The topic of this post is something that I call “Thought Cover”, which measures how much error one makes while performing an action like writing or playing a video game. I was inspired to write this article by my frustration at making mistakes when trying to act quickly and when put on the spot. Thought Cover is my latest attempt to capture this phenomenon, and it informs some guesses at how to alleviate it.
Before going on, I want to give a warning that I make up quite a few words in this post. Here, and for other concepts I assign technical names to, my goal is to condense a cloud of vague concepts into an object that with our minds we can see, hold and manipulate. While my new terminology can be awkward, I think they help towards this goal.
I find the human capacity for intellectual blunder to be as fascinating as human intellect itself. When a parent is in a hurry, she might confuse Sarah for her sister Elise. When a math professor delivers a lecture, he might say one thing, write another, yet mean another. And if you've tried to write something nicely, you've probably noticed that a good night's sleep can make you question whether the you from the day before was in the right mind.
Something I call Thought Cover underlies each of these cases. In each situation, there's a sequence of actions. For the mother, it's the words she's saying. For the professor, it’s both what he’s saying and the symbols he writes on the board. When you write a document, each word you choose is an action. If there are 1579 words in this article, and we call each of these 1579 words an action, we can say that as I write my first draft, a good portion will be erroneous. For example, if my final draft and my initial one have only 1000 words in common, 579 of the words would have been "erroneous". The Thought Cover in this case would be 1000 divided by 1579. Thought Cover measures how much of whatever you’re doing has been properly thought through, or at least are performed as if you had thought through them; it measures your error rate.
The concept of "error" is hard to define. Heuristically, it's when you do something other than what you wanted. But what does this mean precisely? Error needs to be defined with respect to a reference, and this leads to two definitions: Internal and External Error.
In the case of writing, you might look back and find a terribly awkward phrasing and immediately replace it. This is an example of what I call Internal Error: something that you yourself designate as an error, when you can give your full attention to it. The reason why you made the error initially is simply because it was too difficult to focus on both the proper wording and the overall idea when writing the first draft.
But even the sober and fully attentive you can't recognise all errors. As a simple example, you could have misspelled a word and not recognised it because you don’t know the actual spelling. Another example is in Tennis. Playing tennis involves around a hundred actions a minute. You could play with exactly equal performance today and tomorrow, today playing with a novice and tomorrow with an ATP-top 200 player. The exact same action, say, hopping slightly to the left when the opponent's racket hits the ball, would not be a noticeable error against the novice, yet it could be an exploitable and thus consequential error against the expert. Additional examples include stand-up comedy (what routines are boring and which are funny?) and coding (does the code do what it’s supposed to?). Errors that are only noticeable with the help of others or when evaluated against the world I call external error. Internal and External error result in Internal Thought Cover and External Thought Cover, and depending on the context I mean either type going forward.
The natural question now is what determines our Thought Cover. What differentiates the fumbling mathematician mis-writing every other symbol and the pianist striking thousands of notes with perfection? To answer this, we’ll need to define two more types of Thought Cover.
While thought-cover underlies both the quality of a written report and whether someone wins at Tennis, it’s clear that there’s a big difference between the two. After all, writing is a gradual process, where you can improve on the initial output draft upon draft. In comparison, lecturing or Tennis happens in real-time.
One-shot Thought Cover describes how “perfectly” someone can do things in the first run-through. How good can you write your first draft? How flawlessly can you play a Nocturne? A related concept is one-shot thought bandwidth, which looks at the rate at which one can perform error-free actions. If one's one-shot thought bandwidth is thirty words a minute and they force themselves to type at fifty, a simple model would say that their resulting Thought Cover would be 30 divided by 50. This isn’t too helpful to look at however, since it depends greatly on how familiar one is with the task. For a detailed look at this concept, see Appendix 2.
How can we improve our one-shot Thought Cover? I’ve found that the following simple concepts are useful:
Chunking: Actions are easier to do correctly when we group them together. For example, it’s easier to correctly recall telephone numbers when remembering them in groups of three.
Representations: We can free up our focus by finding more efficient ways of thinking about things. For example, it’s easier to measure the length of a week in days rather than seconds.
Object of Focus: How does a teacher simultaneously speak, write and recall what she’s going to say next? The answer is probably via very quick context switching between each of the three tasks. I’ve found it helpful to be mindful of how I’m splitting my attention. In conversations, I often focus too much on the overall direction of the conversation and what I’ll ask next, rather than what my partner is actually saying.
Sink-in Time and Sequentialism: Try to read and solve the following problem in 5 seconds:
Five friends are getting two pizzas and are deciding on toppings for each. All four eat one quarter of a pizza. They would prefer to eat from both pizzas, but it’s fine if they’re forced to stick to one. Each pizza costs $15 and each meat topping costs $2. Specify two reasonable pizza choices for the following preferences:
| Friend | Preferences |
|---|---|
| Bob | Hates sardines, likes pineapples |
| Alice | Loves sardines |
| Ben | Wants all meat options (ham, bacon, sausage) |
| Nelly | Wants vegetables, and the total price to be under $35 |
| Daniel | Wants all meat options (ham, bacon, sausage) |
One solution is a vegetarian pizza shared by Bob and Nelly, and depending on who wins the argument, a pizza with sardines and one meat topping shared by Ben and Daniel. Alice could eat from both pizzas. If you rushed the question, you would probably be much more likely to have made an obvious suboptimality, simply because there wasn’t enough time to load everything into working memory. Sink-in Time is important because of context switching; if we switch tasks so quickly that we can’t properly update context, we’ll probably be doing a lot of guesswork.
Sequentialism is the principle of completing one task before proceeding with another. By reaching a proper conclusion before moving on, we can free up our focus and memory completely for the next task, rather than quickly switching back and forth and dropping context everywhere. I’ve found this to be very useful for working for increasing my endurance and Thought Cover in coding projects.
If one-shot Thought Cover measures one’s performance on the spot, iterated Thought Cover measures one’s ability to polish something over time. Across drafts of a paper, or revisions of a composition.
This is a separate concept from creativity; for how creativity relates to Thought Cover, see Appendix 1. The act of writing will be the running example in this section.
Going back to the definitions of error, it’s helpful to distinguish between internal Iterated Thought Cover and External Iterated Thought Cover. For the former, the limiting factor is one’s working memory and attention. By the time one reads through their article a few times, they typically exhaust all the obvious improvements they can think of, and thus achieve perfect internal Thought Cover.
As soon as we get a good first draft, it’s simple to converge to good internal Thought Cover. But the hard part is getting started. In order to converge into some direction when iterating, the first draft needs to be of a sufficient quality; its one-shot Thought Cover needs to have been good enough to be worth building upon. I find that if my first draft is too shaky, I find myself changing the fundamental ideas and rewriting the article, rather than polishing it, between drafts!
But usually when you write something, it’s for others to read, so the more relevant metric is external Thought Cover, which looks at how flawless your work is to others. We often lose external Thought Cover through mistakes we’re blind to, and bad assumptions on the background knowledge and interests of the reader.
While the best way to improve external Thought Cover is to simply ask your target audience what they think of the article, it’s embarrassing to do so unless the article is already at a decent level. In the context of writing, how can we polish our work as much as possible before sharing? Two concepts to think about are:
The Curse of Knowledge: Courtesy of Steven Pinker. As one dives deeper into a topic, it becomes harder for them to clearly discuss it with a layman. This is because of issues like the expert using technical terminology without being aware of it, and functional fixity, which is when the expert sees objects for what they do rather than what they are. A sentence with functional fixity would be “Participants were tested under conditions of good to excellent acoustic isolation”. A sentence without it would be “We tested the students in a quiet room”.
Framing: Framing is simply the context through which you see your work. Needless to say, applying the wrong frame can be a disaster. As an illustrative fiction, imagine a young and naive McKinsey analyst is hired to make a marketing campaign for McDonalds. McDonalds has the implicit frame of making as much money as possible without getting into legal trouble. The analyst assumes the frame of providing long-term value to the restaurant-goers, and realizes that fries are terribly unhealthy and are hurting the people who eat them too much. The minute before he’s fired, the analyst presents his marketing proposal. On the front page is the slogan: “McDonalds, I’m lovin’ it! But in moderation, and without the fries!”.
Thought Cover looks at how much error we make in the things that we do. Since it’s such a broad topic, we taxonomize it in various ways: * Internal versus External Thought Cover: Do you or others determine whether something is considered an error? * One-shot versus Iterated Thought Cover*: Are you playing a game of tennis, where you have one shot at making as few errors as possible, or are you partaking in the more leisurely activity of writing?
With this concept, I’ve tried to capture a phenomenon that has recurrently plagued me. I’ve generally had confidence in my creativity and ability to hold context and say relevant things. I can occasionally make leaps of brilliance, and see beauty where others might miss it. Yet as soon as I define myself on these maximal moments, I slip into regretful errors in unrehearsed conversations; I say things that not only “sound dumb”, but that I often don’t even believe in. When writing reports, I write in a style that is completely clear to myself, and yet as soon as the people I wrote it for start evaluating it, they discover buckets of embarrassing errors. How could I have been so blind and careless? Thought Cover has provided me with a measurement system for this phenomenon, and what we can measure, we can control.
How can we compare a consultant’s slide deck to a writer’s poem? Clearly Thought Cover, which just measures whether or not things are erroneous, doesn’t suffice. Thought Cover is fundamentally about competence. The soccer player that occasionally roundhouse kicks the ball into the net from half the field away but has terrible stats otherwise isn’t competent; the unglamorous defender who consistently blocks opponent passes is.
Perhaps a more relevant measure for artists would be “Wow Cover”, which measures how much of their work amazes us. The Wow Cover would look at the Wow across the different components of their work. A Wow of 0 means an error and of 1 means a dry and boring non-error. If, for example, a passage in a book had a Wow of 10, it would probably be remembered for years.
Here are some examples of what different levels of Wow Cover and Thought Cover could look like:
The Consultant: Good Thought Cover, low Wow Cover. Everything she does is defensible, but where’s the beauty in that?
The Playmaker: Good Wow Cover but poor Thought Cover. For example, a foosball player that can score goals from across the table and snake shot but occasionally scores on himself.
The Darwin: Good Thought Cover and Wow Cover. Darwin came up with revolutionary ideas, then rigourously defended them in the Origin of Species. Mastery of Thought Cover and wow cover, plus a bit of luck, can lead to a paradigm shift.
As an illustration of one-shot Thought Cover, let's discuss the act of writing in more detail. I find writing to be an exhilarating and sometimes excruciatingly difficult task - a game of working memory and selective attention. For example, as I type these sentences, I translate vague ideas into words and sentences, while consciously limiting the amount of real-time editing I do, resisting the urge to edit words two sentences back that I realize I don’t like.
Previously, I talk about priming capacity, which is one’s ability to load context into their minds, and, based on that context, generate their next actions or words. The priming capacity can be seen as the size of a box, the inputs of which determine what comes out of the writer’s fingers. If the box doesn't have any items relevant to what he’s writing about, you can expect the fingers to type gibberish. On the other hand, if the box contains not only the ideas he’s planning to write, but everything he’s already written, you can expect what’s written to be well in context with respect to the rest of the piece. Let's call this box the priming buffer.
In the case of writing, coding, speaking and similar tasks, priming buffer probably determines Thought Cover. I say that writing is a game of managing context/working memory because the job is to keep only what's relevant in the box. This explains why agonizing over word choice during the writing of the first draft can be such a danger. It's very expensive. Say you don't like the word "gregarious". You load several synonyms into your working memory and cycle through them a few times, seeing how well they fit in with the sentence. Before you know it, you’ve replaced all of your context - what you wanted to write next, what you’ve just written - with fifteen synonyms of “gregarious”!