Complete summary of the course Complex Systems Theory of the Master course Pedagogical Sciences. With use of this summary I obtained a 9/10 on the exam.
Complete samenvatting van het vak Complex Systems Theory van de Master Pedagogische Wetenschappen. Met behulp van de samenvatting heb ik een 9 ...
HC1
Take-home exam, open book. Three hours to complete. Discussion is allowed among students but be
aware of plagiarism. The course will consist of lectures with part A & part B. Part A is a topic
introduction, part B is the application from a CST perspective. Each topic relates to one of the master
tracks.
Introduction
Complex systems is a different view compared to linear sciences, which you have learned until now.
There are several characteristic features that are shared by almost all complex systems. A complex
system can often be seen as a large collection of small elements that interact with each other at a
micro-level. Such elements may be atoms in physics, molecules or cells in biology, or consumers in
socioeconomics. However, ‘more is different’ in complex systems. Phenomena observed at a global,
macro-level, typically cannot be reduced to the properties of the constituent elements: these are
emergent properties that arise through ‘self-organizing’ local interactions. This is in sharp contrast to
the classical reductionistic idea that nature can only be understood by reducing of decomposing its
processes into elementary building blocks that can be studied independently. The concept of
‘complexity’ has been introduced as de associated paradigm shift in the study of natural phenomena.
Linear systems v.s. Complex systems:
There’s also a difference between complicated systems and
complex systems: a complicated system on the left vs. a complex
system on the right. We often treat complex systems as what we would like to refer as complicated
systems. In both cases we’re the system is made up of components. But a complicated system is a
predictable system. You can understand it as a whole by understanding what each part does. A
nervous system (complex system) is more difficult: if you would like to understand one part of the
system, you must take in account all the other parts.
A complex system consists of components and interactions. We often treat a complex system as it
were to be a complicated system (reductionism). This reduces complicated problems into simpler
parts. The behavior of the system exists of the sum of the component’s behaviors. But if you only
know the components, you actually know very little about the system. The opposite of this is the idea
of self-organization: there are local interactions between components and a global emergent system
behavior. This does not reduce to the behavior of the components.
If we think about the brain, we often think about it like a
complicated system, where you have all of these components. But
we also look at it like a computer: a video card, an audio card,
memory, working memory, etc. But the brain mostly consists of
water, sugar, and fat (milkshake). How can we perform all these
functions with these simple components if they’re not specialized as
in a computer?
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This is another way of showing how we look at the cognitive system as a set of components that each
do their independent thing.
When a child is experiencing problems, it doesn’t behave the way it should behave, we think about a
faulty component → one single cause for the behavior. We mostly think a component is missing or
isn’t doing its work. We need to cure the broken component! But we’re missing a very important
thing: the interaction.
Here you see to different brains performing the same task. How can it be that none of the same
“components” are highlighted? None of it is overlapping.
Most cognitive science focuses on time scale; with complex systems theories we’re going to broaden
that quite massively.
What did we learn from linear statistics so far?
- Statements about groups: e.g. women are more emotional than men, lesbians only have sex
with women, people with ADHD have weakly developed EF.
- Statements are often linear: e.g. the older one gets, the less impulsive their behavior will be
or the more repetitive behavior, the clearer the autism.
- Compare means:
- Compute correlation: age * impulsiveness: r = -0.30, p < .05, 9% variance explained
- Run ANOVA:
But we’re forgetting conclusions about the individual!
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Traditional statistics only concern the group, not the individual. They test linear relationships (e.g.
correlation, t-test, ANOVA, regression) and the components explain the behavior (Autism + noise =
ToM). The independent components added together explain the behavior: 3% of variance caused by
gender + 10% caused by the group equals 13% of variance in total. The observed score exists of the
true score and the noise (error). In formula:
Complexity theory concerns the group and individual, measured over time. They test nonlinear
relationships (e.g. phase transitions, CUSP catastrophe, small cause -> large effect, large cause ->
small effect). The interactions explain the behavior (local interactions <- -> global pattern,
emergence). The components are dependent: it’s not about ‘from A to B’, but the entire system
matters. The observed score = the dynamical change process. In formula:
Linear: a change in X is associated with a proportional change in Y.
Nonlinear: a change in Y is nog proportional to X.
Nonlinearity is far more common than linearity in human behavior.
Static: typically, each data point represents one measured value for one person.
Dynamic: typically, each data point represents a change process (many values measured over time)
of one individual.
An example of nonlinear and dynamic: vocabulary development:
You can see this is far from linear, at one point the child will
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experience a vocabulary spurt. If you take enough individual data, it will become linear. It’s crucial to
analyze individual data before analyzing group averages!
A quick note about causality in complex systems. When we compare variable X and Y, we look at age
as some kind of predictor for the number of words a child knows. The most important thing that
explains how many words a child knows at a particular moment in development, actually depends on
how many words a child already knew beforehand. And if you look at how much the mother talks
with the child and how that relates to the child’s lexicon, you will notice that it will also work the
other way around: not only will the child’s lexicon increase when the maternal talk increases, the
maternal talk will also increase when a child’s lexicon increases.
In individual data, the mean is not very meaningful. Maybe it’s more useful to look at how the mood
of someone with depression is fluctuating.
Diversities A
Why should we care about diversity? Almost everything you’ve learned so far is based on population
statistics. Interventions are effective on average, but they’re not effective for everyone.
Blue = intervention group, pink = control group. These distributions differ for effect sizes that we
typically see for interventions in youth care. There are many individuals for whom the intervention
doesn’t do more than if they were placed in the control group. What if the treatment doesn’t work
for a person? You won’t say “I’m sory, it did work on average. I can’t help you”. So, what we want
when we encounter diversity to know what works best for whom, with what condition, under what
set of circumstances.
The traditional view on diversity is the one where
diversity is seen as an error. We might say the mean
is “normal” and that deviation from the mean equals
error. What we take from this is that when we design
something made for the mean, it will help most
people. But you will find out that’s not the case. The
average person, face or brain doesn’t exist.
What’s happening? The average size includes the
length, arm length, leg length, neck circumference,
thigh circumference, wrist circumference, etc. Nobody scores average on all multidimensional
constructs; Nobody scores average when there are many dimensions involved.
You might say: “that’s fine, but I can still use the deviations from the mean as ranks”. You might say
individuals are deviations from average within a certain rank. Two variables are positively correlated
when a high rank in X is associated to a high rank in Y.
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