8.1 Orders of Understanding

Often the simplest and crudest explanation is sufficient to understand a phenomenon, without the need to worry about the finer details. For any given phenomenon, we encourage students to consider the most important, first-order, causes, before moving on to far less important, second- and higher-, order causes. This structured scientific way of thinking is crucial for policy making when resources are limited.

The Lesson in Context

This lesson introduces a practical framework for discussing cause and effect in this complex world. Specifically, the students should learn that there are usually multiple causes contributing to a certain effect, and it is possible to compare the magnitude of the effects from different causes. We wish to encourage students to develop the habit of considering multiple possible causes, rather than just claiming that "[math]\displaystyle{ X }[/math] is the cause of [math]\displaystyle{ Y }[/math]".

Earlier Lessons

1.2 Shared Reality and Modeling

• Simplification is necessary when modeling a phenomenon. A first step is to extract and describe the most important feature of the phenomenon (first-order effect) and then add refinements to the model to describe finer details (higher-order effects).

6.1 Correlation and Causation

• Causation is defined as correlation under intervention, or in other words, a clear effect is observed when the intervention is done as contrasted to when the intervention is not done (the control condition). Orders of explanation can be argued by considering the magnitude of the effect when each causal factor is turned on or off.
• RCTs are an idealized way to study the size of the effect due to a certain cause, enabling researchers to hold all else constant (in the ideal case). It is possible to compare the magnitude of the effects due to two different causes by conducting an RCT with more than two conditions.

6.2 Hill's Criteria

• When RCTs are impractical or impossible to conduct, Hill's criteria may be used to argue about the existence and magnitude of the effect due to a certain cause.

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Later Lessons

8.2 Fermi Problems

• The next lesson will introduce a practical method that can help us quickly estimate the magnitude of numerical quantities when there is little available information. We will use the Fermi estimation method to compare different sources of US government spending.

Takeaways

Learning GoalsDefinitionsExamplesCommon MisconceptionsExpanded Learning Goals

After this lesson, students should

1. Recognize that there are usually multiple causes that contribute to an effect to varying degrees, ranked first-, second-, third-order, and so on.
2. Recognize that there are often multiple causes of the same order of importance.
3. Understand that a model is inevitably a simplification of the real world. As one includes finer and finer details, one is taking into account higher and higher order causes.
   1. The order of a cause is determined by the magnitude of its effect, relative to other causes.
   2. When creating a model, there are some factors (causes) for which we don't consider the order, because we assume them to be constant (for example, they are the underlying environment or circumstance). Whether or not we assume something to be constant may be partly a question of values. (For example, when considering a model of traffic accidents, we typically don't include oxygen content in the air, even though if the oxygen suddenly went out, everyone would crash.)

Order of Magnitude

Factors of ten. A is one magnitude higher than B if it is approximately 10 times larger than B. (Orders of magnitude are typically used for very rough approximations of quantities, "to the nearest order of magnitude.")

This is an intuitive, rather than exact, concept. For example, we may say 2,340 is one order of magnitude higher than 488 but on the same order of magnitude as 977. Fermi estimates only have to be accurate up to a couple of orders of magnitude, so numbers can be replaced by other more convenient numbers on the same order of magnitude.

Order of Understanding/Description

Orders of understanding are a framework of modeling in which we separate all the details relevant to a system or phenomenon into different levels or "orders." Some details are more important than others, in that they have a greater impact on the model's predictions if included.

Orders of Causes

The orders (of importance) of causes are based on the magnitude of the effect if each cause were removed or altered. The one(s) that produce(s) the overwhelmingly largest effect are called first-order cause(s), and subsequently second-order, and so on. There may be multiple causes at each order.

Shape of the Earth

At zeroth order (even more basic than first order), we can model the earth as flat; this works for many purposes (e.g. navigating a city or country) but is incomplete. At first order, a sphere. At second order, an oblate spheroid (pear shape). At third order, one can include the terrain features such as mountains and valleys in the model. Further refinements can still be made. (See The Relativity of Wrong by Isaac Asimov.) To put this more numerically, the curvature of a flat earth is 0 feet per mile, while that of a perfectly spherical earth would be 0.667 feet per mile, a refinement from 0. On the earth's oblate spheroidal surface, the curvature varies from 0.6644 feet per mile to 0.6689 feet per mile, which is a tiny refinement from a sphere.

Commute to Work

When describing the route from home to work, the zeroth order description may just be a straight line. The first order may include the actual roads and turns along the way, and the second order may include the lanes and traffic lights. At higher orders, one may include the traffic condition and pedestrians.

Maslow's Hierarchy of Needs

Since the hierarchy is constructed such that each previous level must be satisfied before the higher ones become relevant, you can consider the lowest level as first order and each level up as one order higher.

Exemplary Quotes

“Ok, at first glance this dramatic increase in breast cancer in Korea seems like an intractably complicated problem, but maybe there is one aspect like diet or environmental change that is the primary driver. If we can identify it first, then we can look for the next most important cause.”

“It turned out that the prices of these stocks was to first order being determined by the buy/sell orders of just a few major pension funds. After that, the second order effect was the automatic buying and selling from the index funds. In fact, the small investors that we thought were important barely affected the prices of these stocks at all—a third or fourth order effect at best.”

“It used to be that the annual population of predator bears was the first order determinant of the annual salmon population, but nowadays the bears are a second order effect, and the fishing industry is the primary determinant.”

“Generations of Americans have been told that they live in the world's richest nation. But the United States today might more accurately be described as the nation with the world's richest rich people.”

Quoted in Oakes et al., 2012, Teaching to Change the World

In every century people have thought they understood the universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern "knowledge" is that it is wrong.

There are different levels of "wrong," and each correction to the previous wrong idea is typically a refinement (by including a higher order effect), rarely a total re-evaluation. Even if the new idea turns out to be wrong or incomplete also, it is still less wrong than the one before.

You know what the real cause of unemployment is? It's the stimulus cheques that the government is distributing discouraging people from finding a job.

While the distribution of stimulus cheques may have an effect on employment, the more important question is to ask whether it is a leading cause of unemployment, or if there is another lower-order (more important) cause. Such a way of reasoning makes it possible in a debate to concede that X is a cause of unemployment, without fully conceding that it is the cause or even a primary one.

After this lesson, students should

1. Concept Acquisition
   1. Multiple Causation: Any given effect may be brought about by a complex combination of many causes (which may interact with each other), with varying degrees of influence on the outcome.
   2. Orders of Understanding: When there are multiple causes of a given outcome, it is often the case that some causes are much more impactful than others. In these cases, we draw a rough qualitative distinction between the cause(s) with the greatest impact for a given effect (first order cause/explanation), the causes with somewhat less impact (second order), and the much less influential causes (third and higher order).
   3. Effect Size: The size of the effect under examination (e.g. how much being overweight affects health is the effect size of obesity on health).
2. Concept Application
   1. Distinguish first order, second order, & lower orders of explanation.
   2. Identify multiple causes for a given effect or outcome and evaluate the relative importance of each with respect to different contexts and goals.
   3. Given a concrete example, identify good and bad examples of evaluating and using the relative importance of causal factors.
   4. Given a concrete example, recognize and critique poor decisions that result from considering only the ranking — and not the relative magnitude — of causal factors.
      1. For instance, differentiate a case with one huge first order factor and many tiny ones from one involving several factors of comparable and large magnitude.

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