Ultralearning Ch. 11 - Principle 8 - Intuition

Dig Deep Before Building Up

“Do not ask whether a statement is true until you know what it means.” — Errett Bishop, mathematician

The chapter starts off by talking about Richard Feynman, an eccentric professor and Nobel Prize-winning physicist. Many considered him a genius. Feynman could take problems others had worked on for months and immediately see the solution. He won various math competitions. He also created the impression of being a human calculator.

Demystifying Feynman’s Magic

Feynman was certainly a genius. Many people, including his biographer, are satisfied to leave it at that. Though Feynman was smart, his magic had its gaps. He excelled in math and physics but was abysmal in the humanities. This, along with other facts, remind us that Feynman was mortal. He explained that for his mental calculations, he happened to remember certain arithmetic results and had an intuition with numbers that allowed him to interpolate. Even his magical intuition for physics had its explanation: “I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples.” Instead of trying to follow an equation, he would try to imagine the situation it described. As more information was given, he’d work it through on his example.

Magic, perhaps, Feynman did not possess, but an incredible intuition for numbers and physics he certainly did. This might downplay the idea that his mind worked in a fundamentally different way from yours or mine, but it doesn’t negate the impressiveness of his feats. How has Feynman developed this incredible intuition in the first place?

Inside the Mind of the Magician

Psychological researchers have investigated the problem of how intuitive experts, such as Feynman, think differently about problems than novices do. In a famous study, advanced PhDs and undergraduate physics students were given sets of physics problems and asked to sort them into categories. Immediately, a stark difference became apparent. Whereas beginners tended to look at superficial features of the problem — such as whether the problem was about pulleys or inclined planes — experts focused on the deeper principles at work. “Ah, so it’s a conservation of energy problem,” you can almost hear them saying as they categorized the problem by what principles of physics they represented. This approach is more successful in solving problems because it gets to the core of how the problems work.

If the principles-first way of thinking of problems is so much more effective, why don’t students start there instead of attending to superficial characteristics? The simple answer may be that they can’t. Only by developing enough experience with problem solving can you build up a deep mental model of how other problems work. Intuition sounds magical, but the reality may be more banal — the product of a large volume of organized experience dealing with the problem.

Feynman focused on principles first, building off examples that cut straight to the heart of what the problem represented rather than focusing on superficial features. His ability to do this was also built off an impressive library of stored physics and math patterns. However, his intuition, too, would fail him when the subject of his study wasn’t built on those assumptions. Feynman’s magic was his incredible intuition, coming from years of playing with the patterns of math and physics. Could emulating his approach to learning enable someone else to capture some of that magic? Let’s look at some of Feynman’s hallmark approaches to learning and solving problems and try to reveal some of the magician’s secrets.

Feynman is an interesting person for sure. I hope to emulate his learning techniques as a programmer, to build a strong intuition in solving problems in code.

How to Build your Intuition

Simply spending a lot of time studying something isn’t enough to create a deep intuition. There’s no recipe, and a healthy dose of experience and smarts certainly helps. However, Feynman’s own account of his learning process offers some useful guidelines for how he did things differently.

Rule 1: Don’t give up on hard problems easily

Feynman was obsessed with solving problems. Feynman was a master at pushing farther on problems than others expected of him, and this itself might have been the source of many of his unorthodox ideas. One way you can introduce this into your own efforts is to give yourself a “struggle timer” as you work on problems. When you feel like giving up and that you can’t possibly figure out the solution to a difficult problem, try setting a timer for another ten minutes to push yourself a bit further.

The first advantage of this struggle period is that very often you can solve the problem you are faced with if you simply apply enough thinking to it. The second advantage is that even if you fail, you’ll be much more likely to remember the way to arrive at the solution when you encounter it.

Rule 2: Prove things to understand them

Feynman didn’t master things by following along with other people’s results. Instead, it was by the process of mentally trying to re-create those results that he became so good at physics. This could be a disadvantage at times, since it causes him to repeat work and reinvent processes that already existed in other forms. However, his drive to understand things by virtue of working through the results himself also assisted in building his capacity for deep intuition.

The challenge of thinking you understand something you don’t is unfortunately a common one. Asking whether you understand a concept is hard because you may understand it a little, but not enough for the purposes at hand. The illusion of understanding is very often the barrier to deeper knowledge, because unless that competency is actually tested, it’s easy to mislead yourself into thinking you understand more than you do. Feynman’s and Einstein’s approach to understanding propositions by demonstrating them prevents this problem in a way that’s hard to do otherwise.

Rule 3: Always start with a concrete example

The process of following along with one’s own example forces a deeper level of processing the material as it is being presented. A finding from the literature on memory, known as the levels-of-processing effect, suggests that it isn’t simply how much time you spend paying attention to information that determines what you retain but, crucially, how you think about that information while you pay attention to it.

Feynman’s habit of developing a concrete instance of a problem can be seen as an example of this deep form of processing, which not only enhances later retention but also fosters an intuitive understanding. This technique also enables some feedback, because when it’s not possible to imagine an appropriate example, that’s evidence that you don’t understand something well enough and would benefit from going back a few steps and learning the material better before continuing. Using feedback-rich processes to test whether or not he knew something was a hallmark of Feynman’s learning style.

Rule 4: Don’t fool yourself

Feynman was deeply skeptical of his own understanding. He had cultivated such rigorous standards for what he counted as knowing. One way to avoid the problem of fooling yourself is simply to ask lots of questions.

The Feynman Technique

The author extensively applied this technique during his MIT Challenge. The purpose of this technique is to help develop intuition about the ideas you are learning. It can be used when you don’t understand an idea at all or simply when you understand something a little but really want to turn it into a deep intuition. The method is quite simple:

1. Write down the concept or problem you want to understand at the top of a piece of paper.
2. In the space below, explain the idea as if you had to teach it to someone else.
   1. If it’s a concept, ask yourself how you would convey the idea to someone who has never heard of it before.
   2. If it’s a problem, explain how to solve it and — crucially — why that solution procedure makes sense to you.
3. When you get stuck, meaning your understanding fails to provide a clear answer, go back to your book, notes, teacher, or reference material to find the answer.

The crux of this method is that it tries to dispel the illusion of explanatory depth. Since many of our understandings are never articulated, it’s easy to think you understand something you don’t. The Feynman technique bypasses this problem by forcing you to articulate the idea you want to understand in detail. Now any gaps in your understanding will become obvious as you struggle to explain key parts of the idea. The technique itself has some nuances and can be applied in a few different ways that might be helpful, depending on your specific intuitive deficit.

Application 1: For things you don’t understand at all

In this case, the easiest way is to do it with the book in hand and go back and forth between your explanation and the one in the book. This lacks the benefits of retrieval practice, but it can often be essential when the explanation you’ve been given baffles you.

Application 2: For problems you can’t seem to solve

In this instance, it’s very important to go through the problem step by step alongside the explanation you generate, rather than simply summarizing it. Summarizing may end up skipping over the core difficulties of the problem. Going deeper may take time, but it can help you get a strong grasp over a new method in one go, rather than needing numerous repetitions to memorize the steps.

Application 3: For expanding your intuition

Apply this method to ideas that are so important that it would really help if you had a great intuition about them. In this application of the method, instead of focusing on explaining every detail or going along with the source material, you should try to focus on generating illustrative examples, analogies, or visualizations that would make the idea comprehensible to someone who has learned far less than you have. Imagine that instead of trying to teach the idea, you are being paid to write a magazine article explaining the idea. What visual intuitions would you use to pin down the abstractions? Which examples would flesh out a general principle? How could you make something confusing feel obvious?

Demystifying Intuition

Feynman worked hard on understanding things, and he put incredible amounts of his pare time into mastering the methods that made his intuition work. He even made a meticulous timetable to allocate hours to his many intellectual pursuits.

How can I start applying these ideas to my own OSSU journey? I think I will revisit this chapter. Whenever I come across an important concept or a concept I have difficulty understanding, I will apply the Feynman technique. The ideas of putting in more effort to understand what I’m learning I will apply to my own journey. I’ll have a notebook ready to use this technique in my next OSSU run.