The Great Mental Models Volume 3: Systems and Mathematics

by Rhiannon Beaubien

How much you know in the broad sense determines what you understand of the new things you learn.

Although these subjects can appear abstract, as soon as we start taking them apart, we quickly see that they describe so many of the behaviors and interactions that govern our lives.

The more moving parts you have in something, the more possibilities there are.

a mental model is simply a representation of how something works. We use models to retain knowledge and simplify how we understand the world. We can’t relearn everything every day, so we construct models to help us chunk patterns and navigate our world more efficiently.

Using them means synthesizing across disciplines and not being afraid to apply knowledge from different areas far outside the milieu they usually cover.

Not every model applies to all situations. Part of building a latticework of mental models is educating yourself regarding which situations are best addressed by which models. This takes some work, and you’re likely to make some mistakes. It’s important to constantly reflect on your use of models. If something didn’t work, you need to try to discover why. Over time, by reflecting on your use of individual models, you will learn which models will best help you tackle which situations. Knowing why a model works will help you know when to use it again.

Systems thinking is a discipline for seeing wholes. It is a framework for seeing interrelationships rather than things, for seeing patterns o...

The more you know, the easier it is to design solutions that will work.

Because systems are so ubiquitous, it’s not useful to try to apply these models outside of systems. Rather, we try to give you ideas for considering just how much of life is part of a system so you can expand your application of systems thinking.

Finally, reflect. Take some time to evaluate your success and failures. In doing so, you will begin to learn the full potential of the toolkit you are building.

follow a system wherever it leads. It will be sure to lead across traditional disciplinary lines.

Feedback loops are everywhere in systems, making them a useful mental model. Think of “feedback” as the information communicated in response to an action.

Our body language is a form of feedback for people interacting with us. The tone you use with your kids is feedback for them.

Once you start looking for feedback loops, you see them all over the place, giving you insight into why people and systems react the way they do.

The incentives we create for ourselves and other people are a form of feedback, leading to loops that reinforce or discourage certain behaviors. If you get visibly upset whenever someone at work offers you constructive criticism, you’ll incentivize your colleagues to only tell you when you’re doing something well—thereby missing out on chances to improve.

A critical requirement is learning how to filter feedback. Not all of it is useful. The more quickly you learn to identify good feedback and accept and incorporate it, the more progress you will make toward what you want to achieve.

Learning to communicate your feedback in a way that makes it easy for others to receive is a valuable skill to develop.

A feedback loop is when the outputs (information) of a system affect its own behaviors.

Depending on the complexity of a system, there may be a single source of feedback or multiple, possibly interconnected, sources. While it helps to first consider feedback in a simple system as we will do below, we are all part of many large systems that contain many interconnected feedback loops.

There are two basic types of feedback loops: balancing and reinforcing, which are also called negative and positive. Balancing feedback loops tend toward an equilibrium, while reinforcing feedback loops amplify a particular process.

The faster you get accurate feedback, the more quickly you can iterate to improve.

The feedback loop of others’ reactions to our actions is the basis of civilization.

“Once books and music exist, there’s a great case for free distribution of them. But then they are less likely to exist at all next time.”

Using feedback loops as a lens, we can understand influencing behavior at the margins as instituting a series of incentives that create loops. Over time this feedback changes the system to produce the desired outcomes.

The concept of feedback opens up the idea that a system can cause its own behavior.

“People draw inferences from what they see others doing and do the same; now even more people are doing it, and they create a still stronger impression on the next.”

Feedback loops are one of the key mechanisms that provide the information we use to make trust-based decisions. What happened before in your interaction with a person provides feedback that may cause you to modify your behavior.

The point here is that we can trust the feedback loops of the system to enforce micro-interactions so we can establish trust. We can imagine that after a few interactions, those gains that come from cooperation contribute to a feedback loop that encourages people to prioritize cooperation in those situations.

Feedback loops are a common component of many systems. They carry the information that a system responds to. Complex systems often have many feedback loops, and it can be hard to appreciate how adjusting to feedback in one part of the system will affect the rest. Using feedback loops as a mental model begins with noticing the feedback you give and respond to every day. The model also gives insight into the value of iterations in helping adjust based on the feedback you receive. With this lens, you gain insight into where to direct system changes based on feedback and the pace you need to go at to monitor the impacts.

Usually when systems stray too far from their equilibrium, they fall apart. When we consider just the pure functioning of a system, equilibrium is a good thing.

A system can be said to be at equilibrium when it is in a stable state. All the forces acting upon it and within it are in balance.

When we use the term equilibrium, we’re typically referring to a state where things within a system are consistent and not changing, known as static equilibrium.

But most real-world systems are more apt to experience dynamic equilibrium, meaning things fluctuate within a particular range. They achieve this using balancing feedback loops. If a variable becomes higher or lower than t...

One way to conceptualize the idea of equilibrium is to imagine a hypothetical family whose overall household forms a system. For the household to run in the way that’s best for everyone on average,...

If they get out of that range, the family makes adjustments to restore balance. If they can’t bring a variable back to the ideal range, the househol...

Homeostasis is the process through which organisms make continual adjustments to bring them as close as possible to their ideal conditions.

Physician Walter Cannon* coined the term homeostasis in his iconic 1932 book The Wisdom of the Body. Cannon marveled at the many variables our bodies manage to keep within narrow parameters, including blood glucose, body temperature, and sodium levels. Although systems theory did not exist as a field of study at the time, Cannon was espousing a view of the human body as a whole system that needed to maintain a stable internal state in response to its ever-changing environment.

Just because a system is at equilibrium, that doesn’t mean it’s functioning as well as it can. It just means things are stable.

If you’re feeling ill one week and struggling to focus on work, you might work extra hours each day to get your usual work done. You’ve maintained equilibrium, but you would have probably been better off overall if you did less. Short-term deviations from equilibrium are often what is needed to maintain it in the long term.

“Homeostasis refers to the process by which the tendency of matter to drift into disorder is countered so as to maintain order but at a new level, the one allowed by the most efficient steady state.”

Organizations, communities, and countries—all are systems that must respond to environmental changes with modifications intended to bring them closer to a desired state.

Damasio argues that feelings act as the key to understanding the biological role of homeostasis. Our feelings are a feedback loop that provides information to our body system about how we are doing. You have to be able to monitor the adjustments and responses to make changes that put you back on track.

After a disaster, for instance, homeostasis does not need to (and frequently doesn’t) return the system to its previous state. Instead, it’s more useful to think of homeostasis returning a system to a place where it “feels good” under new conditions.

When your blood glucose drops, you feel terrible, which causes behavior that seeks to bring you back to where you feel okay. But that level of okay is a range, and Damasio’s idea is that homeostasis normally keeps us at the end of the range that allows us to develop.

When we look at biological systems, we can easily see that information is required to maintain homeostasis, or dynamic equilibrium. In our bodies, various components are constantly communicating an incredible amount of information about everything from the sensations on our skin from the external temperature to the potassium levels in our blood. Without accurate information, our bodies cannot work properly. Using this model as a lens, we can understand which situations might benefit from information to maintain an equilibrium.

People who are actively supported in making decisions about their health care often experience more favorable health outcomes, including less anxiety and a quicker recovery.

One definition of dynamic equilibrium is “when the system components are in a state of change, but at least one variable stays within a specified range.”

Although the terms are sometimes used interchangeably, a bottleneck is different from a constraint. A bottleneck is something we can alleviate; a constraint is a fundamental limitation of the system. So a machine that keeps breaking down is a bottleneck, but the fact there are twenty-four hours in the day is a constraint.

Medical science tends to advance the fastest during wars. Facing new demands and shortages of essential supplies, people find creative ways to deal with injuries and diseases.

Using bottlenecks as a mental model not only helps us conceptualize them in the literal sense when looking at a system but also teaches us that they are not something to fear. When there are no severe bottlenecks, we may not think to improve things. After they emerge, we’re forced to be more creative and watch that we don’t transfer the pain somewhere worse. In the long run, they can make us better off.