Surprising Understanding
Last summer, I wrote a post detailing various strategies for reading mathematical proofs faster.
Last week, I stumbled across a new strategy that I think may be relevant for many different types of deep information processing.
I came across this strategy while peer reviewing a complicated computer science paper. As I read, I quickly became frustrated. I was processing lemmas and theorems, one by one, but as the details for each slipped from my short term memory to make room for the next, there was no sense of a coherent whole. It was as if I couldn’t get my metaphorical arms around this mathematical beast.
After an hour of this blind processing I decided to step back and try to summarize what I understood so far.
It was here that things got interesting.
As I wrote, I discovered to my surprise that I actually understood way more than I expected. My short summary stretched into a longer digression on the problem, why it was hard, what their technique did differently than previous results, and, in the final accounting, where the real contributions could be found.
To be clear, I didn’t have the math all worked out. If you asked me to recreate all the proof details, I couldn’t. But somehow during my frustrated slog from one step to the next, another part of my mind was dutifully collecting and organizing the pieces — work which didn’t become apparent until I tried to write down what I knew.
New Thoughts on Thoughts
Not long ago, when researching a yet to be announced new writing project, I stumbled into a large research literature on what is sometimes called Unconscious Thought Theory (UTT). At the core of UTT is the following idea: the parts of our brain supporting conscious thought represent only a small fraction of our neuronal horsepower. When it comes to complex tasks, therefore, our conscious attention can help intake and understand only a limited amount of information at a time.
Other parts of our brain, however, that operate below the level of conscious attention, are able to dedicate a lot more resources to processing these tasks: even though we don’t always realize this is going on.
I suspect this is what was happening during my paper review. While reading the paper, my conscious mind could only hold a limited amount of the complex information in my working memory at any given moment. The result was the frustrating feeling that I didn’t understand how the pieces fit together.
In the background, however, other parts of my brain were processing this information, trying different configurations and looking for effective ways to fit things together into a more coherent assembly.
When I then tasked myself with summarizing what I knew, my conscious brain tapped into this large reservoir of unconscious work, surprising me by how much I actually understood.
At least, this is one possible explanation.
Process then Summarize
Regardless of the exact source of the phenomenon I encountered, I suspect the strategy that generated it provides a useful deep habit for many cases where you must make sense of a large amount of complicated information.
Spend time to process the information, piece by piece, with full concentration. Once you’re done, step back and try to summarize what you learned. Though the process of digesting the information might feel frustratingly scattered, you’ll likely be surprised by how much work the other parts of your mind accomplished on your behalf. By writing down what you know, you cement this effort.
Maybe there’s another explanation: https://www.scientificamerican.com/article/unconscious-thought-not-so-smart-after-all1/
I agree that it’s up for debate, but psychological studies are inherently flawed. Scientists try to gain understanding about the inner working of the mind by observing college students in lab experiments. I say this as someone who spent college learning about those experiments.
that metastudy involved cherry picked sample, so it’s results have been met with skepticism. There is a lot of support for utt
Benedict Carey dedicated a whole section on this in “How We Learn.” This is where forgetting is a good thing–the previously learned info are being organized in the unconscious mind for full concentration on what you’re learning at the moment.
In fact, research showed people recall more info with more insights a DAY after they learned the info than right away, since the unconscious mind had more time to process. So it’s possible you might have organized the materials better the day after you read the paper.
That fits neatly with the theories of an AI researcher who is working on what she calls “Artificial Intuition” : Syntience Inc.
Reminds me of a quote by E.M. Forster that I learned during a summer Graduate Student Writing Workshop.
How do I know
what I think
until I see
what I say?
The quote is to help remind us that we don’t need to think, “okay, I know everything that I’m going to write down.” before we starting writing, because part of our thinking process happens during the writing process, e.g., connecting the different parts of the proof together.
Amen to this idea!
The header for the last section says
Process than Summarize
I wonder why use ‘than’
should it be ‘then’ ?
Another writing project?! Hurrah!!
I have always called this the “crossword puzzle effect”. After going through the Saturday NYT crossword a couple of times, only yielding ~30% of the answers, I put it down until Saturday night or Sunday morning. Amazingly, here come the rest of the answers!
Thanks!!Great advice!
For some years now I have had an ongoing project to study a particular subject in great depth. As I read books and articles I have been writing my own summary, analysis, abstracts and reviews. Some of the material I read is fairly technical in that field of study and I have frequently experienced the confusion and frustration you describe–although the more I understand the topic, the less this happens. I have found writing summaries, etc., to be very helpful, although I have not experienced the phenomenon you describe. Rather, I find that the summary is much easier to write if I outline a difficult article before writing the summary. That process brings to my attention more clearly the logic, arguments and details that may be missed the first time through. Once I have this done (and I admit it is a laborious process, but the information is very important to me), writing the summary or review is easier. I can generalize easier if that is my purpose, or add as much detail as I want. The bottom line, however, agrees with your notion that writing such summaries of new information is helpful and satisfying. Moreover, I don’t have to read an entire article or chapter over again to be reminded of its contents. And if I want the details I often have an outline to fall back on.
This sounds remarkably like Scott Young’s idea of the Feynman Technique — writing down what you want to learn as if you were teaching it to someone else. It helps debug your knowledge gaps, because you inevitably run into the areas you don’t know as you try to explain things. I’m not a huge fan of Scott’s but this idea is rock solid.
Cal – could this phenomenon be related to / explained by the “Default mode network” – which as I understand it has not itself been definitively proven or defined. And thanks again for a thought provoking post.
I am a homeschooling parent, and I have been telling my kids for years now that with challenging problems (for me these would be math or when learning a foreign language), I usually don’t get the answer in one sitting. After struggling with the material for awhile, I have to walk away and do something else. When I sit down again, I either get the answer (or discover that I can suddenly speak/conjugate/whatever) or I discover that I understand much more than I thought. I always assumed that my brain keeps working in background mode, and that this is necessary when trying to do work that is creating new connections of one sort or another, as in figuring out a new math approach or a foreign language. It’s hard for kids to accept that some things just take time, especially if you want to do a good job and increase your long-term understanding rather than your short-term memorizing skills. I like your added step of writing out what you DO understand. I think we do that in math when we start out by establishing what we know to be true about the problem, but I think sometimes we leave out that step in other subjects when we are tired and frustrated. It’s a good way to actually celebrate your understanding instead of just being upset at what you can’t figure out.
I’m a medical student and this really does work.
When I’m digesting knew information, I first read in blocks of each subsection. I then look up and summarize what I’ve read. Once I’ve done that, I input the information into my spaced repetition (ANKI) flashcard program and make simple questions so I can recall the information at a later date. In this way, I’ve stimulated multiple ways to learn (visual, auditory, etc…)
Jack, thanks for summarizing your process. This is very helpful to me!
I do this on a regular basis Cal! I work in project management and on an almost daily basis I need to make a decision that has implications for many stakeholders. I used to get overwhelmed and just procrastinate for days, not knowing what to do with the many emails and meeting notes and reports being thrown my way.
Last month, I created a “problem solving sheet for problems I will rather not have.” Since then, anytime I sense frustration and apathy building up, I open up that Word document and start typing out a summary of the situation, reviewing the implications of various strategies. Then I make sure to list the next steps that will consecutively lead me to my end goal.
I usually feel much better after going into my problem solving sheet, and I had no idea why until I read this blog.
Sounds like you somewhat sq3r’d. Or just 2R’d. Read recite.
Cal — fascinating post on the importance of writing and summarizing to learn. Some parallel thoughts from Warren Bennis on leadership:
“Codifying one’s thinking is an important step in inventing oneself. The most difficult way to do this is by thinking about thinking — it helps to speak or write your thoughts. Writing is the most profound way of codifying your thoughts, the best way of learning from yourself who you are and what you believe.” (Warren Bennis)
It’s as if our conscious brain is the ram, and our subconscious brain the hard drive. We just can’t have it all in our conscious mind until we’ve summarised it.
Hello Cal, I don’t think it’s unconscious work when you step back and try to summarize.
Actually I think you took a holistic observation again for your problem and mind other things.
…and then sleep on it.
I believe our brains are always, consciously and unconsciously seeking to connect all new conceptual information to previously held concepts. But it’s more than making relatable connections, our brains are continuously evaluating the relative nature of the new concept’s relate-ability to any/all previously helds, based upon varying strengths; whether the new conceptional information reinforces a held concept that has been “repeated reinforced” before, all the way down to those that haven’t which now/for future become held only as “weak signals.” And it’s even more interesting than that. There are 7 connection types that can be made; classification, categorization, generalization, aggregation, association, commonality, and I’m forgeting the last one.
The thing about this, it’s not that important. We can’t manipulate our brain’s connection fucntion efficiently enough to make any real difference. And as far as AI, we can’t emulate it effectively enough to replace or brains in this process.
What we should be concerned with, is augmenting our brain’s natural capabilities with supports that make this “connection engine function’ more useful to our work/learning purposes. That’s another can of worms…
‘I had undertaken to give the Lowell Lectures at Boston, and had chosen as my subject “Our Knowledge of the External World”. Throughout 1913 I thought about this topic. In term time in my rooms at Cambridge, in vacations in a quiet inn on the upper reaches of the Thames, I concentrated with such intensity that I sometimes forgot to breath and emerged panting as from a trance. But all to no avail. To every theory that I could think of I could perceive fatal objections. At last, in despair, I went off to Rome for Christmas, hoping that a holiday would revive my flagging energy. I got back to ‘Cambridge on the last day of 1913, and although my difficulties were still completely unresolved I arranged, because the remaining time was short, to dictate as best as I could to a stenographer. Next morning, as she came in at the door, I suddenly saw exactly what I had to say, and proceeded to dictate the whole book without a moment’s hesitation.’
-Bertrand Russell, from How I Write
I noticed something perhaps similar when I started studying Shakespeare. When I first approached it, I tried to parse each sentence, each phrase. And I found it very difficult. So I tried reading sections at a time and it got much easier.
Part of this is simply complex sentence structures. I don’t know what this clause means until I read that clause it modifies. Part, I suspect, is what you describe. Read reflect read reflect.
I read somewhere long ago that this unconscious thought process was called “consolidation.”
In my attempt to explain consolidation to my freshmen students, I came up the example of when someone tells you a joke and you don’t immediately get it, but then after an hour of doing something else, your brain gets it and you have that moment of, “oh, now I get it!”
For the last 15 years, I explicitly teach summarizing and have been requiring my first-year developmental college students to summarize and reflect during their reading and note taking. Many of them are very inexperienced readers and writers and are reading well below college level. They have few strategies for making sense and remembering written material.
Thank you for your great example of how these processes lead to greater understanding even for professors.
Your should check out a course on coursera.org
Called learning how to learn
They go into great depths explains this.
Here’s what I summarized from this article:
Cal Newport was finding difficulty in making sense of a computer science paper because there was so much information to process and digest. By summarizing the article, he finds that although the engaged parts of the brain had a short-term memory, the rest of his brain were also retaining information.
This technique has often helped me as I prepare for exams in college. I grab a piece of paper and re-write/summarize what I have learned from the lectures. I have found that when I study in this way, I do much better on the exams.
I believe that what you describe it’s part of the learning/understanding process. It allows you to take foreign knowledge and facts and to connect them with what you know and understand (your internal picture, that makes sense). Which makes addressing the rest easier.
From what I read on your blog, I believe you might be interested in a recent book on learning : Make it stick. Some parts of it will not come to you as a surprise, from what I read from your advice, but it is quite interesting :
https://makeitstick.net/
Anyway, thank you for the good material, advice and current discussions.