tehgeekmeister’s blog

May 23, 2009

memorize the mundane

Filed under: Uncategorized — tehgeekmeister @ 1:59 pm

A common theme is developing, so I thought I’d point it out. The lessons I’m sharing are from my own mistakes, entirely. In this case, the mistake was neglecting to fully grok the trig functions and identities while trying to learn calculus. Now, whether you choose to fully understand trig before you work on calculus, you absolutely do need to be able to work with the functions a bit, and be aware of some identities. This is what I meant my mundane in the title. There will inevitably be tidbits you don’t want to study for their own sake, but need to understand for something else you’re trying to learn.

Memorize it. Use flash cards, mnemonics (these have always worked great for me.), whatever you need to. There are a few reasons, as I see it, to do this:

  1. To prevent frustration.  Frustration is inevitable when teaching yourself, but you don’t want to go looking for it.  Too much frustration caused by jumping in over your head is, I suspect, one of the major reasons people give up on teaching themselves.
  2. To enable you to move forward quicker.  Instead of stopping and reading a full on trigonometry book, I’m memorizing the identities necessary to manipulate equations enough for calculus.  Since I’ll now be able to effortlessly recall these values, problems that would have required groping around in the dark before will now merely be challenging.  You need to build up islands of techniques and facts, to use as tools in understanding the big picture.
  3. To support intuition.  As I think of intuitive insight, it works like this: You build up the aforementioned islands of techniques and facts.  Having internalized these techniques and facts makes higher level patterns that were incomprehensible before, just jump out at you.  But you absolutely have to learn those mundane, seemingly irrelevant facts first.

It’s a balancing act.  Rote memorization is not learning, our generation is well aware of this.  Perhaps, though, rote memorization of mundane facts is the quickest way to mastery of higher level concepts.

A final note: I had this post written up yesterday, when it was scheduled to be posted.  In fact, it was a much better post then.  Unfortunately I lost internet while writing, the better content wasn’t saved, and I couldn’t post.  The bulk of it’s still here, but I apologize for the delay and lower quality.


  1. I too have felt the pain of malfunctioning I-net connection, malfunctioning computer, malfunctioning website – and combinations thereof.

    I’d suggest composing your posts offline, and either upload or cut -n- paste when ready. That way, you can do it again, if you decide to use another blog engine. Or if you like to go back and review whatever the heck you thought was comment-worthy some-odd years ago.

    Comment by BMeph — May 23, 2009 @ 5:57 pm

  2. It’s interesting you used trigonometric identities as an example — even after taking, and passing, the whole calculus sequence among other things at school, I could never retain those identities until I studied linear algebra on my own and learned how to derive the identities myself from matrix transforms. I do sometimes memorize e.g. language vocab by rote, but to retain it I need to immediately apply what I memorized to something

    Comment by contextfree — May 23, 2009 @ 6:27 pm

    • Blech. Matrix transforms? Euler’s formula and vector (geometric) algebra. Even now I don’t have the law of cosines perfectly memorized and I don’t bother trying to recall it when I do want to state it. I just rederive it. It takes less than a minute and it never interrupts my flow in a problem because it turns out you never really need the law of cosines. Really, trigonometry is probably the worst way to do any trigonometric problem.

      Particularly for “technical” fields, I don’t recommend rote memorization. There are several problems with rote memorization which you are probably familiar with. First and foremost, it is boring = hard to motivate one’s self to do. Next, it doesn’t generate understanding or allow generalization. It’s fallible; it is easy to subtly misrecall some fact. Finally, it’s wasteful, if you are considering rote memorization, you are probably not in a position to know what is actually useful to memorize. Memorizing too little or the wrong things is a complete waste, and so to avoid that, most people will simply memorize -everything- which is also wasteful.

      Most of this hasn’t directly been a reply to your post. The thing to do to avoid the need for rote memorization is to work on an application (or failing that, exercises.) You will memorize what you need naturally, and it will be the facts that are actually useful. This is what you are doing/describing for the most part, however, instead of choosing some facts and memorizing them by rote, why not just write them down somewhere handy, e.g. a card, and refer to them as necessary?

      Comment by Derek Elkins — May 23, 2009 @ 10:42 pm

  3. BMeph: I started doing that at first. I’m going to restart now. I was using evernote, since it composes offline, but syncs to their servers and my iPhone.

    contextfree: You certainly need to understand content before you attempt to memorize it. Applying it is important, too, but probably overrated. If you can retain knowledge of the basics, you can flit around from subject to subject without too much trouble, if you so choose. The key is really to use good memorization techniques. I have found some pretty good ones, and that’s been a huge help to me.

    Derek: Rederiving trivial facts can be useful in math. On the other hand, if you can skip the rederiving entirely with minimal effort, you may be saving time. It’s a balance, it all depends on how much you’ll use it. I know at least in the calculus books (but perhaps not in real applications) you run into situations where you need trig all the time. That’s why I’m memorizing it, so that doesn’t get in the way of the good stuff.

    As for not recommending rote memorization for technical subjects, I both agree and disagree. I don’t think it’s hard to motivate yourself to do, if you use the right memorization techniques. I spend less than five minutes a day between all my flash cards, and I’m memorizing more than just trig identities. You’re right, it doesn’t generate understanding: you MUST understand what you memorize. At least enough to apply it. The point is that if you’re considering memorizing it to get it out of the way, you probably don’t want a deep understanding of that specifically. I’m actually memorizing every identity I’ve found myself, and as I mentioned before, it’s taking less than five minutes a day. Perhaps I’m memorizing things I don’t need to, but I am certain I’m not wasting much time at all on it. As for working on an application, you run into the same problem there: you don’t know what the applications will be ahead of time, so you can’t choose them realistically.

    Your point is good, overall. I think you are emphasizing the holistic approach, which I appreciate and think is just as important as what I’ve described here. I’ve found that memorizing trivial facts has actually enhanced my ability to take a holistic approach, as I can now focus on the big picture instead of trivial details. Finally, as for the card suggestion, and perhaps why our thinking differs so much, I simply don’t have space or time to refer to something when I’m studying. I study on my breaks at work, and that’s basically it when I’m on the road. One minute out of my time to look something up, a few times in a row, can kill a whole study session for me. This is why memorizing en masse ahead of time is more efficient in my case. I really appreciate your comment, Derek, I’ll cover some of the specifics in more detail in a post soon, I think.

    Comment by tehgeekmeister — May 24, 2009 @ 1:58 pm

  4. As far as rote memorization goes, do you use the spaced repetition systems like Mnemosyne or Anki?

    Comment by gwern — May 25, 2009 @ 7:01 am

    • I’m using iflash because It has support for my iphone and laptop. It has a variant of spaced repetition that’s not as efficient, but still much more efficient than just going through every card. In the future I’ll probably use another app so I can get true spaced repetition.

      Comment by tehgeekmeister — May 25, 2009 @ 12:27 pm

RSS feed for comments on this post. TrackBack URI

Leave a Reply to tehgeekmeister Cancel reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

Create a free website or blog at WordPress.com.

%d bloggers like this: