The oral tradition at the University of Chicago attributed the observation that “sloppy writing reflects sloppy thinking” to Milton Friedman. Of course, it echoes George Orwell’s claim that “the slovenliness of our language makes it easier for us to have foolish thoughts.”

Neither Friedman’s word “reflects” nor Orwell’s phrase “makes it easier” go far enough. The right verb is “produces.” Clear writing produces clearer thoughts. Sloppy writing produces sloppier thoughts. This is a natural consequence of the fact that anything stored in connections between neurons is part of a biochemical and electrical dynamic feedback loop. When we access one of these loops, we change it and connect it to other loops. To use an analogy from computer science, accessing neurons is never just a read. It is always a read and a rewrite.

Good mathematical theory is valuable because it encourages clear writing and thereby produces clearer thoughts in the mind of the author. It encourages clear writing by limiting the vocabulary that the author uses. The mathematical equations depend on a limited set of symbols. In good theory, each symbol is tightly bound to specific, precisely defined word or phrase from the vocabulary. The combination of the equations and the words used in the theory give the words and symbols precise meaning. The prose in good theory does not pull in vaguely defined terms that are not in this vocabulary.

Many people have commented that they do not understand what I mean when I say that mathiness lacks these precise bindings between symbols and words. One way to make clear how important these links can be is to provide an example that shows what it means for these bindings to be present and the ambiguity that can arise when they are not.

In my 1990 paper – the focus of a series of posts triggered by its 25th anniversary–the equations of the model contained two symbols, ||H|| and ||A.|| I bound the symbol ||H|| to the phrase “human capital” and the symbol ||A|| to the word “knowledge.” As I emphasized in my previous post about human capital and knowledge, one of the main points of the model was that it is important to distinguish between these two abstractions. Information stored in neural connections is different from information on the printed page.

There was nothing particularly radical about this. Many growth models that relied on exogenous technological change had two independent variables, ||A|| and ||H||. When I wrote, new models were exploring ways to let change in ||A|| be influenced by things that people chose to do. All I did was propose a model with both of these features, one in which someone could decide to use her ||H|| to produce some ||A.||

The distinction between ||H|| and ||A|| can accommodate different inherent characteristics for these goods and different policy choices about the legal protection they receive. In the model, ||H|| (stored in neural connections) is rival and excludable; ||A|| (codified knowledge stored in a document that I called a design) is nonrival and partially excludable.

As I emphasized in the first post in this series, the assertion about rivalry vs. nonrivalry is a claim about the production possibilities that the physical world makes available to us. We can copy codified knowledge at low cost. We cannot copy directly the configuration of some neurons; at least not yet. In contrast, the assertion about excludability reflects assumptions about policy decisions. For example, a society can change the degree of excludability for codified knowledge ||A.|| The assertion in the model that ||A|| is partially excludable was an “is” statement not an “ought” statement. In the 1990 paper, I avoided any “ought” statements about intellectual property rights and focused on an analysis of “is” statements. One must walk before trying to run.

In response to my claim that it is physically impossible for information stored in neurons to be nonrival or nonexcludable, someone wrote:

Human ability is socially determined as well as individually developed, and all use of human ability other than the most basic, shared with animals, is also socially embedded.

The notion that human knowledge is essentially rival and excludable is socially pernicious and it is the antithesis of a fundamental assumption of scientific method, that of shared results.

This response nicely illustrates the ambiguity that arises when prose does not rely on the clarity that a restricted, precisely defined vocabulary allows. It uses two different phrases–“human ability” and “human knowledge”–that might be synonymous references to a single abstraction. But they might also refer to different abstractions with different characteristics– human ability capturing something like the content stored in neural connections and human knowledge capturing the content stored in text and symbols that I called knowledge. It is impossible to know.

Just to be clear, this response is not mathy. To layer in some mathiness, one would have to add a bunch of opaque mathematical symbols that do nothing to clarify whether these two phrases refer to one abstraction or two.

My hunch is that while writing, the author did not realize that there was a question about whether these refer to different abstractions and if so, how they might differ as economic goods. Clear writing might usefully have surfaced this question for the author. Clear mathematical theory would certainly have done so.

Part of what makes the economics of ideas intellectually interesting is that it is inherently self-referential. To construct a theory about producing ideas, one must produce some ideas. Writing clearly is a fundamental part of the production process that generates new ideas.

The author’s words phrases “socially determined” and “socially embedded” point toward something that is true. Part of the human capital (qua information stored in neurons) that any person possesses is the result of exchanges of codified knowledge (qua information stored in words and symbols) with other people. Often, a person acts like a passive relay, taking in a message and re-transmitting it without modification. When many people relay the same message back and forth, it can come to be seen as a truism, even part of group identity. These people form their own dynamic feedback loop.

One such loop sends around the message that “there are human capital externalities or spillovers.” When I point out that there is no way to make sense of these words, the natural reaction from people in the loop is to get angry and to express moralistic judgments through the use of such words as “pernicious.” The question for them is whether it is really in their self-interest to express these emotions in sloppy writing.

Clear writing would give them agency to be more than a relay. They could edit and clarify the messages they receive from others. If for no other reason, they should want to write clearly because doing so will make them smarter. If the message makes no sense, acting as a relay makes you dumber.

To write more clearly, anyone can learn the basics of mathematical theory and use it to clarify written prose. These basics can be as simple as letters and arrows like the ones I used in my last post:

$$H \rightarrow A \rightarrow H$$

The strategy here is to start by identifying the abstract concepts that interact. Give each one a symbol; here ||H|| and ||A||. Use arrows to show the most important interactions. Then find specific words that you can bind to the symbols; here, human capital with ||H|| and codified knowledge with ||A||. Use those words to write about their interactions. “Someone with human capital can produce knowledge that is codified in the text of a message and send it to someone else, who reads the message and stores the insight as human capital.” Then give yourself the freedom to play and explore. See if you can surprise yourself.

For example, return to the assertion from the title. What symbol and arrow diagram can we draw to capture this? Start by adding some decorations to the symbols. Let ||H(t)|| stand for the neural connections that a specific person has today, so that ||H(t+1)|| stands for the neural connections she has tomorrow. To allow for the possibility of communication, let ||H^*|| stand for someone else’s human capital, so ||H^*(t)|| is what the second person has stored in his neurons today and ||H^*(t+1)|| is what he has stored in his neurons tomorrow.

The diagram I wrote above can now be redrawn to show more clearly that it is shows how one person can use a message that contains codified knowledge to communicate with someone else:

$$H(t) \rightarrow A(t+1) \rightarrow H^*(t+2)$$

The first person, who starts with human capital ||H(t)|| in her neurons today, produces a codified message ||A(t+1)|| that is available tomorrow. The day after, the second person reads that text, and this changes what he has stored in his neurons.

But the timing is probably less important than the actions. So I can redraw the image to suppress the timing and instead to bind the first arrow to the verb “write” and the second to the verb “read”:

$$H \xrightarrow{write} A \xrightarrow{read} H^*$$

Treat this as a creative process. Don’t worry about whether there are any rules you have to follow. At first, just make up things that make sense to you. (Later you may want to revise to make sure that your symbols will make sense to others, but in the beginning, don’t worry about them.) For example, if you want to show that it is the second person who reads, you could add the symbol * as a superscript for “read.”

So what might a representation of the title of this post look like? I’ll use brackets to group things together and display it this way:

$$H(t) \xrightarrow{write} \Big[A(t+1),\ H(t+1)\Big]$$

The diagram tells you that writing produces two outputs. In the jargon of economics, the codified message and the new human capital are “joint products” of the production process that we call writing.

Even if you don’t care about the difference between the effects that clear versus sloppy writing will have on readers, you may want to pay attention to the difference it has on you, the author. For better or worse, writing changes your mind.

This is #3 in a collection of posts that mark the 25th anniversary of the publication of my 1990 JPE paper.

#2: Human Capital and Knowledge

#1: Nonrival Goods After 25 Years

Thanks to Joshua Gans for spurring this series with this post.