Iterative Versus Incremental Learning

I know this makes me seem like an enormous nerd. But one of the great joys of my life is learning. I enjoy few things more than figuring out a problem in an area that interests me, researching a question nagging me, thinking through arguments that are capturing my attention, and reading books that intrigue me.

So, over the years, I have gravitated towards friends with similar interests. Almost without exception, these close friends and acquaintances are autodidacts (i.e. a self-taught person). Though each of them is college educated, and most have postgraduate degrees, each has developed an impressive level of knowledge and skills in areas outside of their academic training. Each of these friends can learn new concepts, fields, and skills quickly — impressively quick.

Recently, I was thinking about the way many of these friends approached learning and how it differed from my friends who are not autodidacts (and, in addition, how it differs from the approach to learning in much of our education system). And I came up with a short, descriptive phrase to describe the difference:

For autodidacts, learning is iterative; for everyone else, it is incremental.

This may not seem too insightful at first, but it describes two drastically different approaches to learning a subject matter or skill. Let me describe it using a common experience many people (especially geeks and nerds) have: learning a new board game. When you learn a new board game, you have to learn the purpose of the game, the rules, and basic strategy.

Take the incremental approach to learning: you would read through the rule book, going at a pace that ensured understanding. First, you’d learn the objective of the game. Then you’d study the basic rules, the flow of the game, the board itself, and so on. You’d start thinking about basic strategy. And you’d do all this before you started playing the game. You’d start with the most basic rules and slowly build up your knowledge until you felt ready to play a game.

The iterative approach to learning a new board game is to just begin playing it as soon as possible. What’s the objective? What are the basic rules? Once you get that, you start a game. As you encounter a difficulty or confusion, you might ask a friend, read the rule book, or google the answer. Some game rules and concepts only become clear after several different situations cause you to think through the more complex rules several times. As you play, you revisit some of the rules and get deeper understandings of them; as you play, you slowly get better at strategy.

In the same way, the fastest learners I know don’t try to learn a subject piece by piece. They don’t start with basic introductions to a subject matter or to a person’s thought (e.g. if studying the philosophy and theology of Thomas Aquila’s, they don’t buy an introduction to his thought). They jump right in. And though the beginning can be confusing and frustrating, they eventually make rapid progress. It’s almost as if jumping into the deep end of the pool, they learn to swim more quickly than if they had slowly waded in from the shallow end. And this hold true whether what they are learning is to program, to remodel a bathroom, to understand a difficult area of theology or philosophy. They get a faint idea of how something works, tries it out, and then revisits and revises their understanding until it works.

So, how do they do this? What are different ways that they dive into learning, iteratively deepening their understanding, improving their concepts, testing out their competency, etc.?

  • Start with a project. They almost always start with a project that will force them to learn the subject matter well in order to complete it. If you are learning web design, start designing a website. Learning a language? Start with something you want to translate. Learning how to remodel or repair something in your house? Just jump in. Learning how to program? Start with an app you want to design. Learning John Rawls’s political theory? Write up a blog post on a section of how theory and your criticisms of it. Basically, jump into project that forces you to learn and use the concepts/skills you are developing.
  • Use introductions or tutorials only to be able to start your project as fast as possible. The fastest learners I know do consult introductions or tutorials. But they spend remarkably little time with them. Introductions and tutorials are just springboards to launch them into their projects; the hard work on the project, not the introduction or tutorial, is what causes them to learn the skills/concepts.
  • Iteratively revisit concepts/skills that are important. Core concepts and skills are employed frequently in projects like these. When they first begin their projects, they have a shallow, incomplete, and muddled understanding of the core concepts or skills involved in what they are learning. But when they try to employ these concepts or skills in their project, they quickly hit areas where they realize that their understanding of a particular concept or skill needs to be improved. Then they revisit these concepts and skills, correcting misunderstandings and deepening their grasp on it. For example, when first learning a language, they might get a very vague and simple understanding of the verbal system. But when they start translating a work, they encounter verb forms that they don’t understand, forcing them to iterate over their grasp of the verbal system in that language, correcting and deepening their understanding.

Now, this seems relatively straightforward. In fact, if you’ve never learned a topic or skill in this way, you might be tempted to through yourself into a new project and learn it this way. But let me end with a warning some attributes of these fast learners that is necessary for taking this approach. If these don’t describe you, you might find it harder to utilize this approach:

  • Intensely interested in the subject matter. The people I know who learn the fastest usually have broad interests, and they only use this approach in areas in which they are interested. In fact, these fast learners might have performed abysmally in school (or abysmally in certain subjects in school). If they are not interested in a topic, they tend not to employ this approach to learning and so often learn as slowly as the rest of us.
  • Passionate, almost obsessive, about the chosen project. Whatever the project is, they are passionate about it. That’s why they can dive into it with so much energy and master a lot of material and skills quickly. They almost become laser-focused on it. In many cases, they are more passionate about the project than the subject matter. For example, they might not care to learn programming languages just for the sake of programming, but their obsession with complete a certain program or app makes them obsessive about learning anything necessary to complete it.
  • Comfortable with confusion, frustrations, and being wrong. This is an undervalued quality in rapid learners. Many people give up or slow down when they are confused, or quit when they get frustrated at how difficult something is. Others might just hate being wrong or making mistakes, and so they venture to make progress on a project out of fear of making a mistake or messing something up. But rapid learners don’t seem to get very frustrated. They are comfortable with being confused about a topic, but they will keep throwing themselves into the subject matter in hopes that their confusion abates. If they are wrong, they correct their errors. If they mess something up, they try to fix it. But, ultimately, they don’t give up when they are confused or frustrated. They understand that learning to swim by jumping in the deep end means that you’ll spend a lot of time with your head underwater. That’s just a part of it to be accepted.

I am not sure that people unaccustomed to this approach to learning could successfully employ it in their own attempts to learn something. And I am not sure that this accurately describes the normal “fast learner.” As I said, this is only an observation about the people I know who learn the fastest. But if you are trying to learn something that you really want to learn, it is worth trying this approach. You might find that you can learn it much more quickly this way than through your normal approach.

C. S. Lewis on the Problem of Unanswered Prayers

I admire much about C. S. Lewis’s writings. He’s a great model of thoughtful engagement with his faith. The more I read of his, the more aware I am of how much deep reading and deep thinking lie behind his sentences.

But I am equally impressed – honestly, maybe more impressed – by how clear his prose is. He can be writing about difficult topics, and he phrases things carefully, with a clarity rarely matched. I often pause to think more deeply about the subject he is addressing, but rarely do I have to stop and work hard to understand him.

A few months ago, I was reading his essay, “Petitionary Prayer: A Problem Without an Answer.” I’d been meeting weekly with a group of college students, discussing Origen’s work on prayer. (Origen was an early Christian theologian.) And when I read how Lewis set up a common theological problem with prayer – that we are told that God would answer our prayers and that the Bible and our own experience show us that there are unanswered prayers – I found it to be another occasion when Lewis worded a problem so well.

Lewis mentions that one “pattern of prayer” is to qualify our prayers with “Thy will be done.” In praying so, we recognize that our specific prayer requests might go unanswered, but that what God wants will be done. But, yet, we are also called to have faith that God would “give precisely what we ask” and not simply that He would give us “the best.”

Lewis writes:

“It is as if God demanded of us a faith which the Son of God in Gethsemane did not possess, and which if He had possessed it, would have been erroneous.”

C. S. Lewis, “Petitionary Prayer: A Problem Without an Answer” in Christian Reflections, p. 144

What a great way of stating the problem of prayer. Some verses read as if we are called to have a faith that our requests will be answered, which is precisely the kind of faith Jesus did not have the night before his death.

How could one not read that sentence and grasp both the logic and the emotion of the problem?

Finding Your Identity By Asserting Yourself

While reading Thomas Merton’s classic, New Seeds of Contemplation, I came across a passage that might be the most powerful passage on identity and self-assertion I have ever read. He writes:

People who know nothing of God and whose lives are centered on themselves, imagine that they can only find themselves by asserting their own desires and ambitions and appetites in a struggle with the rest of the world. They try to become real by imposing themselves on other people, by appropriating for themselves some share of the limited supply of created goods and thus emphasizing the difference between themselves and the other men who have less than they, or nothing at all.

They can only conceive one way of becoming real: cutting themselves off from other people and building a barrier of contrast and distinction between themselves and other men. They do not know that reality is to be sought not in division, but in unity, for we are “members one of another.”

The man who lives in division is not a person but only an “individual.”

I have what you have not. I am what you are not. I have taken what you have failed to take and I have seized what you could never get. Therefore you suffer and I am happy, you are despised and I am praised, you die and I live; you are nothing and I am something, and I am all the more something because you are nothing. And thus I spend my life admiring the distance between you and me; at times this even helps me to forget the other men who have what I have not and who have taken what I was too slow to take and who have seized what was beyond my reach, who are praised as I cannot be praised and who live on my death…

The man who lives in division is living in death. He cannot find himself because he is lost; he has ceased to be a reality. The person he believes himself to be is a bad dream. And when he dies he will discover that he long ago ceased to exist because God, Who is infinite reality and in Whose sight is the being of everything that is, will say to him: “I know you not.” (47-48)


(By the way, I am starting a podcast. The Thinking and Believing Podcast should launch at the start of June. I am already working on the first episode. It will be about topics that I’ve written about over the years on this blog — theology, philosophy, politics, etc. — but with an approach that is quite different than the one I take on this blog. Stay tuned for more updates about it.)