On remembering better
How to learn to remember technical things better.
We re-started our regular lab meetings recently. In one of these lab meetings, we discussed strategies for remembering things, specifically technical things: concepts, math, methods, research studies and literature. The following is an account of our discussion, my thoughts with inputs from Aya, Noah, Hansol, Sriram, and Zhengcan. Thanks to Aya for suggesting the topic. I don’t think there is anything original here, but here goes.
Convince your brain it is important to remember it.
As much as the brain is a remembering machine, it is mostly a forgetting machine. The brain forgets almost everything it encounters. The brain only remembers things it deems, for some reason, important, unusual, interesting, emotional, poignant, enjoyable or useful.
So, if you want to remember something, convince your brain that this is important and you will need to remember this forever. Really believe this.
Sometime during high school, my chemistry teacher, after explaining some important concept, said, “Try to remember this. Learn it well enough that a few years from now, someone asks about this suddenly when you are walking down the street, you should be able to explain it to them.” I don’t remember the important concept she was trying to have us remember. Maybe balancing chemical equations. But this advice of hers I remember forever, and is the first thing I remember when someone asks about how to remember things better. I must have thought that her advice was more important than the chemistry concept.
So, convince your brain that whatever you want to remember is important and that you will need it forever. I don’t think you can switch your brain to this mode of thinking in a day. It is likely not a one-time thing, but a practice to be worked on through life. It is a key value to cultivate in kids. But it is never too late.
And, while it may be possible, it is probably not broadly useful to tell your brain, “please remember the value of square root of 2”. You just try to get into the habit of applying the “remember this” label to large coherent classes of things, say, the topics you care about. People overuse the term “passion”, but I assume this is one part of what means to be passionate about something — that you’ve told your brain that are a particular class of things you care about, so it remembers it better and more generally allocate more resources to it.
Don’t learn only for exams.
Many students forget a lot of what they learned in a course a few days after the exam. I used to do this too. I think this is partly because the students have successfully convinced their brains that the primary objective of the newly learned stuff is to do well on the exam. Of course, this means that the brain forgets the material immediately after the exam, as remembering it beyond the exam no longer helps get a better grade. If you are lucky, the brain forgets stuff only the day after the exam, not the day before.
Don’t give your brain this excuse to forget. Change your internal monologue. Don’t just worry about your grade or the exam (although useful to prioritize those too), but also focus on your ability to recall the material at arbitrary times. Don’t cram just before the exam, as cramming may also increase the salience of the exam as an end in itself. Instead, learn through the semester. You will still forget a lot, as to forget is human. But perhaps you will remember the important ideas better.
When I first noticed this phenomenon, I thought, wouldn’t it be nice if there were no exams at the end of the semester. Instead, you are tested on the material one random day in the following year. This surprise test will incentivize learning for the long-term and your brain will really believe that it needs to remember stuff for a long time. Most students I told this idea to did not like it, as it seems too stressful. But perhaps there is a non-stressful version of this. Maybe this surprise test need not have the high standards of a typical final exam and you get an A even with a 70% grade. Something to think about.
Pay attention when you learn it first.
If you are not paying full attention when you learn it first, you may not remember it as well. First, because you aren’t paying full attention, you may not learn it well enough, understand it well enough, or even hear the idea well enough. Second, because you aren’t paying full attention, maybe your brain thinks that this stuff is not important, and is not gonna waste its precious resources on remembering it.
Paying full attention means not checking your email or messages when listening to a lecture, or otherwise multi-tasking or constant context-switching.
Remember it like a story.
It is easier to remember ideas if they are part of larger story, a conceptual framework or a narrative account consisting of neighboring ideas, simpler ideas, more complex ideas, the history of the subject, the persons that were involved in developing the ideas, evidence for it, evidence against it, etc. The more detailed the conceptual context or real world context you embed an idea in, the more likely you are to remember the idea.
A single point in idea space is a fragile thing, easily forgotten. But once you connect an idea to neighboring ideas, once you see the larger picture, it is easier to remember the details. Even if you can’t remember all the details, you can re-construct the details if you remember some neighboring details.
Remember better by understanding better.
It is easier to remember some technical thing if you understand it better. So, when learning a new idea, try to understand it better. Try to understand it as well as you can. If you don’t understand something well enough, go back to a more basic topic, and learn that better. The more basic topics you have command over, the more easily advanced topics can be learned and remembered. It is often more efficient to take some more time to build a stronger foundation, rather than build on a shaky foundation.
Learning something efficiently is often about finding just the right text, video or lecturer that is teaching at just the right level, neither too easy nor too hard. So when you want to learn a new subject, find some material on the subject, and if that’s too hard to understand, go to a level easier, and so on, until things are easy to read. Find the optimal challenge level. To learn a completely new subject to you, don’t be shy to read or watch stuff meant for elementary school or middle school kids first before going to read more advanced stuff. This is totally fine and may often be optimal.
Watch different perspectives on the same subject. For example, there are lots of ways to internalize linear algebra, and understanding these different perspectives helps.
Never be shy to go back to the basics, to re-learn the basics, and review something you learned in first year of undergrad or high school or middle school. This is fine. No one has a perfect memory and no one learns everything well enough the first time. Make learning an iterative process through life.
Re-learn what you learned to remember better.
Learning sticks better if you re-learn things at some intervals. For example, one random day some six months after you’ve taken a course, just look through all the notes for that course, or watch a video on the topic. Put yourself in situations that give you an excuse to re-learn things you care about. But re-learning goes only so far.
Test your learning to remember better.
Learning sticks better if you test your memory periodically. So rather than look up answers, see if you can remember what you learned, or apply what you have learned in a new context. Do an independent or mentored project that relies on your learning. Try to internalize your learning in a manner that it becomes part of your reasoning in everyday life, so you don’t just associate it with a course, but recall it as part of life.
For better remembering something long-term, repeated testing (possibly with some re-learning) is supposed to be much better than just repeated re-learning. I assume that this is because your brain wants to do well on the test and so decides to remember better what it is constantly tested on.
Teach what you learned to remember better.
Learning sticks better if you teach it to someone. For example, explore being a TA, tutoring opportunities, or presenting at lab meetings. Teaching is a specific form of testing yourself or recalling your understanding. Teaching something makes you learn a topic much better. Teaching something tells you how well you understand something and holds you to a higher standard of understanding. Teaching is about telling stories about the topic, so being a good teacher will force you to organize the ideas better in your head. Teaching calls for reasoning on your feet and incentivizes holding and manipulating ideas in your head.
Good memory is often hierarchical.
You don’t remember addresses by their latitudes and longitudes. Instead, you remember them as door number, street, neighborhood, city, state, country — a hierarchical description. You don’t remember time by their representation in seconds. Instead, you remember them as century, year, month, day, hours, minutes, and seconds. For some locations, just the country information is sufficient, and for some events, only the century it happened is sufficient. But if you want to remember something with more precision, you use the hierarchical representation. The decimal system or more generally, the positional notation of representing numbers is another example.
Similarly, books are organized into chapters, sections, and paragraphs. It may be useful to have an understanding of a subject in such a hierarchical way, so you can call upon a high level description at the level of chapter titles, or a more granular description at the level of individual sentences.
Don’t keep everything in your head.
It is intrinsically hard to remember arbitrary context-free information. So, no need to remember things that you can look up, if it is not important for you to remember them. For things you may need but don’t have enough mental space for, write them down.
When you learn how to use some weird software or some obscure equipment with non-obvious sequence of operations, remember to take good notes with pictures, links, and videos the first time you learn it, so you can use those notes to remember how to use it again. Try to be organized, so you can find things easily on your computer.
Especially write down your to-do lists and your plans for projects, because having them in your head messes with your ability to focus on anything. As David Allen emphasizes, writing things down gives your brain permission to not obsess over these things.
Make arbitrary seeming things more concrete.
If you want to remember some arbitrary seeming numbers, try to see if you can convert the numbers into vivid imagery or a concrete example.
For instance, how much energy does a human consume sitting down? A typical 70 kg human consumes about 100 Watts. Now, visualize that old-timey 100 Watts bulb.
Also, simplify the numbers. In this example, I didn’t try to remember 107 Watts or whatever. More generally, see if you can simplify an idea to first understand it better and then to remember it more easily.
A more elaborate version of this example.
A 70 kg adult human, when sitting down, consumes about 100 Watts of energy. About the same as that old timey 100 Watts bulb. Your laptop adapter has a 50-100 Watts rating.
When walking, the metabolic energy rate of walking in Watts per kilogram of body mass is 2 + 1 v^2 where speed v is in m/s. Of course, the real coefficients are a bit different, but good to remember these simple round numbers, 2 and 1.
People walk at around 1.4 m/s. How can you internalize this? Think about a typical person walking. They take about two steps a second and each step may be around 0.6-0.7 meters long. So that’s 0.7*2 = 1.4 m/s.
1.4 m/s which is suspiciously close to sqrt(2). Why?
People walk close to the speed that minimizes the energy per unit distance. Presumably because this speed helped in their hunter-gatherer past, maximizing the likelihood of food discovery on a single stomach-full’s worth of food.
Energy per unit distance is given by metabolic rate divided by speed v, so (2 + v^2)/v = 2/v + v. This expression goes to infinity for v = 0 and v = infinity, and has a minimum at v = sqrt(2) ~ 1.4 m/s. You can show this by differentiating 2/v + v with respect to v and setting it equal to zero. So, we think, that’s why people walk close to 1.4 m/s.
Using the above formula, we see that when people walk at 1.4 m/s, they consume about 4 Watts/kg, or about 300 Watts if you’re a 70 kg person. So, while walking, you burn about three times as many calories as you are sitting down.
If you lived your life sitting all day previously and your weight is stable, how much more energy do you need if you now started walking 1 hour a day?
How much more or less energy do you need than a 30 mpg car for traveling a given distance? What about a full train per person?
For completing a marathon, walking all the way at your optimal walking speed will take the least energy. How long will this take?
How many cups of rice is 1 hour of walking, over and above sitting down?
In this example, I used rough numbers for everything, talked about how humans walk close to the energy optimal speeds, said that the speed is close to sqrt(2), showed how to derive it from the metabolic rate expression, gave ball-park numbers for sitting and walking costs, and asked you to use these numbers in daily contexts. Hopefully, learning this network of inter-related things will make you remember all of these facts better, or at least one of these facts better. Some more details are here.
Learn to guesstimate things you don’t know.
Learn to do what are called Fermi calculations or estimate order of magnitudes. Here is a fun one to do order of magnitude estimates. What is the size of the square (length of side) into which you fit all the people on earth if they are standing next to each other in a crowd? Try this calculation using rough numbers you know about world population and human dimensions. The answer is surprisingly small. Similarly, what is the size of the cube into which you can fit everyone on earth (if densely packed)? What if each person gets a 1000 sq. ft. house?
Avoid gimmicks for context-free memorizing.
There is a technique called memory palace, which can be used to learn and remember arbitrary things, like a 40 digit number by providing the context-free information into a made-up context like a palace you walk through. Such memorization techniques, while useful for memory competitions, are probably not helpful for conceptual things and I do not recommend them. People use flash-cards to memorize and re-call things. I’ve never used them myself, so don’t have insight into them, but they also seem like a gimmick for short-term memory rather than lasting memory.
Be kind to yourself.
Everyone forgets most things they learn. So be kind to yourself if you forget something. Just try to do some of things above some of the time to get a bit better at remembering things you care about.
So, to remember something better, convince your brain that it is important, pay attention when you learn it, don’t give your brain an excuse to forget it by focusing on exams and grades too much, learn it with better understanding, learn it with lots of neighboring context, test yourself on it occasionally with some re-learning, and teach it. Try to simplify things you want to remember and don’t try to remember everything, because we can’t and it’s probably not optimal. Be kind to yourself if you forget something you want to remember and just gently get back to re-learning it.
Of course, you are your brain, to a good approximation. I assume you know what I mean here when I say “convince your brain.” I use these words in a conventional way. You could understand the word “you” as the conscious part of your brain that is processing this text and “your brain” as the unconscious part of your brain, conceived as a distinct agent that can be influenced by actions by the conscious part. Surely this is not a valid distinction, but perhaps a useful one for the purposes of this essay, perhaps analogous to Kahneman’s Systems 1 and 2.
As a corollary, even if you just want to do well on an exam, practicing solving some problems in an exam-like setting is much better than just looking at the solutions to example problems.
This is called the maximum range speed. For more details, see M. Srinivasan. Optimal speeds for walking and running, and walking on a moving walkway. Chaos: An Interdisciplinary Journal of Nonlinear Science. 19.2 (2009): 026112. PDF.
Perhaps, as Noah said, learning things within a conceptual framework, making links to neighboring ideas, is kinda like the memory palace technique, as you are situating your learning in a grander palace of related concepts. For a more detailed discussion of memory, note taking, and memorization techniques like memory palace, see the book Moonwalking with Einstein by Joshua Foer. I have not read the book, but I recall listening to the interview of Foer by the old Stephen Colbert many years ago.