#002: Your method of studying is wrong — Part One [DD/WP]

Maybe. I could be wrong too lol.

(DD: Deep Dive, WP: Waxing Philosophical. I’m not sure which classification type is ideal for this piece. Info on my type and scale system)

Introduction

So, this is my full statement, with all of the clarifications:

You are, often, applying techniques for studying a subject that is not the most appropriate or best for said subject. Particularly in maths/natural sciences.

A weak statement I know, but read on — the rest of the piece is a lot more insightful.

Do note, this piece is about identifying these subjects & incorrect techniques. The next piece will be about what could be the correct techniques, a much harder question to answer.

Now, my above statement is based on series of pretty intuitive claims.

• Claim 1: There are broadly 3 causes for a subject to be difficult, i.e. subject types.
• Claim 2: Each difficulty “cause” has its own unique problems.
• Claim 3: These unique problems require their own unique solutions (which will be given in the next piece).
• Claim 4: Using appropriate solutions/methods (rather than a general one) will make studying significantly easier.

From these 4 claims, I make my ultimate claim: you can identify the specific type of a subject you have, and learn to study in a way that best suits that type.

But before all that, let’s start with the first claim and some elaboration on it.

Claim 1: There are broadly 3 causes for a subject to be difficult

These come down to the following:

• Difficulty through repetition (“repetitive subjects”)
• Difficulty through application (“application subjects”)
• Difficulty through alien-ness (“alien subjects”) : Alien here meaning completely unknown.

(I have thought about this from the natural science & mathematical perspective, so this idea mainly works for such subjects.)

Repetition

This is pretty easy to understand : the difficulty comes from the sheer effort needed to complete a task within the subject. These subjects often, but not necessarily, have simple concepts. Sometimes, they might have concepts that need not even be understood for finishing the subject.

Take the example of Arithmetic. Multiplying two 4-digits numbers by hand is painful, sure, and requires like sixteen digit-wise multiplication steps, but the individual steps itself require little mental effort.

Another example is any memorization heavy subject. I’d be horrible at remembering the names of all 206 bones or so, not because the names are particularly difficult but because I have to remember two-hundred-and-fucking-six of them.

Application

Here, the difficulty comes through, well, applying the concepts of that subject/field. Definitely not obvious, I know (/s).

This often manifests as a subject having a few core concepts, but dozens, if not hundreds of ways to apply said concepts for problems.

If you’re more into the maths side, a good example might be indefinite integration — there are roughly a dozen methods of solving an integral, but they can be applied and combined in likely a thousand or more different ways. Or perhaps, engineering mechanics. The basic concepts of Forces, Conservation laws, Constraints, etc are applied in highly complex ways that often seem unelievable when compared with how simple the concepts itself are.

A general example is the entire medical field. You have your concepts: the medicines, surgery, and other methods. And your applications: curing an ailment/disease/injury. There are a variety of ways of using your concepts here to solve one among thousands of issues.

Alien-ness/Foreign-ness

I could have named this kind of difficulty, conceptual, but 1) Alien sounded cooler, and 2) Conceptual difficulty isn’t limited to this.

So what do I mean by subjects are difficult through (them) being Alien.

Here, the concepts/ideas itself in the subject are truly new. These aren’t extensions of stuff you know already (which I’d argue comes under application-based-difficulty. After all, an extension of an idea is often an application of said idea in a new situation). These are effectively unknown, unconnected — Alien, Foreign — ideas.

Again, I will explain this using some college level math subjects (if you dunno, skip ahead to the general example).

— College Subjects Example —

Linear Algebra is a textbook example of this Alien difficulty, to the point that I had to pause writing this piece for 6 hours trying to think of a way to simply explain what it tries to do. lol. But yes, Linear algebra is a field in maths that tries to take all the theorems, formulas, results, etc of vectors; and generalize it to any object satisfying certain rules. This kind of maths is something that most students wouldn’t have experienced before, using techniques unknown & methods too abstract to feel like maths. That’s often why most people don’t really get Linear Algebra the first time around, even if they are able to apply the formula to cookie-cutter problems.

Another example is College level Probability and/or Statistics (I’ll abbreviate it as PnS). Till before this subject, maths was deterministic — it might be painful to solve it, yes, but (provided no mistakes) you can be 100% confident in your answer. In comes PnS, a subject whose entire premise is based on uncertainty and random chance. You could calculate everything, but you’d never (well, mostly never) get a certain answer. This is not deterministic maths, it’s probabilistic maths: A whole new language.

— A more common example: Algebra —

Algebra, I’d argue is one of the earliest subjects whose difficulty primarily came through its alien-ness. Before it, pretty much all of maths one learnt just involved calculations, or something that’s “direct” like shapes / geometry.

Algebra brings in this idea that you can perform maths with the question “what value” i.e. “x”, and all the intricacies that results in.

You have most likely normalized the above, but just take a minute to really consider how batshit insane that idea would have sounded initially to a kid: “Hey buddy, we are now gonna do maths with question marks!”.

Exactly.

(This is an assumption (well this entire piece is), but I believe the reason we learnt Algebra over multiple years is because of the fact that it took so long for us to understand such an alien idea compared to our previous calculations-based maths.)

And with an overview of the causes, we come to my second claim:

Claim 2: Each difficulty “cause” has its own unique problems.

This basically just means subjects that are difficult through repetition feel different than subjects that are difficult through application, and so on.

An obvious claim, really, but nonetheless profound (bish, you know I am dramatic). But first, what are the problems for each cause?

Repetition

The common problems here are often the following:

• Remembering all the repetitive shiii, basically having shit memorization.
• Maintaining accuracy (basically no silly mistakes, which is hard when the repetitive shit is tiring and your brain isn’t as active on the 50th step)

These subjects aren’t really making your brain think, they are just tiring it out/overwhelming it with, well, repetition.

Application

Here, your issues arise from not knowing the versatility of the concepts — tools — you know. A problem might be unsolved here because you didn’t know/realize you could apply concepts this way, or combine them that way, etc to solve said problem.

Often, but not always, this can arise from not knowing the underlying the concept perfectly. But even in cases where you do know them perfectly, you can still find a subject difficult through application. After all, even if you know how a phone works completely, you can still find new applications (pun definitely intended) for it.

Alien-ness

What are the problem of a subject being alien?

Well, I have noticed that it’s often similar to the problems one faces when learning a new language, especially foreign ones. Hence why I also call it foreign-ness.

That could mean any of the following:

• Not understanding the core concepts itself (i.e. the words in my analogy)
• Not understanding how these concepts relate with each other (i.e. grammar and so on)

There’s more, but you get the idea.

Often times, these alien subjects are taught directly, tantamount to someone teaching you a new language by only using the new language. You can guess what all are the problems of doing that.

— A lil detour —

If we analogize studying alien subjects as learning a foreign language; we can treat studying repetitive subjects as learning the alphabet of your current language, and studying application subjects as learning how to write well in your current language.

Conclusion?

Well, this is more of an intermission.

And with that part one is done. Part two will try to justify the remaining claims, and more importantly, try to give you methods that will work better for these different kinds of subjects. I will tell you in advance that I don’t have great answers, but the first step to solving a problem is to understand it, and I hope this & the next part will help you do so.

PS: you can already start to think of ideas to solve the above mentioned problems. Perhaps you’ll find some ideas I didn't think of.

The Scale for this piece.

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