How to Think with Models?
Why Abstraction is Key for Critical Thinking
The ubiquity of patterns
You’ve already probably heard the saying that humans are pattern-oriented creatures. We think in patterns: if we see clouds, we think of rain, if we see kitty cats, we think of play and cuddles.
Think of it this way:
Everything we experience is almost immediately slotted in one of the appropriate ‘drawers’ in our minds. We make connections between experiences, ideas, and objects and bundle them together in these drawers. In the ‘cloud drawer’, we also have umbrella, water, wet socks, cold, but also traffic, lateness, as well as coziness, romance, and many others.
Each person has their unique way of organizing these drawers and their contents. Some contents belong to more than one drawer (there are identical copies of them in many drawers). Some drawers are full of things; others have just a few.
Why do we do this?
Reality is too complex for us to think of every moment as its own class. Imagine thinking that every cloudy day is fundamentally and in every way different from any other cloudy day. Of course, in some sense it is, but in matters we might care about (for example, deciding what to wear for work that day), it is not. It would be cognitively demanding to act as if it were; we’d have to spend too much energy thinking about it.
Instead, we rely on shortcuts; that’s where these drawers play a crucial role. They give us instant access to things that relate to the experience of a cloudy day in a useful and functional way.
What is a model?
Let’s change the name now: instead of ‘drawers’, let’s use a fancier (but more useful) word, models. What we do when we organize these drawers (deciding what to put in them and when to retrieve them) is ‘modeling’, or model building.
Every drawer is, basically, a model containing numerous elements that are related to one another in some way.
We use models all the time to understand and make sense of the world. As humans, we cannot understand anything in isolation: everything we know is connected in something we could call a ‘knowledge network.’
If you choose any possible concept or idea, that concept never exists on its own. You need, by necessity, other concepts, even to define it. Sometimes, we need many other concepts to define one; other times, we need a few.
Exercise 1: Here's an interesting exercise. Try finding two concepts, one which needs fewer, and another which needs more other concepts to be defined. What's the difference between those two concepts?
We do all of this to reduce the complexity of the world and make it more simple to understand and interact with. Another word for this is abstraction, the process of eliminating the details of some situations and keeping only certain features, those necessary to understand and use the concept in reality.
Geographical maps are a great example. They represent the main features of the landscape but ignore a gazillion details; not every tree, rock, or squirrel is represented because we don’t need those details when we use the map to go somewhere.
This map is a model of midtown Manhattan, an abstract representation of the real thing. It’s extremely useful, even though it is a very simplified version of the real thing.
So, models are indispensable in real life, we use them every day, but understanding them in more detail can give you superpowers and help you become a much better thinker.
How can we understand them better?
By being complete nerds and digging deeper behind the idea.
We’ll do it by building a model of models. In other words, we will simplify the idea of a model and see what it’s made of and how it works.
To do that, we will use a simple tool: a graph. Graphs are just collections of some shaphes (nodes) and lines (edges) connecting these shapes.
For example, here’s the simplest graph ever:
In this graph, we have two nodes and one edge.
Although very simple, it can help us represent some aspects of reality. It can connect the concepts in our model to help us organize our thinking. Moreover, it can stand for the model itself.
Here’s a simple application, where we assign some concepts to nodes and use an edge to connect them:
This basic model helps us establish a special connection between two concepts, which may be useful when thinking about what to take with us on a rainy day. Of course, this is a radical simplification (most models are much more complex), but serves to describe what models are: conceptual systems for representation of reality that bring order to our minds. We use models to resist entropy of everyday life.
Graphs are very useful in modeling many real-life situations. Here’s another one:
Here we use a graph to represent a group of people and describe their Instagram connections. Arrows represent ‘follows’, so, in this case, Mary follows Amir, but Amir does not follow Mary. He follows Josh who also follows Amir. Double-pointed arrows describe the mutual following.
The benefits of representing complex phenomena with graphs are plentiful. For example, it allows us to describe and understand these phenomena with ease. Imagine how much more burdensome it would be to write out all of these connections in words.
You already know the saying ‘a picture is worth a thousand words,’ and a graph is just a very useful picture.
Graphs can help us tease out more information from our system than would be initially available. Even a glance at this social network tells us that John does not belong to this group of people because he has no connections. Similarly, we see that Josh is the most popular guy in the group (he has the greatest number of incoming and outgoing arrows). All of this information is contained in our little system but could be hidden from us if the system were represented in some other way.
Exercise 2: Choose any other complex system and model it using a simple hand-drawn graph with nodes. Here are a few ideas, but bonus points if you come up with something else: transportation networks, internet and web links, family trees, supply chains.
Graph theory is a serious field of mathematical study, and we have neither time nor space to go deeper here. If you would like to get a more serious, yet beginner-friendly introduction to graphs, I sincerely recommend this blog.
But for now, you have enough idea about models: they are simple, often graphical, representations of some complex systems. They allow us to abstract from messy detail and understand the essence of these systems.
Types of models
Developing models is part science, part art. Since reality is complex and we often wish to model some aspects of this reality, the models that we develop will significantly differ from one another, depending on what situation we wish to capture with the model.
In this section, we’ll cover a few types of models and show their possible applications.
Descriptive models
Descriptive models are usually the simplest models to make. Their job is to accurately represent the structure and components of some system.
For instance, organizational charts are descriptive models that identify departments (or positions) within an organization, such as a company or an institution.
Here’s an example:
Descriptive models give us a useful overview of the inner structure of some system, identifying its main components and defining how they relate to one another.
Predictive models
Sometimes we want more than just a description. There are cases when we’d like to predict the outcome of some complex process, and we can make a model to structure the prediction process.
For example, if we want to predict the weather for the next day, we must take into account a number of relevant parameters, such as the temperature, humidity, wind speed … etc.
Graphical representation of such a model could be useful for identifying and computing the effects of these parameters on the outcome.
Something like this:
Normative models
Models are also great for providing us guidelines for action when the process is complex and has a lot of moving parts. Many businesses use decision trees to model the decision-making procedure and guide individuals through the maze of rules, criteria, and outcomes.
Here’s a simple example of how a company can use the decision tree model to decide whether to launch a new product or not:
Probabilistic models
Life is uncertain and in most realistic situations we can’t really know whether some outcomes will materialize or not. That’s why we use probabilistic models, which help us understand how randomness affects some complex processes and allow us to make decisions amid uncertainty.
Let’s say you are a student choosing between two different majors, accounting, and visual arts, but you’re unsure which one to pick. Both paths have uncertainty in two aspects: getting a job, and making a lot of money.
With accounting degree, the probability of career success (landing a job) is high, but the probability of making a huge amount of money is low; with visual arts, the probability of career success is low, but the probability of making a huge amount of money (if the career is successful) is high.
What would you choose? How much would these probabilities have to be different for you to change your preference?
Without modeling this situation in some way, it would be hard to tell, since any particular choice depends on the features in the whole system.
Under the hood
In modeling, understanding the internal structure of models is crucial. A well-structured model allows for better understanding, predicting, and manipulating complex systems.
How can we structure our models well?
The first step is understanding the elements that constitute the internal structure of any model.
Here are some of the most important elements:
Components
Components are the fundamental building blocks of any model. They represent the entities or elements that make up the system. Components can be tangible (parts of a machine) or abstract (variables in an equation).
Examples:
In a traffic model: vehicles, traffic lights, pedestrians
In an economic model: consumers, firms, government
States
States describe the conditions that components can be in at any given time. States can be static (unchanging over time) or dynamic (changing over time).
Types of States:
Static States: Fixed attributes that do not change during the simulation (the structure of a bridge, eye color)
Dynamic States: Variables that change over time (the speed of a car, the temperature of a room)
Examples:
In a traffic model: a traffic light can be in the states of red, yellow, or green
In a biological model: an animal can be in the states of resting, hunting, or feeding
Inputs
Inputs are external factors that affect the components and states within the model. Inputs drive the behavior and evolution of the system, often relate to dynamic states in the model, changing them in some way.
Examples:
In a weather model: temperature, humidity, wind speed
In a financial model: interest rates, market trends, economic indicators
Outputs
Outputs are the results or outcomes produced by the model after processing the inputs. Outputs give us valuable insights and predictions about the system's behavior. Oftentimes, they are the reason behind the act of making a model.
Examples:
In a weather model: predicted weather conditions, such as rain or sunshine
In a financial model: forecasted stock prices, economic growth rates
Interactions
Interactions define how components and states within the model influence each other. These interactions can be linear (read: simple) or nonlinear (read: a bit complex) and can involve feedback loops (situations when components influence each other).
Examples:
In an ecological model: the predator-prey relationship, where the population of predators and prey affect each other
In a social network model: the influence of peer connections on individual behavior
Parameters
Parameters are constants within the model that define specific characteristics or behaviors of components. They are typically fixed during the simulation but can be adjusted for different scenarios (they are sometimes similar to static states).
Examples:
In a traffic model: the average speed of vehicles, the duration of traffic light cycles
In an economic model: tax rates, consumer spending rates
Exercise 3: Choose a real-life system (a school, a business, or similar) and a) identify components and states; b) define inputs and outputs; and c) describe relationships and interactions.
Why abstract way?
There are many other model types, each corresponding to some aspect of reality that is being represented. While they may differ in the ways they capture the features of each situation, all models share one important thing: they abstract away from reality. By doing so, they omit many details and focus only on the most important things.
What happens to be most important is not fixed, however. It depends on the purposes of modeling, as well as the particularities of each situation.
Critical thinking requires understanding the importance of modeling. We rarely can solve any problem without resorting to this process of abstraction; it is a necessary part of problem-solving in any domain of life.
The sheer diversity life situations in which we find ourselves every day, points to the need to adopt what some people call a ‘many-model thinking’ approach. In order to think critically in different situations, we must be able to use abstraction in many ways.
In other words, we must have many model types at our disposal, and know when to use them.
Great post! I have two questions if you don't mind:
One, regarding abstraction, are you familiar with general semantics? They tend to get nutty once they apply the tool-as-worldview, but they've got interesting writings on abstraction itself.
Two, regarding the graphs, are you familiar with dual coding theory? I didn't hear the word until last summer, but it consolidates a lot of thinking regarding visualization. Lately I've loved the accessibility of Caviglioli's book: https://www.olicav.com/#/posters/.
I’d say everyone always thinks with models. Some are just more explicit and transparent. You run a meteorological model in your head when you decide to carry an umbrella or not.