A reading of the essay Maps

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Maps

One might ask why this initial essay is labeled 'Maps.’ After all, this is a course in microeconomics, not cartography. We'll explain that shortly. The purpose of this essay is primarily to address the question of motivation: why study the model of supply and demand and the other core models of microeconomic theory? What is knowing those abstract models good for?

Students, particularly those taking a first course in a subject, either take on faith that the models they are presented with are important, because their professors say they are, or ignore the issue entirely, lest they become too disheartened about having to study stuff that is irrelevant. But that approach creates a real risk --- the models get studied as things in themselves and we lose track of what we are modeling, which is where the real interest lies.

To make the case transparent we will proceed by first considering maps, thinking about how they are useful and why they are important. The approach may be a bit painstaking for some students, but since this should be familiar terrain for all we'll go through it quickly. So please be patient. We'll also try to bring in the obvious that maps themselves don't tell the full story. Indeed, it is story telling (or narrative) that is needed to fill in what the maps omit. So we'll consider the role of maps and the role of story telling and the interplay between the two.

Then we'll reason by analogy and think of the microeconomic models as playing a similar role as maps and think of story telling pretty much as story telling, but noting that economists do it in a way that is disciplined by the models and to some that makes their stories seem a little different. We'll also look at a few well known economists who are good story tellers.

Let's begin by having you reflect on your experience with maps. Can you give an example where the same map is used for several different functions? What about another example of different kinds of maps, where the focus should be on maps that are designed for different uses.

Here are some suggestions for how to respond as you either write comments to this and subsequent posts or write such a response in a document on your own computer.
(1) Do try to answer the question(s). Doing that will help you understand the flow of the argument.
(2) Since some of the questions refer to the preceding discussion, it might help to write a summary sentence of that.
(3) You might also want to write a sentence about what the question is trying to elicit from you, e.g., to have you reflect on the previous discussion, to get you to examine a particular Web site, or to have you compare the theory to a particular realistic example.

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You can compare your response to the bolded green text below to see if you are on track.

As an example, consider a map of your state or your province. One use of that map would be to concentrate on a particular county, perhaps the one in which you reside, and to locate adjacent counties. Another would be to locate the various major cities and urban areas. Yet a third would be to find routes of transit from one location to another within the state. There are maps that show weather patterns, other maps to show the distribution of natural resources, maps to illustrate topographical features and maps that focus on roads. And don't forget Flint's map from "Treasure Island."

Let's contrast a map of a region to an aerial photograph of the same region. While both represent the same area there are clear differences between the two. The map emphasizes certain features and lets other aspects blend into the background. The photograph displays a likeness of all elements the camera can pick up, in proportion to their size in actuality.

This is a key feature of maps. While each includes information that is specific to its function, each also excludes other information that for the purpose at hand is extraneous. The act of excluding information to bring to focus that information which is retained is called abstraction. Maps are a particular type of useful abstraction of reality. Indeed, abstraction is a necessary part of the scientific method and good abstraction should conform with the principle known as Occam's Razor, which asserts that the simpler explanation should be preferred.

To see a definition of a map, follow the link below. The site also makes a nice tie between maps and mathematics. We'll see a similar tie to math with the microeconomic models.
Mathematics of Maps
Occam’s Razor

Now consider specifically maps used for travel and in this case we want to contrast a map, on the one hand, to directions for taking a trip, on the other hand. Which is simpler? Are there instances where you would want to have a map even if you already had directions? What is the relationship between the two? To make this even more concrete, focus on a trip where you are driving.

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Directions are simpler and very specific. They concern how to get from a point of origin to another point of destination. If followed precisely (assuming they are correct) they will allow you to get to where you are heading. But to keep them simple they may omit helpful landmarks that allow you to find your way. The reason we suggested that you focus on a driving trip was to encourage you to consider the possibility that you could drive past a turnoff specified in the directions. Directions are less useful if you make a mistake and get lost as a consequence.

Maps are different in this respect and hence useful to have even if you also have directions. Since maps contain many locations and many routes all in a single view, with the aid of a map it is possible to re-orient yourself after you have missed your turnoff and having done so to find a way to get back on the correct path. You can construct directions from maps and do this for many pairs of origin and destination points. Maps are more complex than directions but also more general.

There is power in this generality. It means you need have only one map to handle many different routes. That map can help you frame location information, even for items that don't appear on the map. Those items are situated between roads or other markers that do appear. There is also another important generality about maps that applies in a different way. Reading a road map is a skill that takes time to acquire but once you've learned to read one road map you should be able to read any road map. So the skill of reading a map is broadly applicable. Maps are designed to conform with certain standards to make them generally readable.

While maps are generalizable abstractions of reality they also distort reality in certain ways in that in actuality things appear other than they appear on the map. Can you give some examples of how maps distort and in addition for each example provide an explanation why the distortion occurs?

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One example of distortion that occurs in road maps is that there are some roads which are displayed as "thicker" than would be accurate. Interstate highways, in particular, are represented more thickly than would be correct based on proportion. The added thickness is to indicate a major thoroughfare with no traffic lights. This is a distortion of emphasis. But there are also distortions of representation. Fundamentally, these distortions occur from depicting three dimensional space onto a two dimensional surface. One such well known type of map which manages this representational issue in a clever way is the Mercator map. Mercator maps make land masses nearer to the poles, for example Greenland, appear larger than they actually are. These maps also depict lines of longitude, which in reality are great circles that intersect at the poles, as parallel lines.

Background on Mercator Maps
Examples of Mercator Maps

Does the presence of these distortions render the maps useless? Should we instead focus exclusively on representations that are perfect replicas?

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Absolutely not. Distortions of emphasis are placed into a map deliberately to make it more readable and therefore more useful. And even distortions of representation are fine, as long as the reader of the map understands the nature of the distortion and how to interpret the information that is being provided. Mercator designed his maps to enhance navigation. His aim was to promote usefulness. Exact replicas may be too hard to work with because they are more complicated and they may be too unwieldy to use. Distortion is not a fatal flaw at all, but distortion that is unrecognized can create errors in interpretation. Therefore it is important to understand the limits of the representation, to avoid making these errors.

Now let's imagine you are planning a drive trip for vacation. Can you think of information you'd want to learn for the trip that you won't find in a map? How would you acquire that type of information?

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You might want to know about places to stay, good restaurants, and sites to visit. Much of what you'll want to know is a matter of opinion rather than fact, but it may be that the opinion is shared widely enough that you treat it as truth for making your choices. Sometimes, however, you'll get conflicting views. In this case you may adopt one for your own based on which comes from the most credible source. Barring the ability to determine credibility, you may be swayed by how well the view is articulated. To get this information you might talk with a friend who has previously taken a similar trip, or visit a travel agent, or buy some travel books, or visit a variety of Web sites. Indeed, you might do some preliminary investigation of this type of information just to determine whether making the trip will be enjoyable.

After having acquired this information you'll be filled with stories about your trip. And if you take the trip you'll modify those stories and come up with new ones based on your own adventures and experiences. The richness of the experience will be remembered via the richness of the story. This too is an important point. Rather than build ever more complex maps to incorporate the detail that makes up this richness, we move from a map framework to a narrative framework to bring in that information. Good narration is full of rich information woven in to make the story compelling. Indeed some of the most famous fiction books are stories about trips. For example, consider The Odyssey, Gulliver's Travels, and Journey to the Center of the Earth, to name but a few.

We've concluded that maps themselves are not sufficient to provide all the information about a trip. Narrative is also needed. But what about the other way around? Is narrative sufficient? Can you tell a good story about travel without reference to a map? What do you think?

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A good story about travel is based on experience, real or imagined. We've already indicated how a map can be helpful in charting a trip. Is it absolutely necessary? Of course not. The more familiar the terrain, the less the map is needed; the information is already in the head of the story teller. But when the trip is to a new location, surely a map is helpful. Likewise a map is helpful to a reader of (or listener to) the story if the places in the story are not already part of the reader's experience. It helps the reader frame how the various places in the story relate to each other.

For the novice traveler, there is an overt and symbiotic relationship between the map and the story. As the traveler gets more experienced, the relationship persists but it becomes more tacit. The map serves as a metaphor for the trip in that the traveler thinks about the map, plots a course there, and then transfers that thinking to reality, rather than thinking directly about the reality. For the novice this is a laborious process. For the expert it may seem so intuitive as to not happen that way. But it does. And the reason should be clear. The map is simple and it is that simplicity that allows the ready plotting of the course. It is easier to do it that way and then transfer the conclusions.

We will now take the symbiotic relationship between maps and travel stories itself as a metaphor, in this case the metaphor is for the economic models we will encounter and the stories about the economic phenomena being modeled. Just as you need to learn to read a map and use it for making directions for a trip you need to get familiar with the economic models and learn to analyze them to draw conclusions that can be applied to understanding economic phenomena. The analytic modules done in Excel are aimed at giving you practice in developing these modeling skills. Likewise, you need to hone your skills as a story teller. You do this by reading the stories of economists who are skilled at story telling and by writing some yourself. Because economics is so much a part of world around us, you also learn story telling by reading news and commentary with economic content. The modules delivered as blog posts are aimed at improving your story telling skills.

Lakoff and Johnson, in 'Metaphors We Live By' make the case that metaphor is intrinsic to language and the way we think. Indeed we humans may be hard wired to use metaphor.
Lakoff and Johnson at Amazon.com

Other than your instructor, do you know the names of any professional economists? Have you read anything they have written?

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One way to identify the superstars of the Economics profession is to do a Web search on 'Nobel Prize in Economics.' This will give a good set of the giants of the profession. Less well known but also important is the John Bates Clark medal awarded every other year to the best American economist under 40. The recent Clark medal winners are having a profound affect on the current directions that economic research is taking. Many professional economists spend a good deal of their time writing for other economists. You can find their published work in such journals as the American Economic Review, Journal of Political Economy, and Quarterly Journal of Economics. A smaller number of economists also write for general audiences, where the intention in the writing is to be literate but not require formal economics training in the reader. There are an increasing number of blogs by professional economists.

Below we briefly describe a few of these economists and give some links to their work.

Let's begin with Paul Krugman. He is an extremely prolific writer. His renown originally came from work on International Economics, in particular on strategic trade policy. He is a former Clark Medal winner and a good bet to the win the Nobel prize in the not too distant future. He has a column that appears twice weekly on the op-ed page in the New York Times, where he writes on political as well as economic matters.
Unofficial Krugman Homepage
New York Times Krugman Page (free but you must register).

Next, let's consider Steven Landsburg. He is fun to read, not the least because he is so frequently outrageous in his claims. You may not always agree with him, but he will challenge you in your own thinking. He analyzes ordinary human behavior by taking an economics slant and comes up with provocative analysis and commentary.
Landsburg Homepage
Fairness and Employment

Finally, let’s consider Gregory Mankiw. His Principles text is one of the market leaders. His blog can be considered an adjoint of his text.
Mankiw Blog

I would appreciate getting any comments on the tone, style, or substance of this essay.