Discovering the Other Path
There is a story back when me and my brother still studied the same subjects (he is a doctor now and wicked smart). It is indicitive of the different approachs we took to knowledge acquisition. Ben would spend many an hour revising, creating materials and summaries. Putting his nose to the proverbial grindstone. I was less interested in revision. I claimed that I didn’t need to revise, and I wasn’t fooling anyone (not even myself) with my excuse. I was a lazy teenager. Ben would go on to exceed my grades because of his rich attention to detail. But he wouldn’t necceserily go on to exceed my understanding.
The final question of our Human Biology A-Level illustrated this. The exam ended with the “monster question”, a 14-mark essay. They were notorious for their difficulty to revise for. They often integrated disparate knowledge not encountered together before. It asked why if you had both kidney failure and diabetes mellitus, you wouldn’t detect blood in the urine. I remember it not because of the question, but our comparison of the answers afterwards. Ben had written many pages building up a description of all the systems at play. Honing in on the cause by leveraging the huge informational database in his head. My answer was simpler. I didn’t know so I made a reasonable assertion based on my understanding of the systems (a subtle distinction!). It was only a few sentances. Both were right.
(For the curious, the increased water content of the urine causes any blood cells in the urine to explode due to osmosis, making them harder to detect. At least, at my A level understanding of the topic)
In transition to university the choice in learning style became adapt or die. Students that flourished at college often crumbled in their first year of study. Rote learning falls apart at this level. There is too much to memorise, it is too complex and courses introduce too many new ideas. You must derive your answer from the underlying principles or you will fail. I started to develop an understanding of what I had unconciously understood for most of my life. Facts and understanding aren’t quite the same thing. One was much more effective than the other.
When you list the downfalls of rote learning - it’s ineffectiveness, inflexibility, time consuming nature - most people agree it’s a bad way to go. And yet it remains prevelant. It is sad every time I see a beautiful binder of mindmaps, highlighted revision notes and summaries. Huge amounts of energy go into learning like this. And it works for your GCSE’s, it works for your A-Levels, but it doesn’t work anywhere else. As adults trying to understand a complicated world, we need better tools.
It turns out many thinkers before me have known what my lazy teenage brain had also discovered. To understand ever more complex concepts you must first make simple concepts intuitive. By building up the layers of ideas you find intuitve you can think in increasing depth about any domain. Once a concept is intuitive, there is no need to memorise it - it will never leave you.
A concept that has become intutive is easy to understand. It has become unthinking. You work with it in the mind without cthe oncious effort of understanding it again. You reutilise the work you did long ago. Before a concept becomes intuitive it requires your full energy to reason about. This limits the number of other concepts that you hold in the mind at once. By building intuition we can combine those ideas. Merging them with other intuitive concepts and forming strucutres of ideas. We can also go in reverse. By breaking doing complex ideas into simpler pieces we already have intuition about.
I avoid the term Intuitive Learning and the associated pseudo-science of learning styles. Learning by building intuition attacks a problem from as many angles as possible. Every “learning style” is available. It builds up from a focus on axioms and definitions. Then primitive examples, complex examples, predictions and finally practice and (essential) memorisation.
How to Build Intuition
Building intution is more difficult than rote learning and spends more time in the “basics”. By spending 80% of our time learning the core 20% of the topic, we can spend 20% of our time learning the other 80% that depends on those core ideas.
At first the initial work will be on definitions. Don’t get out a glossary and a flash card deck. There is no need to start memorising the jargon of the domain you are studying. Our primary knowledge acquisition will come from reading or hearing information. We use definitions to pack larger ideas into single words. It increases the density of information. This parralel to our own goal of understanding intuitive concepts that fit together. Understanding what these words define is our map to locate underlying principles.
Understanding often stalls because your definition of a word is unclear. The use of similar words to mean differing topics confounds this further. Consider how process and procedure aren’t quite the same thing. It’s so easy to skip over the words without questioning them. Their familiarity is deceiving. We know the word, we know how to use it but out understanding of it is fuzzy.
You must ensure that you do not construct your foundation from half-truths and fuzzy assertions. I like to apply a technique I call “expanding the terms”. Given a difficult sentance, I expand out each definition with simple language. Then I look for further oppurtunity to expand in that sentance. Each time expanding out the terms to the simplest possible langauge. When you can’t expand a term you have uncovered an area of fuzzy understanding. Work can now proceed to correct it.
The Feynmann Technique is similar. Write the topic of study at the top of an A4 page. Explain the topic in the plainest english you can - at the level of a bright twelve year old. The original method calls for an actual twelve year old to explain too. Not very convenient. Instead stop and pause at each fuzzy definition or usage of jargon (as above). Question your understaning. This directs your efforts to what you need to learn and avoids study of what you already understand.
As part of our study of definitions, and as a continuation of it, examples are key to the intuitive learner. At first we seek the most primitive form of the problem. Stripped back from special cases and exceptions we can focus on building intuition. In contrast, the rote learner tries to memorise every possible example. Trying to enumerate every possible paramater. The madness of this method needs no further explination.
Find a primitve version of the problem that is the simplest possible case. We are able to it hold in the mind all at once and play with its parts. “Turning the knobs” as Daniel C. Dennett would say. Any given example is a set of paramaters and the output of them. Change the paramaters and see what happens. As you develop more understanding, don’t only see what happens but predict it as well. This predict-verify cycle is a powerful generator of intuition. It forces us to consider the relationships between the parts. Our familiarity with the mental grows. Learning it’s strengths and weaknesses without ‘revision’ or ‘study’. It is a generative process. From a little source material we are developing a wealth of examples and tests. As we understand more our examples will grow in complexity as our curiosity expands.
The process is remarkable in it’s similarity to the play of children. This is deliberate. Uncorrupted by learning styles and mind maps, children solve their problems with pure, undadulterated, fearless intuition. Think on how you learned your mastery over your spoken language. It’s many hundreds of tiny rules and nuances that still eludes formal specification by academics. You did so through play, example and definitions. You never needed a single highlighter.
Intuitive learning does not preclude the use of practice. One of the keys to intuition is the easy recall of the idea and the rapid processing of the results derived from it. This comes only with experience. But through the process of “turning the knobs” this comes as a natural result of the process. We focus on the doing, the using of the ideas. We limit memorisation to the special cases and exceptions to the rule. The rote learner tries to memorise all the common results of an idea in the avoidance of calculation. The intutive learner memorises them through engagement the calculation
As a rule of thumb, for each hour of study of a text you are best served spending another hour building intuition. This 50% time rule ensures you spend the proper time thinking about a problem in intuitive terms. By engaging with material you can not skip over the difficult parts. Make your predictions out on paper. This way when you get them wrong you are not tempted to change the past to serve the egotistical need to be right. Fight back to embrace the failure so that you learn from it rather than ignore it.
We’ve explored this idea of intuitive learning vs rote learning from many angles. Let me summarise the key takeaways. These are the reasons to avoid rote-learning:
- Boring, hard to motivate self to memorise facts
- Doesn’t emulate the way we learn
- Builds inflexible, hyper context-dependant knowledge
- Focuses on facts rather than concepts
- Rarely leads to novel conclusions
- Focus on learning just enough to pass (the exam, the interview, the job requirement)
By using the intuitive learning techniques I’ve described we gain the following benefits:
- Playful, fun and interesting work that you’ll want to spend time doing
- Emulates the way we learn - experimentation and example
- Knowledge is flexible you apply it across domains
- Focuses on foundational concepts rather than facts
- Leads to novel and exciting conclusions
- Focus on learning deep enough to thrive
A sense and skill for learning by building intuition comes over time. Thinking hard, turning the knobs, and embracing the failure of your predictions is a triplicate of uncomfortable thinking patterns. It feels hard. It is hard. Progress feels much slower at first but if you stick with it you feel a deep appreciation for its ability to push you further than you have before. The true richness of knowledge lies deep below the surface.
But I suppose the final question to answer would be, what should you study? The short answer is “whatever and wherever your intellectual curiosity takes you”. The long answer I’ll save for another time. Though that short answer does capture most of the truth. The world is endlessly interesting once you start digging in.
And though learning new things is hard and uncomfortable, it is free and rewarding. With the combination of Open Textbooks and Library Genesis the worlds knowledge is at your fingertips. Never in history has there been more access to it. It is possible to learn almost anything given the aptitude, the discipline and the time to try. It is a special moment in history that we have this oppurtunity. Let’s not waste it.