For long-term learning endeavors (chess, BJJ, etc) you’re going to encounter plateaus. These can stall progress by weeks or even years.
A great way to break through plateaus is to improve fundamentals. Either improve ones you suck at, or find new ones you’re not aware of and get good at them.
This article focuses on the latter: overcome plateaus by getting large improvements from finding (and then training) core concepts you’re currently overlooking.
There is also a brief section at the bottom about increasing temperature, a technique to break out of local optima to overcome plateaus.
What are fundamentals
For any concept, the fundamentals are the subconcepts make up large fractions of it.
They’re the 20% of subconcepts that make up 80% of the useful knowledge.
That’s why fundamentals are taught to beginners. Generally, learning them provides the fastest increases in competency. This comes from Amdahl’s law in computer science.
Amdahl’s Law:
Improvement to a system’s subcomponent can improve the whole system by how much of a fraction the subcomponent is.
Some fundamentals are very obvious.
Others are extremely hard to notice. Even though they’re right under your nose. In this article I give techniques I use to find them.
Get skilled at finding core concepts, and then target them for the fastest improvement in learning.
Strengthening fundamentals can be done recursively, because each concept is composed of subconcepts, whose impact seems to (from my observation) have a power law distribution (meaning, the 80/20 Pareto principle works on them).
You may find that sometimes, your concept is 90% composed of a subconcept 10 layers of recursion down.
Get skilled at finding overlooked fundamentals
You should aim to get skilled at finding fundamentals on your own. You do this by practicing finding them (I go over some techniques below).
Asking others can be a great sometimes! Especially at the beginning. As a beginner don’t worry too much about rigorously adhering to ‘the perfect’ way of learning, try new things and do what seems to work. But over time, you probably want to move away from relying on others for learning, so you can improve the amount of improvement/depth of knowledge you can get long term.
Some fundamentals are super super obvious
Usually these are called basics, and are taught to beginners. Generally most people can benefit from improving them, even if they’re at master level.
In my online chess experience, players as strong as 1900 Elo still often don’t adhere to basic opening principles. Even expert level players can gain from improving obvious fundamentals, even if they have the skill to be able to break away from them and still win.
In The Art of Learning (insanely cracked book), Josh Waitzkin talks about GM Michael Adams (former chess world #4), who is so good at controlling the center (a basic idea taught to beginners) he can do it with so little resources it looks invisible (this is what Waitzkin calls ‘making smaller circles’ – using less and less resources to accomplish a fundamental goal).
John Waitzkin on controlling the center: “[Michael Adams‘] pieces are often on the flanks and he appears to casually give opponents central dominance – and yet he wins. The secret behind this style of play is a profound internalization of the principles behind central domination. Michael Adams knows how to control the center without appearing to have anything to do with the center. He has made the circles so small, even Grandmasters cannot see them.“
Examples of easy to find fundamentals
Chess examples: how the pieces move, putting your pawns in the center, developing your pieces one by one, castling
Writing examples: have a title, have good grammar, write something interesting
Programming examples: programming languages, front end, back end, databases, scalability, UI/UX, security, common algorithms/data structures, ML, data analysis, time and space complexity, etc
These are non-exhaustive examples, each of these has more fundamentals.
Some fundamentals are very hard to notice
We tend to overlook many core concepts. Often we undervalue certain foundational ideas and sometimes they escape our attention completely. Its a really, really bad weakness, but luckily is not that hard to overcome.
Reevaluating how much attention you should pay to specific fundamentals is a tremendously useful source of wisdom/improvement
Examples of hard to see core concepts
Chess examples: pawn structures, attack where the pawn chain points, when to play dynamic vs static, holes in the position, creating weaknesses, exploiting weaknesses, creating winning chances
Chess examples, but even harder to notice: visualization (this is a fundamental of calculation, strengthen it with blindfold exercises to strengthen calculation, works for many things other than chess) learning the map (practicing visualizing the board, gradually, with all colors, will make you better at calculating and recalling games) recall (increasing your ability to recall games with detail will make you learn way more useful patterns across time)
Writing examples: outline speedrunning (article), compress information (idk any more, I’m new to writing)
Programming examples: outline speedrunning to build things quickly (article), building new things to learn new skills (article), learning to navigate up/down abstractions quickly
Techniques to find overlooked fundamentals
Listen for words experts commonly use, then double down on understanding those concepts
Simple as.
Example: In chess, I always heard master players talk about ‘positional chess’. I ignored it because it sounded kind of irrelevant. One day, I decided to read a bit about it.
Turns out it was an extremely foundational concept of the game. Just by going from 0 to OK at positional chess my lichess blitz Elo instantly spiked from 1600 to 1800. Took two days.
Zeroth principle analysis
Recursively break a concept into its subcomponents by asking ‘origin questions’ and putting energy into figuring out specific and actionable answers, rather than general useless ones.
This isn’t some weird complicated thing. It’s just first principles analysis, but you don’t stop going deeper when the questions get extremely tough to give specific, actionable answers to.
NEVER GIVE UP
For some concepts, doing this can take months or years of thinking. If you can’t come up with a specific answer, after a long time of bashing your head into the problem, don’t conclude the null hypothesis that there is no answer (this is a common antipattern, and it prevents fruitful long-term analysis of systems). Stay humble, it’s an advantage, you don’t have to conclude anything, and you shouldn’t conclude null hypotheses anyways.
What are ‘origin questions’?
Origin questions are any question that probes into the nature of there a thing came from. “Why”, “how”, “what”, etc.
They can be very ‘outside of the box’. For example, you could consider the sqrt function to be an origin question (“what x what = this?”). And, in fact, asking it can produce some extremely tough questions that yield extremely useful results when answered in specifics. For example, asking the sqrt question of negative numbers leads to ‘escaping’ the reals and discover a new fundamental – complex numbers.
This is why you shouldnt assume the null hypothesis that there is no answer (‘negative numbers have no square root! how could they?’ ‘imaginary numbers dont exist’ etc) or conclude something general and useless (‘the sqrt of -1 is the thing you multiply by itself to get -1’) but rather bang your head against the question for as long as it takes to produce a specific and useful answer.
This is similar to ‘5 whys analysis’ in industrial engineering, except with an emphasis on high specificity at each layer of ‘why’, and without stopping until you’ve found extremely useful, actionable information.
Psychology example
Metacognition is a fancy term that just means thinking about your own thoughts. In my experience it’s one of the most useful and important concepts in psychology.
Zeroth principle analysis, combined with metacognition, is an INCREDIBLY powerful tool for solving most of your mind-based problems (which are a large portion of your problems in life, because your mind is a fundamental of your life).
Practicing paying attention to your own thoughts will improve your ability to understand them.
As you practice metacognition, you’ll often notice interesting phenomena you don’t understand. For example, maybe every time you come home you feel sad, or maybe you have a hard time starting homework, but after you start it’s incredibly easy.
Ask yourself why this phenomenon happens, and keep thinking about why it happens until you have an extremely specific answer that leads to leveragable information.
At first, many questions of this nature seem impossible, like trying to scale a perfectly flat cliff face. However, after putting your mind to it for long enough, you eventually make footholds. It’s like beating your fist into the cliff wall for a few months or years until theres a slight dent that allows you to plant your foot into the wall of the cliff.
For this, and any other long-term endeavor with high payoff, it helps to imagine the giant pot of gold at the top of the cliff face. “If I understand why I have social anxiety, or procrastination, or whatever, I’ll be able to solve it, and my life will be so different, I’ll have xyz and abc and yadda yadda yadda.” Horses won’t chase the carrot if they can’t see it. If they can see it, smell it, taste it, and they’re hungry, they’ll do anything to get it.
Chess example
A fundamental of chess is controlling the center, usually by putting your pawns in the center. Why? because it works very effectively. Why does it work effectively? Because it has the highest restriction-of-opponent-ness per move of any moves you could make in the beginning. Why is restricting your opponent effective? Because then you can do what you want, while they are tied up/slow. Why does that matter? because your plan is directly opposed to theirs, and so the d(prob_winning)/d(moves) becomes positive if you maintain a standard speed of plan execution. Conclusion: control the center to restrict your opponent, making the your relative velocity of winning positive by slowing them down. (specific, actionable information)
Continuing from there to find even more actionable information: if you are too slow (because you make bad moves, or because your opponent’s defense slows you too much), your slowed-down opponent can match your speed, or even overtake you, so you have more leeway on being slow, but should still avoid it. This relative-plan-progress-velocity concept also means that you don’t want to allow your opponent to ‘cut the ropes’ on being restricted. For example if you are slowly constricting them, moving your pieces in for the attack when they are low on space, don’t allow them to trade off pawns and open the center, thus freeing themselves.
- This explains why you want to attack on the side where you have space. If I have space on the kingside, it means my opponent is tied up on their kingside, and that’s where I have the advantage. If your opponent’s legs are tied up, attack there. If your opponent’s hands are tied up, attack there. This creates deadly threats, which now not only binds your opponent’s pieces physically but also binds their attention mentally, as they have to focus on addressing the threat.
Other techniques for finding more fundamentals?
There are probably more techniques out there that I am unaware of. If you know of more, or find more, DM me on X or comment here (I see every DM/comment). Its probably possible to apply these techniques to the fundamentals of finding hidden fundamentals, but I haven’t focused enough on that problem to have come up with more specific actionable information.
(Tangent: This kind of meta-stuff sounds esoteric and useless, but often I’ve found that if you put in the energy to come up with a specific way to do it, rather than settling for a general-level understanding, you can actually pull them off. Examples that seemed BS at first but ended up becoming extremely useful after months/years of thought: ‘getting good at decision making in general’ and ‘learning how to learn’)
Raise the temperature
Temperature is a term used in ML that you can think of as ‘randomness’. I believe it comes from simulated annealing, which is an optimization method that attempts to find global solutions to problems by slowly lowering the ‘temperature’ to reduce probability of accepting changes that move away from the goal.
Action produces information. Doing new things leads to new information that can break you out of plateaus. For something like chess or bjj, try playing in a different style than normal. For programming, try new technologies that you normally try to avoid using. Etc.
Some things in life tend to lower your propensity to do new things. For me personally, drinking caffeine tends to do this. Whenever I stop drinking caffeine for a few days, I feel less constrained in my decision making. That may just be a thing for me personally, but there’s probably stuff that changes your temperature – maybe exercise, or a cold shower, or sleeping more.
If you found this helpful, you can follow me on X @ dnbt777. I post my articles there. I also post about ML, learning, and building things.
Great article!