8.1 Orders of Understanding

Because each event and/or phenomenon has many causal factors, it is often important to distinguish which factors affect it the most and which factors play a smaller role.

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 "X is the cause of Y".

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.

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 Misconceptions

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 (e.g. they are the underlying environment or circumstance). Whether or not we assume something to be constant may be partly a question of values. (E.g. 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.

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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.

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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.

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.

Useful Resources

Lecture VideoDiscussion SlidesHandouts and ActivitiesReadings and Assignments

Discussion Slides Template

The discussion slides for this lesson.

Identifying Orders of Understanding Worksheet

Worksheet used for the activities in this lesson.

The Relativity of Wrong

Isaac Asimov on using orders of understanding in our descriptions of reality.

Recommended Outline

Before Class

Familiarize yourself with the worksheet and print it.

During Class

3 Minutes	Ask your students the warm-up questions.
8 Minutes	Have your students discuss the introductory example.
25 Minutes	Have your students work on the traffic accident activity. You should skip parts 3 and 4 if you're running short on time.
15 Minutes	Happiness activity.
24 Minutes	Government spending activity. (This is the most important activity. Make sure you leave sufficient time for it.)

Lesson Content

Warm-up Questions

Normal Minecraft and Minecraft with shaders.

Referring to the provided image, ask your students the following questions. We're modelling natural scenery with computer graphics.

1. What first order details of the scene did the graphic designers include on the left?
2. What second order details were included on the right?
3. What further higher order refinements could we make?

Introductory ExSAMple

Bigger blocks are lower order than higher blocks. They’re refinements of the model.

First poll your class on their answers following question. Claim: "Sam makes a lot of money because she works hard." Do you think Sam's hard work is:

1. A first order cause of her high income.
2. A second order cause of her high income.
3. A third or higher order cause of her high income.
4. Not a cause of her high income.

After the poll results are revealed, tell the students that you forgot to find out whether Sam was born in a Bangladeshi slum or to a family of lawyers in the Upper East Side of Manhattan. What if Sam attended college?

Poll the students again and give them another minute to discuss before answering.

The extent to which "hard work" plays a role in how much money Sam makes is a second (or higher) order cause in all of these cases. The first order cause would be what her circumstances are. If she was born in the Upper East Side then there's a much higher floor and ceiling to what Sam could conceivably earn than if she were born in Bangladesh.

Orders of understanding are a part of the modeling process, which in turn requires first defining the scope of the problem. This question is tricky because it does not specify the scope, i.e. the success of a random world citizen or a New Yorker/Bangladeshi. This is why, once the scope is clarified, the orders of understanding in modeling the causes of success change.

Traffic Accidents

This activity lets students practice assigning orders to various causes. In particular, it frames the orders of causes in terms of intervention (c.f. 6.1 Correlation and Causation). It also highlights the importance of first considering the set of relevant or realistic interventions, before studying the magnitude of the effect of each intervention.

The orders are somewhat based on one's intuition, and there are no correct or recommended answers for this activity. The purpose is to let students reflect on and discuss the relative impact of various causes of traffic accidents, as well as the relevance of interventions as a way of studying the effect size.

Identifying Orders of Understanding Worksheet

Worksheet used for the activities in this lesson.

Instructions

20 Minutes	Have students follow instructions on the worksheet and answer any questions they may have. If they only finish Parts I & II, that's fine; be sure to save time for Happiness and Government Spending.
5 Minutes	Bring everyone back for a whole-class discussion and to share results.

Activity 1

[Brief description of and motivation for the activity]

[Common misconception or thing to look out for.]

[Thing you really need to look out for!]

[Title]

[Useful tip, guideline, or other background.]

Instructions

[n] Minutes	[Activity.]
[n] Minutes	[Activity.]

Discussion Questions

[Question 1]

[Possible misconception that may need to be corrected and clarified.]

[Intended answer to the above question.]

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[Question 2]

[Possible misconception that may need to be corrected and clarified.]

[Intended answer to the above question.]

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8.2 Fermi Problems