a model to changes in its basic structure
Identify model features responsible for certain results
Evaluate which similarities and idealizations matter to learn about the world
building a mathematical model
Although, at least in the beginning, the representation is very rough (i will) schematize the phenomenon by isolating those actions that we intent to examine, supposing that they take place alone, and by neglecting other actions
A mathematical model: Lotka-volterra
dV/dt = rV - (aV)*P
dP/dt = b(aV)*P - mP
V = preys
P = predators
rV = prey birth rate
(aV)*P prey capture rate by predator with a = constant
mP = predators death rate
b(aV)*P = predators birth per prey capture
biocide
Any substance or event which has a harmful effect on both predators and prey
