Rote memorization versus integrating your knowledge
One of the most important issues about learning has to do with the contrast between rote memorizing and actual learning. If you do lots of your thinking by rote memorization, then you’ll fail to learn much useful knowledge. This can be expected to lead to failing your tests and failing at life in general.
Now it’s important to understand that there is a process involved with learning and that not doing this process makes it easy to fall into the trap of rote memorizing. So what is that process?
The process involves solving a problem — guessing and criticizing your way to the solution. Now if it’s a problem that you don’t care about — one that you’re not interested in — then you’re already starting out in a bad situation.
Without interest, you are working against yourself. If you try to learn something that you’re not interested in, then what you’re doing is setting yourself up to spend time hating what you’re doing — which can only be expected to lead to failure. A common response to hating what you’re doing is to take shortcuts — like rote memorizing.
So if you’re taking a standardized test and you find yourself bored out of your mind, then you’re in a dangerous situation. You’ve started on a path towards a goal which involves learning things that you don’t find interesting — so failure is the expected result. There are two broad ways to fix this. Find out what’s interesting about the problems within the path you’ve chosen, or reconsider your chosen path.
What does it look like to not be doing rote memorization?
Now let’s say that somebody is not doing rote memorization. What does that look like? Well it implies a couple of things.
One implication is that you’re creating useful information that can be reused later. The fact that the knowledge is reusable is what makes it useful.
A second implication is that you’re creating information that you can readily correct in the future when you find flaws in it.
I discuss these two implications in the following two sections.
Explanations have reach
Creating useful and reusable information implies that the information has a lot of reach. This means that instead of only being able to use the information for the purpose that it was originally created for, it can be used for lots of other situations too, even ones that you’ve never encountered before.
Now I’ll do an example of an idea that is not very reusable in it’s current state, and then I’ll explain how to make a reusable version of it.
Consider the math idea of solving for a variable (y) by getting it all by itself on one side of the equation, like so:
x = y * 4
Most people would know that we should divide both sides of the equation by 4, thereby leaving y all by itself on the right side, like so:
x / 4 = y * 4 / 4, which leaves…
y = x / 4, and we’re done.
Now if you’ve only memorized this, then you won’t know where else this idea applies. You won’t know the reach of the explanation. You won’t be able to apply it in other types of situations.
Consider this other type of situation:
x = ey
What should we do here to get y on one side all by itself? Well some people have already memorized what to do, but again that’s not a good way to learn. It doesn’t help you apply the knowledge to other situations.
What I’m going to do is generalize what we did in the first situation, and then I’m going to explain how that generalized idea can apply to both the old situation and the new situation.
What we did before was to figure out what operator is being done to y (it was multiplication), and then we figured out the inverse to that operator (division), and then we applied that inverse operator to both sides of the equation. It can be written like so:
Take y and operate on it with operator O, then take the result from that operation and operate on it with the inverse operator I, and the result is y.
In short notation we have:
(y o O) o I = y, where I is the inverse operator of operator O.
Now let’s see how this general idea applies in the first situation.
In the first situation, the operator was “*” (multiplication), and the inverse of that operator is “/“ (division). So we have:
(y * 4) / 4 = y
This is what we used to get y all by itself on one side. The equation was x = y * 4, and we took y * 4 and used this universal theory (an explanation that has a lot of reach) to figure out that we should divide both sides of the equation by 4 so that we can get rid of everything around the y.
Now let’s see how this general idea applies to the second situation.
x = ey
So “e” is the operator. And the inverse operator to that is “ln” which means “log base e”, or “loge”. So we take both sides of the equation and do this inverse operator to it, which gives us:
ln x = ln ey, which reduces to…
y = ln x, and we’re done.
Notice how I took an idea that applied to one situation, then I generalized it so that it applies to lots more situations, then I reused the general idea in a situation that was slightly different than the first situation.
So instead of memorizing what to do in these two types of situations, I’ve created an explanation that applies to lots of situations — it applies to all operators, not just the multiplication operator. And without having created this universal explanation, I’d just be rote memorizing specific methods to be used in specific situations. This kind of knowledge is not very reusable, and it’s very fragile, in the sense that it’s not designed well enough to make it easy to find and correct flaws in it.
In the next section I talk about a special case of the general idea in this section. The general idea is explanations have reach. The special case idea is criticisms have reach. It’s a special case because a criticism is a type of explanation. A criticism is an explanation of a flaw in an idea.
Criticisms have reach
When you create a new criticism to an idea, often times that criticism does not only apply to just that one idea, and instead it applies to lots of ideas. In this sense, criticisms have reach.
This idea of having reach is crucial to learning. Without ideas having reach, they couldn’t be reused. You’d “learn” an idea for one situation and never be able to apply that idea to any other situation. That means you’re not learning much. It’s just rote memorization.
If you memorize answers to questions so that you can get through tests, you’ll fail horribly. Analogously, if you memorize specific methods for solving specific problems (as I explained in the last section), you’ll fail horribly. But instead, if you actually learn, by integrating new information with the rest of your knowledge, then you’ll be able to reuse it throughout your life, and you’ll have the potential to succeed (at tests and at life in general).
So when you create a new criticism to an idea, you should make a concerted effort to figure out the reach of that criticism too. In other words, you should try to figure out the situations that that criticism applies to. Let’s do an example.
Say you are working on a practice test and you answered a question wrong. Then you go to the answer guide and you find out what it is that you missed while working on that question. You learned about a flaw in one of the answer options — a flaw that you never knew about beforehand. So you’ve learned a new criticism. Let’s say that the criticism was that whenever you have the words “the boy swim,” if the words “boy” and “swim” are in grammatical disagreement, then that’s a mistake.
Now if you apply this criticism only to situations where you have the words “the boy swim,” never thinking about what other situations the criticism can apply to, then you’re not learning much. You’re basically just memorizing one mistake and its fix. You’re not organizing your knowledge in a way that can help you fix this type of mistake going forward. What you should do is figure out the reach of this new criticism. And part of doing that is to generalize the criticism. So let’s do that.
Whenever you have a subject and a verb, they should agree grammatically. For example, they should either both be singular or both plural. Note that this applies to “the boy swim,” as well as it applies to any other subject-verb combination. It applies to all possible incorrect subject-verb combinations. How many is that? I don’t know but maybe it numbers in the millions. So this criticism applies to millions of ideas.
So creating criticisms is crucial to learning, and so is figuring out the reach of criticisms because that’s what allows you to reuse them, and it’s what helps you find and fix flaws in your knowledge.
In summary, think of an explanation as a tool. Each time you create a new explanation, that’s a new tool that goes in your toolset. So each time you create a an explanation (like a criticism), you expand your toolset, thereby expanding your error-correction ability.
What does this toolset idea imply about how you should study?
One thing it implies is that you shouldn’t spend time studying without also making a concerted effort to expand your toolset. What’s the point of spending time passively “studying” if you’re not going to learn much of anything? That would be a huge waste of time. So for example, if you spend some time doing a practice test, you should also spend the time necessary to go through each of your wrong answers, figure out what mistakes you made, and expand your toolset.
More importantly, you want your tools to be resilient to breakage. Strong tools are the ones that have a lot of reach. Fragile tools are the ones you learn by rote memorizing.
How should you study?
When you study, do you also study your mistakes? If not then you’re missing out on a huge opportunity to find and fix gaps in your knowledge. And without finding and fixing gaps in your knowledge then you’re just rote memorizing. This means that the new ideas you learn won’t be integrated into your knowledge well enough to allow you the ability to reuse those new ideas in situations different than the situations you originally “learned” them in.
Studying your mistakes involves thinking about them critically with the goal of finding out why you're making the mistakes and creating error-correction methods to prevent you from making those mistakes in the future. Part of this process requires figuring out the reach of the criticisms that you created about your mistakes. Knowing the reach of a criticism is crucial to be able to reuse it in all the situations that it reaches to.
I’m studying but I’m not making much progress. How can I start making progress?
One thing you can do is to seek help from others. There’s something wrong with your method of thinking but your blind to that because those are your blind spots. By exposing your ideas to others, since they don’t have all the same blind spots that you do, you’re able to cover some of your own blind spots.
So let’s say you’re having some trouble with a certain passage. What you can do is expose your ideas about the passage to a discussion group and ask people to look for flaws in your thinking. This works especially well when the other group members have a good attitude towards critical discussion and where they know the things explained in this book about how knowledge is created.
Now let’s say that you’re having trouble understanding the material in this book about how to create knowledge. The thing is, it’s possible that you think you know it well when actually you don’t. This is a result of having blind spots. You’re blind to the things that you’re ignorant of. So you should expect to have lots of misunderstandings about the content of this book. And you should account for this fact by exposing your ideas to external criticism and making a concerted effort to improve that criticism.
Why is critical discussion crucial to learning?
In a previous section I made the claim that critical discussion is good for learning. Actually it’s crucial to learning.
Without critical discussion, a person would be limited by his blind spots. With critical discussion, he would still be limited, but by a smaller set of blind spots. Having fewer blind spots implies finding more mistakes.
Why is it a smaller set? Let’s say that John has 5 million blind spots and Paul has 6 million blind spots. Many of those blind spots aren’t the same ones, so let’s say that 4 million of John’s blind spots are ones that Paul has too. So this means that John has 1 million blind spots that Paul doesn’t have and that 2 million of Paul’s blind spots are one’s that John doesn’t have. Now since John and Paul are discussing together, that means that between the two of them, they have only 4 million blind spots. Now imagine that for every person you add to the critical discussion group, you reduce the number of shared blind spots. So each person benefits from the addition of each person sharing his ideas in the critical discussion group.
So consider what scientists do. They publish their work worldwide for all scientists (and anybody else) to review. And the review takes the form of critical analysis being published again worldwide for all scientists (and anybody else) to review the critical analysis. So each scientist is benefitting from the worldwide group discussion because a huge portion of his blind spots are being covered by other scientists who do not have those same blind spots.