Comment by simpaticoder

Memorizing is a super power / skill. I work in a ridiculously complex environment and have to learn and know so much. Memorizing and spaced repetition are like little islands my brain can start building bridges between. I used to think memorizing was anti-first principles, but it is just good. Our brains can memorize so much if we make them. And then we can connect and pattern matching using higher order thinking.

Hmmm... It's the other way around for me. I find it hard to memorise things I don't actually understand.

I remember being given a proof of why RSA encryption is secure. All the other students just regurgitated it. It made superficial sense I guess.

However, I could not understand the proof and felt quite stupid. Eventually I went to my professor for help. He admitted the proof he had given was incomplete (and showed me why it still worked). He also said he hadn't expected anyone to notice it wasn't a complete proof.

During my elementary school years, there was a teacher who told me that I didn't need to memorize it as long as I understand them. I taught he was the coolest guy ever.

Only when I got late twenties, I realized how wrong he was. Memorization and understanding go hand in hand, but if one of them has to come first than it's memorization. He probably said that because that was what kids (who were forced to do rote memorization) wanted to hear.

My controversial education hot take: Pointless rote memorization is bad and frustrating, but early education could use more directed memorization.

As you discovered: A properly structured memorization of carefully selected real world material forces you to come up with tricks and techniques to remember things. With structured information (proofs in your case) you start learning that the most efficient way to memorize is to understand, which then reduces the memorization problem into one of categorizing the proof and understanding the logical steps to get from one step to another. In doing so, you are forced to learn and understand the material.

Another controversial take (for HN, anyway) is that this is what happens when programmers study LeetCode. There’s a meme that the way to interview prep is to “memorize LeetCode”. You can tell who hasn’t done much LeetCode interviewing if they think memorizing a lot of problems is a viable way to pass interviews. People who attempt this discover that there are far too many questions to memorize and the best jobs have already written their own questions that aren’t out of LeetCode. Even if you do get a direct LeetCode problem in an interview, a good interview will expect you to explain your logic, describe how you arrived at the solution, and might introduce a change if they suspect you’re regurgitating memorized answers.

Instead, the strategy that actually works is to learn the categories of LeetCode style questions, understand the much smaller number of algorithms, and learn how to apply them to new problems. It’s far easier to memorize the dozen or so patterns used in LeetCode problems (binary search, two pointers, greedy, backtracking, and so on) and then learn how to apply those. By practicing you’re not memorizing the specific problems, you’re teaching yourself how to apply algorithms.

Side note: I’m not advocating for or against LeetCode, I’m trying to explain a viable strategy for today’s interview format.

Fortunately that was not my experience in abstract algebra. The tests and homework were novel proofs that we hadn't seen in class. It was one of my favorite classes / subjects. Someone did tell me in college that they did the memorization thing in German Universities.

Code-wise, I spent a lot of time in college reading other people's code. But no memorization. I remember David Betz advsys, Tim Budd's "Little Smalltalk", and Matt Dillon's "DME Editor" and C compiler.

I would wager some folks can memorize without understanding? I do think memorization is underrated, though.

There is also something to the practice of reproducing something. I always took this as a form of "machine learning" for us. Just as you get better at juggling by actually juggling, you get better at thinking about math by thinking about math.

Interesting I had the same problem and suffered in grades back in school simply because I couldn't memorize much without understanding. However, I seemed to be the only one because every single other student, including those with top grades, were happy to memorize and regurgitate. I wonder how they're doing now.

My abstract algebra class had it exactly backwards. It started with a lot of needless formalism culminating in galois theory. This was boring to most students as they had no clue why the formalism was invented in the first place.

Instead, I wished it showed how the sausage was actually made in the original writings of galois [1]. This would have been far more interesting to students, as it showed the struggles that went into making the product - not to mention the colorful personality of the founder.

The history of how concepts were invented for the problems faced is far more motivating to students to build a mental model than canned capsules of knowledge.

[1] https://www.ams.org/notices/201207/rtx120700912p.pdf

Depends on the subject - I can remember multiple subjects where the teacher would give you a formula to memorise without explaining why or where it came from. You had to take it as an axiom. The teachers also didn't say - hey, if you want to know why did we arrive to this, have a read here, no, it was just given.

Ofc you could also say that's for the student to find out, but I've had other things on my mind

>Memorization is not a panacea.

It is What you memorize that is important, you can't have a good discussion about a topic if you don't have the facts and logic of the topic in memory. On the other hand using memory to paper over bad design instead of simplifying or properly modularizing it, leads to that 'the worst code I have seen is code I wrote six months ago' feeling.

Your comment about memorizing as part of understanding makes a lot of sense to me, especially as one possible technique to get get unstuck in grasping a concept.

If it doesn’t work for you on l33t code problems, what techniques are you finding more effective in that case?

Is it the memorisation that had the desired effect or the having to come up with the novel proofs? Many schools seem to do the memorising part, but not the creating part.

Indeed, not just math. Biology requires immense amounts of memorization. Nature is littered with exceptions.

I find it's helpful to have context to frame what I'm memorizing to help me understand the value.

> But an amazing thing happened - I realized that it was impossible to memorize a proof without understanding it!

This may be true of mathematical proofs, but it surely must not be true in general. Memorizing long strings of digits of pi probably isn’t much easier if you understand geometry. Memorizing famous speeches probably isn’t much easier if you understand the historical context.

It's funny, because I had the exact opposite experience with abstract algebra.

The professor explained things, we did proofs in class, we had problem sets, and then he gave us open-book semi-open-professor take-home exams that took us most of a week to do.

Proof classes were mostly fine. Boring, sometimes ridiculously shit[0], but mostly fine. Being told we have a week for this exam that will kick our ass was significantly better for synthesizing things we'd learned. I used the proofs we had. I used sections of the textbook we hadn't covered. I traded some points on the exam for hints. And it was significantly more engaging than any other class' exams.

[0] Coming up with novel things to prove that don't require some unrelated leap of intuition that only one student gets is really hard to do. Damn you Dr. B, needing to figure out that you have to define a third equation h(x) as (f(x) - g(x))/(f(x) + g(x)) as the first step of a proof isn't reasonable in a 60 minute exam.

memorization + application = comprehension. Rinse and repeat.

Whether leet code or anything else.

Mathematics pedagogy today is in a pretty sorrowful state due to bad actors and willful blindness at all levels that require public trust.

A dominant majority in public schools starting late 1970s seems to follow the "Lying to Children" approach which is often mistakenly recognized as by-rote teaching but are based in Paulo Freire's works that are in turn based on Mao's torture discoveries from the 1950s.

This approach contrary to classical approaches leverages torturous process which seems to be purposefully built to fracture and weed out the intelligent individual from useful fields, imposing sufficient thresholds of stress to impose PTSD or psychosis, selecting for and filtering in favor of those who can flexibly/willfully blind/corrupt themselves.

Such sequences include Algebra->Geometry->Trigonometry where gimmicks in undisclosed changes to grading cause circular trauma loops with the abandonment of Math-dependent careers thereafter, similar structures are also found in Uni, for Economics, Business, and Physics which utilize similar fail-scenarios burning bridges where you can't go back when the failure lagged from the first sequence, and you passed the second unrelated sequence. No help occurs, inducing confusion and frustration to PTSD levels, before the teacher offers the Alice in Wonderland Technique, "If you aren't able to do these things, perhaps you shouldn't go into a field that uses it". (ref Kubark Report, Declassified CIA Manual)

Have you been able to discern whether these "patterns" as you've called them aren't just the practical reversion to the classical approach (Trivium/Quadrivium)? Also known as the first-principles approach after all the filtering has been done.

To compare: Classical approaches start with nothing but a useful real system and observations which don't entrench false assumptions as truth, which are then reduced to components and relationships to form a model. The model is then checked for accuracy against current data to separate truth from false in those relationships/assertions in an iterative process with the end goal being to predict future events in similar systems accurately. The approach uses both a priori and a posteriori components to reasoning.

Lying to Children reverses and bastardizes this process. It starts with a single useless system which contains equal parts true and false principles (as misleading assumptions) which are tested and must be learned to competency (growing those neurons close together). Upon the next iteration one must unlearn the false parts while relearning the true parts (but we can't really unlearn, we can only strengthen or weaken) which in turn creates inconsistent mental states imposing stress (torture). This is repeated in an ongoing basis often circular in nature (structuring), and leveraging psychological blindspots (clustering), with several purposefully structured failings (elements) to gatekeep math through torturous process which is the basis for science and other risky subject matter. As the student progresses towards mastery (gnosis), the systems become increasingly more useful. One must repeatedly struggle in their sessions to learn, with the basis being if you aren't struggling you aren't learning. This mostly uses a faux a priori reasoning without properties of metaphysical objectivity (tied to objective measure, at least not until the very end).

If you don't recognize this, an example would be the electrical water pipe pressure analogy. Diffusion of charge in-like materials, with Intensity (Current) towards the outermost layer was the first-principled approach pre-1978 (I=V/R). The Water Analogy fails when the naive student tries to relate the behavior to pressure equations that ends up being contradictory at points in the system in a number of places introducing stumbling blocks that must be unlearned.

Torture being the purposefully directed imposition of psychological stress beyond a individuals capacity to cope towards physiological stages of heightened suggestability and mental breakdown (where rational thought is reduced or non-existent in the intelligent).

It is often recognized by its characteristic subgroups of Elements (cognitive dissonance, a lack of agency to remove oneself and coercion/compulsion with real or perceived loss or the threat thereof), Structuring (circular patterns of strictness followed by leniency in a loop, fractionation), and Clustering (psychological blindspots).