I volunteer tutor high school kids in my local community. Particularly math and history. The biggest differentiator between the students who scale up quickly and those who scale up a bit more slowly is their aptitude for memorization.
Recent history curricula and pedagogy in HS has placed an emphasis on “analysis” and “critical thinking.” But the students who struggle all struggle for the same reason: they cannot remember at the moment of writing their paper the basic facts that give context or even give meaning to the documents they are to analyze. I can teach a kid how to do the ACT of analysis to a great level of competency but their papers will be filled with bad analysis and illogical conclusions because they do not know what they read. So, much to their protests, I train them to memorize. And that is often the last push they need to not only get good grades, but realize the joy of critical thinking itself. For now they are not wasting brain cycles trying to conjure up the facts.
Good memorization skills are a huge leverage and it is something that can be learned and practiced. It is a shame that schools are letting children let their mental muscles atrophy like this.
I'd claim (perhaps not even contrary to what you're saying) that memorization and competent analysis/understanding are really two sides of the same coin.
"Here is some long sentence that doesn't really say anything and which you've probably never read in your life before."
You could now probably recite that sentence with near perfect accuracy; at worse changing it in very slight ways that are still functionally identical. That's an absolutely remarkable degree of memorization - one pass for 22 words, 119 characters!? Of course the reason it's easy and natural is because you have an intuitive understanding of what you're memorizing and so one word kind of flows into the next to create the singular whole.
Amateur chess players often find chess masters able to recite their games from memory as evidence of some sort of super-human memory that must be what enabled them to become masters in the first place, but it's completely false. It's the exact same story - when a strong player plays or sees a game, the game tells a story to him not especially different than a very short story. And so people are not recalling random moves or positions from memory but instead the story that those moves and positions tell. A master reciting a game is no more impressive than a "normal" person reciting the plot of a famous short story, let alone one that they wrote!
So for instance I remember from high school memorizing the order of the presidents (yeah... great school...) but finding it relatively easy by instead remembering the logical stories there. For instance instead of just remembering JFK-LBJ-Nixon, etc you remember the story of JFK getting assassinated, LBJ coming to power (and JFK's wife's view of him), then Nixon coming to power and grinding the old axe he had with JFK and scrapping the space program, followed by his VP (Ford) becoming president after Watergate, then losing to good but incapable Carter which led to TV Star Reagan, etc, etc.
I couldn't tell you the order of the presidents at all, unless you give me one and then I can recount the story of how we got from him to where we are now. Because like most of all people I suck at memorization, but also am pretty decent at recalling interesting stories.
Strongly agree with everything you've said, and I'd add that elite athletes have the same seemingly-incredible recall (e.g. https://www.youtube.com/watch?v=dHibkh57FFA) - I think for the same reasons.
This is fantastic! And a method I teach to students who I find to be narratively inclined. Works wonders, and is similar to my main method of memorization of historical facts.
The opening epigraph of the textbook used by my AP Euro teacher still sticks with me 15 years later: "good history is a well-told story". Teaching the cause-and-effect greatly eases the memorization. Even if you do not remember which year Martin Luther nailed his 95 theses to the cathedral door, knowing it happened after the voyages of Columbus helps point you to the correct year.
There is a lot of evidence that I think backs up your anecdata. For example Massachusetts has the highest performing public school system in the US (arguably, but by many measures) and their curriculum is based on the content heavy Core Curriculum (not to be confused with the watered down Common Core) created by E.D. Hirsch. Hirsch was a college professor and his argument is that knowledge is a significant portion of literacy, he witnessed this first hand trying to teach college freshman that simply didn't have the background knowledge to understand the college level books Hirsch was teaching, even though they had no problem reading the words. Hirsch's books "Cultural Literacy" and "The Schools We Need and Why We Don't Have Them" go into detail about this and he has some essays available online that are worth reading.
Anecdata plus one. My exact experience tutoring high school kids. Some could totally solve the problem, but the inability to remember the basic facts to start with meant getting the wrong answer, despite an impeccable logic trail.
The cost in time to derive basic facts that would have been instantly available had they been memorized also harmed the ability, especially on tests, to get to the end within the time available. 'Drill and kill' has its merits and, if done right, gives the kids a sense of accomplishment and progress.
If you start with the wrong facts, or missing facts, you don't end in the right place.
> The cost in time to derive basic facts that would have been instantly available had they been memorized also harmed the ability, especially on tests, to get to the end within the time available
I can relate to this amazingly well. I'm dyslexic, so I have trouble remembering thing in the correct "sequence" they need to be memorized in. While taking some of my math classes in college, I particularly struggled with finishing statistics exams in the allotted time since a lot of the rules were (for me) difficult to keep straight in my mind. So, I memorized the bare basic "truths" and would basically start each problem from first principles. I knew them well enough to go very quickly, but I still ran out of time in some of the exams.
I wound up with a C in the class, but the professor commented that I probably would have received one of the highest grades in the class if I had taken the time to commit more of the "shortcuts" to memory and actually finished all the exams. Nearly all the points I'd lost on the exams were from incomplete solutions.
That being said, it was still one of my favorite classes ever, and was immensely useful to me as a newly minted manufacturing engineer in a foundry.
>The biggest differentiator between the students who scale up quickly and those who scale up a bit more slowly is their aptitude for memorization....
>But the students who struggle all struggle for the same reason: they cannot remember at the moment of writing their paper the basic facts that give context or even give meaning to the documents they are to analyze.
It sounds like what you're describing isn't about students' ability to memorize, but rather about students' ability to develop their own mental models. Luquet and Piaget demonstrated that the ability to synthesize information to develop mental models isn't particularly connected to the ability to memorize the same information.
It substantially comes down to the amount of language practice those students have had over the years, starting from listening to large amounts of varied material (from conversations/books read aloud) as young children, and then from reading a wide variety of material. The kids who read, and read, and read (especially those who have someone discuss with them the meaning and structure of what they are reading, hearing, or experiencing) learn these skills to great fluency. The kids who don’t, don’t.
Some kids live in households where they listen to thousands of books by age 5 or 6, including not only stories of increasing complexity but also natural history, biography, science, technology, ..., and other kids never get that kind of attention or experience, and end up far behind in those skills.
The ability to “memorize” (i.e. learn) rests on a vast subconscious structure built up by fitting together language, starting from little bits and pieces of vocabulary, and building to subtle understandings of complicated ideas.
The way to train it is by giving the little neural net of the brain as much meaningful input as possible about the relevant parts of the world, and letting the brain fit them together in a web of connections. Not by trying to practice/drill rote trivia (say, reciting state capitals or the multiplication table).
I hypothesized that after 3/4 very different languages you start to build a different, more abstract model of linguistics (syntax, phonetics, semantics) that helps absorbing more. Just like music.
I don't disagree with any of what you're saying. But piecing little bits and pieces of things together is seen as a higher-level cognitive trait in most of the cognitive literature, quite distinct as a learning concept from memorization.
My point is that when someone says “the biggest differentiator between the students who scale up quickly and those who scale up a bit more slowly is their aptitude for memorization....” this is a mis-interpretation of the evidence that the “quicker-scaling” students remember facts they read more readily. What actually distinguishes these students is fluency in comprehending and associating material conveyed in writing/speech. Which may vary slightly based on inherent traits but comes down substantially to cumulative past practice listening/reading to complicated language. By high school students have more than a decade of practice, and between the most prepared and least prepared students there is probably something like 10x difference in amount and quality of past practice, most of it outside of school. Some students are barely reading the few assigned novels and textbooks while others are reading multiple (extra-curricular) difficult books per week on a variety of subjects and having extracurricular conversations where they construct and parse complicated arguments, etc. The latter group have a huge advantage.
Students’ skill at specifically remembering lists of atomized trivia (what people often mean when they say “aptitude for memorization”) is not as important, though this is also a trainable skill for anyone who really wants to do it.
Similarly, between the kids who play sports or do other physical activities all the time and have some amount of expert coaching and the kids who only play sports in PE class, there is probably something like a 10x difference in cumulative quantity/quality of past practice. Which ends up making it seem that some students are “athletic” and others aren’t.
And similarly for music, electronics, carpentry, abstract mathematics, cooking, shooter games, or whatever other skills you look at.
I was having a conversation/debate with a friend this past weekend along similar lines:
I have an extreme amount of trouble memorizing basic facts, and so I can't recall a lot of historical dates. Things I didn't know which bothered her included the year America signed the declaration of independence and the year we entered World War I.
But, I knew how long World War I lasted, and that it coincided with the Spanish flu, and proceeded an economic boom period which ended in the Great Depression and then World War II. I'm quite good at remembering stories, and so I knew the context of these events—just not the specific year they happened.
Which I think is fine. Context is what matters.
My friend said that for her, knowing the date is what lets her recall the context. Because of what she memorized as a child, she's able to form a timeline of history in her head, and see when things happened and how they coincide. And I will admit that I sometimes have trouble forming a similar timeline, and it's a handicap. But I mostly manage; I have a limited number of hours in my life and I focus my energy where it makes the most sense.
I guess what I'm trying to say is that people are different. It may be that most students are like my friend and the children you tutor (which is something I should keep in mind, as I'm actually training to become an elementary school teacher). But it's not necessarily true for everyone. I resent the fact that when I was in high school, I had test questions which asked "what year did Christopher Columbus arrive in America". I studied for hours trying to commit these facts to memory, and I still got the questions wrong. But if the test had asked "how did Christopher Columbus's arrival in America affect the European economy", I could have answered easily.
Perhaps that explains why Indian and Chinese secondary education can perform so well for their top students: even if they emphasize memorization rather than critical thinking, at the end of the day they can still pick up the latter without suffering from the former.
I have dyslexia (specifically a weakness in memory) and agree with everything you say. When not armed with a decent computer I can use as a crutch for my memory I'm noticeably weaker at critical thinking given the time spent recollecting fundamentals.
What software do you use? I have a poor memory and heavily used Notational Velocity as an external brain, but it's Mac only and I'm looking for alternatives.
I use Google Docs because it’s available on all platforms. I also carry a paper notebook.
I rarely refer to my notes again but the act of jotting them down creates a context, which acts as a hook for me. Even then my recall isn’t perfect but I haven’t run into situations where this has disadvantaged me greatly.
Anki (or similar). Spaced repetition is the most underrated tool I know of. And I barely use it: 8 cards per day, probably 1.5 minutes total with a noticeable bump in ease of professional life
Ah.. I thought it was more of so you could practice remembering stuff. Like some people remembers what somebody said in a meeting 3 months ago and some don’t even knew we had a meeting about it
You know, funnily enough, as someone who considers themselves to have a good memory, I cannot for the life of me remember most meetings, or most conversations for that matter in any sort of verbatim.
What I do focus on is remembering key details, as well as key emotional responses and postures. I try to take away from any sort of interaction any 1) new details that I find to be important and 2) how they reacted to other bits of information.
This helps me create a sort of holistic picture of a person, which I then take with me to my next interaction with them. I find this ultimately more useful than remembering the actual things said, as for the most part the counterparty does not either. However, their fundamental emotional posture(s) and motivations rarely change that quickly and having that knowledge helps me shape conversation faster and better.
My understanding is that "learning memorization" is really the process of learning to do the work to memorize, through explicit strategies like spaced repetition.
I don't think people become better at "effortless" memorization. Instead they learn what it is they need to do if they want to remember something.
It's possible to get to the point where you can become better at effortless memorization, but that takes a LOT of work. I studied 6 languages in high school and undergrad, and by the time I was in my senior year (taking Arabic + Chinese concurrently + over a decade of cumulative language classes) I remembered pretty much everything and reviewing for things like formulae/terms in other classes wasn't necessary.
It wasn't a process so much as an accidental by-product of what I was studying. By the time I left high school, I was taking German, Latin, and French. In undergrad, I expanded that to include some Old English, Mandarin Chinese, and Arabic. You can't get around memorization to learn languages.
The reason my memory ended up so nuts is that I was only interested in the nuts and bolts of the language, so I didn't continue on with French when it became about literature, I just picked up a new language instead. After a while, languages become more about things like context clues, but at the beginning and intermediate stages, you have to memorize a lot. Since I wanted to go for linguistic breadth (since I was interested in how languages were related/how features travel), I did the memorization stage of language learning a lot.
So I'd say it's down to consistency and longevity of practice. I used spaced-repetition as my main technique, but it's really down to spending 1+ hour a day for 8 years on memorizing.
You also have to keep up with it, or your memory degrades. It's been a good 10 years, and I don't have nearly the memory I used to.
I've been working on an app [0] for the past few years that attempts to synthesize note card style note taking (a la zettelkasten method) with spaced repetition flash cards. Spaced repetition is the single most effective tool for efficient memorization that I've discovered.
If we're slinging anecdata around I may as well offer mine up as a long-underperforming student that also somehow took night classes at college for software when I was 11 years old.
The teachers may force the kids to memorize, but that doesn't mean it does them any good in the long run. I met tons of kids that memorized mathematics from 8 to 13 years of age in Canada. I struggled badly with fractions when I was 8 years old. The fact that there wasn't one canonical representation broke my little brain. Before in mathematics you could always "keep going until you were done" and the number looked like 1.75 and that was it. Now you could stop at 14/8 or 1 6/8 or 1 3/4 or 7/4 or even 1.75 again! And sometimes they made me round it all the way up to 175/100 instead! Madness!
But unlike the kids in my class that seemingly did better than me in grade 4 while I was wasting my time trying to make this slippery math reliable I naturally ended up memorizing little gems like 7/2 being 3 and 1/2 because I kept at doing the actual work over and over again until my brain remembered it for its own sake. I'm not fighting my brain and trying to squash stuff that I don't care about into it, I'm letting it make the tradeoff as to what to memorize and what to keep as I keep doing the work over and over again.
By grade 6 (age 11, same time I started college) I was starting to wonder why we hadn't learned anything in a couple years in math. When you understand the building blocks or "first principles" so well, what looks to be a new lesson (the area of triangles!) barely registers because it's such a basic application of what you've already learned before. By grade 8 (age 13) I was actually complaining that we'd barely made any progress in 5 years of education. I believe my exact words were "we've basically learned nothing other than maybe the Pythagorean theorem" and I still mostly believe that.
When it comes to things like science, computer science, visual (ie, non-statistical) mathematics, and probably economics, physics, optics, and some areas of statistical mathematics we could probably move 3x as fast if we would just really hammer home the first principles until we were absolutely sure they were sticking.
We don't let babies fill containers with soup because they haven't demonstrated that they understand what a hole is and does. I feel like too often we force children to remember that 3*7 is 21 without really making sure they understand multiplication. The key to getting a child to really learn something isn't by jumping to intentional memorization. Not with mathematics, anyway. The key is to get them to reason about it and to practice over and over again. Not to memorize, but to understand and though knowledge and understanding are different things, understanding always comes with some knowledge though the reverse is not necessarily the case.
On the other hand, a good memorization skill must not necessarily mean you come to the right conclusions. Your sources, peers, genetics and a mind that is by nature chaotic, do it's part.
For example, having good memory may lead you to become more arrogant. If other people praise you for your skill, you become so confident in your conclusions that you stop questioning them and rather see confirmation in an echo chamber of sources.
This arrogance is the source of much evil, I think. You see it a lot in politicians and management.
There is a type of person who can only reply with "smart people can do bad things" when discussing competence in any form.
But there are only so many ways you can say "smart people can do bad things" without sounding repetitive, and it looks like they're scraping at the bottom of the barrel.
Of course not. My point was that there are more important parts of the mind that need training. You can't overcome the mind's evolutionary weaknesses in perception of the world and in being in control over its inner workings by having a good memory.
Memorization might be a part of it, but imho the important part is (emphasis mine):
> So they ended up reading *reference manuals* and writing down or memorizing the answers to their questions because they couldn't look up information very easily.
Good reference manuals are dope and they're so much better than tutorials or FAQ like stackoverflow because they are written to be general, you don't have to generalize yourself (which usually isn't trivial). You're almost never reading about a particular problem but about a class of problems, not about a technic but about a class of technics. In freshman we learnt ocaml (actually caml light, yeah you guessed i'm french) and we were all handed a text copy of https://caml.inria.fr/pub/distrib/caml-light-0.74/cl74refman.... To this day i still love reference books, usually when i have a problem i look it up, get my answer, and then end up reading the whole chapter or so giving much more background knowledge.
Recently I realized that when you had paper documents—books, manuals, libraries, filing systems, whatever—the only way to make them accessible at all was to have organizing principles. Some of these were brilliant.
Most people gave all that up because "search."
But aside from search being flawed (good luck finding an old Google Doc), when information was actually organized, you might be able to remember where it was. Without structure, you can't remember where it is because it isn't really anywhere.
I'd say that being able to make use of a good reference manual is still the process of learning the basic outline of the material, learning what it is that you know and what it is that is contained in the manual (and what isn't in the manual!), and even learning your way around the manual itself in order to find stuff quickly.
I'd say this skill is very different than never learning any geography because you "could" look it up on Google Maps some day if you wanted to.
I've never regarded memorization highly. Whenever we had to learn the times tables or the squares at school, I would just work them out in my head instead of memorizing them.
Of course, I still ended up learning the squares and the times tables by heart, but not because I actively memorized them, but because I just used them so much that I couldn't help but remember them eventually.
I'm of the opinion that this leads to a good rule of thumb: never memorize anything - if you use the thing often enough, you can't help but memorize it anyway.
Of course, you could argue that how often you use something isn't necessarily equivalent to how much utility you might get out of memorizing said thing, and I don't disagree with that.
All that being said, I do agree with the article's premise that an expansive knowledge base aids reasoning, which does seem to be in conflict with my principle. I definitely do possess a basic knowledge of geography, and it does definitely aid my reasoning, but I don't ever remember actively memorizing that - not at school, nor elsewhere.
I had a similar view as a kid, driven mostly by the fact that I wasn't very good at memorisation. I found that I could get by in maths without it, eg. deriving the quadratic formula by completing the square rather than memorising it. I didn't value memory much as a tool in maths.
After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths. The main reason I don't think I could ever have been a professional mathematician is that I would have reached (and have reached in my own learning as an amateur) a ceiling.
I have maths books that are beloved to me, that I have read multiple times (actively, working with pen and paper as one should) and which I will enjoy again in future. But the concepts in those books do not remain in my mind. I don't reach a point where the structure of basic linear algebra, say, is baked in.
I am good at the problem solving, but maths is an edifice, one people have been building onto for millenia. I explore that edifice, and keep returning to my favourite bits of it, but the portion of that structure that is resident in my mind is, and I think always will be, small. It's a window, and as more comes into it, more slides out. Everybody must have such a window, but I know others have much larger windows than me. And that's fine - I'm a programmer, not a mathematician. But I think it's something I would have benefitted from understanding earlier in my life. Perhaps I would have set about "learning to learn" differently. Rote memorisation and active curation of memories already formed could have benefitted me greatly.
> I had a similar view as a kid, driven mostly by the fact that I wasn't very good at memorisation. I found that I could get by in maths without it, eg. deriving the quadratic formula by completing the square rather than memorising it. I didn't value memory much as a tool in maths.
Isn't the structure of the school curriculum also at fault here? If concepts like the quadratic formula being presented without context on why you will need to memorize them, and you're able to succeed without doing it, it's clear why you might choose not to memorize it. That wouldn't be the case if they presented you with challenging, applied problems where having the quadratic formula memorized really is actually necessary.
The curriculum seems to be structured under the assumption that the students will memorize the facts for the sake of memorizing (as most students do) in order to get good grades, and only later apply them on more advanced classes. If you're able to derive the results fast enough, and as such you see no point in memorizing them, then that assumption is broken, and the curriculum won't work the way it is expected to. Those students would need to take initiative themselves to adapt their learning style to the way books and classes are structured, as it's not obvious for them that such memorization is necessary.
From my personal experience, I find that schools often fail to prepare their top students because the exercises meant to teach you how to work hard for real this time are still passable with a last-minute cram session by the fastest students. By the time the assignments are actually too long to be crammed, it's often well past the safety of K–12 education.
I’ve had a similar intuition and approach as a kid though in school I had to memorize definitions and formulae, I never fully commited them to memory, instead choosing to derive them on the spot thinking I was practicing a different muscle, understanding. The bad part was building a bad habit of avoiding rote memorization at all costs whict lead to similar limitations later on. Only later on did I understand that it’s all about building good habits that yield great returns over time.
> After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths.
Same story here. Undergrad engineering math curriculum came easy to me, and it stuck as it was our bread and butter (calculus + diff eq). Once I got to grad level courses, the frequency with which we would utilize the material elsewhere dropped dramatically, and the net effect of that was I could never recall the topics until I needed them.
The next problem was even more significant: If I took even higher level courses, they relied on knowledge of the material I took in one of those prior courses that had not been burnt into memory, and may have taken 2+ years prior. The only reason I did poorly was because I had not memorized enough of the prior material.
On my own, I studied/reviewed the undergrad statistics course 3 times over many years and it never stuck. Finally, in 2018 I used spaced repetition to memorize much of the material, and over 3 years later I can still read material that utilizes those statistics and understand what I'm reading.
Memorizing is useful for things you don't use often.
>I'm of the opinion that this leads to a good rule of thumb: never memorize anything
Did you ever learn another language? It's impossible without memorizing a massive amount of things, especially when the writing system is different than the one one is familiar with. In fact the most famous researcher in vocabulary learning (Paul Nation) states in one of his book that rote learning is one of the most efficient use of time.
I'm of the reverse opinion that memorizing things is a "secret trick" particularly effective, that is put aside by a lot of people because it takes effort.
I can't speak for the GP, but my personal experience is also that I really dislike memorization. That being said, I speak 5 languages, have written books in two of them, have given public presentation in three and can introduce myself and go and buy bread in a few more.
That's in addition to computer languages, of course :)
I suspect that the parts of the brain involving in learning by rote and learning a new language are somewhat different. When I learn a new language, I'm desperately trying to connect anything I see to something I already know. When I learn a multiplication table or a list of unrelated dates, it doesn't work nearly as well.
I speak 7 languages (learning an 8th) and can relate to remembering things in context being more effective than rote memorization.
That said, some types of rote memorization do help accelerate learning. In language learning I often come across fundamental words that don’t occur frequently enough for me to internalize automatically but yet occur frequently enough to block comprehension when encountered (it’s little words like “put” or “place”). For these words, I just put them in Anki in sentence context and do a few rounds of spaced repetition to get them in my system.
In my opinion Anki shouldn’t be used for core vocabulary but it’s useful for reinforcing and “cleaning up” words on the fringes that one doesn’t encounter that often but that are very useful.
I also dislike it. As a small child, I remember hating the boredom of needing to learn by rote the times tables at school. That left my appreciation of mathematics scarred for many years. Only when I was approaching my teens I started to like math again, when presented geometry at school. That makes me think, does this traumatic experience with arithmetic tables right at the beginning is what gives math a bad reputation among lots of students, setting them in a course to hate the subject for life? Sometimes I think it would have been better for society to settle in a number system with a smaller base, say 8 or 6, instead of 10, so the tables got a lot smaller (64 or 36 entries, respectively, instead of 100), giving young students a better experience with aritmethics from the outset.
I speak two languages, one of which is English. I learned them in my early formational years, so I wouldn't consider myself to have learned them using "active" memorization. I was also conversational in Finnish as a child, though I've since completely forgotten the language.
Learning new languages no doubt involves a lot of memorization no matter which way you look at it, but I think you'd agree that the "active" kind is much more mentally taxing than the passive "immersion" kind, the latter of which I take no issue with. I also don't contend that learning a new language as an adult necessarily involves active rote learning.
I have had to learn other languages at school, including ones with non-Latin writing systems. It did involve a lot of rote learning, which I did to pass the classes, shortly after which I forgot everything. I personally don't value learning new languages, an opinion which I realize might come across as a bit uncultured.
One doesn't, but there is a clear distinction between attempting to learn a language by memorizing its words and grammar, and learning it through context.
To actually understand a language in the same way we understand our native language, we cannot learn the language by memorizing the meanings of words and treating each sentence like a logic puzzle to be solved.
Practical knowledge of language is largely tacit.
A native speaker does not need to know what tense a word is in to use them, they do not even need to understand what a verb is. Explicit grammatical understanding can help us reason about a language, but it is not necessary to learn it.
This seems to focus on the wrong part of the benefit of memorization, I don’t think the method of putting the information in or ‘active’ memorization is what provides the benefit so much so as it is that the information is available for active recall.
I draw a distinction between active learning (which takes place when you practice a language) and rote learning. I speak quite a few languages (with varying success) and learned most of my vocabulary from practice (which includes reading). I never thought of learning words as exercising my memory, it's just practice.
Active recall is a key component of successful memorization, which is why the popular system of spaced-repetition flashcards is very much based on it. Actually, even pre-flashcard systems of organized rote learning tend to feature it, e.g. via being asked to recite some short text (the "lesson") word-for-word until it is learned by sheer habit.
For me a language is easier to learn if I can actually use it. For me his rule of thumb is less a rule and more like how my mind works (and to agree all I guess). I can memorize unused facts, but it gets lost in big life changes usually which is really frustrating.
You were probably taught that memorization means "memorization, plus you will be examined and punished and rewarded accordingly, in many cases against any natural inclination to memorize the object of conditioning".
I doesn't, but you're right to not regard this highly.
> never memorize anything - if you use the thing often enough
> Whenever we had to learn the times tables or the squares at school, I would just work them out in my head instead of memorizing them.
I took a slightly different approach: memorize what is important.
For some reason, they wanted us to memorize the times table up to 12 when I was a kid. I quickly recognized that it was only important to memorize it up to 9, and even then there were patterns. Why is 9 more important than 12? Because it is incredibly inefficient to figure out a product each time you need it, but the rules for multi-digit multiplication were generals whereas the rules for single-digit multiplication only worked for single digit (and were necessary for multi-digit multiplication anyway). The trick is to figure out when the efficiency outweighs inefficiency.
I never learned times tables in schools. Just struggled on through until they stopped asking me to memorize them.
Then way later in my 20s, when it was handy to know how to remember some multiples quickly, I realized that obviously there's a lot of patterns in there, and of course the magic of looking for an easier problem to do mentally to solve a more complex one.
No amount of effort at memorization ever succeeded in even trying to give me those tools, and they're so general - you can apply them to everything.
My entire 90s educational experience is a memory of teachers saying "you need to know your times tables" and no one actually trying to teach even basic reasoning about how numbers worked (which I suspect is why programming lept out at me - it's all number manipulation but it's all about the algorithms and patterns and finally things started to make sense).
My brain works the same. When it comes geography, I tend to learn and remember a lot about the countries I visit. But empty learning just doesn't work for me.
When encountering a new concept (a definition, a theorem) memorization is more important than understanding. Yes, you can spend time trying to crack the meaning, but you won’t unless you spend enough time contemplating examples and trying to imagine counter-examples. It’s a struggle. A more efficient way of gaining understanding is, first, to have things you do not (yet) fully understand memorized to the letter, and then use this to do exercises and solve problems. Only then you can more or less fully appreciate the concept, its raison d'être, and why it is formulated the way it is; no amount of explaining on the part of the instructor can be as helpful as your own practice actually using the thing.
Excellent comment. This is exactly how I explain it to the students I tutor.
I tend to use the term "contextual recall" rather than the term "memorization", since the former emphasizes that it's okay to rely on a combination of memorization and pithy resources.
Hand anatomy is the best example I can think of. A good diagram can help you recall enough information to answer complex questions that would otherwise require an incredible amount of memorization. You still need to memorize some things in order to answer questions -- mostly the kinematic aspects and various properties of the things being represented (tendons, bones, muscle, etc.) -- but far less than you would need otherwise.
The one pager of theorems and proof construction techniques sometimes allowed in mathematics courses is another example.
This is why generative models are exciting as the next "tool for thought" for me, up there with calculators and search engines. Contextual recall is a powerful tool, especially when combined with memorization, and is a limiter for lots of folks (including me).
I think people are confusing "memorization" with "practice". "Practice" is really important and "memorization" is both the prerequiste and result of "practice".
I often tell people "Calculus is just algebra. However, it's fast, repeated algebra. If you aren't excellent at algebra, calculus is going to be terrible for you. On the flip side, calculus forces you to use your algebra so much that you get much better at it."
This reminds me a brilliant article [1] by Barbara Oakley, who has a _superb_ course on Coursera on "Learning How to Learn" [2].
In this article, Barbara talks about how memorization helped her with Mathematics, a subject that she had previously struggled with. In particular, this line stands out to me
> Continually focusing on understanding itself actually gets in the way.
This is something I miss from the era when I learned to code: thick books of reference material, designed to be comprehensive. At the time, your compiler was called Superlative Language Number, and you had confidence that as long as you double checked the Number.Subnumber supplement, it would keep working the way the thick stack of paper promised it would.
What you memorize here is the table of contents, and approximately where each answer is inside the book. Search might be better at first but it doesn't scale like logarithmic search over a static pile of paper.
There are programs I can still apply this approach to, vim comes to mind, but for the most part documentation is ambient now, with the leading search engine delivering meaningfully worse results year over year.
Yes! I learned a number of languages from O'Reilly books and it is a qualitatively different experience than learning through a bunch of disconnected StackOverflow questions.
Both modes of learning have their place and a combination of a comprehensive overview plus detailed treatments of specific corners gives so much more understanding than either alone.
In University I had a prof that gave us 600 facts at the start of the year. All printed and easy to read. Each class we went over a few of them.
He said if you mastered 100% you'd get 100% on the exam. He would pick from the lot and that's the exam question.
His reasoning was. These are the basics, we were all smart, and we could use the basics to go beyond them. But only if we had them.
20+ years later and I still remember most of the things in that class. I can still write code in assembly (8086). I don't need to, but I have the knowledge, and it's helped shape my code.
This is honestly so important. Almost every issue or confusion I have had while studying is because I didn't remember or never learned a fact from "the basics". Over time I like to think I've corrected most of them, but only by finding and saving high-quality references that help me learn them again quickly - although ironically the process of conciously doing that usually means I no longer need the reference!
I avoided memorizing mathematics for a long time, but eventually created some spaced-repetition flash cards about math. I find the math I have memorized gives me something to reason about. While I'm in the shower, for example, I can think about stuff I've memorized and gain deeper insight. The memorized facts are hooks upon which I can hang new knowledge.
Sounds like a great prof. Mastering the basics cannot be overstated, if you ask me. Everything else can build upon those basics, worst case it can just be looked up when needed.
Anyone who's interested in this way of learning, I'd recommend you to check out retrieval-based learning (1):
"Retrieval is the key process for understanding learning and for promoting learning, yet retrieval is not often granted the central
role it deserves. Learning is typically identified with the encoding or construction of knowledge, and retrieval is considered
merely the assessment of learning that occurred in a prior experience. The retrieval-based learning perspective outlined
here is grounded in the fact that all expressions of knowledge involve retrieval and depend on the retrieval cues available in
a given context. Further, every time a person retrieves knowledge, that knowledge is changed, because retrieving knowledge
improves one’s ability to retrieve it again in the future. Practicing retrieval does not merely produce rote, transient learning;
it produces meaningful, long-term learning. Yet retrieval practice is a tool many students lack metacognitive awareness of
and do not use as often as they should. Active retrieval is an effective but undervalued strategy for promoting meaningful
learning."
Memorizing is a lost art. It breeds understanding, because the symbolic surface makes itself apparent to the mind so readily—and without understanding, the symbolic surface has no grounding.
Only once the lines are memorized can you say them with feeling. And, when you know the feeling, you can make up new lines.
Understanding and memorization should not be seen as opposites.
This resonates with me and my experience of memorisation in the context of botany. A few years back I started going on urban plant survey walks with my local natural history society. The process of learning and memorising the names of the different plants, and then feeling the patterns start to take shape and the flow of recognition on the following walks was so rewarding. It starts to change the way you see things around you. Rather than just being arbitrary bits of data that you're memorising, names become like markers that amplify the unique aspects (however minuscule) between the different living things that surround us.
Memorization also forces you to "reduce dimensionality" in the data—find the underlying patterns of correlation and causality that cause the world to be structured the way it is. You can't feasibly fit every single event in the history of every country in the world into your head, but it becomes a lot more feasible once you extract a narrative that explains the data effectively.
Memorization implicitly requires learning and characterizing them entirely separately as modern education does is pretty faulty.
Absolutely, so does external storage (optimized note taking) btw. If you try to cram data on paper in succint way, you'll have to find redundancy, structure which ultimately is easier to store in your mind too.
I largely agree with the author. Even the quickest internet search is many orders of magnitude slower than recollection from memory. The analogy with retrieving from cache vs RAM / disk / network is probably well known. But we should not go overboard in either direction. Everyone's memory is limited, and there are appropriate uses for both calculations and lookup tables.
Quoth Sherlock Holmes:
"I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has difficulty laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones."
I'm one of those people. I haven't memorized all of the Python standard library, but whenever I run into things that I need to do on a monthly frequency (which is not enough to remember things just by using them), I add them to my Anki deck.
I memorized half of If when I was younger. It seemed especially impressive to certain people.
These days I combine mnemonics with memory palace journeys. In a few hours of practice I went from being able to memorize 6 digits to around 70.
My penultimate challenge is to memorize texts verbatim. I haven't been able to find a straightforward method. My next thought is to research theater performers' methods and Hafiz methods. If anyone has any specific pointers to share I'd be grateful.
To memorize text verbatim, you might find value in learning GMS. Mattias Ribbing has a course (search on coursio.io for his name) called "First Steps to a Complete Master Memory" and a follow-up course. This course is like the abridged version of GMS. To summarize in one sentence: GMS has you make palaces/journeys constructed from objects and their parts and you attach mnemonics to the parts. It is effective, but requires a decent amount of training. There is a second course called Pmemory (phenomenal memory) that has disappeared from the internet except for certain torrent websites. GMS (via Pmemory) was brought to the English-speaking world by an "interesting" character, but it was not invented by this character. I would suggest digging into the Pmemory material if you are serious, even though it can be a little confusing and overly prescriptive. But yes, I was able to memorize theorems and mathematical formulae verbatim. The time/energy cost was too high to maintain in my schedule, but I look forward to returning to the system in the future.
Memorize blank verse, aim for a stanza a day. There's loads of it, and you can be that guy who spouts just a bit too much Shakespeare at parties.
It's closer to prose, but the meter makes it harder to swap words out, and teaches you that words aren't fungible in memorizing a text (as opposed to learning from it, which is most of what we do with texts).
> If anyone has any specific pointers to share I'd be grateful.
I recite a pair of lines multiple times until they feel natural. Then I put overlapping quintuples of words into my Spaced Repetition system. So with Ozymandias I read the first section:
I met a traveller from an antique land who said:
"Two vast and trunkless legs of stone stand ..."
Then into my SR system I put:
I met a traveller from | traveller from an antique land ...
traveller from an antique land | antique land who said: "Two ...
The ancients put rhythm to their poems for a reason. It aids memorization of long passages.
But also, text I find is something that resists mnemonic systems. Rote repetition to make the text lived and part of you, to burn into your brain and tongue the very act of saying the words in that specific order seems to rule the day still.
I've worked with devs who never looked up anything on the internet and tried to do everything from memory and their code was shit. I think here it may have been something else that made this team highly productive.
Maybe they had more autonomy than most dev teams are allowed to have. I know I would have never been allowed to create a compiler for any of my previous jobs (to high risk).
I do agree you shouldn't just Google every problem you have.
You crossed a major line here in bringing in someone's personal material as ammunition in an argument (if this can even be called that). That's a form of personal attack, which we don't allow here, and which we ban accounts for doing, so please don't do it again.
I wonder if there should be a distinction between memorization and intuition. The author alludes to the fact that if you can build an intuition to the fact that daylight savings time was right in the middle of world War 1, then you can remember more easily that it was in 1916.
I have found that I cannot remember certain mathematical properties at all. For instance I always forget whether to use sin or cos to get the x component or y component. But, I had a few teachers force us to memorize the fundamentals: SOH, CAH, TOA. Using the fundamentals allows me to prove to myself very quickly what I should use. It's the same thing with the quadratic formula. I can never remember it, but I had a calculus teacher show us how the equation is derived. I can remember what a parabola is, and I also remember the fundamentals of calculus. Using these two things I can derive the quadratic formula pretty easily.
So I wonder if there's a 2nd metric that we're missing. Where we need to memorize fundamentals, and critically think about how to use those fundamentals. I don't know, this could just be more anecdata though :)
You know those fancy electronic notebooks? They're barely better than actual notebooks. They all seek to emulate the pen and paper experience, they go to great expense and make it a focus of their advertising that they feel like real pen and paper. Why wouldn't I just use pen and paper?
I believe electronic notebooks haven't yet realized their greatest potential, spaced repetition. I want to take my notes in an electronic notebook, then review my notes and extract parts of them to become spaced repetition items. This is something I would happily have a dedicated device for, and would pay $1000+ for such a device, but they don't yet exist.
After taking notes, natural hand made notes, I imagine creating spaced repetition "flashcards" would work like so:
1. Review notes and draw a square around something I would like to memorize; perhaps a fact I have written, or a hand drawn chart or diagram. This square becomes a "flashcard".
2. Optionally, I may hide (by blurring, or pixelating, etc) part of the flashcard.
When the time came for study, these flashcards would be presented to me following a spaced repetition algorithm:
3. Present the flashcard, including all blurring and pixelation.
4. When ready, the user is shown the full unobscured flashcard. The user may also toggle the surrounding page the square was originally extracted from, this gives the user context.
5. The user can then judge how well they remember the flashcard. The user presses a button indicating how well they remembered the flashcard. This feedback goes back into the spaced repetition algorithm.
The important innovation here is that users can easily combine hand-written and hand-drawn notes and a spaced repetition algorithm. In Anki, you can import pictures, but this is burdensome. You can write markdown or LaTeX, but those suck compared to just drawing something by hand. Studies have shown that hand drawn notes aid in memorization. The would has never seen hand drawn notes easily combined with spaced repetition, and I believe it would be better than any other memorizing scheme we've yet encountered.
The Art of Memory by F.A. Yates is still a nice read.
In the article, the engineers admired by the author were intel ops who
were stuck in an airgap and had to use their minds. That's a principle
I try to use in life - to some extent deliberately making things hard
for myself. As with all exercise, what was impossibly hard becomes
commonplace.
Part of this discipline is knowing what not to do (yes, attic
theory). I never create new accounts on anything or unless I've a
clear cost-benefit rationale that makes memorising a new 32 character
passphrase worthwhile. That excludes a huge heal of crap that wants
you to "sign up" for it.
Speaking of airgaps, here's David Beazley's wonderful classic PyCon talk about using Python as a secret weapon while locked in a secret vault with no internet connection or floppy disks allowed:
>David Beazley: Discovering Python - PyCon 2014
>So, what happens when you lock a Python programmer in a secret vault containing 1.5 TBytes of C++ source code and no internet connection? Find out as I describe how I used Python as a secret weapon of "discovery" in an epic legal battle.
Here's some stuff about how The Art of Memory, Memory Palaces, and the Method of Loci relate to adventure-like games, and some apps I developed along those lines, which I discussed with Scott Adams when he dropped by HN (the kind and brilliant old school text adventure game developer, not to be confused with the terrible Trump loving misogynistic troll and right wing nut job cartoonist who was outed for using sock puppets to gushingly praise and flatter himself on Metafilter and Reddit, and who besmirched the original Scott Adams' good name):
>How do you think Adventure games are like the Method of Loci, or Memory Palaces, in that they can help you remember and retrieve vast amounts of information geographically?
Or as we call it,in infant school "rote learning" which incurs a huge penalty in popular opinion, despite driving recall of basic arithmetical facts like the times-tables, alphabet order, spelling "rules" &c
Understanding that memorization should be key for the reasons laid out in the article, would it be better to forgo note centered workflows such as Zettelkasten or Wiki for flashcard centered workflows such as Anki or Supermemo? What gives the most value?
I'm going back and forth between these two workflows and I feel like progressing at a steady rate before getting bogged down, not because I have difficulty with the subjects I study per se, but because every month or so there is an article confuting the previous one, prompting me to switch to the other workflow, slowing me down considerably, every single time.
I've been working for the past few years on an app that attempts to combine the two (Zettelkasten / wiki + flashcards / Spaced repetition). [0] I personally really like the zettelkasten method and it's the only note-taking method that has really worked for me. Being able to then take a subset (or all) of those cards and put them into a spaced repetition review schedule makes them even more useful.
Pick something that works for you and stick with it. There will always be aricles of people talking about what works for them, you shouldn't just drop everything and switch entirely, just incorporate some aspects of their advice that sound good to you.
I think heuristics are much more important than knowing semantics. Someone who can memorize all the notes on a piano faster than their peer isn't necessarily going to be better at piano in the long run.
Similarly, there was an idea expressed in chess where some people rely on memory to reproduce thousands of similar scenarios, while others rely on the "feel" of the chessboard and the various heuristics related to it (e.g. is the king "safe" -- e.g. castled and not exposed etc., are the bishops "powerful and free to roam" -- e.g. not blocked by pawns or heavily contested etc.).
My argument partially comes from self-defense; my memory is comparatively poor. But I'm able to use heuristics developed over years of experience to make generally good decisions.
So in this case:
"Who would you rather hire: the person who knows exactly what features are available in PHP 7 and which are only available in PHP 8, or the one who will figure it out by trial-and-error of while writing each application and seeing what fails?"
I would hire the person who is able to write the best application, and understand when to use what features or not: similar to the Bond quote "Sometimes a trigger needs to be pulled -- Or not pulled, it's tough to know which in your pajamas". If memory was the most important part of cognitive ability computers would serve a much larger role in society than the (already large) part they do today.
> Subconsciously, when you learn a piece by heart, its message penetrates deep inside you. It lies at your fingertips, ready for you to make use of it. Many cultures have long understood this. In Islam, people who memorize the entire Koran are given the special title of hafiz, or guardian. In a secular equivalent, I know people who have memorized Rudyard Kipling's poem If— to give them a moral helping hand at times of crisis.
What poems you all think serve as good reminders of truths of how to work well in teams and build good software?
Honestly the ancient Latin's dict "est modus in rebus" (there is a measure in anything) IMVHO is still generally valid, witch means that yeas we also need memorization but there is no reason to stretch it like in the old time before printed press. I fail to found a purpose to remember exact date of birth and death of historical figures, remember poetry etc
Similarly I see no point in doing the opposite, like certain "GTD fanatic" who pretend not to remember what they need to do in next few hours because their GTD system is more efficient than their memory and so they need to keep memory free to focus on current thing.
Est modus in rebus.
We need to eat, eating too little is harmful, but also eating too much is harmful. We need oxygen to breathe but too much exigence fry our lungs and brain. Sport is important, a sedentary life is not healthy, but too much physical activity means being broken in the old age with a consumed body.
The most important thing to operate with their own brain IMVHO is having in memory "the big picture" so to being able to recall anything via computer as needed. Without the big outline our searches are limited, probably biased, we can't correlate things we encounter etc, but there is no need to do more and no reasons to do less.
Use method of loci. It's an almost trivially learned skill, and once you've got the technique down, you can expand it as needed, or riff on the basics with other mnemonics to amplify the speed and volume of memorization capacity.
Rote learning is difficult, and unnecessary. Your brain already automatically memorized places, faces, and novel things. If you can imagine Elvis in a wizard robe holding a block of cheese on your front porch, you have a one item memory palace. That's the level of difficulty a memory palace requires - it's a hack of built in automatic functions your brain is already performing.
Elite memory athletes who memorize the order of thousands of cards, or tens of thousands of digits of pi, or a travel dictionary, or any other assortment of things - these people are often average intelligence, otherwise normal folks who just practice a neat trick.
There are dozens, if not hundreds of "advanced" memory, mnemonics, or method of loci primers. Get one and develop a superpower.
I like "Memory Improvement" by Ron White - you can grok it in an afternoon, but it's structured into 30 daily exercises, and captures all the important features without fluff or filler. The audiobooks is great, 4 hours long. A motivated person could master the skill over a weekend with nothing but the audio.
Seriously. Method of loci is a basic human skill that gets attributed to genius characters like Sherlock or Tony Stark or Einstein level intellects, or to shamans and druids and mystics. It's a default feature that comes in every install - it's how your brain wants to work. Every single person can do it, and should.
This analysis is only relevant for neurotypicals. There are ways that your brain can work that flip this whole thing on its head, and if you have one of those brains you need to do exactly the opposite of what this article recommends: You can only remember the details by understanding the context. I do not understand that Oman is powerful because it controls the Strait of Hormuz; I do not understand that Russia wants Crimea because it has Mediterranean access. Rather, it's only possible for me to remember that Crimea has Mediterranean access by understanding that Russia wants Mediterranean access and wants Crimea and using those facts to infer the relevant geography. I am able to remember that Oman controls the Strait of Hormuz because I understand that Oman is powerful and that the Persian Gulf is important and I can work backwards from there. So be careful about the directionality of causation when you're looking at observations like "The most understanding-capable people I know know a ton of details" - they may be able to know details because they understand rather than being able to understand because they know details.
Memorization alone and in itself is nothing but just a curiosity. But coupled together with good analytic and connection skills it is an incredibly powerful asset.
Very much in agreement with the article. The analysis about the current Ukrainian situation is a little bit limited, though, because Russia controls Sevastopol since it annexed Crimea in 2014; it didn't need the current war to control it more.
Also, probable typo:
> A second example: at the time of the writing of this article, Russia is a month into an invitation into Ukraine.
invitation => invasion? I don't think anyone invited Russia in Ukraine.
> Very much in agreement with the article. The analysis about the current Ukrainian situation is a little bit limited, though, because Russia controls Sevastopol since it annexed Crimea in 2014; it didn't need the current war to control it more.
Agree. That was my first thought even when they invaded Crimea.
> invitation => invasion? I don't think anyone invited Russia in Ukraine.
Could be a tongue-in-cheek? I understood that as being said in a sarcastic tone.
>, because Russia controls Sevastopol since it annexed Crimea in 2014; it didn't need the current war to control it more.
Crimea's fresh water supply came from a canal originating in Ukraine. After Russia's annexation, Ukraine retaliated by blocking the water flow with concrete so Crimea was running out of water. Deep link to explanation: https://youtu.be/If61baWF4GE?t=16m27s
So it was no surprise that on the 2nd day of the invasion, Russian soldiers used explosives to blow up Ukraine's dam to to re-open the canal: https://www.youtube.com/shorts/313jB_tLSxQ
Also, Russia controlling Ukraine's land and coastline from Donbass through Mariupol and down to north Crimea means they have a more viable "land bridge" for supplies than the tiny man-made bridge that links southern Crimea with Russia. Ukraine becoming allied with NATO (or a defacto "NATO ally" via EU membership instead of a Russia puppet) means that tiny bridge over the Kerch strait becomes a vulnerable chokepoint that threatens Russia. Deep link to that explanation: https://youtu.be/l5KXeFdpyaE?t=7m22s
From Russia's point of view, there are many desirable military objectives for them to take over southeastern Ukraine.
EDIT reply to: >, because a naive look at the map suggests that even without Crimea, Russia already has coastline onto the Black Sea between its borders with Ukraine and Georgia... there must be a strong reason in favour of invading another country rather than developing ports on the land they already have,
Russia's existing coastline with the Black Sea (e.g. Sochi, etc) has no deep water ports that connect to their major navigable rivers. The 2nd video I linked illustrates that. You can also see on the wikipedia diagram that the Russia's existing Black Sea coastline around Sochi doesn't connect to Russia's main river system: https://en.wikipedia.org/wiki/Unified_Deep_Water_System_of_E...
When Ukraine had pro-Russian president Viktor Yanukovych, the Crimea chokepoint wasn't as big of a threat. With the 2014 regime change to pro-NATO presidents Poroshenko & Zelenskyy, that mindset changed.
I'm obviously missing some facts about the region, as per the OP's hypothesis, because a naive look at the map suggests that even without Crimea, Russia already has coastline onto the Black Sea between its borders with Ukraine and Georgia... there must be a strong reason in favour of invading another country rather than developing ports on the land they already have, if the goal is simply "control over the Black Sea and trade access to the Mediterranean Sea".
As per the video https://youtu.be/If61baWF4GE), above and beyond the geopolitical reasons for Russia's invasion of Ukraine, the main motive is economical:
1. Russia is in effect a petrostate; it lives and dies by its exports of natural gas and oil.
2. Immense fields of underwater natural gas and oil were discovered in 2012 in the Crimea maritime exclusive economic zone.
3. If Crimea stays with Ukraine, it lets Ukraine become a new petrostate and challenge Russia (take over its European customers), which to Russia is an existential threat. Hence the annexation of Crimea in 2014: not only for Sevastopol and access to the Mediterranean, but to exploit the oil fields (and/or prevent Ukraine from exploiting them).
4. But the supply of 80% of the fresh water to Crimea comes from a canal [0] that connects it to the Dnieper river in Ukraine; after the annexation, Ukraine shut the canal down, effectively thirsting Crimea to death.
5. If Russia wants to stay in Crimea (which it believes is necessary for its own survival), it needs to reopen that canal, and therefore control at least the southern part of Ukraine and possibly its whole Mediterranean coastline.
(It's not just about the canal, but the canal is a very big part of it.)
Russia's Black Sea coast is shallow and lacks large, sheltered harbours. It would cost billions and takes decades to build a proper port there.
Russia had actually be leasing the port at Sevastopol from the Ukraine since the fall of the USSR and had their Mediterranean fleet based there even before the invasion in 2014. They had a lot to lose in an anti-Russian Ukrainian government.
For math, when I was in school I tried memorizing all the formulae, and well, my life was miserable. I hated it.
Recently just for fun (I have a job that (perhaps unfortunately) does not require any advanced math), I started taking math MOOCs from top universities. I discovered that, when I looked into how the formulae is derived (starting from elementary math), I find it substantially easier to keep in mind the formulae. Or even if I don't remember the formulae, I know how to derive them.
I now feel like I've understood certain concepts much better, even though if there's a timed test I might end up being worse off than others who memorized. But then again, I'm learning for fun and is not preparing for any test :)
What I'm trying to say is, for math atleast understanding the underlying concepts work better for me, even if at a given point it's beyond your grade.
(Thank goodness MOOCs exist. I should probably donate.)
I get the impression that memorization fell out of favor in education
because in the past, it was used as an ends in itself
rather than a tool to generate insight.
In school, my dad had to memorize a lot of dates
with precision down to the day.
That seems mostly-useless to me.
Just knowing the decade is sufficient
for most analysis.
To take the article's example,
the putative link between
"Row v. Wade (1973) → Downswing in crime since the 1990s"
only really requires that you know
that the ruling occurred sometime in the 70s.
I think the strategy, then, should be to memorize things
that are likely to generate insights
and to the level of precision that will likely be necessary to do so.
You should probably commit to memory that Andrew Johnson
was the president after Lincoln in 1860s
-- but you probably don't need to remember
that Millard Fillmore succeeded Zachary Taylor on July 9, 1850.
One of the big advantages of memorization is that you can work on problems in your sleep.
Sometimes when I have a very difficult problem, I will memorize all the information related to the problem and then go to sleep. Many times, I have woken ip in the middle of the night with a solution to the problem.
> “An overly precise memory is maybe not really what we want in the long term, because it prevents us from using our memories to generalize them to new situations,” she said in San Diego at a recent meeting of the Society for Neuroscience. “If our memories are too precise and overfitted, then we can’t actually use them to … make predictions about future situations.”
I guess it depends on what is meant by "memorization." I feel like I have a good memory but I suck at memorizing things. I would say I have knowledge but when it comes to dates and quotes I am terrible. I can remember things that happened and my friends and I usually do well at pub trivia. However, in school there were two times we were supposed to memorize poems and I sucked at it. I screwed it up both times. When we would take a test and afterwards people would ask what I got in question 4, I would have no idea.
While I agree that factual data points are necessary to test the hypothesis and reach a better conclusion, I disagree that one needs to memorize them. Facts are stored in databases and books. One can always look it up. Maybe a matter of minutes or hours.
There is no point in memorizing a readily available fact that virtually has no effect on your life.
"Subconsciously, when you learn a piece by heart, its message penetrates deep inside you. It lies at your fingertips, ready for you to make use of it. Many cultures have long understood this. In Islam, people who memorize the entire Koran are given the special title of hafiz, or guardian. "
Mentioning Muslims who learn by heart the Quran as a means to illustrate how memorization makes the message penetrating deep inside us, is something totally wrong. VERY wrong.
There is no single Muslim in the world (and in the history of Islam, including Muhamad himself) who knows the meaning of Quran. One of the obvious reasons you may understand is that a large amount of the Quran vocabulary is not Arabic (even the word "Quran" itself, is not Arabic). Basically you can pick up any random Quranic text and you will not find one single Muslim in the world who knows at least the meaning of certain words.
If you read the Islamic resources which explain the Quran, you will find dozens, and sometimes hundreds of explanations for the same text just because some words are not even Arabic.
So memorizing the Quran by heart does not help you in anyway to understand its message.
I could have said similar things about other examples you mentioned. But the point of my comment is that between programmers we should stick to programming concepts when we try to explain something instead of picking examples from fields which are beyond our knowledge and which approach is merely a waste of time and confusing at best.
Also do not try to overthink a concept. It's easy to be quickly off-topic.
I still believe one the biggest problems new students have at community college from their math classes is lack of memorized basic math. When you have to take any time to do the basic math when learning college math, you are at a time disadvantage. Flash cards are apparently the devil, but you don't need to work out the simple stuff and calculators are context switches.
I volunteer tutor high school kids in my local community. Particularly math and history. The biggest differentiator between the students who scale up quickly and those who scale up a bit more slowly is their aptitude for memorization.
Recent history curricula and pedagogy in HS has placed an emphasis on “analysis” and “critical thinking.” But the students who struggle all struggle for the same reason: they cannot remember at the moment of writing their paper the basic facts that give context or even give meaning to the documents they are to analyze. I can teach a kid how to do the ACT of analysis to a great level of competency but their papers will be filled with bad analysis and illogical conclusions because they do not know what they read. So, much to their protests, I train them to memorize. And that is often the last push they need to not only get good grades, but realize the joy of critical thinking itself. For now they are not wasting brain cycles trying to conjure up the facts.
Good memorization skills are a huge leverage and it is something that can be learned and practiced. It is a shame that schools are letting children let their mental muscles atrophy like this.