Models

Yair Mau

Semantics

Meaning

Models represent a selected part of the world:

the model’s target system.

🤔 What does this mean?

Scale models

Yair’s fun etymology break: model

latin

modus = measure
diminutive modulus = measure, standard

vulgar latin

word becomes modellus

old french

modelle

originally

small-scale representation or a standard to be imitated or followed

fashion

human figures to showcase garments or products

science

simplified representations of real-world systems

Analogical models

Idealized models

Aristotelian idealization: neglect stuff

mass
length
color
material

Galilean idealization: distort stuff

point-like mass
massless string
no friction

Toy models + Minimal models

Phenomenological models

observable properties
hidden mechanisms

Speaker notes go here.

Exploratory models

starting point of further explorations
proofs-of-principle
specific target system
particular experimentally established phenomenon

Models of data

data cleaning
data munging
smoothing, etc

# exclude rows with missing values
df.dropna()
# resample into daily freq, take average, and forward fill gaps
df.resample('D').mean().ffill()
# 7-day running average
df.rolling(7, center=True).mean()

Epistemology

Knowledge

models are vehicles for learning about the world

by studying a model we can discover features of, and learn facts about, the system the model stands for

Learning about a model happens…

during model construction

during model manipulation

Explanations

Some models explain. But how can they fulfill this function given that they typically involve idealizations? Do these models explain despite or because of the idealizations they involve? And what kind of explanation do models provide?

Causality

the causal relations between facts or processes does the explanatory work

explanations:
information about patterns of counterfactual dependence between what is explaining and what is being explained

enable us to see what sort of difference it would have made for the explanandum if the factors cited in the explanans had been different in various possible ways.

But why do models play such a crucial role in the understanding of a subject matter?

Elgin (2017)

this is not despite, but because, of models being literally false. False models as “felicitous falsehoods” that occupy center stage in the epistemology of science