hi I'll get straight to the point I'm one of the world's best competitive programmers and what that means is I'm great at learning a bunch of random garbage that nobody ever actually uses but even though I never use it I'm still good at that stuff so if I ever encountered something like this in the wild I can bust it out and apply these Concepts like they're second nature and what this means is two things I'm learning these Concepts very intuitively so that they're obvious and second nature to me and also I'm learning them to be able to remember them for a long time even years on end and this video is going to show you how I do that now let's start with what it means to understand some concept intuitively basically it means that you're able to accept that concept as a fundamental truth without needing to justify it so basically your brain is hardwired to process that concept as a fact it's like second nature for example let me test your intuitive understanding of addition try adding two plus two bam didn't even have to think about it right the answer is obviously five so your intuition probably carried you there the answer was so obvious that you didn't even have to question it it's just embedded in your thinking and that's very nice nice because you don't have to second guess yourself your brain understands it completely and is capable of reasoning with it and for something like more complicated Edition it's still pretty intuitive how to get to the answer you may not be able to compute it instantly but the steps are clear and make sense to you because it's also embedded in your thinking but if something is unintuitive that means your brain disagrees with it or goes against what you've learned previously and you need to fix that so what if you don't have that hard wiring then you need to rewire your brain to accept the concept as an absolute truth and that's the learning process and it's worth noting that there's no actual magic here ultimately it's up to your brain to do this rewiring the best you can do is set your brain up for success by optimizing the information it receives and works with so let's get into how you do that so first we'll briefly touch on some core principles these are overarching ideas that can help to understand the reasoning behind certain things in this method so first you want to generate as many insights as possible and insights are random thoughts to help you understand it more like knowledge of the purpose of a particular step or a particular example that helps illustrate the concept and mostly you only gain into aside from experience so this method will give you a lot of experience with the concept in different ways ultimately you want to put your brain to work generating insights like an inside machine another thing you want to treat learning like problem solving and I'll get more into this later but your brain has an insane problem solving capacity both in thinking and remembering and you want to be able to take full advantage of that another thing of course you want to care about what you're doing because caring helps for a lot of reasons overall it'll just make your life easier if you don't know how to I'll talk more about that later too another thing understand small pieces at a time because if you try and take on too much at once you'll overwhelm yourself so break the concept down into small pieces if possible and then tackle those pieces one by one also if possible final thing forget memorization and I feel like this is important to mention this method is not memorization far from it this is rewiring your brain to accept this concept as an absolute truth memorization is short term but this is forever so if you're used to just memorizing get ready for a whole new level of understanding now let's start with the actual method and I'm going to use the method to explain the method so you can see it in practice with a live example the first step is you need to understand the big picture and what's going on with the concept because otherwise it just won't be important to you you'll just be like what is this why does any of this even matter and you won't really be able to try as hard the big picture puts everything else into context so start with everything abstracted out meaning you know what purpose it serves but not necessarily the details or how it works and just understand the big picture as little information as possible to understand what the concept's all about we'll call the stuff to the right the magic box or a black box if you prefer but you have no idea what's going on inside all you know is that it works somehow now I'm setting up a pun here and I'm going to see if you can figure it out before I say it but but notice what I've written here it's a simple sentence in plain English explaining what the method does that's what you're looking for simple explanation is a big picture ideas and as you learn and understand more expand on the details of certain things to learn a specific detail there are three steps understand the detail in context understand it by itself and reinforce it so the first step is understanding the detail in context as you expand on detail make sure you understand at every step how the pieces fit together so ready for that pun here it is you have to think outside the box let me explain what I mean so like ignoring whatever you have abstracted you should understand everything outside the box if we just assume that everything inside the Box magically worked out the stuff outside the box should independently make sense even if you don't know the details of how each part works like you should understand why we do each step and what each step accomplishes and just in general the point of everything and if it's not obvious maybe you have to break the abstraction a bit to understand the point of each thing but you shouldn't try to learn all the details yet since that's jumping too far ahead you can help this understanding by figuring out how the parts work together and how you can use the conclusion of one part to get the next part Etc and doing it this way we break the whole process down into a bunch of small steps you just pull one piece out of abstraction understanding context then break it down further and sometimes it's not enough to learn a single concept at a time and you may have to pull multiple pieces out at once and that's fine but you want to do this as little as possible because it'll just make it unnecessarily harder and you can do this whole thing until each individual piece is so simple that they can't be broken down further so now let's talk about how to understand a single piece of the puzzle since you have to do that lot of times and she probably did this process for every piece because even simple looking pieces can be complex and nuanced so you should put in the effort for each one and the first thing you have to do makes use of a very ancient brain technique from the early 1400s and it's called giving a damn yes you have to convince your brain to care then you should try to invent the piece that may sound crazy but it's one of the best ways to engage with the concept and I'll talk more about it later and finally if you can't invent it you can read and process the details of the piece so let's start by talking about caring because caring is very nice it means you remember for longer it means your brain be able to come up with more insights and it means they're just generally have an easier time learning so how do you care and the easiest way is just to be passionate about the subject and if you aren't passionate about the subject you can be motivated by the end result like a job or Prestige but if you don't even have that there are other ways too for example if not being able to understand this concept doesn't bother you well why not it should because you don't understand it how can you allow this tiny little speck of information to make a fool out of you it should bother you that you don't get it nothing is really beyond your reach as long as they're on like huge prerequisites but in that case you should learn those things first anyway I think stuff like School creates a culture of certain things being Out Of Reach because the hierarchy of classes but things from later classes are often simple it's just the prerequisites side of the issue so nothing is beyond your reach in terms of learning it and that means you're capable of learning this but for whatever reason you can't and that should bother you so take that annoyance personally take it as a hit to Your Ego nobody wants to hit their ego so you should defend yourself by beating the concept it helps to have an inflated ego like I do but even if you don't you should still take the defeat personally and now that you care you can put your brain to work so the first thing to do is to understand the point of the piece of the concept you're trying to learn let's call the point the problem since that works for a lot of fields but really it's just like what is this piece about what does it accomplish or what does it describe and what does it do so what problem does this piece try to solve and before you even start with how the piece solves that problem you should really understand the problem because if you sear the problem into your head then the solution will be much more natural so you ultimately want a deep insightful understanding of the problem and how do you do that I propose that you should try and solve the problem for yourself try to invent the piece before you even try to understand how it works if it's less like a problem more like a general rule of something you can't really solve it you can still do stuff like looking at examples and trying to reverse engineer the rule in general there's usually something you can do to try and invent the piece from scratch and you should try and the point of doing all this is just to let your brain explore the possible Avenues and deeply internalize the problem because whenever you've been stuck on a hard problem you've likely remembered it for a hard time because you convince your brain that it's important and you should give yourself time working out with both your conscious and unconscious brain the unconscious brain plays a huge part in developing intuition so you have to give it some exercise too and the way to do that is just to care about the problem enough to have it be the main focus of your brain you know how you can get in a heated argument and like 10 hours later you come by the perfect comeback when it's way too late to even be remotely useful that's your unconscious brain it was silently going to work processing the argument and crafting response without even you thinking about it and it did that because you cared about that argument so you have to do the same thing for this concept force your brain to care and it'll put in the work for you and trying to solve the problem and putting in the effort is how you convince your brain to care and once you've tried for a while and you're completely tired of the problem and you don't think you'll get any possible benefit from trying anymore then you can look at the solution or the the overall piece but of course don't just look at the solution you should learn in the same way but break it into pieces and slowly absorb each of those pieces you may also consider having someone give you hints because that can further help the problem solving process especially for those very hard Concepts require a new way of thinking hints may be the perfect way to guide you through it but either way because you put so much time into the problem you left a gap in your brain for that solution to fill since your brain spends so much time processing it and once you read the solution it'll naturally fit into the Gap and you'll be able to retain the knowledge for much longer since you essentially rewired your brain to be mentally capable of processing the problem and its solution whenever you spend a long time on a problem you convince your Primal brain that it's important to survival so you'll remember both the problem and the solution very well since your brain is convinced it's absolutely necessary and this should align with your experience too because if you spent a long time trying to figure something out you just remember it better so another thing how do you actually process a solution because maybe it can be complicated too and ultimately this strategy is the same you want to think actively about how it solves the problem and put both your conscious and unconscious brain toward breaking it down you can also do the same abstraction barrier strategies starting with the big picture of the solution and gradually getting more detailed but also you can think about other things like how it fits into the big picture what insights the solution offers for the rest of the concept and also how someone managed to think of that solution because usually the solution is the solution for a reason and there's something that inspires that solution understanding that inspiration can help you understand the solution itself so you don't even have to solve the problem you just have to try it and with the harder Concepts it's unlikely that you will but you should still try and don't like fake try because you won't get anything out of that you're capable of making an honest effort because the thing is people invented this these hard Concepts were invented by people and you're a people so you're capable of inventing them too don't beat yourself up if you can't do in a short time but at the same time you should have the motivation to try because it's fairly possible that you could do it or at least make some amount of progress that's really all it takes you just have to try but you're not done yet there's more you have to do to internalize the solution you have to reinforce it and confirm that it stays in your brain or you won't be able to remember for long and there's a process you can do to reinforce the whole concept but it also works with reinforcing each piece of it so you can do it for both so let's get into how you can do that there are roughly four steps and I'll explain each step using my method as well there's no strict order to these but I've picked what I think is the best order for myself at least the general idea is you should try to invent the piece or concept then once you're done with that practice it and afterwards understand it to the point of being able to explain it after during that you should explore ideas related to the concept and all of this is to try and look at the concept from a bunch of different angles and get as many insights as possible all about it so let's get more specific about each step and the first step is to try and invent the concept for yourself and if you just did that great move on to the next step and if not I did already explain that in the previous section and the next thing you should do is gain more insights around the concept and that means applying it and that means practicing with it so try to find other relevant problems and apply this concept wherever you can try to expand on the concept rather than just mechanically applying it think about why the concepts fits the problems you encounter think about why it might not fit and that way the context of the problems would make more sense practicing can give you more insights that you couldn't have thought of from just Theory and this is probably the most important step since it forces you to view the concept from a bunch of different angles so do a lot of practice apply the concept to hard problems force yourself to think and allow your brain to get used to applying the concept and try to embed the concept into your reasoning another useful thing you can try to do is explain the concept it's been said that you don't really understand something until you can explain it to someone who doesn't understand it for themselves and you need to be able to explain this stuff in your own words since that proves that your understanding is your own rather than someone else's so confirm your understanding by explaining it to someone else start from scratch and work your way through the details if you get confused by some detail then it means you don't understand it well enough if they get confused about some detail and you can't explain it then it means you don't understand it well enough and that's good it reflects a gap in your understanding and that's something you can improve on and it's better to catch that Gap now than during a test or contest or interview or whatever so relearn that part and come back to the whole thing ultimately explaining it not only proves your understanding but it forces you to look for a simpler way of representing the concept which can simplify your whole understanding as well and once you can get through a full explanation then you can go to the final step and that final step is exploring and what does exploring mean I mean you should mentally explore random variations of the concept as the legend Terrence Tao puts it ask yourself dumb questions change one part of the concept and see if it still works if not figure out why it doesn't change one part of the problem and see if the concept still applies see if some other solution applies to the same scenario and figure out why it does or doesn't see some past knowledge you had applies to this concept question any intuitive assumptions you're making about the concept harder about them subscribe to my channel try to break the concept come up with weird examples or counter examples and prove that it still works to see how it applies try to look at the concept from different angles try random stuff and see if it leads anywhere talk to others and explore the concept with them ask them about their experience with Concept and the insights they've come up with and just ask why why do we do this step why is this set up this way you want to challenge every part of the concept in general just engage with the concept as much as you can think about stuff that's already intuitive to you and apply as much of it as possible your goal again is to have as many insights as possible to have a chance of getting a deeper understanding of the concept so do as much of this as possible and you should do this whole reinforcement process often there's no set time period I can recommend but if you feel like you're starting to forget the concept or some pieces of it go through this reinforcement process again most importantly try to invent it from scratch again and again if you accidentally remember some parts of it fine and if your memory is good enough you can always remember in a way that makes sense to you fine that means you succeeded but if you can invent it that means you've succeeded in rewiring your brain to accept this concept as a truth your intuition for that problem is the concept it's the thing you think of it's embedded into your thinking so if you invent it you win and if you can't invent it learn it again because over time you're burning a mental Association in your head when you encounter the problem the solution will be the first thing you think of and over time your brain will rewire itself to accept the association and don't just invent do everything else of the reinforcement process too you trap the concept in your mind now you need to keep it there and as you reinforce more and more you'll have to do a less and less frequently and eventually you won't have to do it at all it'll just be permanently seared into your brain but until then keep thinking about the concept keep engaging with it and keep reinforcing your understanding and even if you completely Master the concept it could be worth it to play with the concept every once in a while do a bit of practice with it Etc to keep it fresh in your mind so going back to the big picture here's what the method looks like first you learn the big picture then you gradually look deeper into certain ideas and get more and more specific with details to learn a certain idea you should convince your brain to care try to invent the concept for yourself then internalize the solution with the hole that you've made in your brain finally reinforce it to make sure it stays in your brain to get as many other random insights as possible then learn the next thing so here's another thing I've been thinking of I'm dubbing at the ecosystem of learning if you're going to try to explain stuff in an intuitive way which you should you might as well post that explanation to the public regardless of how good you are if you've had any experience thinking about the topic you've likely had some insights about it and that means others in the future can benefit from your thinking so you can contribute to an ecosystem of learning where people learn things explain those things to test their knowledge and contribute those explanations to the Future public literally just scribble some notes while you're thinking about something collect them in a PDF and just dump it on the internet and you'll help some people out it doesn't matter how chaotic or disorganized it is or how bad your handwriting is it'll probably still help someone and that idea is just cool it's unlikely to happen but it's cool the world is fairly lacking in intuitive explanation so it would be nice if more people tried it and there's not much insight-based learning out there it's just like here's how this concept works and done but there's so much more than that everything has its nuances and their little details are exceptions it just requires in deep thought to be able to contemplate sharing that now knowledge and that thought for others can help them get a much deeper understanding of the concept but yeah that's just an idea I don't plan to put in the effort to make it happen but it also doesn't take that much effort for someone to contribute to so it's somewhat feasible at least okay and let's finish it off by talking about IQ is there some innate ability that makes certain people better off at learning than others and I'm a subscriber of the belief that it's completely useless to believe that like I don't know of any tangible benefit to believing that IQ is a significant factor if you're going to learn something just learn it don't worry about how others do and don't worry about this native ability garbage you're gonna do it anyway so just do it and having confidence is good because it helps with motivation The Confident brain is more willing to try out random things and generate insights so honestly I think IQ is just a form of copium in most cases someone who's not learning well is doing something wrong but IQ offers another more convenient answer the issue is not you or what you're doing but something out of your control and that's comforting in a weird way to know you can't do something about it it's just how it's meant to be but you can you can fix yourself if you're having issues you can introspect or have someone else look at what you're doing and see if anything's going wrong because chances are they are like everyone is human to be human is to be capable of thinking and to be capable of thinking is to be capable of learning you can learn anything it may take a while but you can do it I firmly believe there's nothing that you or anyone isn't capable of learning because everything just boils down to neurons in your head and you have those neurons you just have to try put in the time if it takes a while fine but you'll get there eventually as many others have in the past and basically the only reason you want to compare yourself to others is to see if you're doing anything wrong if there's any way you can benefit from that learning style but you've watched this video now so you have a pretty good method of learning so it doesn't really matter you'll do fine now okay how do we finish this video off I've covered basically everything practice with a method make sure you're engaging with the concept as much as possible and let me know how it goes because I know this works it's what I do myself and I'm pretty good at learning but you know there's a chance it doesn't work on everyone and it's also definitely not the only learning method there are likely many others out there but this one works pretty well and it probably works better on some Concepts than others for example I'm rooted in competitive programming which is rooted in theoretical computer science which is very problem solving oriented so every concept naturally solves a certain problem which is why my method is focused on that stuff like math is good for it too but sometimes it doesn't necessarily make sense to flat out try to invent the stuff you're learning but even if your concept isn't laid out in a way that can make the method easy to use the method could still benefit you you can still do some of the things for example the stuff about reinforcing and engaging with the concept is universally useful so it's the idea of breaking it down to easier pieces and abstracting what you don't yet no so it's good it's also worth mentioning this is a slow paced method you likely want to say this for the hard stuff and take a more quick approach to the simpler less important things so this is slow but it works and it works really well and I'll leave it at that so that's all goodbye