Navigate through the Oxbridge Notes Guide to Autodidactism series
1. Employ spaced repetition systems (SRS)
Spaced Repetition Systems ask their users to formulate “items” of knowledge in a question and answer format, input these pairs into a computer program, then answer mini-tests based on these pairs at increasingly long time intervals, intervals determined by memory research to minimise the lifelong time cost of goading knowledge into memory.
I’m a big fan of this technique and possess thousands of cards spread across various topics. But, don’t take my word about SRS—consult the science, where you’ll find that SRS has a brilliant track record.
I started using SRS in its typical intended manner, which was foreign language vocabulary. Upon seeing how well I retained vocabulary, I asked myself whether I could use SRS to speed up learning programming, a topic I was struggling with. It worked just as well (read my experiences here), and now I use SRS to memorise all sorts of topics, such as algebraic formulae, German grammar rules, (native) English grammar and style, music theory, and rationality ideas. (These decks are available for free download here.) All of these topics contain large sets of facts or rules that I’d like to have on rapid access. For example, the music theory deck contains cards to train for sight-reading or chord spelling (naming the notes that constitute a chord), knowledge that I don’t want to spend more than a millisecond recalling when improvising on a piano. While these decks do not remotely equate to the full skill in question, they are a useful supplement for the knowledge component.
Having regularly reviewed cards in SRS decks for about four years, I’ve noticed advantages beyond memory, advantages that other authors do not emphasise half enough: Firstly, like prose writing or software unit-testing, SRS forces you to restructure your thoughts through its simple question and answer format. Even if you never reviewed the card you created, this restructuring and simplification of your thoughts promotes honest understanding and beats underlining your text ten times out of ten. Secondly, the unpredictable order of flashcard reviews promotes creative connections within and between your chosen disciplines. For example, I might see an English grammar card, followed by a Natural Language Processing card (using computers to understand human language), followed by an algebra card. Sometimes seeing these cards consecutively forges a welcomed connection between the three in my head. Juxtaposition is, for me at least, the first step to creativity. Thirdly, my flashcard decks form notebooks where I store ideas worth remembering, albeit with a superlative advantage over conventional notebooks: the SRS algorithm causes you to revisit old notes instead of leaving them forgotten in some drawer. Through reviewing your old thoughts, you combine, question or build upon them, forming richer and more nuanced ideas that grow to proportions not possible through conventional note-taking alone. In my prior Evernote/pen-paper notebooks, I found that I’d sometimes note the same ideas two years later, showing that my thinking had run around in circles all that time, never really progressing.
I love SRS and find it amongst the most effective learning strategies in my toolkit, but as an SRS power-user I know it ain’t perfect. The following list of drawbacks presumes you are already familiar with SRS; if you aren’t, you may want to come back to this later.
1 SRS mostly delivers on its promise of not forgetting, albeit somewhat literally in that remembering a flash-carded question/answer pair is not necessarily equivalent to learning the underlying idea. With SRS, you sometimes train yourself to only have answers to the specific questions you input, so your learning becomes overfitted to the data; you remember the specific example instead of the general rule; you remember that answer instead of building the ability to calculate answers on the fly. For example, I’ll remember the application of a German grammar rule to the particular sentence in the example, but not necessarily to unseen sentences.
This danger can be partially overcome through the mental discipline of challenging yourself afresh whenever you review. In terms of the example given, this means inventing new sentences that exhibit the rule whenever you review that grammar card.
I wish there were dynamic SRS decks for language learning (or other disciplines). Such decks would count the number of times you have reviewed an instance of an underlying grammatical rule or an instance of a particular piece of vocabulary, for example its singular/plural/third person conjugation/dative form. These sophisticated decks would present users with fresh example sentences on every review, thereby preventing users from remembering specific answers and compelling them to learn the process of applying the grammatical rule afresh. Moreover, these decks would keep users entertained through novelty and would present users with tacit learning opportunities through rotating vocabulary used in non-essential parts of the example sentence. Such a system, with multiple-level review rotation, would not only prevent against overfitted learning, but also increase the total amount of knowledge learned per minute, an efficiency I’d gladly invest in.
2 SRS has become conflated with flashcards for the overwhelming majority of users.This isn’t ideal because some types of knowledge are process-oriented or require physical skills, therefore reduction to your typical flashcard is insufficient for sustained learning. I know that I have until recently never even considered SRS outside of a flashcard context, and for the convenience of avoiding too many abstractions in my explanations, I also equated the two in my preceding paragraphs.
The format of a spaced repetition could be anything: “solve an equation using this trigonometric technique”, “draw a venn diagram demonstrating the differences between these six medical diseases”, or “sing a perfect 5th interval”. The key to SRS is repetition at scheduled intervals, but that which you repeat can and should vary with the type of material you are studying. Khan Academy, an online learning platform with a special focus on math, has taken a step in this direction with their dynamically generated exercises that drill previously learned topics.
3 SRS reviews take time out of your schedule every day. Personally, it takes me about half an hour every day. I’m willing to live with this, justifying the time expenditure as a long-term capital investment in my knowledge that will lead to increased opportunities and efficiencies in the future. Nevertheless, I would welcome more intelligent review systems that pack in more learning per minute, systems such as the multi-level review rotation I espouse above.
As I mentioned above, I’ve written extensively about my experiences with SRS in 2011 and in 2013. Read those articles then add these further refinements from the past year, refinements based on the deeper principles of learning I explain in the earlier Malgorithms piece.
Have a fresh thought every time your review the same card. When reviewing my deck on cognitive biases/logical fallacies/rationality, I challenge myself to think of an example of that specific flaw in thinking that either I or someone else committed in recent memory. Failing this, I construct a fictional example. The point here is to use the knowledge in a manner parallel to its real world usage, rather than mindlessly press a button within my Anki application. In other words, I’m increasing the activeness of an active review.
Challenge yourself with possible confusions. In my German grammar deck, I noticed that the verb conjugation rules for present tense are similar to those of the present subjunctive tense. When I was next reviewing subjunctive tense I paused and asked myself to verbalize the differences between these two tenses, thereby confronting early a confusion I was sure to encounter naturally later when speaking or comprehending German in the wild. This practice of confronting potential confusions is another form of the classic learning technique “making connections”, and the technique can partially alleviate the problem that flashcarded knowledge is too removed from real-world complexities.
Resolve suspected inconsistencies. As soon as you realise that two flashcards have (or suggest) different answers to the same question, you need to examine the area and figure out whether one card is wrong or whether there is a subtlety that has escaped you. For example, in grammar flashcards one card might describe a general rule, whereas another shows an example of a class of exceptions you hadn’t realised existed. Primary school teachers in English-speaking countries belaboured the incorrectness of sentences such as “My mom and me went to the supermarket”. Here, the objective case first person pronoun (“me”) was used instead of the correct subjective case pronoun (“I”). You add a flashcard and learn that rule. Months later, your teacher might correct your sentence “Between you and I, I have a secret identity” to “Between you and me, I have a secret identity” and you spin up a new flashcard for that particular error, without fully understanding why (you're in a rush that day). Only after reviewing both cards sequentially might you realise that the two cards appear inconsistent; you rectify their differences through research and find that “between” is a preposition and therefore must use the objective case, i.e. "me". However "I", as in "My mom and I went to the supermarket" is acting as the subject for the verb "went", and therefore needs to be in the subjective case. Now you have a general rule that explains what previously seemed like an arbitrary exception. I’ve had some genuine eureka moments of understanding through confronting and resolving inconsistent knowledge in this way. Similarly, with conflicting “best practice” advice, no matter what the field: figure out what advice applies in which situations by performing experiments, and then delete the rest. Evict knowledge that does not pay rent.
Avoid ambiguous questions. This might be specific uniquely to me, but I include it for the benefit of my spiritual clones. In computer science, I like to create flashcards with the format “What’s wrong with the following?” then display a picture of a deeply flawed piece of code. Reviews of this card become problematic when there is an additional problem with the code: despite my only intending to quiz the specific major problem, I might answer with the secondary problem during my reviews, thereby usurping my intended question. To relieve this issue, I reworded the question part of the card to direct my attention. For example, the above card would become “what’s wrong with the function names in the pictured code?”, and now I know I can safely ignore issues with something like variable naming.
Give names to techniques, associating them with a person, adjective, and/or place. For example, I describe a piano-playing techniques that my musical mentor showed me as “Fred’s Calypso Technique” and note that he taught me it in Portugal. In naming the previously unnamed, I believe you grant your memory a convenience in later recalling. I’ve written elsewhere about the value of naming concepts.
Not only can an image sum up a thousand words, but—critically, for our purposes—images are much easier to remember than even a handful of those words. Given the massive availability of images online and available through Google Image Search, the ease of taking a screenshot of all or part of your screen, and the convenience of using your phone to take a photo of something you scribbled, we now have unparalleled ease in making rich, colourful, visual notes.
This image from Drum Nuts helps you remember the parts of the drum kit easily because you map your memories of playing your friends’ kits as a teenager onto it, or you remember a concert where a favourite band played a certain part of the kit and associate the sound you remember in your mind’s inner ear with that part of the drum-kit.
The above graph from Purple Math shows two common mathematical functions—one exponentiation (multiplying something by itself X times: 2^3 = 2 x 2 x 2 = 8) and the other a log (the number of times the base of the log must be multiplied by itself to get X—e.g. log base 2 of 8 is 3) . The diagram shows how these functions behave at various values of X or Y in a far more vivid and information rich way than a solely verbal description. You can see how exponentiation output quickly approaches 0 as the X value decreases below 0, and how it quickly tends towards infinity as the X number increases above 0. Likewise, you can see how the log function behaves and even notice how the two functions have similar contours.
3. Document internal realisations
When you were in math class at school, I bet you noticed convenient simplifications that either sped up or expanded the scope of arithmetic. For example:
to multiply a number by 10 add a zero to the end (=> 2x10= 20)
to multiply by a multiple of 10, such as 20, 30, or 40, just multiply by the initial digit (2,3, or 4), then add a zero at the end (=> 2 x 30 = (2 x 3)0 = 60)
to multiply a number by 9, multiply by 10 (add a zero to the end) then subtract the original number (=> 6 * 9 = (60 - 6) = 54)
to multiply by 8, do the same, except subtracting two times the original number (=> 6 * 8 = (60 - 6 - 6) = 48)
I used these simplifications haphazardly because they only presented themselves to my awareness in a haphazard manner. Adult Jack, existing in a hypothetical world where calculators weren’t built into phones, would document these simplifications in a deck of flashcards for spaced review. The point of documenting is not just to remember, but also to stimulate myself into thinking of more advanced simplifications. When reviewing the rules above, the happenstance and chaotic (both meant in a positive sense) placement of the cards might trigger fresh insight or a connection between two previous rules. Indeed, while I was writing the above list of examples I realised:
to multiply by a number ending in 9, such as 29, 39, or 49, just multiply by a digit one higher (29 becomes 30, 39 becomes 40 , and 49 becomes 50), then subtract the original number. (=> 2 * 29 = (2 * 30) -2 = 58)”
Given a place in your memory, these insights accumulate and mature into richer connections. Sparks of insight and momentary flashes of understanding can be so rare and valuable that I find it appallingly wasteful to effectively throw them out through failing to document them; you may never arrive at that spark again. These insights have fantastic pedagolical power, and Kalid Azad at BetterExplained.com has harvested his personal realisations when studying computer science to create perhaps the most fun and memorable math resource ever compiled.
4. Extract, document, and improve the process.
Let’s start with a definition. By “process” I mean the workflow you use to actuate your skill; I mean your criteria for choosing your online advertising photos; I mean the checklist of potential issues you check before submitting an essay for grading or an article for publishing; I mean the order in which you compose sections of your song (and your reasons for doing this); I mean the time of the day you choose to deploy important code changes; I mean the little things, like how you tile your programs on your Macbook screen to see as much text as possible at once, or the keyboard shortcuts you press to speed you up.
We already have processes for everything we do—we just may not be aware of it. Indeed, process may be too strong a word for what might start out as inconsistent and rough intuition. Process matters in skill-based learning because it enables you to attain higher quality results, more consistently, and in less time.
I learn process best by watching experts at work. I watch videos of expert programmers at work and paid attention to the keyboard shortcuts they use, the way they name variables, and the various other factors that the textbooks leave out as “trivial” but real world workers consider indispensable.
I say that you might need to “extract” a process because the process isn’t always spelled out for you in an apparent manner. When you read a solution to a mathematical problem, it’s not enough to see how the author solved that particular question; a solution so closely fitted to the previously seen problem does not help you with unseen future problems. Instead, you need to identify an abstract reusable technique, a tool available to you when faced with a future problem. Ask yourself “what general rule would I need to have formulated in order for me to solve that class of problem?” and “what tell-tale sign in the problem should have prompted me to consider this particular technique as a candidate solution?”. For example, you might formulate the rule that seeing three sides of a triangle should prompt you to consider the Law of Cosines.
Extracting a process is particularly valuable when you have mentors or teachers. These experts are likely to have rich internal processes, albeit processes that might exist only as intuition that these experts never verbalised before. Your job is to ask probing questions about what thoughts fired through their head when performing certain tasks, and thereby reverse engineer their expertise. I have found that experts’ descriptions of their workflows only form the tip of their proverbial knowledge iceberg, so do not settle with these explanations alone. Search for the points so obvious to them that they would never think to mention unless pressed.
I say “document” your process because human memory isn’t reliable. A twelve-month break from applying your processes may result in you forgetting the subtle skill in how you once made magic happen. Process is accumulative, but our minds can only juggle a limited set of factors at once. Therefore, to arrive at sophisticated processes, some work on pen-and-paper pays dividends. For the same reasons that an architect builds on paper before plot, you’ll arrive at better results by planning your process beforehand, where edits are cheap and the full picture becomes apparent at the scroll of a page.
In anticipation of potential criticism, I do not argue that those in possession of process ought to close themselves off to potential changes and only adhere strictly to their existing workflow. The process is always a work-in-progress, and improvements are ever welcome. Improvement necessarily requires that you try something different, so I advocate some element of locally inefficient exploration in expectation of long-term efficiency gains. Think of process as a way to spare the expenditure of mental energy in areas where it doesn’t matter or on matters where you’ve already reached a good enough decision; by doing so, you save energy to invest in creativity where it has the chance to impact most spectacularly.