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Ask HN: Concepts that clicked only years after you first encountered them?

• Simon_O_Rourke 4y ago
  The concept of decorators in Java and Python - I know what they're supposed to do, but each time I find myself grinding my teeth when using them, thinking there's a better way of doing the same things more simply.
• dionidium 4y ago
  I was at a Denny's around 2AM once and in an instant became totally convinced that I understood the Ontological Argument perfectly and that it was 100% correct and undeniable proof of the existence of God. But then I lost it.
  • 082349872349872 4y ago
    which of the many Ontological Arguments? (eg Gödel's https://en.wikipedia.org/wiki/Gödel%27s_ontological_proof#Outline https://en.wikipedia.org/wiki/Gödel%27s_ontological_proof#Ou... is an exercise in order theory, in which one proves that a certain axiomatically presented mathematical structure has to have a maximum, which then, for the religiously inclined, could be identified with God)
• 99failures 4y ago
  "The Innovator's Dilemma". I read the book and I took the class in b-school. At the moment I thought it was OK, fast forward a decade and it's one of the pillars of my business thinking.
• sciencesama 4y ago
  Basics of software planning by reading phoenix project.
• bsuvc 4y ago
  Unit testing and using dependency injection to write test-able code. I'm not sure if it was years, but it wasn't immediate. I just didn't understand why dependency injection was good at first, and not just someone's weird personal code style choice. I thought it was just people being "Enterprisey" which I'd encountered many times over the years. Once I committed to unit testing, I realized how necessary it is. Unfortunately I still encounter customers who haven't bought into it and as a result have untestable code. It's so hard to go back and retrofit testing.
  • everybodyknows 4y ago
    > dependency injection The term is unfamiliar to me -- is it related to "fault injection"?
    • la_fayette 4y ago
      No it is a design pattern to structure code. It is also known as the hollywood principle (don't call us, we call you). Meaning that dependencies of a class are provided from the outside, the class itself doesn't know how to create instances of dependencies, just relys on the dependency container (also named inversion of control)...
    • ngc248 4y ago
      It is a pattern where you inject the dependencies of a class into it rather than create the instances of the dependencies within the class. for more info --> https://en.wikipedia.org/wiki/Dependency_injection https://en.wikipedia.org/wiki/Dependency_injection it makes the code cleaner and testable.
      • everybodyknows 4y ago
        What I find troubling about that page is that it does not qualify up front whether the dependencies are: A. Also depended upon by other, coequal unrelated classes, possibly maintained by others, OR B. Depended upon only by a single class (of higher functionality) Situation A is sometimes called a portability interface; B might be called an internal structuring interface. The difference has crucial implications for social power relationships between the human developers and users involved.
• ergonaught 4y ago
  Basic music theory. Almost no one I encountered bothered to actually explain anything. They simply regurgitated things and I guess expected me to somehow intuitively understand something or other.
  • linuxlizard 4y ago
    Sadly, mathematics classes are like that as well. Instructors start throwing equations on the board, expecting us to somehow connect it all together. The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used.
    • gen_greyface 4y ago
      Do you remember what the book was called, or the writers.
    • luuuzeta 4y ago
      Sadly many professors fall victim to the Curse of Knowledge. It doesn't help they need to follow a tight schedule and intuition isn't something you can develop in a single lecture. I suppose self-study and repetition is the most likely solution. >The best math textbook (Theory of Algebra) I ever read had little sections about the person who revealed a particular subject, why they were studying it, and how the subject is used. I've found the best type of books provide motivation for concepts, how they have evolved, etc. Take Computer Science for example, many of its concepts were area of research for decades but from a student's perspective it seems these concepts were always here instead of being constantly refined until the states they're now in.
      • voidhorse 4y ago
        Exactly, understanding the intentions and history behind a concept is key to achieving comprehension. I've had to teach myself nearly all of the more advanced mathematical concepts I know, and I'm finally starting to reach a point where I feel I have a nice approach toward achieving an understanding: - Learn the definition - Learn the motivations and history - Peruse a few examples - Try to map the above to a brief synopsis that explains the concept in intuitive terms that relate to your own life. Rely on pictures. Finally, I find it helpful sometimes to try and "deduce" identities from "first principles". e.g. assume I didn't know that n^0 = 1. How might I reach that conclusion? If I have an understanding of what exponentiation means I should be able to come up with a few different propositions (these could even be relatively informal) that make such a conclusion make sense. My childhood was rife with mathematics teachers that focused more on rote memorization of identities instead of careful explanation of definitions and development of "intuition". There's pretty much no better way to ensure you'll produce students that dislike and suck at math for the rest of their lives than proceeding by mind-numbing rote memorization.
• sokoloff 4y ago
  Systems in equilibrium. A lot of my college engineering courses had these (what seemed to me to be) hand-wavy assertions of equality and what seemed like just an assumption that the system would converge to that point. I was probably in my late 30s or early 40s before I really grokked why that tended to be true. (I could blindly accept and grind through the equations to get the answers in college, but it was decades later that I developed a feel for why.)
• W0lf 4y ago
  Discrete mathematics and all sorts of its application in real-world (software development) related problems. Also how any given solution to a problem in one problem domain can be transferred to a problem in another unrelated domain. Think Galois theory but waaaay less fancy :-)
  • philjohn 4y ago
    When I did Mathematics A-Level's, we had to select four modules. I chose pure 1, pure 2, stats 1 and, new that year, discrete 1. So many useful groundings in various super important comp sci concepts.
• recursivedoubts 4y ago
  i didn't really understand hypermedia, and, in particular, the uniform interface/HATEOAS until a few years after i started building intercooler.js (htmx predecessor) https://intercoolerjs.org/2016/01/18/rescuing-rest.html https://intercoolerjs.org/2016/01/18/rescuing-rest.html much later: https://htmx.org/essays/hateoas/ https://htmx.org/essays/hateoas/
  • NeutralForest 4y ago
    I'm reading the HyperMedia book right now, thanks!
• ISL 4y ago
  That professors were thinking real hard about which problem sets to give us in hopes that we would actually learn something. I don't think I really understood that completely until I started TA-ing.
  • luuuzeta 4y ago
    Tangentially related but that's something I've come to realize too as of recent. Asynchronous programming in JavaScript is new to me so as an exercise, I'm writing a document where I explain the concepts to myself and once I shifted from "how I understand" to "how I would this to someone else", figuring out a good enough scenario/problem harder. Good problem sets that aid studets' intuition aren't easy to come by, oftentimes they're either too easy or too hard.
• robg 4y ago
  The autonomic nervous system and the adrenal cortex. Homeostasis is taught as a textbook fact, the body reverting to a baseline over time. What’s not taught is how much the impacts of daily life events drive a continuous stress response. Fight or flight is not just a reaction to deadly threats. It’s active every moment of every day to ensure survival. The adrenal cortex is always active, to traffic, your boss and colleagues, relationship struggles, and overall health and wellness like sleep and nutrition. Yes, the system reverts to a baseline over time but how much that baseline varies is obvious in tracking resting heart rate.
  • rzzzt 4y ago
    "Understanding Stresses and Strains" from 1968 presents a good depiction of the mechanism with familiar-looking cartoon characters: https://archive.org/details/understandingstressesandstrains https://archive.org/details/understandingstressesandstrains The caveman pressing the alarm button is something I think of a lot.
    • eternalban 4y ago
      I had to see it. Thanks for sharing.
  • rramadass 4y ago
    Any books you could recommend? I presume you already know of this book: The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma by Bessel van der Kolk.
    • sirsinsalot 4y ago
      Thank you. Bought and reading.
    • robg 4y ago
      That’s a great one. I’ve been looking for something that links the physiology with knowledge work and life demands, but I haven’t found it yet.
  • 4y ago
• linuxlizard 4y ago
  Blue Noise dithering based on a HN post from @todsacerdoti. https://news.ycombinator.com/item?id=25633483 https://news.ycombinator.com/item?id=25633483 At my previous job we had an ASIC hardware block to implement blue noise dithering. No one, even the people who created it, could explain to me how I needed to use it. Years latter, I read their blog post and a light bulb went on.
• tails4e 4y ago
  The fourier transform. Encountered it first in my undergrad engineering degree, it was presented as dry mathematics, with no real explanation, just threw complex exponentials at us, and pages of derivations. Years later I actually use it in my job, and through that and other material can see its beauty, and how its actually not that complicated. Some great resources like this helped a lot: [0] https://betterexplained.com/articles/colorized-math-equations/ https://betterexplained.com/articles/colorized-math-equation...
  • sjaak 4y ago
    This is what made it click for me, can recommend it: 3Blue1Brown -- But what is the Fourier Transform? A visual introduction. https://www.youtube.com/watch?v=spUNpyF58BY https://www.youtube.com/watch?v=spUNpyF58BY
    • kippinitreal 4y ago
      That video did the same for me. I also like the reducible video for Fast Fourier Transforms as well as the Veratasium piece that shares some fun history. Reducible - FFTs the most ingenious algorithm ever https://youtu.be/h7apO7q16V0 https://youtu.be/h7apO7q16V0 Veritasium - The Most Important Algorithm of All Time https://youtu.be/nmgFG7PUHfo https://youtu.be/nmgFG7PUHfo
      • Akronymus 4y ago
        The FFT is something I still can't quite grok, for some reason.
        • Gibbon1 4y ago
          I had the same problem. Then I took a math course where we covered the general fourier transform and it made way more sense. An the FFT is the result of a simplifying transformation based on discrete regularly spaced points and that's really opaque from the other side.
        • rramadass 4y ago
• btrettel 4y ago
  It took a couple years in college for me to understand entropy. Entropy in classical thermodynamics is presented in a mysterious way that leads to confusion. Entropy in statistical thermodynamics, however, is logical. Once one understands basic statistical thermodynamics, entropy isn't mysterious. The book in my statistical thermodynamics class was An Introduction to Thermal Physics by Daniel Schroeder, which is an excellent book that I've referred to many times since.
  • luispauloml 4y ago
    I had to study entropy twice in college for different courses that were 2 years apart from each other, and I still remember this one quote I read somewhere: The first time you study entropy, you won't understand it. The second time you study it, you'll think you understood it until you realize you didn't. By the third time you study it, you just don't care anymore and just use it. 10 years after graduating, and I haven't encontered entropy again after the second time, so you can guess where I'm at in this quote. But thank you, for now I know how to attack it if I ever need it again.
    • btrettel 4y ago
      Entropy is basically a useful quantity. It's no more mysterious than enthalpy or Gibbs free energy, both of which have also caused me confusion in the past. To me, the issue with entropy is that it's initially presented without clear justification, so people don't know why it's important. Statistical mechanics made it clear to me that the state with the most entropy is the most likely to occur in equilibrium. (Statements about entropy representing "disorder" and whatnot in my opinion are handwavy, often lead to confusion, and should be avoided.)
  • atemerev 4y ago
    I also have chosen entropy for my most memorable grokk! :)
  • lambdatronics 4y ago
    For me, it was approaching it from the information-theoretic perspective. E. T. Jaynes' paper was what made it all click for me: https://bayes.wustl.edu/etj/articles/theory.1.pdf https://bayes.wustl.edu/etj/articles/theory.1.pdf Edit: but that was only after I had grokked Shannon's paper on information theory, which I felt was pretty intuitive.
• mumblemumble 4y ago
  The monitor model in second language acquisition. Or, more accurately, the more contemporary synthesis that it's developed into in the decades since it was first proposed. The model itself is easy enough to grasp. But concretely understanding what it implies about how I should be studying took much, much longer.
  • _xnmw 4y ago
    Very intriguing! Any links you can share on this theory? A quick Google search gave me an overview, but I don’t see how this is particularly useful for second language acquisition.
    • mumblemumble 4y ago
      The big take-away is that explicit study of grammar rules, and even vocabulary to some extent, is kind of a waste of time. They encode information in a format and region of the brain that generally isn't accessible to the areas that are used in fluent communication. The way our brains have evolved to build up a functional language model is by observing lots and lots (and lots) of examples of the language being used for communication. Which implies that, even from the very beginning, graded readers, level-appropriate dialogues, etc. should be the foundation of a language study program and not, as most language instruction courses and apps make it, just a little bit of icing on top. The primacy of input is also kind of a big deal, and, at least for me, it took a long time before I was willing to let go of forced production exercises such as "translate this sentence into your target language". Perhaps in part because they're so endemic to language learning resources. You can't abandon them without also abandoning Duolingo and most formal classroom programs. But the problem with these kind of practice exercises is, we now know that it's normal for there to be a long delay between when someone can comprehend a grammatical structure, and when they can use it in a natural setting. (Anyone with kids over a certain age should be familiar with the phenomenon.) Forced production relies on - and reinforces - that aforementioned misplaced encoding, and there's a mountain of research demonstrating that skill in performing those sorts of exercises simply doesn't correlate with the development of communicative fluency. Tangentially, the transformer architecture that's taken natural language processing by storm has some interesting similarities to the leading model among SLA researchers for how language is represented in the human brain. Which isn't the monitor model itself, but might hint at a mechanism for a few parts of the model. Acquisition order, for example.
• Overtonwindow 4y ago
  Staying out of debt. A simple concept that took me until I was 37 to appreciate and understand.
  • djmips 4y ago
    Yes, don't rent money unless you have a very good plan.
• sdenton4 4y ago
  Lie Groups... I signed up for a grad level course in my second year, and had no idea what was going on. Eventually I did my PhD on algebraic combinatorics, which works with Lie Groups quite a lot, but it took years to internalize all the ideas needed to have any intuition at all. https://en.m.wikipedia.org/wiki/Lie_group https://en.m.wikipedia.org/wiki/Lie_group
  • fooblaster 4y ago
    Although I still don't understand liegroups with significant mathematical rigor, I do think I finally understand why they are used in code for computer vision and state estimation. It took me a shockingly long time to understand why. This paper was the catalyst to me finally grasping some of the details: https://arxiv.org/abs/1812.01537 https://arxiv.org/abs/1812.01537
• throwaway98797 4y ago
  blockchains as a single source of truth always seemed like a shitty expensive database for 7+ years
  • pintxo 4y ago
    What made you believe that they are not a "shitty expensive database" after all?
    • throwaway98797 4y ago
      in the ecosystem of a single blockchain, they are the single source of truth that is an open api-like thing that no company can control therefore it’s safer to build then on twitter, facebook, apple, etc. the entire ecosystem may be a fraud, but if it is not then it’s incredibly enduring. i have more faith that i can get what the balance of an account is in 10 years from ethereum than i do from my banks api staying stable or open.
• rramadass 4y ago
  The use of Predicate Calculus in coming up with the Proof along with the Program. Predicate Calculus is used to show that the path followed by a Process through a Cartesian Product space (created from all the memory variables in a Program) is the one you had in mind w.r.t. its Specifications. Suddenly you start to understand basic Set Theory, Types, Relations (Functions) and Logic.
• kozak 4y ago
  Entropy. Both in information and in thermodynamics, and how brilliantly they are connected. The audiobook "The Big Picture" by Sean Carroll has helped a lot.
• itsmemattchung 4y ago
  The power of an outline when writing. Over the past few years, I've been teaching myself how to write better. I'm not talking about elementary syntax or grammar. I'm not talking about writing the traditional, American English five paragraph essay. I'm talking about writing longer pieces of prose, articles or blog posts or short chapters with word counts ranging anywhere between 1500-3000 words. On this journey of improving the craft, I realized that one of my biggest struggles was writing cohesively. Although I've been able to get lots of words on (digital) paper, eventually I'd get lost in my own web of thoughts, the article itself totally incoherent, no structure, no organization. Constructing outlines and reverse outlines[0] has helped me tremendously. It's not easy ... but the concept itself is finally — years later — starting to click. [0] - https://explorationsofstyle.com/2011/02/09/reverse-outlines/ https://explorationsofstyle.com/2011/02/09/reverse-outlines/
  • catears 4y ago
    This summer I read "On Writing Well" by William Zissner which was an eye opener for me. I'm far from an expert in writing clear texts, but I am definitely noticing more text which are just... big balls of blurb that don't actually say anything. All because of that book. It sounds dumb, but this year it clicked for me how big of a difference a poorly written text compares to a well written text. Hope your training pays off, itsmemattchung!
    • luuuzeta 4y ago
      Zinsser's "On Writing Well" is one of my favorite books, I like how clear and concise its prose is. I got Joseph M. William's "Style: Toward Clarity and Grace" recommended [1] so you might be interested in it. I read the introduction (I'm planning to read it this year) and with the few examples the author presents it sells the idea that prose doesn't need to be utterly complex to communicate ideas and concepts succinctly and clearly. [1]: https://news.ycombinator.com/item?id=33601492 https://news.ycombinator.com/item?id=33601492
    • grantc 4y ago
      This is the first book I recommend to anyone who wants to improve their writing. With Minto's Pyramid Principle as a follow-on. My top 3: 1/ Edit ruthlessly. Every single word is reduced to its simplest form and pulls its weight--it has a damn good reason for being there. 2/ Aspire to write at a third-grade reading level. Readers prefer simple writing even when reading deeply technical content. 3/ Start your most important conclusions up front, not at the end. You're not writing The Sixth Sense. Do your reader a favor and tell them the big reveal first. You can then follow through and persuade the reader why your conclusions are right.
• lqdc13 4y ago
  Forward-Backward algorithm before there were all sorts of resources and explanations on how it works online. The wikipedia page for it explains it well.
• parasti 4y ago
  One of the biggest realizations recently for me was realizing that a nearly all of software development is basically about turning a slow, manual process into a faster, automated process. Modern CI/CD stems from a bunch of shell commands that somebody wrote and manually executed to test an app and upload it to a server. Modern automated software testing stems from humans writing small test apps and running them to confirm correct behavior. Many modern development practices stem from allowing small test apps to be written easier and faster. It's all just a giant manual process-to-automated process time-saving machine.
  • jstummbillig 4y ago
    To add on to this, when you think in term of software development, that's already pretty meta because you skipped level 1: Formalizing any type of process. Something that is the entry level requirement to get, well, anything done via programming, is actually only done sporadicly in a lot of not-software fields.
  • tantalor 4y ago
    This is a great way to understand complex, new-fangled technologies. Ask "what manual process does this speed up"?
    • metadat 4y ago
      Okay, I'll bite: What manual process does ChatGPT speed up?
      • derwiki 4y ago
        Writing peer reviews at work
      • celeritascelery 4y ago
        Googling
      • RajSinghLA 4y ago
        Interpreting search results
• deepersprout 4y ago
  Haskel monads.
  • jvans 4y ago
    There is a common saying that if you can't explain something to someone else then you don't really understand it yourself. Monads made me realize that some things need to be experienced in order to be understood.
• mejutoco 4y ago
  Complex numbers, as a convenient representation for certain operations, in the same way as we use negative numbers to represent debts.
  • klysm 4y ago
    The certain operation almost always being rotation in my experience
• nycdotnet 4y ago
  I didn't really understand HTTP until I started using Fiddler which was probably 10 years after I had written my first web server application. "What do you mean I can't change the headers because they've already been sent?"
• harimau777 4y ago
  Socialism When I got out of my middle class bubble, made friends with people working multiple jobs and struggling to make ends meet, and experienced a period of financial instability; I began to realize that something wasn't working in our current system. Then I started struggling with burnout and other issues and found that corporations were happy to just replace me. I also found that management wanted programmers to be replaceable cogs instead of professionals. At that point I started to suspect that the idea of a dignified professional lifestyle may not be true. I observed that technology and products were getting worse over time. For example, Google search has become mostly useless and it's hard to find products that are made to be repaired. I concluded that the invisible hand and/or the price theory of value were not true. Then I saw Republicans gain power and run up the national debt. I also observed that when wages actually started increasing the economy fell apart and the Fed started taking steps to prevent wage increases. I concluded that "free market" rhetoric was a lie. At that point I looked for alternatives and found socialism. In particular the "social democracy" strains of socialism as opposed to those advocating central planning or anarchist organization.
  • rramadass 4y ago
    >In particular the "social democracy" strains of socialism as opposed to those advocating central planning or anarchist organization. Yes; Most people get hung up on terminology and/or specific interpretations but i am convinced this is the natural order of things for the Human species. The balance without going to extremes is what is important.
    • zozbot234 4y ago
      > Most people get hung up on terminology and/or specific interpretations Because terminology matters, and some terms are quite misleading. What some people tend to miss about the "Socialism with Scandinavian Characteristics" that folks claim to like these days is that Scandinavian countries are actually near the very top rankings by economic freedom and lack of excess regulatory burden. I.e. they're actually some of the most free market and capitalist, while applying effective redistribution after the fact (leading to moderately high tax rates). So I don't get why people decry capitalism and free enterprise while praising Scandinavia as "successful" socialism? It makes no sense.
• rolisz 4y ago
  Differential equations took a couple of years to grok. I first encountered them in high school, while preparing for physics Olympiad. I could solve basic differential equations by following the "rules" (such as for dampened oscilator), but I didn't understand what was going on under the hood. When in university I did some more math courses, suddenly differential equations clicked and made sense (and I could even derive some of the rules)
  • rramadass 4y ago
    Any books you could recommend?
  • atonse 4y ago
    I failed calculus twice in college. Then a summer went by before the third time I took it. When I stepped into class that third time, everything clicked and it all felt very obvious to the point where I could anticipate where the lecturer’s equations were headed. I stopped attending class and still got an A. I even ended up helping classmates in a study group. I still can’t explain what that brain process was that resulted in the pieces subconsciously lining up over the summer.
• nmca 4y ago
  The meaning of "adaptive" in the sense of evolutionary theory, and the capacity of species to evolve to extinction. Reading the selfish gene as a youth I missed the point; "an alien god" [0] and some Hanson articles got the point across finally. [0] https://www.readthesequences.com/An-Alien-God https://www.readthesequences.com/An-Alien-God
• lebaux 4y ago
  theory of reliativity, took me a while, but now I think I got the main gist
  • 7373737373 4y ago
    I'm not sure if this even possible, but I'd appreciate a "relativistic simulation for dummie programmers" handbook
• jefftime 4y ago
  For me it was pointers. I used C throughout college and I never really grokked the "address to a value" description, but one day it finally just clicked and now I love pointers
• nkrisc 4y ago
  Two concepts that I never really understood until I encountered them together: functional programming and recursion. When I first encountered recursive functions when I began learning programming I had a really hard time understanding what the function would do and how it would play out as it called itself. I couldn't think through the recursion and imagine what would happen. Nor did I really understand how to usefully apply one to a situation. I would either use a loop or a recursive function that utilized lots of external state to work. When I later encountered functional programming, having learned programming with OOP languages, it was a real mind-bender. I finally started to understand it but when I encountered the need for recursion in FP, it really threw me for a loop. How the hell was I supposed to do this without external state? So it was that restriction that really let me understand how to create a recursive function that could return something useful with nothing more than the initial input. This new understanding also gave me a better appreciation of functional programming and the idea of pure functions.
  • sokoloff 4y ago
    I had a similar experience with tail recursion that I only fully grokked much later when I had to implement some stack-trickery in C for a computer game. I realized then that tail recursion was typically optimized as a jump to code within the same stack frame rather than creating a new stack frame.
• amorroxic 4y ago
  the null concept being referred to as “the billion dollars mistake” - until discovering optionals and gradually opening up to FP, category theory, etc
  • bazoom42 4y ago
    The “billion dollar mistake” was not the null concept itself, it was having all reference types be nullable, i.e no distinction between nullable and non-nullable in the type system.
• XCSme 4y ago
  It took me like 4 years of playing/training table-tennis to understand what being relaxed when hitting means and how it feels like. It's very easy to tense up and not have all your muscles work harmoniously, but it takes years of practice to simply "be relaxed" when playing.
• whacked_new 4y ago
  I love this as a research topic. Here are a few examples close to me. 1. The nature of variance in regression methods. The first time I heard about "soaking up the variance" in modifying stat models in brain imaging I had no idea what was going on. Then I spent a few years doing brain imaging and modified models to "soak up the variance" differently. Over the few years I came to grok the concept. I had a electrical engineering PhD colleague with an impressive resume who would argue with me about the effects of models. I realized that he knew the textbook stuff (which I didn't), but he didn't actually grok the concepts (which I did). 2. Once in an office was I mystified by hot spots and cold spots of wifi signal. One of my colleagues, a brilliant engineer, then explained to me what might affect the shape of the hot and cold spots, which is why he sits in certain places. I asked him if he had an intuition of how RF fields are distributed and he said yes, so I asked him how. He said, "I used to do a bit of tensor calculus".
  • jeffreyrogers 4y ago
    I used to work in an office where I only got cell service on cloudy days, I assume it had something to do with the clouds reflecting the signal.
• djmips 4y ago
  One of the big aha moments which clicked for me only fairly recently was staring at some physics equations my own internalized realization that light doesn't experience time and then I had to tell everyone haha - but that one eureka moment unlocked a whole lot of understanding and certainly a lot more questions. This of course was after all the schooling and physics where it somehow sailed over my head the whole time.
  • 7373737373 4y ago
    I'm not sure how this works out in media which slow down light https://en.wikipedia.org/wiki/Cherenkov_radiation https://en.wikipedia.org/wiki/Cherenkov_radiation There, e.g. gravitational waves will be at c (in a vacuum), but wouldn't photons experience time there? Edit: I suppose the photons are still actually moving at c
    • djmips 4y ago
      I had thought because light was absorbed and re-emitted but that and scattering ideas are incorrect. See this video for an explanation of why light travels slower through a medium with an index of refraction greater than one. https://youtu.be/CUjt36SD3h8 https://youtu.be/CUjt36SD3h8
  • richardw 4y ago
    I was going to put this as mine. It’s astounding how important this is. I woke up at 2am with the intuition that light was like a lightning strike across spacetime, with no time and no distance between the emitter and absorber. Why and how, though. What are the fully-baked implications.
    • peterfirefly 4y ago
      I remember that we found that entirely obvious (well, most of us) in my high-school physics class. What I still don't understand, though, is how photons can "wave" or how "long" a photon is (or how they can have any "length" at all). What I also didn't understand back then was how light can be slower when there is matter present -- or how a photon could somehow know that it was supposed to cause another, very similar, photon to be released in just the right angle when it hit something that, if zoomed out enough, looked like a mirror. How on Earth could the photon know that the photon it was hitting was part of a flat surface and what its orientation was? I even started using that mirror question as a litmus test of physics students once I started at uni (comp.sci.) -- pretty much all of them failed, not by not knowing the answer but by not understanding that this was even a question that required an answer. I now know that the photon -- the wave(s) in the electromagnetic field -- cause atoms (and in particular their electrons) to move about a bit, which in turn cause waves in the electromagnetic field. And by adding up all these waves, we get the resulting wave which moves slower than c and which might seem to have been reflected at an angle. Why my physics teacher in high-school didn't tell us that, I don't know.
• catears 4y ago
  I have one example and an anti-example. Both are related to algorithms and computer science. A) Packing a binary tree into an array. Anyone that has attended an algorithms course has likely created a binary tree with nodes, leaf nodes, left and right child etc. Seen the pine-tree like sketch with a larger example where each node except the leaf nodes have a left and right child. So how do you pack this tree into an array and traverse it efficiently? Well you turn it 90 degrees side-ways, slightly shift all nodes on the same level so that none align and put them into an array by going from leftmost to rightmost. (or other way depending on if you shifted 90 degrees or -90 degrees). Congrats, you've packed nodes into an array. How do you traverse it? Our root node is at index 1 and if you packed the array correctly then `idx = (idx * 2) + 1` will move down one side and `idx = (idx * 2) + 0` moves down the other. I don't have a good visual explanation of this but you can think of the integer/index as a bit-sequence describing when in the tree a left vs. right path was taken (with the exception of the root node). B) Anti-example: Ford Fulkerson algorithm for finding shortest paths between all nodes in a graph. The algorithm is basically just three for-loops stacked on top of each other, but I still can't grasp why it works. Something with dynamic programming and incrementally building on prior established intermediate paths. The algorithm is truly the product of a beautiful mind.
  • arjvik 4y ago
    A) I've seen this before but I've never thought of the "index as a bit-sequence describing when in the tree a left vs. right path was taken" before! This is a very nice intuitive explanation that'll really help in describing this to others. B) Did you mean Floyd-Warshall's?
    • catears 4y ago
      On B) yes, of course. Aaagh, all these algorithms and their indistinguishable names!
• hakanderyal 4y ago
  Power of static typing, that it allows one to develop complex programs faster and better, not slower.
  • klysm 4y ago
    I think the develop faster thing is a poor argument for static typing. The refactoring piece of the equation is the most important to me. Static types provide confidence (and speed) while making sweeping changes to code.
    • hakanderyal 4y ago
      That's what I meant by developing faster. Refactoring is an indispensable part of the building process.
      • klysm 4y ago
        Yeah totally agree that refactoring is part of development but I don’t think people frequently think about in comparison to maintenance.
• em-bee 4y ago
  object oriented programming. i must have encountered it during my computer science classes and i certainly did some form of oo programming with LPC in MUDs, but only when i was programming modules in Pike for the Roxen webserver, it really clicked how oo programming worked. in Roxen each http request causes a request object to be instantiated which lives for the lifetime of the request. further, each Roxen module gets instantiated as an object for the lifetime of the server process. the request object would call module objects to process the request. the modules would make changes to the request object which would produce the response to the http request, whereas storing data in a module object caused it to be persistent. i have been working on this for a while when one morning i woke up with a literal eureka moment as i realized how objects and encapsulation worked. this happened a few decades ago and it was the most clear moment of this kind that i can still remember.
• dplgk 4y ago
  Steely Dan
  • ilvez 4y ago
    (got a smile out of me, both because the band name and original meaning) Do you mean whole discography? Because I really like their earlier stuff but lost interest at one point. Asking since if there was enlightenment with whole discography then I have more interest to take new dives.
    • ilvez 4y ago
      Actually skip the question .. I took their albums not linearly and got to Aja, so basically I already got nearly everything but have skipped few. Still a smile:) I thought they did more stuff on 80s..
• colinwilyb 4y ago
  Formal logic.
• rolenthedeep 4y ago
  It took me an embarrassing amount of time to fully grok what object oriented programming really means. It's one thing to have someone tell you what an object is, but it's another thing entirely to build a fully object oriented system. I remember what made it click: I was designing an animation system, which had a bunch of different interdependent moving parts. Once I started treating each part like an object and letting it manage its own state it all just clicked. I started with this massively complex functional-like system that managed four or five different motions, but once it was broken into objects most of the code just fell off and it became a nice clean system. I was super proud of it at the time, but it's pretty bad by my current standards.
  • zabzonk 4y ago
    I've always found OO programming completely natural. n fact, it's the only kind of programming i've ever really done - create a structure with data members, and then create functions to work on that structure. you can (and should) do this in low-level languages such as C and assembler. Of course, if you want to go the whole polymorphic route, i'd suggest using something like c++, but the key ideas are really structures, and functions that operate on those structures.
    • opportune 4y ago
      As someone who started programming in BASIC, OO is a really good way to think about stuff (it introduces the abstraction of “conjoined data” that is typed and has functions) but it was not natural. It just feels natural now that I’ve spent so long in school and at work dealing with OO languages. I imagine if you had started with BASIC you’d feel the same
    • sureglymop 4y ago
      I've always had a hard time because I was thinking.. why would I carry the performance hit of instantiating objects for a bunch of stuff?
      • rolenthedeep 4y ago
• Nimitz14 4y ago
  Fourier transform
• klysm 4y ago
  The expression problem. I had vague notions of “horizontal” and “vertical” abstraction but they weren’t concrete enough to discuss or make informed decisions about.
• DylanSp 4y ago
  Matrix multiplication. First encountered it in high school, where the textbooks presented matrices without any real motivation, and matrix multiplication just seemed like a weirdly-defined operation. Once I got to linear algebra in college and matrix multiplication was presented as the way to compose linear transformations, it made a lot more sense.
  • rkp8000 4y ago
    A big one for me was realizing that a matrix times a vector returns a weighted sum of the matrix columns, with the vector's elements as weights. It's not particularly profound but it has definitely clarified my intuition around a number of matrix problems.
  • XCSme 4y ago
    Related, this always amazes me: https://news.ycombinator.com/item?id=32195262 https://news.ycombinator.com/item?id=32195262
  • enkid 4y ago
    It took me taking a class in neural networks in my thirties to really understand matrix multiplication
    • jliptzin 4y ago
      Which class?
      • thamer 4y ago
        A sibling comment to your mentioned Andrew Ng's class, and I actually had the same experience as them with the same class. You can find it by searching for Stanford CS229; the lectures are available on YouTube.
      • enkid 4y ago
        It was Andrew Ng's machine learning class on Coursera
    • 4y ago
• tobyhinloopen 4y ago
  Shaders. I tried shader tutorials multiple times for years and they only started to click recently.
  • baby 4y ago
    Any good resource on that? Bonus if it’s for Unity
    • mmcconnell1618 4y ago
      Ben Cloward - Shader Graph Basics for Unity - https://www.youtube.com/watch?v=OX_6_bKpP9g&list=PL78XDi0TS4lEBWa2Hpzg2SRC5njCcKydl https://www.youtube.com/watch?v=OX_6_bKpP9g&list=PL78XDi0TS4...
• ofcrpls 4y ago
  Fourier Transform. I'd been writing DSP code in C and MATLAB during undergrad while thinking I knew every possible aspect thanks to the deep study we had as part of coursework across all the transforms methods in our ECA & Communications coursework in India. Also, dad was a self-taught hands-on Analog electronics whiz whose day job was in Telecommunications Training, and I had uncles and aunts in the Telecom/Electronics/ATC industry, so I had all these resources from a very young age to revisit the concepts that were being taught to me in school, against practical applications over and over. In week 2 or 3 of ECE490 at UofR, Prof. Heinzelman[1] broke a barrier that I did not know existed in my understanding of DSP. It was pinned to me realizing that the intuition between Fourier and Laplace transforms being the same. It was a moment that I haven't experienced since, in that I felt my brain got re-wired within that hour. It must help that her father[2] basically wrote the textbook on speech processing. [1] http://www.hajim.rochester.edu/ece/heinzelman/ http://www.hajim.rochester.edu/ece/heinzelman/ [2] https://www.ece.rutgers.edu/lawrence-rabiner https://www.ece.rutgers.edu/lawrence-rabiner
  • bonzini 4y ago
    Interesting, Fourier transform has never been an issue for me but Laplace never clicked. I know it's kind of similar (convolution, exponential and all that) but I miss the connection with the frequency domain that is there for Fourier.
    • dannymi 4y ago
      The frequency is the imaginary part of the Laplace parameter s (and the attenuation is the real part of the Laplace parameter s). Laplace transforms work on systems with attenuation—that’s the main advantage. Because the kind of transform was swapped out anyway, people used the chance to often only define one-sided Laplace transforms that only work for t > 0 (because as an engineer, thats the systems you want anyway). There’s a direct correspondence between the (usual) one-sided Laplace transform and the (unusual) one-sided Fourier transform for that reason. Since you usually have systems where f(t) = 0 for all t < 0 anyway, the distinction one-sided or not is not so important in practice for understanding.
• lakeshastina 4y ago
  (1) Pointers (2) Recursion
• krosaen 4y ago
  The Kalman filter. I felt like I understood it watching some videos but it always turned out I didn't really understand it well enough to put it to use or explain it to others. Gaining a better understanding ultimately just took a lot of time playing with the equations and understanding how measurement and process noise/uncertainty get incorporated into the Kalman gain, and how that in turn affects the updated state estimate - e.g if you have zero noise in the measurement, you end up fully trusting your measurement. This tutorial [1] is the one I ended up studying. This is a case where memorizing the equations (with the help of Anki) helped me reflect on them and keep everything in my head long enough to improve my understanding. http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf
  • passion__desire 4y ago
    > This is a case where memorizing the equations (with the help of Anki) helped me reflect on them and keep everything in my head long enough to improve my understanding. Dr. Mark Colyvan once preparing for his test couldn't understand a proof. So he went ahead and tried to memorize it anyway but in the process of memorizing he understood the proof so he had no need to memorize it now. https://www.youtube.com/watch?v=KqYh1h2t8WU https://www.youtube.com/watch?v=KqYh1h2t8WU
    • krosaen 4y ago
      That's a great way of putting it - the memorization becomes sustained through deeper understanding.
• thesnide 4y ago
  Working with others. Really. I was super annoyed and insanely annoying to work with for years. Then I understood that difference is hard to cope with, but more often than not, good. As it trades some short term efficiency to long term one. Same with your output. If it is dumbed down to a level everyone can understand it, you really learned it.
  • mattbaker 4y ago
    That’s cool, what kinds of things helped you learn this? I bet those things would be really valuable to a lot of people if you felt like sharing.
    • thesnide 4y ago
      I'd say parenting is the one that really made a difference. Not because I had a strike of common sense, but because I actually cared very much and started to listen to others. I didn't want to be horrible to my kids. So "starting to listening to others". Every troll has a kernel of truth. And sometimes what you consider a troll isn't one in the first place. Which is very apropos those days, where everyone is confined in their own echo chambers by all those clever social media algorithms that always favor short term bliss. And yes. Trying to explain things to my kids enables me to understand those things way deeper.
  • ldx1024 4y ago
    Reminds me of the saying "If you want to go fast, go alone, if you want to go far, go together." But an important corollary is that you should be very selective about who you travel with. In some cases, like a corporate setting where you have no control over the randos you are thrown together with, it can indeed be the least painful option to go it alone. The alternative is knowing that if everyone does their best you can all aspire to be ... mediocre.
• atemerev 4y ago
  The relationship between entropy and states of matter (including pressure and temperature). How “degrees of freedom” are calculated and compared for gas molecules, if they are infinite. All that stuff.
• itsgrimetime 4y ago
  programming in general, i tried probably half a dozen different times throughout my early teens to understand how to write programs in pascal, C, python, java, and it wasn't until I was 18 when I found Zed Shaw's "Learn Python the Hard Way" that it clicked.
• grogenaut 4y ago
  It took me 4 tries over 10 years to get antlr to work/grok.
• khaledh 4y ago
  YAGNI and KISS. When I was a junior developer I used to overthink and overdesign solutions, most of which was never needed. It took many years and a lot of battle scars to realize that less abstraction is more. Today I see a lot of juniors do the same mistake and I ask them to revise their designs to keep it simple.
  • deleted 4y ago
    [deleted]
  • coffeebeqn 4y ago
    I use the rule of threes to kill off any premature abstractions. ie. Don’t think you need to make this generic if you have one or two different variants of it. Most often it’s one- so it’s very easy to see that you’re just solving imaginary problems at this point. Each abstraction has a mental cost for reading and understanding the code so I try to be sparing. Too many code bases in my youth were a nightmare to navigate because I could never find any actual concrete code.
    • fullstackchris 4y ago
      Also don't forget that code (including the complexity you want to add to it) will probably have only something like an aggragate ~1/3 chance of still being used in a production scenario 5 years or so away anyway (for any number of reason, product change, feature removal, company bought / sold, the list goes on and on...) of course these numbers are anedotal but the point is it can be detrimental to think your code will run as is for the next million years, especially after the first draft
    • DrJokepu 4y ago
      That being said, sometimes a good abstraction can really simplify a complex problem by dividing it up to a set of smaller sub-problems. In such cases, the abstraction is worth it even if there is no reuse. As always, rules like this have to be interpreted in a context.
      • coffeebeqn 4y ago
• lamontcg 4y ago
  Big bang didn't happen in a single point in our space-time like a firecracker, it happened everywhere and was just a uniformly much hotter and denser universe that didn't really explode into anything, but space-time just expanded to make the universe less dense.
  • namrog84 4y ago
    Don't some people prefer to say the slow expansion over using the term big bang? Although it hasn't taken off as a term. Or something like that?
  • PUSH_AX 4y ago
    If “everywhere” is an infinitesimal point, is there much difference?
    • rodamaral 4y ago
      Everywhere was not an infinitesimal point, if the present Universe is infinite (as it seems to be). In this case, the Universe was already infinite at the very first meaningful instant of time.
    • lamontcg 4y ago
      To be more pedantically precise: The big bang was not like a firecracker that went off in pre-existing, infinite flat space-time...
      • PUSH_AX 4y ago
        There are two replies to my comment, yours and someone else's. They both say the opposite thing!
• 2devnull 4y ago
  The importance of play.
• dudul 4y ago
  A lot of the math I learned in high school didn't make any sense until I revisited it in college. The difference between stupidly copy/pasting rules and theorems without understanding them and having to demonstrate them from the ground up before being able to apply them made a humongous difference for me.
• jeffreyrogers 4y ago
  Dynamic programming made very little sense to me when I first encountered it, then a few years later I read the DP section of Algorithms by Dasgupta, Papadimitriou, and Vazirani and it somehow clicked for me. Now I enjoy dynamic programming problems when I get them in interviews because they are usually pretty easy once you understand the trick.
  • sethammons 4y ago
    This one is always interesting to me. People mention "dynamic programming" and my gut says "code that writes code" and every single time I remind myself it is just caching earlier calculations. DP is just caching.
  • mesarvagya 4y ago
    DP is just overlapping recursion with caching. That's it. Richard Bellman just wanted to give a fancy name for mathematical work he was doing without being suspected of it.[1] [1]https://en.wikipedia.org/wiki/Dynamic_programming#History https://en.wikipedia.org/wiki/Dynamic_programming#History
• user3939382 4y ago
  f(x) = y etc in linear algebra in school. By the time I was learning this in high school I’d already been programming for several years and perfectly understood the concept of function inputs and outputs. It wasn’t until my early twenties that I realized this was just an alternate notation for functions and was so simple. Sad that my math education was just focused on “memorize steps” for concepts that weren’t clearly explained.
• richardw 4y ago
  In OO, the interface. It seemed like the most useless construct. Zero implementation. Why make something with no implementation? Later I realised that the benefit isn’t the code, it’s the freedom you gain later in choosing the implementation. You can create an interface and add a simple implementation, then later swap it out for something more robust. All you’re agreeing to now is the contract of what needs to be done, without any restrictions on how.
• hospadar 4y ago
  Voltage and amperage for me, years after a college electronics course and a childhood of soldering kits I finally started to get it. I was always tripped up with analogies about how it's like water in a pipe or something, which can be useful, but aren't quite right.
  • marshmellman 4y ago
    Can you share what helped it click? I’m in the same boat, trying to understand it through analogies.
    • carapace 4y ago
      These are physical properties that can be experienced (although there is some risk) for voltage you can touch a Van de Graaff generator, for current you can touch a battery to your tongue. That's the way to understand electricity without analogies. :) Anyway, voltage is always measured between two points (one is typically called "ground" but that's not important here.) It's a difference. (A difference of what? No one knows. That's just the way it is.) Current is always measured through a single point. It's a count of the charge flowing past a point per time unit. (What is charge? No one knows. "Charge" is just a name for the mysterious something that "voltage" is a difference of...) When electricity moves it obeys a (very simple) Law called (Ohm's Law) e.g.: E = V/R The current (E) is the Voltage divided by the Resistance. E.g. is I have a 5 Volt power supply and I put a 100 Ohm resistor across it (remember that voltage is always between two points) then 5/100 Amperes of current will flow through it. Also, If I take just the resistor and drive 0.05 Amps through it, it will develop a voltage of 5 volts, as measured from one end of the resistor to the other end. Now if that doesn't help you, remember the advice of John Von Neumann to Felix Smith: "Young man, in mathematics you don't understand things. You just get used to them."
      • _dain_ 4y ago
        >Current is always measured through a single point. It's a count of the charge flowing past a point per time unit. (What is charge? No one knows. "Charge" is just a name for the mysterious something that "voltage" is a difference of...) I think you're being overly mysterious here. It's the number of electrons passing through the wire per second. And charge isn't the thing that voltage is a difference of; it's potential difference, as in electric potential energy. The "water in a pipe" analogy really isn't that bad; it's gravitational potential instead of electrical potential, and amount of water instead of amount of electrons.
• deleted 4y ago
  [deleted]
• olalonde 4y ago
  It took me a long time to grasp market economics. I knew it worked somehow but I didn't quite understand why. What really made it click was Milton Friedman's "Free to Choose" TV series[0]. [0] https://www.youtube.com/watch?v=dngqR9gcDDw&list=PLXD32Z5YYifX8J3Kp-WBA9Ongy0p1C1u9 https://www.youtube.com/watch?v=dngqR9gcDDw&list=PLXD32Z5YYi...
  • viburnum 4y ago
    I had the same experience (and then I had to unlearn it all because it only applies to trivially narrow examples. MF’s trick is to hide the assumptions well the same way a magician diverts your attention).
• ojr 4y ago
  Objective-C message passing/variable declaration's the syntax is so different from C, C++, Java, Javascript, Ruby, Python and other popular OOP languages
• ngalaiko 4y ago
  for me it was functional programming. and not just fp as is, but it's relation to another popular concept - oop. i was properly introduced only to oop, and grasped a little of fp here and there, especially learning go and javascript. what i consider a 'click' for me is when i realised that all of these paradigms are interchangeable. like, an abstract method is just a function, or a function signature is the same as in interface with a single method. after that i write code however it feels more appropriate for the situation i am in and don't think too much about fancy words and patterns. it really feels like programming languages are becoming 'native' for me.
  • satvikpendem 4y ago
    You should learn Haskell, that's what I'm doing now, in order to learn functional programming from the ground up. Languages like JS which have FP concepts aren't really functional programming fully.
    • ngalaiko 4y ago
      i don't care about idealistic concepts
      • satvikpendem 4y ago
        Not sure what is idealistic, it's a useful programming language.
• iancmceachern 4y ago
  The simple beauty of the calculus integral.
• ww520 4y ago
  Shader and OpenGL programming. It was many foreign jagons, concepts, and computation models. Took me a while and couple tries to get a hang of it.
  • atentaten 4y ago
    What were you trying that allowed you to get the hang of it? Also were there any online resources that helped?
    • ww520 4y ago
      Wrote 3D games and simulations. That forced me to go through the full pipeline end to end. Also UC Davis professor Key Joy's Computer Graphics course [1] is the best intro course on 3D graphics programming, covering many key concepts and math. I found it better than any other courses from MIT/Berkeley/CMU/etc. It doesn't have some of the newer techniques in recent years but is still very much relevant and forms the foundational knowledge to level up. [1] https://www.youtube.com/watch?v=01YSK5gIEYQ&list=PL_w_qWAQZtAZhtzPI5pkAtcUVgmzdAP8g https://www.youtube.com/watch?v=01YSK5gIEYQ&list=PL_w_qWAQZt...
• LAC-Tech 4y ago
  I'm currently doing a dive into classic distributed systems papers, mainly from the 70s (actor model, logical clocks, that kind of stuff). I'd "understood" the concepts before, but now because I am: - brushing up on my math to understand every equation or proof they drop in there - reading them in combination with applied stuff that uses the same concepts, ie the "designing data intensive applications book" - reading over them slowly, I want my fundamentals to be strong and etched into my head Things are clicking in a way they never did before. TL;DR - studying compsci concepts, slowly, from multiple angles (completely mathematical to practical engineering) is just a different level of understanding from doing one or assuming your mind will bridge the gap. YMMV.
• theptip 4y ago
  Domain Driven Design. The book by Eric Evans lays out a bunch of concepts and as a developer that had not owned the architecture of a big domain, it was hard for me to see exactly where they fit. But after reading the book a couple times, and then encountering a few tricky domain modeling challenges, I started to see where these patterns add value. Also, as I started trying to describe the cohesive domain architecture of the system to a growing engineering organization, I also clicked on the advantage of having a standardized set of terminology for the problem, rather than inventing your own. It's nice to be able to link to an existing explanation of what a Repository is for, instead of having to name and document your own ad-hoc architectural patterns (or more likely, end up with you ad-hoc architecture being under-documented). Things like Repositories, Aggregates, Bounded Contexts, and so on are going to be a net drag on your system if you only have a few 100 kloc of code in a monolith. But they really start to shine as you grow beyond that. Bounded Contexts in particular are a gem of an idea, so good that Uber re-discovered them in their microservices design: https://www.uber.com/blog/microservice-architecture/ https://www.uber.com/blog/microservice-architecture/. (Edited to clarify the book author)
  • shortlived 4y ago
    This is the book by Eric Evans?
    • theptip 4y ago
      That's the one. (I edited in a clarification to my original post.)
  • eckza 4y ago
    It's a solid book. I was chugging through it a bit at a time, until I discovered Scott Wlaschin's Domain Driven Design Made Functional. I've dropped the Evans book (as it's mired in mid-00's Enterprise Java patterns) and am enjoying this one quite a bit more. Both books are great. Read whichever one aligns with your practice best. I recommend Wlaschin's book for anyone curious about FP, without hesitation. He's great at explaining things from first principles, without veering off into "monad tutorial" territory. https://pragprog.com/titles/swdddf/domain-modeling-made-functional/ https://pragprog.com/titles/swdddf/domain-modeling-made-func...
• jethkl 4y ago
  The axiom of choice, Tychonoff's theorem, and the open mapping theorem [0, 1, 2]. Each one took me, in my view, much too long to grasp. [0] https://en.wikipedia.org/wiki/Axiom_of_choice https://en.wikipedia.org/wiki/Axiom_of_choice [1] https://en.wikipedia.org/wiki/Tychonoff%27s_theorem https://en.wikipedia.org/wiki/Tychonoff%27s_theorem [2] https://en.wikipedia.org/wiki/Open_mapping_theorem_(functional_analysis) https://en.wikipedia.org/wiki/Open_mapping_theorem_(function...
  • kccqzy 4y ago
    The axiom of choice is the topic of one whole quarter of set theory in my undergraduate years. I still don't think I fully understand it. By "fully understand it" I mean achieving the level of proficiency of my professor who, upon hearing seemingly any theorem encountered in undergraduate study, would immediately tell you whether it requires Axiom of Choice, merely Dependent Choice, Countable Choice, or doesn't require Choice.
• throwaway81523 4y ago
  The purpose of C++ template generics only made sense to me after I started using Haskell.
  • rrgok 4y ago
    I have to agree. I couldn't understand templates until Haskell introduced me to it. But Haskell is expressive enough that the intuition comes naturally.
• hawski 4y ago
  Parenthood. Now I see how much my mom was right, but couldn't put things in proper words.
  • evilotto 4y ago
    Parenthood is the Matrix. Nobody can tell you what it is, you have to experience it for yourself.
• fortituded0002 4y ago
  1. Everyone is the main character in their own story. This manifest in all sorts of ways - from people not being there when you need them the most, from friends dying off as soon as proximity changes, to how and why get people get promoted in jobs. This isn't necessarily bad, but if you don't know how to navigate this it can be quite painful and confusing. 2. Representation matters. I knew this for a long time, but it didn't fully click until years had gone by and I realized I had unconsciously held myself back from pursuing a wide range of things because I just didn't see anyone like me there. 3. Rules in life are just constructs that we as humans have created. Starting a business helped the most on this one. That's when I started to see that "rules" or "procedure" are all made up and exceptions can always be made. (Edit: typos)
  • nivethan 4y ago
    2. Hits home for me as I’ve begun to realize the same thing. Not seeing any person of color in an activity makes it’s so I don’t want to be the first.
    • yieldcrv 4y ago
      Similarly this gives me pause about Ivy League MBA programs. Although a small sample size, despite their ambitions the BIPOC people I know haven’t been able to reap any professional benefits from it. Whether from access to executive roles, getting taken seriously by venture capital firms, or in their attempts to join venture capital firms. There is a level of discretion in these team forming situations that is not extended to them whether it has anything to do with their race or not, its pretty clear the upwards mobility is not coming from this credential. For people with their own capital and leverage, it amplifies their ambition if they want. BIPOC don't really have this. The “average salary” of MBA alumnis is not what is interesting about getting one, for me or them. Some, or more, examples to the contrary would make it seem less like a total waste of time.
      • idiotsecant 4y ago
        I am not an ivy league MBA person but my understanding of these sorts of things is that it's not the credential itself that's useful, but the connections you make in the process.
• antiquark 4y ago
  The idea that atheism is a form of religion.
  • apienx 4y ago
    Or just a personal relationship with reality. :P
• bob1029 4y ago
  I'd have to say... Linear Algebra & SQL. SQL is something that is a permanent journey for me. It is a domain-specific language, so the nature of its use depends almost entirely on how the domain was modeled in the first place. Much of my interest has been drawn towards the modeling aspects and how we can arrive at schemas that business experts can tolerate. Linear algebra properly clicked for me when I started getting into writing my own 3d rendering software. Systems of linear equations are absolutely everywhere. I didn't really tie together their use in control theory, DSP and graphics until I was forced to learn them "for real" to achieve my project goals.
  • pfdietz 4y ago
    Something in linear algebra clicked for me when I realized the infinite dimensional case is different from the finite dimensional case.
    • bob1029 4y ago
      What are some applications / examples for the infinite-dimensional case?
      • pfdietz 4y ago
        The continuous Fourier transform, for example, or more generally linear operators in functional analysis.
      • sampo 4y ago
        Quantum mechanics
• TheAceOfHearts 4y ago
  It felt like my understanding of pointers was a bit vague until I learned assembly. I think programmers would benefit from starting off with a simple virtual machine that runs a tiny set of instructions with everything presented cleanly in a visual format which can be inspected and stepped through. The biggest a-ha! moment I've experienced was in my Comptuer Architecture course when it finally clicked how you could build up a bunch of logic gates into a real modern computer.
• samhuk 4y ago
  Computer networks. For years I was dumbfounded how IP addresses, VPN, ports, etc, all worked and tied together. Then, when I was interning as a software developer a fair while ago, a colleague drew the analogy of "IP address" = house on street, "port" = something you ask for when you knock on the door of a house. Then it all just clicked. I still remember that day all these years later. Other notable mentions, in no particular order: * Perfect is the enemy of good enough. Did n't really appreciate this idea until around 2 years into my career. * How to be professionally displeased at something. Early on my career I would get way too angry at incompetent colleagues peeing in the pool, e.g. bad code, design, management, etc. I would complain quite a bit! It only clicked ~2-3 years later into my career when I figured that one's displeasure at a situation should be a function of both how bad the situation is and how able you are to improve it. When you offer constructive solutions to incompetence (suggest alternative algo, management style, library, tool, etc) whilst not actually mentioning what is wrong, instead of just fruitlessly reminding people of what they did wrong, people become far more cooperative and receptive, etc. My tin-foil-hat pet-theory is that the relatively recent tyranny of low expectations and "participation award" society has on average made younger people much more sensitive to negative comments about their work. The extension of that is that people end up robbed of more detailed reasoning about what they did that was wrong. People are interesting!
  • wellthisisgreat 4y ago
    > Then, when I was interning as a software developer a fair while ago, a colleague drew the analogy of "IP address" = house on street, "port" = something you ask for when you knock on the door of a house. Hey thanks for sharing! Can you maybe expand on this in any form? I'd love to get that kind of analogy. Maybe you have a blog post about it? That'd be amazing!
    • deleted 4y ago
      [deleted]
    • ruune 4y ago
      This[0] blog post explains the basics of IPs, ports, etc. using that analogy [0] http://www.steves-internet-guide.com/tcpip-ports-sockets/ http://www.steves-internet-guide.com/tcpip-ports-sockets/
• narag 4y ago
  That Pareto is everywhere and, when applied to knowledge, a comprehensive study plan, like courses or a book, for most subjects, tend to obscure what's the meat. Waking call: https://sive.rs/kimo https://sive.rs/kimo Corollary: a place where there's a fat-ass book of "best practices" has probably lost its focus.
• tezza 4y ago
  1/2) Trusting Institutions Institutions such as Police, Universities, NHS, Scouts, MsF, Religions, Churches, YCombinator et alia have a hierarchy of internal loyalties in strict precedence: * The Staff Member * The Staff Member’s Family * The Friends of the Staff Member * The Colleagues of the Staff Member * The Group within the Institution the Staff Member belongs to * Wider Groups in the Institution * The actual powerbrokers within the Institution * The acknowledged Leadership of the Institution (may be different to actual powerbrokers) * The actual goals of the Institution * The acknowledged goals of the Institution (may be different to actual goals) * Helping YOU in accordance with what the acknowledged goals of the Institution are… Only when all the loyalties in that list are satisfied is there the slightest chance you may get anything positive from the Institution. Despite the long list of higher precedence loyalties it is still frequently possible to have positive outcomes… But because it is a long list of loyalties far more important than helping YOU, there are often breaks. And because people and families and relationships are involved they can change at any moment. So trusting Institutions to do the best for you or act honourably needs to be carefully weighed against the likelihood that will happen 2/2) Mortgages How mortgage repayments change over time as you pay off some of it (YMMV)
  • _huayra_ 4y ago
    > How mortgage repayments change over time as you pay off some of it (YMMV) This is a big one people buying houses recently due to FOMO don't understand: you're really not building equity the first few years because almost all of your monthly payment is going to interest. The "irrecoverable cost" of owning a home can often be higher than renting in some HCOL areas now, although I understand that people buy for more emotional reasons (e.g. not wanting to yank their family around to a new place each year to avoid being at the mercy of a bad landlord on each lease renewal).
• nathanmcrae 4y ago
  For me it was lambda calculus. I remember in high-school going through the motions of beta-reduction but having no idea what it meant. Much later I think I finally saw an implementation of natural numbers and addition using bare lambda calculus and it clicked that you really can represent any computation with just variables, abstraction, and application.
• apienx 4y ago
  Bayes theorem really clicked when I saw 3Blue1Brown's visual representation. https://youtu.be/HZGCoVF3YvM https://youtu.be/HZGCoVF3YvM
• jonsen 4y ago
  Recursion. I tried and tried and tried. Only when I untried the exact same number of times did it click.
• sowbug 4y ago
  Taking the point of view of others, and learning to view a situation from a "perspective-less perspective." It's easy to think you have people skills because you listen to others and repeat their point of view back to them before telling them they're wrong. And unfortunately you can get quite far in the business world simply by being good at demolishing other people's positions. As a mental exercise, a few years ago in meetings I started deleting the names from the running transcript I keep in my head. "Joe said X and Jane said Y and then I said Z" was replaced with "we said X, then Y, then Z." It was a remarkably effective device to rise above the "who's going to win?" attitude and instead think about the best way for everyone to proceed as a group. I suddenly started to get what people say about meditation and removing the "I" perspective from your life. If instead of being you, you're a quadcopter hovering near the person you call yourself, it's so much easier to get your ego to shut up and start listening for once.
  • nathias 4y ago
    mine is the opposite, you can't get anywhere in life with the perspectiveless perspective
    • sowbug 4y ago
      Maybe it works best as a blend of looking out for yourself and looking out for the group. Or, cynically, maybe it's effective to adopt the group-first mentality once you have the personal momentum from years of being self-centered.
      • hyperthesis 4y ago
        observe selflessly, act selfishly
• dqpb 4y ago
  Data structures are more interesting than algorithms.
• machina_ex_deus 4y ago
  Learning history / literature in school is important. I was a total STEM math nerd in school. I used to frequently complain how I don't get what's the point of it, or how it's a waste of time and I'm learning nothing. I still think the emphasis of school was off, but I get the point of it now. Stories are like code for humans. You can't tell someone what it means to be good or bad, or to give them a course in philosophy and they will become good people. But you can tell them a good story, that engages with them emotionally, and it will change their perception. And history shows that in fact, those stories being told and repeated aren't just interesting minor curiosity, but they have shaped the direction of humanity and they are driving it. A single person with a single story can change history in such a way that it would be completely different without it. And some stories about stories need to be told as a warning so that people will not fall for those kinds of stories again.
  • 9804 4y ago
    I think people come out of school hating reading because nobody likes being forced to read specific books, as everyone's tastes are different. It sounds like this might have been what happened to you.
    • mabbo 4y ago
      I completely agree with this. I loathed Shakespeare in school. Now I try to get a visit every year to the Stratford Festival (in Stratford, Canada) to see at least one or two Shakespearean plays. I also remember reading 1984 on my own time in high school- it wasn't in the curriculum the year I might have. It blew me away. But if I'd been forced to read it, I probably would have been bored.
      • Balgair 4y ago
        For other HN readers: I was like this too. I had no interest in ol' Bill. Then I read his 'best' works. And then I read them again. It takes a bit to get really used to iambic pentameter, to the old words, to the places and people he was writing for, to his limitations of candlelight and lack of amps, etc. Reader, it is totally worth it. There are very many very good reasons that he is still produced and studied. I encourage you in this new year to give him a solid try. Not just a play or two. Read him and watch the plays at the same time. There are hundreds of productions on YT for every play of his, all free, most very good.
• ahmadnoid 4y ago
  That sometimes the extreme needs to manifest in order to pull toward the middle
• leftcenterright 4y ago
  Visual thinking! [1] I had read a bit about different types of thinking but I didn't really understand it so well until I saw a kid who had amazing visual thinking capability and could visualize years' old memories in a very detailed manner. It has also been related to photographic memory according to some research. [1] https://en.wikipedia.org/wiki/Visual_thinking https://en.wikipedia.org/wiki/Visual_thinking Nikola Tesla's Creative Thinking Secrets: https://www.sers.si/wp-content/uploads/2014/10/angle%C5%A1%C4%8Dina.pdf https://www.sers.si/wp-content/uploads/2014/10/angle%C5%A1%C...
  • satvikpendem 4y ago
    You should read Moonwalking with Einstein and look into memory palaces. I have memory palaces I can still walk through and remember after a decade.
    • leftcenterright 4y ago
      Thanks for the suggestion, that does look like an interesting read! I will check it out.
  • Akronymus 4y ago
    https://en.wikipedia.org/wiki/Aphantasia https://en.wikipedia.org/wiki/Aphantasia This could be some fun reading for you.
• thyrox 4y ago
  The power of follow ups (especially in sales) One thing which held me back for a very long time was not following up with people who didn't show much interest initially. I wasted so many good leads thinking it is impolite to follow up with people after contacting them once. My whole life changed once I understood the power of follow ups and understanding that most people are so busy that it takes at least 6 reminders before most people will take any substantial action. The reverse is also true. People say a lot of things and most of the times you never cross the bridge or reach it. Nowadays, I rarely argue about anything and don't act on stuff until a person reminds me once or twice. This small filter can be like a miracle for saving your time and energy.
  • aj7 4y ago
    You were not trained well. The principal element in sales is asking for the order. Everything, and I mean everything, follows from that. If you had been trained this way, following up would be second nature.
    • zeroxp 4y ago
      Some products dont fit well with a one call close and are centered around building long term relationships with your clients. This is especially true in b2b. Maybe you were trained too narrowly.
      • aj7 4y ago
        You can have your great “relationship with your clients.” You will see how illusory that is when a competitor appears with a 50% better value proposition. Oh, and SOMEONE has to ask for the order.
    • abdullahkhalids 4y ago
      I am not trained at all in sales. Can you expand upon this?
  • satvikpendem 4y ago
    Agreed. When I was doing sales, I would follow up with people seven times before they replied. I used to feel bad until I realized that it worked, then I just automated that part and didn't think about it further, the leads once they replied were sent to my CRM where I could then set them up on a call or some other action.
• vegetablepotpie 4y ago
  UML When I first saw it, I thought it was a process step that was unnecessary. Then I thought it was a way to program visually, but generated code only works in narrow domains. I realize that UML is tool to define your system, and it lays bare your assumptions, which is one of the hardest problems in computing.
  • urthor 4y ago
    UML is hard. Any abstraction can evolve into wasted time not making the thing.
• JanisErdmanis 4y ago
  Superconductivity. I did four PhD projects regarding superconductivity properties at nanoscale without really getting hold on the concept. For instance, how zero resistance is related to cooper pair tunnelling and BdG Hamiltonian. Only when I was forced to write introduction a month before my thesis submission I gave my best last try for the farewell and it clicked. Note the title of my thesis “Quantum effects of superconducting phase” ;) Quantum computers. I was so deceived by all the hype that it took me long to see it as SU(N) matrix product accelerator. Zero knowledge proofs and Shamir transform to non-interactive protocol. The tunnel analogy did quite a harm to me, also the math was just unbearable (defining set of languages and etc). Only a year ago when I got an old paper on “Observational wallets” describing how to prove ‘log_g A = a’ and ‘log_g A = log_g B’ the whole ‘proving statement without revealing secret’ after long frustration and angst made sense to me. If I had encountered finding Vodo analogy first, It would have clicked much quicker to me.
  • peterfirefly 4y ago
    Old papers are great. I have often deliberately sought out old papers to get a quick and good introduction to a subject. It doesn't always work -- sometimes a newer paper with better abstractions/examples/terminology wins, of course. I no longer know when I figured out this trick, but I have been using it for at least twenty years. I wish I had known about it earlier.
    • TimPC 4y ago
      There are tradeoffs. Most of the time I find terminology has drifted so substantially over time that reading old papers isn't worth the effort. I instead usually look for literature review type of papers that often have good summaries of relevant results in modern terminology.
    • liketochill 4y ago
      I have also found old papers to be the best for learning a new concept - they make it as simple as it can be. A colleague of mine wrote a paper that proves that negative numbers exist and would often cite archimedes, Galileo, newton, etc in his bibliographies. I think he loved crediting the first person to come up with whatever idea or concept he was using.
• revskill 4y ago
  Everything is a monoid to be useful. Now i understand more about why 1+1=2.
• ranting-moth 4y ago
  Music theory. I'm not claiming I understand it all. I've had many eureka moments when I suddenly realise what or why this thing from years ago is important. I think teaching music theory with both what and why (with examples) is essential. I still have haven't found a book that does a good job of it and keeps it interesting. Any recommendations?
• hydroid7 4y ago
  OOP on Java.
• mixmastamyk 4y ago
  Not my click exactly, but hearing the “Unicode sandwich” described ~15 years after studying Unicode and using it in production was the last piece of the puzzle no one ever mentioned before. Or perhaps in not so clearly.
• mattsears18 4y ago
  Functions in calculus... I never understood them until I learned about functions in programming several years later. They're the same damn thing! I really wish I had learned to program before learning calculus.
  • peterfirefly 4y ago
    Hopefully, you learned about functions long before calculus... When we learned about functions back in something like 5th grade, I noticed that my classmates were very confused by the concept. I also remembered that I found the explanations in the book and the ones from our teacher quite unclear. My guess back then was that the notation was partly to blame for that -- and I still think that's true. So, my questions to you are: 1) were you taught the "f(x) = 3x + 2"-style notation? 2) have you seen the "x --> 3x+2"-style before? Or the "f: x --> 3x+2"-style, where we give the function the name f? 3) did you find it confusing that f(x) was sometimes used to refer to the function and sometimes to its value when applied to x? The notation of question 2 should eliminate that confusion. I'm guessing that part of the confusion was also that your teachers were unclear on what functions could be used for -- but didn't they ask you to draw graphs for various functions? And didn't they also introduce functions like sin/cos/tan?
• hammock 4y ago
  >longer wires mean more resistance while thicker wires mean less resistance. Intuitively (perhaps incorrectly) I would assume that it's like trying to force a fluid through a skinny long pipe vs a wide pipe - the skinny long pipe will have higher pressure inside. Or, the long thin wire has more distance for the current to travel (= more resistance), while the thicker wire has more "options" for the current to choose a path of least resistance (literally), tending towards a lower overall resistance compared to a thinner wire of the same length
• ruune 4y ago
  Long time ago, but mathematical functions. In hindsight stupid, but it took me embarrassingly long to understand that a function just takes a value for x, calculates it with the rest of the numbers in the function and that way basically assigns a y-value to every x-value. No idea why it took me so long, I didn't have any similar problems with high school math
• evanpw 4y ago
  This is true of almost everything in math. You learn some definitions and techniques in one class, and it doesn't all become clear what's going on until you've used those to as the base layer for solving some other problems in the next class. Part of it is just that it's hard to teach you need the first concept in order to understand the second, but you need the second to understand why you should care about the first, so it's all a bit circular.
• CSDude 4y ago
  Sadly, React. Was using Angular 1, and Vue made much more sense. I'm not a Frontend Developer though, but needed to learn React but it happened to late. At least, when I needed to learn, components were not classes anymore but functions which made learning curve somehow simpler for me although its not much difference.
• zenmacro 4y ago
  Central Banking 101 by Joseph Wang does a great of explaining the repo and reverse repo markets. https://books.google.com/books?id=wPs_EAAAQBAJ https://books.google.com/books?id=wPs_EAAAQBAJ
• dgudkov 4y ago
  Data visualization. I had many years of experience with data analytics, but only when I read "Now you see it" by Stephen Few I started understanding how data visualization is linked to the way the human eye and brain work.
• spritefs 4y ago
  1. Being able to derive bottom up dynamic programming leetcode solutions. The only way I really "figured out" how to do this was by reading the dp chapter out of the Cormen algorithms book. It's crazy how illuminating (and rare) clear explanations are 2. The chain rule. I knew the actual rule from a calc class, but the intuition behind it didn't make sense to me until I read a couple pdfs on backpropagation 3. Money brings out the worst in people
• progJustMath 4y ago
  Programming as “just math”. I got wrapped up sitting there memorizing ins and outs of each language and the ecosystem, others compositions in the form of Apache and the like. Now it seems bizarre we’d think of it as anything but add, div, compare of electrical state in a memory address. It’s not a 1:1 machine translation but it’s the abstraction that’s made me most productive. A whole lot of baggage comes with software that I’m hopeful ML libraries will allow us to retire. Currently wrapping UI around OpenCV to make my own “Photoshop”, for example. I really can’t see any other way of approaching programming as anything but a waste of human agency. There are social problems we could be focused on if we were less focused on butts in chairs cranking out code.
• mmcconnell1618 4y ago
  Compound Interest. The idea and the numbers made sense but it is only with many more decades of life that I understand how much impact time has on compounding. If I had understood this when I was younger, I would have made different choices in regards to saving more. Small sacrifices when you're younger and can easily tolerate them, have massive dividends later in life.
• iddan 4y ago
  Someone once told me he derives his self-confidence from the dialogue with himself. It took me a few years to understand it: 1. A clear dialogue with oneself is establishing certainty about the inner self 2. Certainty with the inner self enables one to see the outside in a clear way 3. That clarity contributes to confidence in one's actions.
• furyofantares 4y ago
  Gender as a social construct, separate from biological sex.
• aj7 4y ago
  That the integral I-V relations for an inductor and capacitor are the fundamental forms, not the differential relations.
• andyjohnson0 4y ago
  The attachment theory of adult relationships [1]. Sometimes you just have to go on the journey to understand what stopped you getting to your intended destination. [1] https://en.m.wikipedia.org/wiki/Attachment_in_adults https://en.m.wikipedia.org/wiki/Attachment_in_adults
• jmorenoamor 4y ago
  Orbital mechanics. It was after playing KSP that I had that "woah! this makes sense!" moment.
• brunooliv 4y ago
  The biggest one has to be design patterns in OO design! I was fortunate to have a great teacher which taught OOP by focusing on design patterns, dynamic dispatch, composition over inheritance, etc, etc, the really foundational concepts. I was too young and naive to fully understand all the concepts, I just thought writing Java was cool! Ah. Many years later, I really realized how to apply design patterns to solve real problems in a large production codebase and it all clicked then and in retrospect that teacher was really amazing, I just was too naive to realize it back then...
• gpsx 4y ago
  This is something that clicked after a few hours rather than a few years, but it is similar in a way. A long time ago when I was a graduate student I was in the library one afternoon studying some idea in field theory (physics). It covered maybe three pages in a small book, but it wasn't making any sense. Finally, hours later it suddenly became clear, and it was so simple. I remember saying to myself, "Why didn't they just say that?" I looked back at the book and they said exactly what I would have said. I guess sometimes words are not enough.
  • mixmastamyk 4y ago
    They need to simmer a bit.
• slotrans 4y ago
  For me the big one was relational modeling & normalization. I took a database class in college and I thought normalization was idiotic. It seemed obviously foolish and wasteful and I couldn't imagine why anyone would do this to themselves by choice. Then ~2 years later I got a job working with data, at a company with quite a big database that was designed largely by experts. Within a few months of starting to work with real data I had internalized the Why of normalization and become a believer. Ironically I've been doing database work ever since. Lately I've worked for a number of companies where no one -- like seriously, absolutely zero developers on the team -- understand normalization. They may perform a shadow of it, because someone somewhere told them to, or some article said this is how you model data that looks like X, but they don't get it. Predictably, their data models are absolute garbage. Teaching them is an uphill battle because they don't care, they're not curious, and their web frameworks (cough Rails cough) have taught them to distance themselves from the database and treat it as dumb. The other one was Rich Hickey's "Simple Made Easy", which I first watched in 2013. I enjoyed it even then but I didn't really understand what he was getting it. After working with, and building, some systems done in a functional style, I feel like I figured most of the ideas. That would have been some time in 2017 so, definitely took a while to soak in.
• buzzert 4y ago
  For me, it was the difference between “is” and “ought”. It sounds obvious when you first think about it, but I spent a vast majority of my 20’s with a view of the world filled with “oughts” instead of “is’s”, especially when it comes to things I can’t control. I.e., people “ought” to behave a certain way, versus the way people actually behave. The way companies/governments “ought” to operate, versus the way they actually do. Thinking in terms of “oughts” can really cloud your judgement in ways that you might not be totally aware of. I guess this is kind of like the “realpolitik” philosophy, but coming to this realization in my early 30’s actually made me a lot happier and less confused about why the world is the way it is.
  • satvikpendem 4y ago
    Are you familiar with the is-ought problem? Somewhat related. https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem
    • buzzert 4y ago
      Oh wow, I wasn’t but this perfectly sums it up! Learned it the hard way. “Fact-value” is another good way of putting it.
      • satvikpendem 4y ago
        Yeah, David Hume has some good works. I recommend you read Treatise of Human Nature if you can, and follow along with commentary rather than trying to parse it all on your own, I took a class on modern philosophy where we covered it.
• skatanski 4y ago
  I think I've read about git multiple times before I started using it. And even then at first it was with a dash of scepticism. I can't put my finger on that moment, the moment of clarity but it had to be quite glorious. Before, I was "what else do you need we have svn". Sounds horrible now that I think about it.
  • rubberband 4y ago
    Pfft. I believe that anyone who read about git, and responded "yeah, duh, it's so obvious" is a dirty, dirty liar. An explanation of "interactive rebasing" to me might as well been an explanation of quantum entanglement to a learning-disabled ant. Sometimes it still trips me up. I have an embarrassingly large number of copies of source folders, despite git's safety net of "don't worry, you can always restore it; pinky swear..."
    • quickthrower2 4y ago
      I would never rebase at the command line and avoid rebasing generally to the chagrin of team mates. A merge retains the information to reconstruct the rebase anyway so might as well use the simpler option. Unless there are a lot of commits such that in aggregate they conflict but individually they apply smoothly.
• 23B1 4y ago
  Simple one: understanding probabilistic vs. deterministic thinking = the serenity prayer* The former is for dealing with any situation where we can't control the inputs and outputs. The latter is for when we can. *"Grant to us the serenity of mind to accept that which cannot be changed; courage to change that which can be changed, and wisdom to know the one from the other."
• andrewflnr 4y ago
  call-with-current-continuation. First ran into it as a teen and the concept pretty much completely bounced off my brain. I think it took a couple more tries before I started getting it, and arguably I'm still working on it.
• mustafabisic1 4y ago
  For me it was basic statistics. Statistical significance and variability. Had Statistics in college, but only understood it now that I use it to understand data.
• I_complete_me 4y ago
  Two are very pertinent for me at the moment: 1. The Monty Hall problem 2. The Wason Selection Task. I read about the first one eons ago and was impressed that Marilyn Von Savant was vindicated. Shoutout to her! The name Wason was unknown to me but I bought a book called The Oxford Companion to The Mind (new in 1987!) and his 'task' was featured in it (pg. 639 in my edition). I spent a lot of time satisfying myself as to the answer and kind of got there. This Christmas I am reading Stephen Pinker's "Rationality" and the description of both have allowed the penny to fully drop. I hadn't been thinking about these puzzles for ages and then when they cropped up "unexpectedly" I grokked them easily. They "clicked". There is a certain type of wisdom that comes with passed time.
  • metadat 4y ago
    New to me me, interesting problem and origin story: https://en.wikipedia.org/wiki/Monty_Hall_problem https://en.wikipedia.org/wiki/Monty_Hall_problem
    • v-erne 4y ago
      That's a great paradox that can be really hard to understand for some but it's quite obvious when it finally clicks. You just needs proper reference or rather point of view that makes You understand that Monty selection and player decisions are not unrelated events and Monty just eliminates a whole branch of possibilities by introducing his knowledge into the system (he cannot show the prize and thus must always select one of the goats). And if You can imagine this problem as a decision tree You suddenly, as a bonus, understand conditional propability.
  • rubberband 4y ago
    Oh thank goodness. Another human not cool enough to "get" the Monty Hall problem at first. I thought I was the only one... Took me years...
    • hinkley 4y ago
      I made a pact with a group of friends never to bring up Monty Hall again, especially not when alcohol is involved. The only things I’ve seen people get more upset about than MHP is infidelity and politics.
• mablopoule 4y ago
  "The road to hell is paved with good intentions.", "Perfect is the enemy of good", and more generally idioms that sound like either paradoxical assertions or obvious platitudes. It wasn't until late teens/early twenties that lots of those piece of wisdom went from "cliché phrases you've heard all your life", to (often) deeply impactful aspect of human conditions. The "road to hell" idiom explicitly didn't click until I had enough experience with counter-productive efforts who looks good on the outside, but actually fail to take into account a more nuanced reality. It also kinda works with the distinction between "values I believe in" and "arguments articulated around shared values". Being able to disagree on something even when (especially when) it's invoking values I believe in is one of the most important thing I've gained as I matured, and yet it needs experience to 'click'.
  • jrockway 4y ago
    I never remember the right "direction" for these platitudes. I feel like "good is the enemy of perfect" is just as valid as "perfect is the enemy of good". Meanwhile, the road to heaven is also paved with good intentions. Good paving material, it turns out, but asphalt is cheaper.
• screye 4y ago
  Related : I have a request for the 1 major concept that has never clicked for me --> Can someone help me understand 'productive value' in an economy ? I have tried hard, and can't for the love of me understand what lies at the bottom of trade, what is the base value of assets / activity. It just doesn't click. Questions like: - Can a services based economy work if the consumers of the services weren't producing some non-services based value ? - How can there be any economic value in middle-men ? - Is speculation on artificially limited assets (housing) just a pyramid scheme ? - How is it NOT a zero sum game ? - Is a Fiat currency just 'vibes based economics' ?
  • bbayles 4y ago
    Here's something to think about: suppose you buy an assortment of candy from the grocery store and distribute a uniform collection of pieces to a room full of middle school students. Some students will like the sour candy; others won't. Some will like coconut; others won't. Some will love nuts; others will hate them. Now you let the students talk to each other and trade candy. The ones who like sour candy but hate coconut will trade with the students with the opposite preference, and so on. At the end of the trades, everybody is happier with their new bundle - why would they have traded otherwise? So value has increased. But this is magic - no new candy was produced! Through trade we have increased overall value - the exercise was positive sum. With some effort you can see that a middle man might add value by expediting trades - connecting people who like coconut with people who hate it (suppose there are thousands of students in the class who all speak different languages). And you can see how fiat currency might make things easier. Rather than having to come up with the barter value of coconut candy and sour candy to nuts, you can convert both to a single unit and then trade units.
  • xvedejas 4y ago
    I can try some of these > Is a Fiat currency just 'vibes based economics' ? I'd think of it more like contract-based/trust-based. If a government has promised you can pay your taxes and debts in a fiat currency, and you believe them, then you'll value that currency. You may need it some day. When the trust erodes, so does the value. I don't think this is simply "vibes", it's people behaving rationally about what they expect the future to hold. And in fact this is just what "value" means for all things generally. Someone thinking rationally about how to value a gold-backed currency is still asking themselves whether they expect gold to be worthwhile in the future. > How is it NOT a zero sum game ? A zero-sum game would be one where there's just a fixed amount of value to allocate however, and you're stuck to the pareto frontier; that is, there is no re-allocation which would leave someone better-off and nobody worse-off. But in reality there's obvious misallocation all of the time! That's why you would ever buy or sell something: because two parties both believe they benefit from that exchange. Whether that exchange is actually positive or negative for society depends on externalities. But it seems pretty clear to me that a lot of activity is a negative-sum game (if it cause pollution, addiction, etc), and a lot of activity is a positive-sum game (most other things), and almost nothing is actually zero-sum. How is it NOT NOT a zero sum game? > Is speculation on artificially limited assets (housing) just a pyramid scheme ? Kinda.
• shrimpx 4y ago
  I studied functional programming and I took terms like "expression", "evaluation", and "value" for granted until it clicked that these terms have intuitive meaning when interpreted in colloquial/human terms. - Expression as in someone expressing themselves, a tentative gesture. - Evaluation as in scrutinizing something to learn what it's really about. - Value as in "valuable". We don't know if an expression is valuable until we subject it to evaluation, or we get an interpreter to interpret it for us.
  • dehrmann 4y ago
    Have you ever studied compilers? You'll gets a good idea of these concepts from a toy compiler for an imperative language.
    • shrimpx 4y ago
      Yeah I've built a compiler and several interpreters in an academic context. I'd appreciate any concrete suggestions for further playing/learning.
• anacleto 4y ago
  Krebs cycle.
• ryanschneider 4y ago
  Calculus, even the basics like derivatives, 2nd derivatives and integration didn’t really click with me until I did some scientific computing/signal processing with SciPy and Pandas a couple years ago. Graphing the discrete versions on time series data, e.g. graphing the difference between consecutive values and seeing the derivative pop out, or a rolling sum for integration, etc finally made it all click.
• sampo 4y ago
  Eigenvectors
• adamnemecek 4y ago
  The fact that essentially all concepts in math, programming, physics etc. are just applications of fixed points which is predicated on the idea of nilpotence. Fixed points go by many names like invariance, spectra, diagonalization, embedding, braids etc. By fixed point I mean something like the "Lawvere's fixed point theorem". https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere%27s+fixed+point+theore... I have a braindump on this https://github.com/adamnemecek/adjoint https://github.com/adamnemecek/adjoint I also have a discord https://discord.gg/mr9TAhpyBW https://discord.gg/mr9TAhpyBW
  • igravious 4y ago
    Also Brouwer's fixed point theorem, and the Y combinator?
• tevon 4y ago
  Anyone who is excels is out of their depth. By definition if you continue to progress (in career or life), you will be doing something you have never done before. This means everyone that we look up to who appears to be on a upward trajectory is making it up as they go.
• erdos4d 4y ago
  Frechet differentiation.
• ttul 4y ago
  When we think about history over any time scale, we tend to think about one region, person, group, etc within that period of time. In reality, “everything” was going on during that time. History is far richer than we tend to realize. So much is going on all the time; it’s impossible to grasp it all.
• darawk 4y ago
  Tensors. Years ago, I would read the Wikipedia page about them every so often, and completely fail to understand what they were. Then one day I was modeling something in a spreadsheet, and I thought to myself "you know, what I really need here, is 3rd axis to this spreadsheet". And for a few minutes, I thought I had invented a new form of spreadsheet/structure, and was considering trying to build a 3d spreadsheet program. But, of course, suddenly everything I'd read about tensors and not understood before snapped into place, and I realized that this is exactly what they are (to be precise, this is a special case of a tensor, the contemplation of which caused me to understand what the general case is, and why e.g. a scalar is a rank 0 tensor, a vector is rank 1, a matrix is rank 2 my 3d spreadsheet idea is rank 3, etc).
  • ninthcat 4y ago
    It sounds like you are describing a multidimensional array, which can be used to represent a tensor, but is not conceptually the same thing. A tensor is an element of a tensor product.
• Tade0 4y ago
  Singing. I was part of a choir in high school and early college, but never managed to get good at this, even though I knew well how skilled singing should sound. More than a decade later, when I was really exhausted after tending to my infant child I let out a sigh of the same type that we did as exercise back in the choir("Aaaaaaaah"). To my surprise it was almost effortless despite making quite the sound due to it being more or less at the resonance frequency of the bones in my skull. And then it dawned on me. It's essentially turning yourself into an elaborate fart pillow. Of course there's much more to that in things like posture and the mentioned resonance, but I had that covered from years of training. The only piece missing was using the diaphragm correctly. Now I sing daily and while my range is pretty average, I don't strain myself any more and can do it for hours. Also the tone is just so much better now.
• rubicon33 4y ago
  Eating fiber.
• college_physics 4y ago
  Graph theory. For the longest time I thought it is an interesting and even beautiful branch of mathematics but somewhat "recreational" and disconnected from my various bread-and butter workhorses for applied work (from linear algebra and PDE's to differential geometry etc). So I never bothered to dig and connect the dots. At some point I realised the connections between the two worlds e.g., graph operations as linear algebra [0] or the transition from continuous Laplacian to graph Laplacian via a discrete Laplace operator [1] [0] https://graphblas.org/ https://graphblas.org/ [1] https://en.wikipedia.org/wiki/Discrete_Laplace_operator https://en.wikipedia.org/wiki/Discrete_Laplace_operator
  • oaiey 4y ago
    Topological sorting! So important
• pfoof 4y ago
  The importance on clean code, architecture and testing. That was during my university when we had a serious diploma group project on the last semester. Also importance of reading books even later. My mother told me this all the time but school books were not the best choice. In high school I started reading fanfics, then occult books and finally I landed on self-helps and ones related to my SWE career.
• ChrisMarshallNY 4y ago
  In my case, almost everything has been like that. 1) I learn rote. 1.1) Almost no improvement. 2) I "get it." 2.1) My development in that area suddenly explodes. This has happened with almost every software concept, from calculus, to Structured Programming ("Whatever will I do without my precious GOTOs?"), to Object-Oriented Programming, to Design Patterns, to Protocols, etc. It usually only takes weeks or months, but I suspect some have taken years.
• wiseowise 4y ago
  Programming languages don't matter.
• criddell 4y ago
  For me it was Microsoft’s COM and how it’s all powered by interfaces. It took a long time before it clicked for me. Fortunately, it didn’t really matter because 20+ years later, it’s still relevant. I’ve had plenty of time to work it out. The other Windows-related idea that took an embarrassingly long time to work out is device / printer / memory contexts.
• abyesilyurt 4y ago
  Specification vs Implementation: There could be only one specification, but many implementations. There is only one Python specification, but it has many implementations, cPython being the most popular.
• pcurve 4y ago
  object oriented programming, with public, private, classes. inheritance, parameters... ugh. It took much longer to internalize these than I'd care to admit.
• _huayra_ 4y ago
  Pretty much anything related to personal growth (however you define it) takes time to click, but it took a while to understand two things at a deep enough level to begin to make change: * everyone has a set of habits that served them well during childhood, but may be maladaptive as an adult (e.g. getting angry is almost universal a sign of this maladaptive childhood habit rearing up). Book recommendation [0] * the fear of hope is a key thing to understand when it comes to why people (myself included) hold themselves back. Taking the first step can feel terrifying because it demonstrates that one is responsible for creating one's own life. Book recommendation [1] The only way out of this is to deliberately design your days so that you get the most out of them, even if it is fumbling at the start. Add in some times to relax here and there, but if you have a plan, it's much easier than staring at a blank Saturday with the vague goal of "I MUST learn JS/Rust/Go/Scala or my career will be over!!!" and then getting nothing done. [0] https://www.goodreads.com/book/show/23129659-adult-children-of-emotionally-immature-parents https://www.goodreads.com/book/show/23129659-adult-children-... [1] https://www.harpercollins.com/products/how-we-change-ross-ellenhorn https://www.harpercollins.com/products/how-we-change-ross-el...
• whalesalad 4y ago
  We are all just children. As kids we always want to be adults but then we become adults and ultimately everyone around us is just a child who’s been on the earth longer.
  • ipnon 4y ago
    I will die knowing a little about programming computers and not much else. Over time this has slowly become acceptable to me.
    • hinkley 4y ago
      You’ve still got time to learn a little bit about half a dozen things, if you’re so inclined.
• a_c 4y ago
  People never change because of YOU. This applies to work, relationship and family. It made me click about the saying that science advances one funeral at a time. It is easier to rally people of similar thought than to change people of opposite opinion. Not impossible, just more difficult. It explains a lot of thing in my opinion. 1. It is easier to start a start up than to convince your boss to take a certain product direction. E.g to not pursue certain pursuit, as outlined by John carmack's departure from meta. The ultimate judgement will be whether YOUR idea survive rather than whether your boss buy your idea. And I prefer bootstrap, at least for now, for that reason. 2. Never attempt to change your spouse. Find the common ground instead. 3. Empathy is mostly about experience sharing. You can't have people feel something they never experience before. If you can empathize, it means you have experience to draw similarity between. Imagine teaching a 18yo to be a father, that's how preaching people to be empathetic felt like.
  • fritzo 4y ago
    Yes, that resonates. But how do people change? Through their own rude awakenings? When they contrast their own selected peer group with other teams?
    • marcosdumay 4y ago
      People change due to their own concepts that take a while to click. You can have an impact there. But you can't cause immediate change.
    • a_c 4y ago
      "Change" is manifestation of idea. If you have the idea that sleeping 8 hours a day is beneficial, you are very likely to act like it. Imo, ideas form within the spectrum of indoctrination and "epiphany". Indoctrination is something that you hear over and over, and sort of taking it as granted. Parent to children, school to students, religion to devotees, government to citizen, social media to general public, hackernews to us developers, all impart their flavors to our mind and we act according to it. Take sleeping for example, sleep well, sleep long enough, sleep early shouldn't elicit much debate, we treat it as truth more of less. On the other hand, dietary cholesterol consumption, which is considered, advertised and indoctrinated as bad for more than 5 decades has now garnered some attention to consider otherwise [1][2][3] Epiphany is circumstantial, event driven. Either you have a lightbulb moment, or reality decides to slap you in the face. Having a close friend/relative die at a young age will either makes you treasure life a lot more, or send you into deep depression. But it will change you forever for sure. On the other hand, again taking sleeping as an example, I have been a night person since teenage, habitually sleeping at 3am, 4am, feeling drowsy in the morning and study/work in the late evening. "I prefer working in silence" is the excuse I gave to the then self. One day it dawn on me that there are only 24 hours a day, if I can get things done in 1am before sleep, I can equally get things done in 6am after sleep. And if I can rest well, I can get things done quicker. No new information just one day I viscerally feel that shifting the biological clock earlier makes more. 1. https://en.wikipedia.org/wiki/Ancel_Keys https://en.wikipedia.org/wiki/Ancel_Keys 2. https://en.wikipedia.org/wiki/Seven_Countries_Study https://en.wikipedia.org/wiki/Seven_Countries_Study 3. https://en.wikipedia.org/wiki/Robert_Lustig https://en.wikipedia.org/wiki/Robert_Lustig
• friend_and_foe 4y ago
  Understanding your data representation is more important than understanding how to write code. It makes sense once you've used code to solve problems a few times, but when you're just starting out you don't get it.
• wtcactus 4y ago
  I wouldn't say years, but it took quite a few weeks, maybe even months: The idea that the expansion universe is akin to the surface of a balloon expanding (albeit in 4D). I don't know why. It is so absurdly simple in my mind now. But when I was first told this (after naively asking where would the center of the expanding universe be), I just couldn't put my head around it, it seemed absolutely gibberish to me at that moment.
  • mixmastamyk 4y ago
    Why is it like that?
• jsonne 4y ago
  You should look up a concept called "Gestalt Learning". I liken it to the "Eureka" effect that Thomas Edison talked about. For any professional educators or other folks more familiar with this I am about to butcher this concept I am sure but my layman's understanding is the following. Basically rather than a bottom up approach to learning it's a top down approach where you see the whole picture first rather than each piece and then dance around it until you just "get it". Think of imagining a house and then learning about it until the entire house system makes sense. You might imagine the house, then learn a large "chunk" which is the foundation, then another chunk which is the plumbing, etc. etc. A more typical learning method might be you learn what a brick is and then you learn how they're put together, then you understand a wall, etc. etc. This style of learning is more common in folks on the ASD spectrum but isn't exclusive to ASD folks. I find for me I'll encounter a concept, then think on it periodically over some period of time until one day I just sort of "get it". It's not better or worse than other ways of learning but it just means you need to approach things differently to learn more efficiently.
  • dev_0 4y ago
    [dead]
• alexmolas 4y ago
  Social constructs aren't less real than other tangible concepts. For instance, I used to complain a lot about the non-sense that's to wear a tuxedo in weddings. I was the typical kid saying that I would like to go wearing my best sweatpants to weddings, and that probably my sweatpants are more expensive than some of the tuxedos there. Then, I matured and realized that what we wear have a meaning, wether we like it or not. It's like words, maybe you don't like the definition of the word "car", but using an alternative word would be useles since nobody else would understand you. So if you care about the people getting married and you want to communicate it you need to wear the damn tuxedo.
  • dgwight 4y ago
    What kind of sweatpants are more expensive than a tuxedo??
    • MaxHoppersGhost 4y ago
      https://www.gucci.com/us/en/pr/men/ready-to-wear-for-men/pants-and-shorts-for-men/leggings-jogging-pants/jumbo-gg-jogging-pant-with-web-p-715192XJETI2270 https://www.gucci.com/us/en/pr/men/ready-to-wear-for-men/pan...?
    • deleted 4y ago
      [deleted]
• iKlsR 4y ago
  I self taught myself c++ many years ago as my first lang (no idea why, I must have googled how to make games and it came up). No internet, just some downloaded word docs and html pages I saved on flash drive and went to a friends house. I was so bad when I think back that it's actually funny now that I've become so proficient in it. I used to think the runtime was the compiler and my very first hello world was done in Word so you can imagine the torture I went through trying to get that to compile. So the topic that took me about 2 years to get at this inefficient setup, (had finally gotten a sam's teach yourself in 24 hours at some point iirc) was pointers. I could never grasp them. It suddenly came to me one night when reading something about letters that it clicked, the concept had something to do with delivering letters to houses and each house has an address. Can't recall the exact details but man was it an enlightening moment. I googled pointer mailbox analogy and this is very close if not what made it click for me - https://www.eskimo.com/~scs/cclass/notes/sx10.html https://www.eskimo.com/~scs/cclass/notes/sx10.html
• alexmolas 4y ago
  Monads are just a design pattern.
• IceHegel 4y ago
  There are no rules.
• MichaelDickens 4y ago
  What an algebra equation is. I could solve linear equations, quadratic equations, and systems of equations by adding/subtracting/multiplying/dividing both sides of the equation and by adding two equations together. But I didn't know why you were allowed to do any of those things, or what else might be allowed. Are you allowed to square both sides? Raise both sides to a power? It wasn't until maybe my third year of algebra that I realized an equation means both sides of the equation are equal to each other, which means you can perform any operation at all to both sides, and the result will still be equal.
  • sgdpk 4y ago
    This is a great example! I was fortunate enough that my father explained it to me when I was in school. An equation is like a balanced scale: whatever you do to one side, you must do to the other, to keep things balanced. I still remember that "click".
  • ipnon 4y ago
    It was long after I graduated and passed symbolic logic that I realized a proof is the “solution” of an equation using logical operators instead of algebraic ones. Proof writing then becomes following branches on the tree of textbook knowledge to new leaves. I envy those who grok this when they’re kids.
    • kamaal 4y ago
      Can you elaborate more on this?
  • xigoi 4y ago
    Just be a little careful: when solving an equation, you're usually asking when the sides are equal, not asserting that they are. So the implication has to go in the opposite order.
• jackcosgrove 4y ago
  It's not really a discrete concept, but the course western philosophy took over the past 500 years, and its dialogue with science, was something that took me decades to appreciate. In college I sort of understood the outlines of this development, but years of learning, reflection, and life experience have really solidified it for me.
• jb3689 4y ago
  Mathematical proofs. I studied math in college and didn't really understand anything I was doing until well after school. When I read Book of Proof a few years later it all suddenly clicked for me and made perfect sense. Half of studying math is just surviving. Same thing for my Fourier analysis and signal processing classes. I didn't grok it until a few years after my classes. Don't even get me started on statistics which I still find difficult to really understand "why do I trust this magic formula?". The hard science behind statistics is actually incredibly complicated when you start to dig into it
• deleted 4y ago
  [deleted]
• cm2187 4y ago
  Coriolis force. It's pretty basic but I never really got it until I watched the Tom Scott video https://www.youtube.com/watch?v=bJ_seXo-Enc https://www.youtube.com/watch?v=bJ_seXo-Enc
• foobarbecue 4y ago
  The Nyquist frequency. Looking back, it's hard for me to understand why I had trouble with it. I remember a friend telling me it was really simple but at the time I just thought it was because he was smarter than me or something. I guess I didn't see a good demonstration of aliasing until years later?
• chx 4y ago
  git. Only https://www.cduan.com/technical/git/ https://www.cduan.com/technical/git/ worked for me.
• shockeychap 4y ago
  The quote below is from a 1995 interview with Steve Jobs. Forgive the length, but the whole thing is quite poignant and there wasn’t much to be trimmed. This particular interview confirmed my own experiences with esoteric processes that people do just because that’s how it’s always been done, and the opportunities that exist because of it. ———————— You know, throughout my years in business I discovered something. I would always ask why you do things. The answers that I would invariably get are: “Oh, that’s just the way things are done around here.” Nobody knows why they do what they do. Nobody thinks very deeply about things in business. That’s what I found. I’ll give you an example. When we were building our Apple computers in a garage, we knew exactly what they cost. When we got into a factory in the Apple II days, the accountants had this notion of a standard cost, where you kind of set a standard cost and at the end of the quarter, you would adjust it with a variance. I kept asking: why do we do this? The answer was, “That’s just the way it’s done.” After about six months of digging into this, I realized that the reason they did this is that they didn’t have good enough controls to know how much it’s going to cost. So you guess. And then you fix your guess at the end of the quarter. And the reason you don’t know how much it costs is because your information systems aren’t good enough. But nobody said it that way. So later on, when we designed this automated factory for the Macintosh, we were able to get rid of a lot of these antiquated concepts and know exactly what something cost. So in business a lot of things are folklore. They are done because they were done yesterday. And the day before. What it means is, if you are willing to ask a lot of questions and think about things and work really hard, you can learn business pretty fast. It’s not the hardest thing in the world. It’s not rocket science.
  • shostack 4y ago
    Agreed with this. One thing I've learned about large established companies is there is a lot of room to deliver impact if you can rework inefficient processes and navigate the politics to have that change adopted. Steve was fortunate in that he could do whatever he wanted which isn't always the case for everyone else.
• foota 4y ago
  Basically all of calculus, but especially multivariable and differential equations. I was first introduced to them in high school and again in college, I struggled with them in high school, but breezed through them in college. Not sure if I just got smarter, worked harder, or some combination of the two :)
• gerbilly 4y ago
  That there will always be work to be done. Whether you define it as working on yourself, on your relationships, fixing up the house, the car, washing the dishes. I guess I sort of lived as if there would be some kind of 'over the rainbow' someday when I could retire and just chill, but this year when watching 'Stutz' on Netflix, where he states that there are three inescapable things in life: "pain, uncertainty, and constant work," the work part really sunk in for me. I've been watching my mother try to create a kind of peaceful cocoon with her new house and her manicured lawns and list of friends curated down to only the ones which don't ever challenge her etc, only to find that even nearing her eighties she constantly has surprises and challenges intruding on the peace she is trying to cultivate. The tldr; of it is that I've been looking at work the wrong way, i.e. I've been trying to avoid it or push it away, but I feel I should embrace it. Some recurring tasks can even be sort of comforting in that it creates a routine.
• Berniek 4y ago
  Accepting the fact that some people are just arseholes and it is no reflection on me. I used to worry that it was something I had or had not done that made them interact in the way they did. Now I will initially give them the benefit of the doubt, (bad day, tired, hangover) but if it continues I no longer interact with them and move on. I no longer even consider or think about them.
• brailsafe 4y ago
  Trig
• derangedHorse 4y ago
  Bitcoin and the need for an alternative to the US dollar and gold as reserve assets
• dmak 4y ago
  This might be a good thread to ask this. I have done all the math in college, but I don't fundamentally understand sine, cosine, tangents, and logs. For sine, cosine, and tangents, I understand how they may correlate on a graph, but that doesn't really give me additional insight into how to apply or use any of this. Similar thoughts on logs, especially when it comes down to O(logn). Maybe someone can direct me to a video to help me develop a deeper insight?
  • fritzo 4y ago
    Consider following John von Neumann's advice "in mathematics you don't understand things. You just get used to them." Write down the first 100 equations involving sin, cos, tan, log. Use those equations in 100 larger derivations. Visualize the functions in 100 different ways (2D, 3D, animated). It's a lot of memorization and "getting used to" the math, punctuated by a few "aha moments" of insight when you realize the 100 examples can be compressed into say only 50 examples. In retrospect its tempting to think the insights led to understanding, but really they were just the dopamine hits on top of the real stuff of understanding: tedious acclimation to a new abstract realm.
  • sgdpk 4y ago
    I don't know exactly from what angle you're looking at this, so let me explain through trigonometry. We know that triangles may be displaced, rotated, flipped and scaled while still looking the same. We have a word for this: we say two triangles are congruent when they are the same up to these operations. This means that there is something intrinsically invariant about triangles. Can we find it? Actually yes! If the sides of a triangle have lengths A, B, C, then the ratios A/B, B/C, etc. are invariant. That is, if you make a triangle twice as big, all sides will multiply by 2, so A/B becomes (2A/2B)=A/B -- it's the same! So, we can come up with names for these invariant ratios. They're most useful for right triangles. To give names, we need to pick any of the two smaller angles as a reference, call it "a". Now, let C be the largest side, A be the side opposite to the angle and B the adjacent side. Then, the ratio A/C can be called sin(a), B/C can be called cos(a) and A/B can be called tan(a). Since sin(a), cos(a) and tan(a) are ratios, they only depend on the angle, not how big your triangle is. But if you know some side of the triangle, then you can know all of the other using these values. So sin, cos and than really capture the uniqueness I was talking about! --- Now the applications. I memorized these as the "divide by C" rule. The Pythagorean theorem says thar A^2 + B^2 = C^2. Divide by C^2, and you get sin(a)^2 + cos(a)^2 = 1. Divide by cos(a)^2, and you get tan(a)^2 + 1 = sec(a)^2. These are all the Pythagorean theorem on disguise.
• ROTMetro 4y ago
  Dancing. I was both horrible at it and or disaster happened when doing it* so I became 'too cool' to dance. One New Year's I finally had a girlfriend I could be authentic with, we were at the city's 'First Night' party, so different activities all over town, and I told her 'I really want to go dance to the big band in the grand ballroom. But I am a horrible dancer and every woman I have danced with has made fun of me'. She was down, was patient, and it was one of the most fun nights of my life. After that we started taking salsa lessons. So just dance. And if the people you are with make fun of you, don't stop dancing, stop being with those people. * Example: Junior prom, slow dancing with my date in her fancy dress with her $200 hairdo. The gum I was chewing (because I took her out to sushi, which she informed me was gross, and therefore would not kiss me until I got the taste out of my mouth) somehow attached to a hair of hers in my mouth. Before I could unstick it she flicked her hair, yanking the gum from my mouth and into the rest of her long hair. Fun times were not had by all.
• jesprenj 4y ago
  • Basic concepts of dynamic programming and precomputation. During lockdown I attended a course that prepared students for IOI. I couldn't focus/follow at home via web conferencing. One year after I attended some lectures from the same course, but physically. I understood everything when it was explained in person. • Basic concept of buckets in distributed hash tables. After reading BEP-0005 I was left puzzled and left the topic for some months. Reading a Wikipedia article about Kademila, first understanding static buckets and transferring this to dynamic buckets with splitting was way easier to grasp.
• geocrasher 4y ago
  Narcissism. My grandmother was a terrible narcissist. I loved her dearly and she had a lot of wonderful qualities, but The quality that stood out the most, sadly, was narcissism. My mother was also a narcissist to a somewhat lesser degree. It didn't occur to me that I too was a narcissist until I was about 35 years old. It took waking up in the corner of the living room in my friends one bedroom apartment Early one morning to see it. I had pushed away my wife and kids because in my mind all of my problems were their fault. I had blamed others for every thing that had ever happened to me or every feeling that I had felt. And in that moment I realized: It's ME. Everything changed in that instant. It was no longer just about me anymore. I stopped seeing the people closest to me as opponents and started seeing them as what they were, family. My support system. The love of my life. As the years have gone by since then I have seen more of my past through that light and things have become so much more clear. Understanding that my grandmother was a very damaged person who turned a narcissist to deal with it, then raise my mother similarly, help me understand two things. The first was that the things I blamed myself for in the past weren't my fault. Secondly, it helped me forgive them for some of the awful things that happened. I'm not saying it's okay to be a narcissist. But recognizing that their narcissism affected my life, and it was something that I could shed in my own personality was a serious life changer. And the funny part is that after I realized all of this, my debilitating depression essentially went away. And that was a big deal. I also learned not even 2 years ago that I have ADHD which was like a light bulb moment for me as well because it explained so much of my life.
  • whimsicalism 4y ago
    I find it interesting when people come from a long family line of narcissists (not uncommon) that they often attribute it to a cycle of being raised by a narcissist making you into a narcissist. it seems more likely that there is a genetic/biological basis for this personality trait
    • chottocharaii 4y ago
      or it could be a biological disposition to developing it as a response to the trauma of being raised by a narcissist
• justinhj 4y ago
  A bon mot I saw on a sign outside a liquor store: When I was young I thought a $1000 was a lot of money. Now I’m older I realize that $1000 is a great deal of money indeed.
• thewebcount 4y ago
  For me it was design patterns. I read the book in the late 90s. I was working mostly on Mac development using PowerPlant. But despite the fact that it used several of the design patterns described in the Gang of Four book, many of them still didn’t seem very clear to me. Then when MacOS became OS X, and I started using Cocoa, it just clicked. Having delegates finally made sense, for example. Previously, it was so abstract, but once I saw it in action within Cocoa, it made a lot more sense for some reason.
• csomar 4y ago
  1. Functional programing It took me a while, but once it clicked, everything changed. Programming became a process of data consumption, transformation and then presentation. It was if/then/loops/classes/libraries/languages before that. 2. Entropy The example of the messy room that gets messier with time is probably the worst. Entropy is everywhere (in real life or in IT); and it’s actually the reverse of that example. For me now, entropy is life. 3. Bitcoin I was quite a crypto/bitcoin skeptic back until 2014-2015. The whole thing seemed like a ponzi/pump&dumb scheme. Until I read the book “Mastering Bitcoin”. It goes into the details of how Bitcoin works. That’s when Bitcoin (as a cool technology) clicked to me. I still see the trading activity as suspicious but I made my peace with it as humans doing what humans always do: speculation.
• jcelerier 4y ago
  it was very hard for me to understand what was the point of classes when I opened my first C++ book when I was.. 11/12? thankfully it became very clear as soon as I started having actual projects and noticing all the C apis I was writing would all look like foo* foo_create(); void foo_destroy(foo*); void foo_set_stuff(foo*, int); void foo_bloberize(foo*);
• snappy173 4y ago
  The bowline
• Eddy_Viscosity2 4y ago
  Here's a concept I still don't get, even after multiple attempts: quaternions! I mean I get what they are and how they are used and could do operations with them by following the rules. But... I still don't really understand them.
• zweifuss 4y ago
  1. Object-oriented programming. At that time, no one gave a clear explanation of what was actually meant by it and how to implement it. The various schools of OOP often did not acknowledge the existence of other (heretical) schools, which caused a lot of confusion in my brain. Critical voices were hounded and silenced. Also, the gap between implementation and theory was always quite wide. I did not know Smalltalk at that time and have not seen it in use to this day. 2. Electromagnetic fields. I'm still not sure I understand them. I found this video helpful: https://youtu.be/XoVW7CRR5JY https://youtu.be/XoVW7CRR5JY
• semireg 4y ago
  I read “Deep Survival” a few years ago pre-pandemic and was pleasantly surprised it wasn’t a book of survival stories. The main takeaway for me was that sure, nature doesn’t care if you live or die, yet surviving in modern life is an illusion - a papering over of the brutal, unfeeling and inescapable “nature.” The author wrote of survivors coming home after a harrowing near-death experience and realizing that survival is one day at a time, even in the comfort of your own home. Once you taste true survival it may haunt you. Survival is an easy concept with subtle and deep physical and mental consequences. Kind of reminds me of David Foster Wallace’s “This is water” - https://youtu.be/eC7xzavzEKY https://youtu.be/eC7xzavzEKY
• wunderlust 4y ago
  Socrates’s “all I know is that I know nothing” and “know thyself” more and more reveal to me something new about life, philosophy, and the nature of being.
• codethief 4y ago
  Special Relativity. E.g. how could it be that observers A and B (moving relatively to each other) both think that time passes more slowly for the other one? How is that not a contradiction? Man, that took me a while. The solution: A and B have different notions of simultaneity and won't agree on which events occur at the same time. In particular, they won't agree on time measurements.
• ryanlitalien 4y ago
  Docker.
• keepquestioning 4y ago
  People like to pretend they didn't work hard for what they have.
• ved_a 4y ago
  For me, it’s the determinism of nature. The clear hard fact that nothing I can do will impact the pre-determined outcomes. This is cold physics as we know of today. Also, the ‘present’ feeling different from past is just a trick our mind plays on us. This realisation has had profound impact on me - but this dawned on me quite late despite reading a lot on this topic for years.
• umarniz 4y ago
  Self fulfilling prophecy. It took several near burn-outs and tons of hours of my life lost due to frustrations before I truly understood this. The world is what you want it to be. Hopeless because everyone in the world is so selfish? You create the world you live in. Live selfless and see the world transform around you. Frustrated you have to constantly interfere to make someone good at their role? You have to yourself believe they are the best in that role and then see them flourish. Afraid your relationship might not workout? The fear itself will make your worst thought a reality. Your life becomes extremely easy once you truly understand the world is what you believe it to be. Note: There are of-course strings attached to this concept, but understanding the power of this is life changing.
• pizlonator 4y ago
  My top ones: - abstract interpretation. It was at least a year after I first heard of the concept that I grokked it enough to try to write my own, and it wasn’t until many goofy failed attempts and something like 6–7 years that I actually understood it enough to write a good one. And then it was another 5-6 years before I understood the theory well enough to understand abstract interpreters designed by others. So, like, that took me more than a decade to understand. Maybe I still don’t fully understand it. - SSA IR design. It’s so easy to understand the facts of what SSA is, and it’s not that hard to use an SSA IR designed by others. But it took me over ten years from when I first read the papers and did my first attempt until when I actually got it. And I still feel like there are aspects of SSA that I don’t fully understand.
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• supernova87a 4y ago
  Quantum mechanics as continuous probability distributions. It took me about 3 tries in taking QM classes to learn and understand that the whole thing was about continuous probability distributions (at least, the beginner, static stuff). And finally to understand how to understand what continuous probability distributions are, and how to use them.
• gregfjohnson 4y ago
  1. The Fast Fourier Transform 2. Quantum computing 3. Godel’s Incompleteness Theorem 4. Denotational semantics In all four cases, I make no claims to real expertise. However, in each of these cases there was a powerful moment of epiphany, when after much groping in a conceptual fog a light seemed to turn on, and an essential clarity, simplicity, and intuition clicked.
• high_priest 4y ago
  Homologation implies not only "the granting of approval by an official authority", but compliance with social agreement about unification of solutions / standarisation of thought. I've always thought that homologated solutions are parts of a bigger whole, bigger "homo". Stating that the producing party has all the right knowledge to make the part fit and adhere to safety guarantees.
• fouric 4y ago
  Monads in a software engineering context ("a particular set of rules for composition of two pieces of code"); defunctionalization; Lisp structural macros; fexprs; the Rust lifetime system; how to structure functional programs. All of these things had a delta in years between when I first encountered them and when I finally understood them, with repeated (4-8) spaced exposures over that time period contributing.
• gawin 4y ago
  Ram Dass - Be Here Now Amazing book with mind blowing illustrations about life, purpose and spirituality. Changed my life. Every time I re-read it I discover something new.
• blaser-waffle 4y ago
  > no one is coming to save you Thought that was about working extra hard to make money and CYA, but really it's about finding your own happiness, regardless of what it may be in a money / status / property sense. > everything related to RSA & trapdoor algos Like I go the rough idea and implications, but didn't "click" until I was trying to explain what the square root of 11 was to my nephew. Was helping him with homework and was doing everything in my head just fine until we hit that and I had to stop and think and it clicked.
• SNosTrAnDbLe 4y ago
  Internet Protocols. Specifically the beauty and simplicity of IPv4
• zagrebian 4y ago
  The cascade in CSS.
• KolenCh 4y ago
  MPI. A prof. teaching a grad level course on parallel computing mentioned in class that even he himself took a few years to get used to program in message passing protocol like MPI. Funny enough, even when I don't need to program in MPI extensively, after a few years my fear of writing in MPI just went away.
• cybersecurity99 4y ago
  [dead]
• gloosx 4y ago
  Fractality of things is all around us. The whole world is inside you, but at the same time the same world contains all of us. Most simple things are fractal, and most complex things are made using this concept. It's very applicable to code as well. I kinda encountered this my whole life, but it started clicking only few years ago on the 5th year of spitting code out of my head
• deafpolygon 4y ago
  Life is actually short. As a kid, you don't really put much stock into that being bandied about by your elders. You feel like things will go on forever, and that you're basically immortal. As an adult, I now have less time than the time I've been alive to make of what time I have left. I'm not left with cripping regret, but I have wondered what I could have done to make better use of my time.. and that time is just simply gone.
• ezedv 4y ago
  One concept that took me a while to fully understand was the concept of decentralization in blockchain technology. When I first learned about blockchain, I understood the basic principles of how it worked, but it wasn't until I started working for a blockchain company that the concept of decentralization really clicked for me. Decentralization is a key feature of blockchain technology, and it refers to the fact that the blockchain is not controlled by a single entity or organization. Instead, it is maintained by a network of computers working together, and every transaction is recorded on a distributed ledger that is available to everyone in the network. Realizing the potential implications of this decentralization - such as greater transparency, security, and accessibility - was a big moment for me, and it solidified my belief in the power of blockchain to transform industries and the way we do business. If you're interested in learning more about blockchain and decentralization, I highly recommend checking out Rather Labs (https://www.ratherlabs.com https://www.ratherlabs.com). We're always looking for passionate people to join our team and help drive the adoption of this exciting technology.
• nobodyandproud 4y ago
  A bit more light hearted, but I would’ve had far more dates (and one nighters) if I’d smiled more and worked on my small talk. It only dawned on me many years later that I was: a. physically attractive to the opposite sex, especially during my teens and twenties, regardless of my ethnicity. b. my blank expression was intimidating.
  • more_corn 4y ago
    Everyone should practice being approachable and talking to strangers. Not just for expansion of romantic opportunities but basically every kind of opportunity.
• more_corn 4y ago
  When I was 12 my wrestling coach was getting his PHD in fluid dynamics. He gave a tour of the lab where he worked. On screen was a simulation. He explained that they fly a plane back and forth through a certain column of air in the stratosphere to get starting data. Then, using his model he predicts what the flow will look like over a period of time. There were specks flowing through the space onscreen. I asked what they were. “Bugs” he said. Six years later I was sitting in the library studying and I slapped my forehead. “Bugs! Of course! Ha!”
  • mixmastamyk 4y ago
    I don’t get it.
• berniedurfee 4y ago
  Leg drive when bench pressing. The idea that anything you could do with your legs could possibly help drive the bar upward was always ridiculous. Many, many years later, I finally found the right combination of articles and videos where it finally made total sense. Instant improvement and I wished I would have understood it sooner. The problem is really the name, which leads to a particular mental image, which is incorrect, but difficult to break. I think naming is important and for me, can cause enough cognitive dissonance that I can’t get past what something is called to understanding very easily.
  • _dain_ 4y ago
    Do you have links to those articles/videos?
    • berniedurfee 4y ago
      Here are a couple videos that provide most of the insight… https://youtu.be/4T9UQ4FBVXI https://youtu.be/4T9UQ4FBVXI https://youtu.be/Bmjr4Q6je8I https://youtu.be/Bmjr4Q6je8I Basically, you can’t bench with elbows straight out, because you’ll hurt your shoulders. So you tuck your elbows a bit, but that means you’re fighting some leverage because the bar is no longer above your shoulders. To fix this, you arch your back, which rolls your shoulders back and puts the bar back above your shoulders, but with your elbows still tucked. One side of the arch, your shoulders, is pinned to the bench by the weight of the bar. The other side of the arch, your butt, is not. So your arched back will straighten out under load, which rolls your shoulders forward, which moves the bar out of position. So, to keep the arch solid, you use your legs to push your butt toward your shoulders, thus reinforcing the other side of the arch, keeping your shoulders rolled back. So, leg drive is _not_ driving the bar, it’s driving your butt toward your shoulders, to keep the arch in your back solid, to keep your shoulders rolled back (and chest up) to keep the bar above your shoulders with your elbows tucked a bit, to keep from impinging a tendon. You could bench with your butt off the bench and make a big arch, though this article explains you’re diminishing your returns by reducing range of motion. https://startingstrength.com/training/keep-your-butt-on-the-bench https://startingstrength.com/training/keep-your-butt-on-the-...
• mo_42 4y ago
  Bayesian probability or Bayesian thinking in general Like many, I learned Bayes' theorem for an exam. I even did well. But it clicked only when I was reading The Scout Mindset (by Julia Galef). I cannot really tell why. I think it helped me connect math formalism with more real-world examples outside of statistics.
• Agingcoder 4y ago
  I learned classical piano, and a bit of music theory, which was mostly about analyzing what I had in front of me. I always found classical music to be a bit dead - beautiful, but dead : I guess I see it as a dead language, like latin or greek. The jazz I was given was fully written, so it was dead too, except in a few cases where I was supposed to magically improvise. Then I 'got' Jazz, 25 years later : it's entirely about learning the language and grammar and vocab of music, and speaking it, creating new sentences and expressing yourself. The process probably matters more than the style itself.
• danielschonfeld 4y ago
  One thing I feel is clicking for me this year is that of inelastic systems. Be it monetary systems or one’s life occupation. The name of the game is being elastic and rigidity is the end all. Unfortunately as we age ?and as systems age) rigidity seems to be the default path and it takes greater and greater power and aptitude to fight that. One I’m working on still is the unfairness of life. I understand it is unfair down to the level of the cell but how to come to terms with that I still grapple with.
• rajnathani 4y ago
  Privacy.
• topologie 4y ago
  Refactoring.