Comment by jqpabc123

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).

> Rather spend $500,000 on the hunt than $50,000 on training someone into the role.

Capex vs opex, that's the fundamental problem at heart. It "looks better on the numbers" to have recruiting costs than to have to set aside a senior developer plus paying the junior for a few months. That is why everyone and their dog only wants to hire seniors, because they have the skillset and experience that you can sit their ass in front of any random semi fossil project and they'll figure it out on their own.

If the stonk analysts would go and actually dive deep into the numbers to look at hiring side costs (like headhunter expenses, employee retention and the likes), you'd see a course change pretty fast... but this kind of in-depth analysis, that's only being done by a fair few short-sellers who focus on struggling companies and not big tech.

In the end, it's a "tragedy of the commons" scenario. It's fine if a few companies do that, it's fine if a lot of companies do that... but when no one wants to train juniors any more (because they immediately get poached by the big ones), suddenly society as a whole has a real and massive problem.

Our societies are driven into a concrete wall at full speed by the financialization of every tiny aspect of our lives. All that matters these days are the gods of the stonk market - screw the economy, screw the environment, screw labor laws, all that matters is appearing "numbers go up" on the next quarterly.

I can’t think of another career where management continuously does not understand the realities of how something gets built. Software best practices are on their face orthogonal to how all other parts of a business operate.

How does marketing operate? In a waterfall like model. How does finance operate? In a waterfall like model. How does product operate? Well you can see how this is going.

Then you get to software and it’s 2 week sprints, test driven development etc. and it decidedly works best not on a waterfall model, but shipping in increments.

Yet the rest of the business does not work this way, it’s the same old top down model as the rest.

This I think is why so few companies or even managers / executives “get it”

That we talk about "building" software doesn't help.

>For regular companies they're infested by managers imported from non-engineering fields

Someone's cousin, lets leave it at that, someones damn cousin or close friend, or anyone else with merely a pulse. I've had interviews where the company had just been turned over from people that mattered, and you. could. tell.

One couldn't even tell me why the project I needed to do for them ::rolleyes::, their own code boilerplate(which they said would run), would have runtime issues and I needed to self debug it to even get it to a starting point.

Its like, Manager: Oh heres this non-tangential thing that they tell me you need to complete before I can consider you for the positon.... Me: Oh can I ask you anything about it?.... Manager: No

Could not agree more. Whenever I hear monikers like "Java developer" or "python developer" as a job description I roll my eyes slightly.

I've worked in education in some form or another for my entire career. When I was in teacher education in college . . . some number of decades ago . . . the number one topic of conversation and topic that most of my classes were based around was how to teach critical thinking, effective reasoning, and problem solving. Methods classes were almost exclusively based on those three things.

Times have not changed. This is still the focus of teacher prep programs.

Parent comment is literally praising an experience they had in higher education, but your only takeaway is that it must be facile ridicule of academia.

In CS, it's because it came out of math departments in many cases and often didn't even really include a lot of programming because there really wasn't much to program.

> Now as a hiring manager I’ll say I regularly find that those who’ve had humanities experience are way more capable and the hard parts of analysis and understanding.

The humanities, especially the classic texts, cover human interaction and communication in a very compact form. My favorite sources are the Bible, Cicero, and Machiavelli. For example Machiavelli says if you do bad things to people do them at once, while good things you should spread out over time. This is common sense. Once you catch the flavor of his thinking it's pretty easy to work other situations out for yourself, in the same why that good engineering classes teach you how to decompose and solve technical problems.

The #1 problem in almost all workplaces is communication related. In almost all jobs I've had in 25-30 years, finding out what needs to be done and what is broken -- is much harder than actually doing it.

We have these sprint planning meetings and the like where we throw estimates on the time some task will take but the reality is for most tasks it's maybe a couple dozen lines of actual code. The rest is all what I'd call "social engineering" and figuring out what actually needs to be done, and testing.

Meanwhile upper management is running around freaking out because they can't find enough talent with X years of Y [language/framework] experience, imagining that this is the wizard power they need.

The hardest problem at most shops is getting business domain knowledge, not technical knowledge. Or at least creating a pipeline between the people with the business knowledge and the technical knowledge that functions.

Anyways, yes I have 3/4 a PHIL major and it actually has served me well. My only regret is not finishing it. But once I started making tech industry cash it was basically impossible for me to return to school. I've met a few other people over the years like me, who dropped out in the 90s .com boom and then never went back.

This is also why I went into the Philosophy major - knowing how to learn and how to understand is incredibly valuable.

Unfortunately in my experience, many, many people do not see it that way. It's very common for folks to think of philosophy as "not useful / not practical".

Many people hear the word "philosophy" and mentally picture "two dudes on a couch recording a silly podcast", and not "investigative knowledge and in-depth context-sensitive learning, applied to a non-trivial problem".

It came up constantly in my early career, trying to explain to folks, "no, I actually can produce good working software and am reasonably good at it, please don't hyper-focus on the philosophy major, I promise I won't quote Scanlon to you all day."

Many top STEM schools have substantial humanities requirements, so I think they agree with you.

At Caltech they require a total of at least 99 units in humanities or social sciences. 1 Caltech unit is 1 hour of work a week for each week of the term, and a typical class is 9 units consisting of 3 hours of classwork a week and 6 hours of homework and preparation.

That basically means that for 11 of the 12 terms that you are there for a bachelor's degree, you need to be taking a humanities or social sciences class. They require at least 4 of those to be in humanities (English, history, history and philosophy of science, humanities, music, philosophy, and visual culture), and at least 3 to be in social sciences (anthropology, business economics and management, economics, law, political science, psychology, and social science).

At MIT they have similar, but more complicated, requirements. They require humanities, art, and social sciences, and they require that you pick at least one subject in one of those and take more than one course in it.

I worked for someone who I believe was undergrad philosophy and then got a masters in CS.

On a related note, the most accomplished people I've met didn't have degrees in the fields where they excelled and won awards. They were all philosophy majors.

Teaching people to think is perhaps the world's most under-rated skill.

I would say you have some bias.

yes, sometimes you need people who can grasp the tech and talk to managers. They might be intermediaries.

But don't ignore the nerdy guys who have been living deeply in a tech ecosystem all their lives. The ones who don't dabble in everything. (the wozniaks)

> "crazy finger syndrome" - the attempts to go straight to the code without decomposing the problem from a business or user perspective

Years ago I started on a new team as a senior dev, and did weeks of pair programming with a more junior dev to intro me to the codebase. His approach was maddening; I called it "spray and pray" development. He would type out lines or paragraphs of the first thing that came to mind just after sitting down and opening an editor. I'd try to talk him into actually taking even a few minutes to think about the problem first, but it never took hold. He'd be furiously typing, while I would come up with a working solution without touching a keyboard, usually with a whiteboard or notebook, but we'd have to try his first. This was c++/trading, so the type-compile-debug cycle could be 10's of minutes. I kept relaying this to my supervisor, but after a few months of this he was let go.

I make a point to solve my more difficult problems with pen and paper drawings and/or narrative text before I touch the PC. The computer is an incredibly distracting medium to work with if you are not operating under clear direction. Time spent on this forum is a perfect example.

Humans will never outcompete ai in that regard however. Industry will eventually optimize for humans and ai separately: ai will know a lot and think quickly, humans will provide judgement and legal accountability. We’re already on this path.

You just did.

My experience as a professor and a student is that this doesn't make any difference.

Exactly the point of his test methodology.

What he asked of students on a test was to *apply* knowledge and information to *unique* problems and create a solution that did not exist in any book.

I only brought 4 things to his tests --- textbook, pencil, calculator and a capable, motivated and determined brain. And his tests revealed the limits of what you could achieve with these items.

Isn't this an argument for why you should allow open book tests rather than why you shouldn't? It certainly removes some pressure to remember some obscure detail or formula.

Isn't that just an argument for always doing open book tests, then? Seems like there's no downside, and as already mentioned, it's closer to how one works in the real world.

Sadly, I doubt 3-day take-home assignments have much future as a means of assessment in the age of LLMs.

>but no jobs are being replaced

I agree that an LLM is a long way from replacing most any single job held by a human in isolation. However, what I feel is missed in this discussion is that it can significantly reduce the total manpower by making humans more efficient. For instance, the job of a team of 20 can now be done by 15 or maybe even 10 depending on the class of work. I for one believe this will have a significant impact on a large number of jobs.

Not that I'm suggesting anything be "stopped". I find LLM's incredibly useful, and I'm excited about applying them to more and more of the mundane tasks that I'd rather not do in the first place, so I can spend more time solving more interesting problems.