Comment by bildung | Hacker News Reader

Comment by bildung | Hacker News Reader

The author doesn't seem to differentiate the different types of learning as they are defined in educational science: associative learning (think Pavlovs dogs salivating if the bell rings), instrumental learning (Skinners rats learning labyrinths for snacks), cognitive learning (grasping abstract concepts, like a "comment form", or "democracy"), and know-how, knowledge about processes, like driving a car, or successfully talking to a bank manager, or approaching a programming problem.

Rote repetition is indeed important for the first (and to a lesser degree the second) type of learning. These types of learning are what the famous forgetting curve experiments dealt with: aquiring non-sensical knowledge. It is mostly unneeded for cognitive learning, which usually happens by having those lightbulb moments when exposed to the concept. And learning about processes is done through practicing (which is different to rote repetition because it involves meaning, i.e. the topic makes sense).

It is mostly unneeded for cognitive learning, which usually happens by having those lightbulb moments when exposed to the concept.

Meaning? Spaced repetition still work there.

Let's use the concept "3D printer". Imagine time travelling 50 years into the past and wanting to get people to learn what that thing is. You would essentially show a single time how the plastic goes in, gets heated, and flows out in molten state, according to a pre-defined program.

Almost every human observer would have an instant lightbulb moment and would probably not forget this for years. The observing people would have instantly formed a mental model - the concept.

That works for the right level of novel concepts. But just because I understand the Taylor expansion of cosine doesn’t mean I will remember it.

Yes, absolutely. In many/most real world cases, different types of learning overlap (these themselves are only mental models, after all). In this case, the cognitive aspect would be the what and why, helping you to get why this exists, what problem this solves, and to how to find out whether the current problem at hand is a good case for an application of this knowledge. And if your mental model is precise enough (say if you have 2 decades of experience as a full-time mathematician), you'd probably be able to recreate the function as needed.

Everyone else still has to memorize the actual terms.

I agree. Strong emotions cause memories to imprint deeply. I would argue that the "lightbulb moment" may use this effect.

taylor of e goes something like 1 + x + x^/2! + x^3/3!...

Well if we look at cos and sin, we know that these correspond to e^x if x = i x So then it’s easy to plug that in to the expression for e and get e^{i x} = 1 + ix - x^2/2! - i x^3/3! ... Taking the imaginary part gives us sin, and taking the real gives us cos.

So all we have to remember really is the pattern for e and to put ix instead of x. e^(ix) = sum((1/n!) * (ix)^n)

This was the Aha! that I got from a professor in my bachelors. Of course there’s still like two or three things to remember, but it’s a whole lot easier to unpack from there than to memorize the expansion of cos

Oh, I don’t have problems deriving the Taylor expansion of anything. It’s just that when I need it my main focus is on something else. My productivity has increased a lot since I started putting those often used things in Anki so I used could use them without having to look them up or derive them every time.

Of course. Yeah, what I was trying to illustrate is that with enough contextual knowledge the amount of things one has to memorize becomes comparatively smaller. Basically if one learns and remembers Euler's Identity and the expansion of e^x = (x^n)/(n!), then you don't really need to memorize the trigonometric expansions.

Reading over it I guess that may have been your initial point.

Spaced repetition doesn't provide benefits for topics that require understanding (hard science) https://www.gwern.net/Spaced-repetition#subjects

I maybe out of my league here, but I think you are confusing conditioning, training, and learning.

I third option: I mistranslated. I studied this in German, and in the German literature conditioning and training are subsets of learning.

Edit: Wikpedia confirms at least associative learning and instrumental learning, though the latter seems to be more often called operant conditioning.

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