Computer simulations of language change notes
This website collects my personal notes on Computer simulations of language change. These notes are provided to bring full transparency to my research process. Of course, since they are only notes, they do not reflect my final thoughts on a topic, and should not be interpreted as such. To read finished papers, please consult my website. Do not use these notes as a basis for your own scientific research. Start from high-quality, peer-reviewed scientific literature instead.
human behaviour silos
why modelling?
Why should you do violence to reality?
1. stepping stone
2. precision
flocking starlings
emergent behaviour?
boids
↓ three rules
1. separation
2. alignment
3. cohesion
Screenshot from a simulation of the boids model
agent-based model
models
model
| direct study | indirect study |
|---|---|
| questions are about the thing you are observing | questions are about something else than you’re observing |
| directly | proxy |
| e.g. weighing a rock | e.g. marshmallow test |
formal models
| formal models in exact sciences | formal models in social sciences |
|---|---|
| elements of a model are direct representations of measurable quantities in the world | models are intended to capture core elements of a theoretical idea |
| (usually) near-perfect one-to-one mapping between measurement and model | no perfect one-to-one mapping between measurement and model |
circularity
assumptions and consequences
model building
Good models can show us how our assumptions lead to unexpected conclusions.
verbal ambiguity
verbal theories
In the social and behavioral sciences, the search for clarity can present a problem for verbal models and can lead to a depressing recursive avalanche of definitions. For example, many researchers are interested in preferences. But before we ask about the sorts of things that influence preferences or are influenced by preferences, we should first ask: What is a preference? Perhaps a preference is a tendency to choose certain behaviors over others. This leads to a new question: What are the available behaviors? Of course, the set of possible behaviors depends on the social and environmental context. What are these contexts, and what determines them? This can go on for a while.
formal models as an escape from recursive abyss
↓ problem
all models are obviously wrong
↓ solution
stupidity as a strength
standard science
↳ problem
A hypothesis is usually a proposal that the parts of a system are organized in some way and/or that because the parts are organized in a particular way, some phenomena and not others occur. But what are these parts? If we want to understand some aspect of a system and form hypotheses and theories about it, we first have to articulate the parts of the system, a process I’ll call decomposition after Herbert Simon, who used the term similarly.
↓ questions we have to answer
↳ decomposition
how decomposed?
The value of a model largely depends on how well its decomposition usefully answers the questions the modeler is asking.
Decomposition visualised (OC)
theory
↓
models
[I]t is the question that determines the relevant parts of the system
building models
↓
canonical models
In practice, [a hypothesis] is a prediction that either (1) the parts of a system are organized in a particular way—in other words, that a particular decomposition carries explanatory power for some observed phenomena—or that (2) because the parts of a system are organized in a particular way, certain phenomena and not others will occur. Good hypotheses allow us to exclude and distinguish between competing theories.
Strong theories allow us to generate clear and falsifiable hypotheses.
An example of a theoretical framework is Darwinian evolution by natural selection, from which many subordinate theories have been derived.
challenges in doing science
hard science (according to Popper)
| science | non-science |
|---|---|
| theory can be falsified through empirical result | theory cannot be falsified through empirical result |
New distinction by Smaldino
| exact sciences | inexact sciences |
|---|---|
| theories involve direct mappings between measurable constructs and model predictions | mappings between measurements and theories are imprecise |
| terms in fundamental equations all have universally-accepted units (e.g. mass, velocity) | model parameters don’t align with empirical measures (typically proxies) |
| ↳ theories are exact specifications of the relationships between quantities that can be measured with high level of precision | ↳ theories are more vague approximations of relationships assumed to hold (nvda.) |
Exactness is more like a continuous variable rather than a binary characteristic.
inexactness of models
prediction from models in social sciences
| statistical models | generative models |
|---|---|
| powerful predictive correlations | qualitative predictions / no predictions at all |
| extremely dependent on conditions of the study | conditions modelled explicitly |
mental models
verbal models
formal models (nvda.)
The most successful verbal model—from a scientific point of view—may be Darwin’s theory of evolution by natural selection, which provides the foundations for explaining much of life as we know it. Darwin’s writings contain no mathematical formalisms, only richly described ideas.
| verbal models | formal models |
|---|---|
| contain ambiguity | cannot contain ambiguity |
| multiple interpretations | unique interpretation |
| useful for prototyping | useful for final product |
(ideas echoed from Gong & Shuai, nvda.)
explicit assumptions
↓ benefits
1. clear scope
2. aids communication
We sidestep the problem of the Cubist chicken, because the formalism tells us exactly what the parts are and how they fit together.
Met ‘tractability’ bedoelen ze hier ‘haalbaarheid’.
tractable models
↓ benefits
1. overcome real world messiness
2. overcome time-scale constraints
3. explore counterfactual scenarios
4. cheap
(more echoes from Gong & Shuai)
gaining insight
interesting models
Newton’s model of planetary gravitation
Earth has a forward velocity 𝑣, which is continuously altered by the gravitational attraction of the Sun, 𝐹𝑔, resulting in an elliptical orbit. In reality, the model is even simpler than implied here, because the Sun and Earth are represented as point masses rather than spheres.
two animal species
relations
model
simplicity
extensions
| equation-based models | agent-based models | |
|---|---|---|
| relationships |
equations specify the relationships between the parts of a system |
individual agents enter into relationships |
| aggregation | necessary | not necessary |
| parameter exploration | easy → plug in new numbers | possible, but less straightforward |
| heterogeneity (spatial/network structure) |
ill-suited | well-suited |
| complexity | complicated | intuitive |
| fine-grained models | coarse-grained models |
|---|---|
| there are data in the world that can be used to precisely parameterize and test the models | focus on broad, qualitative patterns in the data |
| e.g. mass, pressure, voltage | e.g. emotion, perception, norms |
Fine-grained models
In epidemiology, some agent-based models are calibrated using high-precision data on demographics, geography, schools, travel matrices, and so forth, with the goal of predicting the time course of an epidemic.
In neuroscience, biophysical models might exactly predict the dynamics of action potentials or motor behaviors.
Coarse-grained models
The utility of [concepts like norms and perceptions] in lay thought and communication is indisputable, but it is less obvious how they should be measured for scientific study. Even when a concept is precisely defined, measurement is often made difficult by constraints of time, resources, or ethics.
complex systems are complex
Computer simulations of language change notes
This website collects my personal notes on Computer simulations of language change. These notes are provided to bring full transparency to my research process. Of course, since they are only notes, they do not reflect my final thoughts on a topic, and should not be interpreted as such. To read finished papers, please consult my website. Do not use these notes as a basis for your own scientific research. Start from high-quality, peer-reviewed scientific literature instead.