When I started studying it didn’t take long until I was confused and disappointed.
Why were almost all lectures boring and useless?
Typically the lecturer dwelled endlessly on trivialities and rushes with lightning speed through everything complicated. Still, I continued visiting the lectures, simply because I thought that this is how you learn at the university level. I thought somehow something will stick subconsciously even though I didn’t learn anything consciously. The main reason I went to the lectures was that I feared I would miss something crucial if I didn’t go.
I also discovered that most textbooks are boring and useless. When you go the library and read the textbook your professor recommended, you usually end up more confused. As a beginner student, you only know a few textbooks and chances are high that they are all horrible.
Today I know that I wouldn’t have missed anything if I would have skipped the lectures. Today I know that there is no way to magically learn something subconsciously. Today I know why lectures and textbooks are typically boring and useless.
What do bad lectures and textbooks have in common?
The thing that lectures and most textbooks have in common is that they are made by experts. Only after at least a decade of intensive research, you get into a position where you are allowed to give lectures. Analogously, usually, only textbooks written by experts are published or at least recommended by professors.
This sounds reasonable. To teach something you must be an expert. To write a book on something you must be an expert. What’s the problem?
The problem here is the more we know about some subject, the more we think about it in abstract terms. This isn’t a bad thing per so. Abstraction allows us to compress vast amounts of knowledge into manageable pieces. The evolution towards abstraction is the reason why every mature field has its own jargon. If you are an expert, this jargon is immensely helpful, because it allows you to express things correctly and concisely.
However, abstract explanations and jargon are big obstacles for beginners. Beginners need simple words, pictures, and analogies.
The root of all confusion
So… why aren’t experts using simple words when talking to beginners and abstract formulations when talking to fellow experts?
This question was answered in 1990 by a Stanford University graduate student in psychology named Elizabeth Newton.
She conducted an experiment in which a person was instructed to tap out a given famous song like, for example, Jingle Bells, with their fingers. A second person listened to the tapping and had to guess the name of the song.
The tappers had to estimate how many songs the person listening would guess correctly. On average they estimated that 50% of the songs would be guessed correctly. However, the real figure was only 2.5%.
The people who tapped the songs on the table heard the song in their heard and thus for them the task to guess the song seemed easy. Thus, the reason why the tapper’s estimates and the real figure are so different is that once we know something, like in the experiment the melody of the song, it’s usually incredibly hard to imagine what it’s like not knowing it.
This phenomenon is called “the curse of knowledge“. What it boils down to is that most people find it incredibly hard to put themselves in the listener’s shoes. That’s why experts talk to beginners like they would talk to a fellow expert. That’s why most textbooks and lectures are useless for their intended audience.
The curse of knowledge in the wild
Hundreds of perfect examples of the curse of knowledge in action can be seen at Scholarpedia. The project describes itself as a “peer-reviewed open-access encyclopedia, where knowledge is curated by communities of experts.” While this sounds great in theory, it’s worth examining a few articles to see how this works in practice.
Here’s an article I recently stumbled upon http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields.
I was astonished how useless and confusing it is for any beginner. The problems start right at the beginning. The introductory sentences are incredibly overstuffed with buzzwords and jargon. Then in the first section, instead of sticking to the 4-dimensional spacetime we are living in, the article “explains” everything for a general D–dimensional space-time. This is something only experts care about and that can confuse beginners immensely. Finally, check out the references. There is not one article or book among them that I would recommend to a beginner student. Every beginner will be hopelessly confused after reading this article.
So without any doubt, the author of the Scholarpedia article knows what he is writing about. But unfortunately, he is subject to the curse of knowledge.
Another good place to observe the “curse of knowledge” in action is Wikipedia.
Almost any page on a math topic is completely useless for a beginner. The reason for this is, of course, that nowadays almost any math page was (re-)written by an expert. On the one hand, this is a good thing, because it means that most things on Wikipedia are nowadays correct. Wikipedia has reached a high-level of accuracy. Nevertheless, this also makes Wikipedia a horrible place to learn things. Unfortunately, most experts are not only subject to the curse of knowledge but also think that explanations in simple terms are a bit silly, trivial and naive. Thus when you try to add some explanations to Wikipedia that would be valuable for beginners, they almost always get deleted immediately.
Wikipedia wants to offer one page on a given topic that caters to all audiences. However, what experts find illuminating can confuse a beginner endlessly. There is no way to present a topic such that is a great read for any audience.
Okay fine, this is a problem. But what’s the solution?
I quote it all the time, but here it is once more:
“It often happens that two schoolboys can solve difficulties in their work for one another better than the master can. […] The fellow-pupil can help more than the master because he knows less. The difficulty we want him to explain is one he has recently met. The expert met it so long ago he has forgotten. He sees the whole subject, by now, in a different light that he cannot conceive what is really troubling the pupil; he sees a dozen other difficulties which ought to be troubling him but aren’t.” (C. S. Lewis)
The only possibility to fight the curse of knowledge is to write down what you learn while you learn it. This way you can always see what problems you struggled with when you were a beginner. After this realization, I started to write down everything I learn and I encourage others to do the same.
Unfortunately, many beginners feel that their notes are not valuable and their thoughts aren’t good enough to be written down. Nothing could be further from the truth. Only because there are already 50 textbooks on a topic by experts, this doesn’t mean that notes written by a beginner can’t help hundreds of fellow students.
For example, before I wrote my book “Physics from Symmetry” already hundreds (!) of textbooks on group theory and symmetries in physics existed. To quote Predrag Cvitanovic
“Almost anybody whose research requires sustained use of group
theory (and it is hard to think of a physical or mathematical problem
that is wholly devoid of symmetry) writes a book about it.”
Nevertheless, after my book was published I received dozens of messages from students all around the world who told me my book was exactly what they needed. This is not some lame attempt to brag. Instead, I mention this to demonstrate that what beginner writes can be valuable for others, especially fellow students.
Of course, not everyone has the time to write a complete book. For this reason, I started a small project called the Physics Travel Guide.
It’s also a wiki like Wikipedia and Scholarpedia, but it contains multiple layers. This means that it takes the various layers of understanding into account by offering several versions of each page.
Each page contains a laymen section that explains the topic solely in terms of analogies and pictures without any equations. Then there is a student section, that uses some math but is still beginner-friendly. Finally, there is the abstract layer, called researcher section, where the topic is explained in abstract terms and as rigorous as possible.
This way everyone can find an explanation in a language he understands. In addition, people interested in participating can see what kind of information is missing and don’t get discouraged because there is already lots of high-level stuff available.
To get a better idea what I am talking about, compare the Physics Travel Guide page for the Lagrangian formalism with the Scholarpedia page I mentioned above.
PS: Even if you think such a layered Wiki is a stupid idea, please, whenever you learn something, write it down and make it publicly available. There are too few people who currently do this, although such notes are incredibly valuable for anyone who tries to learn something. It doesn’t matter if you publish what you learn on a personal blog, a personal Wiki or if you participate in a Wiki project. The only thing that matters is that we get more explanations for each layer of understanding.
*Of course, there are rare exceptions like, for example, Richard Feynman who was an expert and a great teacher.
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