After mastering the basic rules of a knowledge point (for example, the subjunctive mood in a language or the concept of calculus in mathematics), one typically believes they can apply it to solve problems through practice and reflection. However, in practical applications or high-stakes assessments, you often fail to recall this knowledge point, confuse it with other concepts, or forget its crucial variations. These phenomena all indicate that your “certainty” in this knowledge is insufficient. If many key points within a knowledge system suffer from this issue, you must begin to enhance the certainty of the entire system.
Human civilization has now accumulated countless foundational pieces of knowledge. At the application level, you neither need nor have the time to question every axiom. What you need is to accept them as self-evident premises and commit them firmly to memory.
For instance, in Euclidean geometry, “the shortest distance between two points is a straight line” is a fundamental axiom. When applying this system to solve problems, any doubt about it is counterproductive and inefficient. You must believe in it without question, and in any scenario, immediately recognize that the shortest path between two points is a line. While challenging axioms is what drives the frontiers of science, efficiently solving problems within a given framework requires absolute faith in its foundations.
Therefore, from the very beginning of learning any knowledge system, you must be convinced from your core that you can master it completely. For every fundamental concept, definition, and rule, you must achieve precise memory and absolute trust. In practice, deliberately trace problems back to these foundational points. In this way, with every problem you solve, you deepen your conviction in these fundamental principles, rather than merely memorizing isolated techniques.
Believe You Can Achieve Mastery
Learning is a gradual process, necessarily moving from incomprehension to understanding, from imitation to creation, and from error to correctness. Even if your initial progress is slow or you face setbacks in assessments, there is no need for anxiety. You must believe that you will ultimately achieve mastery. From the moment you begin learning any knowledge system, or any single point within it, you must resolve to master it completely. No matter how daunting the challenge, you must believe you can conquer it.
Sometimes, even when you possess all the external conditions for success—the right methods, sufficient knowledge, a clear mind, and ample time—you still fall short of top-tier performance. This often stems from a lack of internal certainty: in your subconscious, you may not truly believe you can be the best.
Increasing Knowledge Certainty is a Gradual Process
As your learning deepens, the requirements for knowledge certainty should be dynamically adjusted. In the beginner stage, to quickly build a complete knowledge framework and fill in gaps, it can be appropriate to relax the certainty requirement for each point. As you advance to the intermediate and advanced stages, you should deliberately narrow your scope of learning, dedicating sufficient time and energy to increasing the certainty of your core knowledge. This is a process of polishing ambiguous cognition into precise understanding, of transforming internal doubt into intrinsic power. It requires patience and calm.
Methods for Increasing Knowledge Certainty
Depth Over Breadth The acquisition of knowledge values depth over breadth. For a high-quality, foundational text, the more times you study it, the higher the certainty of that knowledge will become in your mind. A superficial reading of many books can easily lead to your energy being scattered on trivial details or unimportant techniques. More dangerously, if the material you read contains errors that you fail to detect, a seed of doubt will be planted in your mind. This is one of the root causes of indecision in critical moments.
A Clear Framework and a Simplified System The clearer your overall knowledge framework and the more simplified its system, the stronger its internal certainty. A good mentor or expert can articulate a complex knowledge system with clarity and comprehensiveness, thereby greatly assisting you in building knowledge certainty.
Absolute Trust in Fundamental Concepts The axioms of mathematics, the laws of physics, the established facts of history, the principles of philosophy—these are the distilled essences of truth, refined from countless trials and errors. You must believe in them without question and commit them to memory with precision. This will save you from wasting energy on misguided paths. On this foundation, use practice and reflection to master their applications and correct any deviations in your understanding. Ultimately, through repeated memory, practice, and reflection, your trust will sublimate into unshakable conviction, and knowledge certainty will be achieved.
Precise Memory For the key elements in any field—the vocabulary and syntax of a language, the formulas and theorems of mathematics, the laws and models of physics, the factual timelines of history—you must strive for absolutely precise memory. The accuracy of your memory directly determines the level of your knowledge certainty.
Deliberate Attribution to Knowledge Points In the beginner and intermediate stages of learning, when solving any problem, you should deliberately and explicitly trace it back to one or more core knowledge points. This practice allows you to achieve flexible application with a minimal set of knowledge. As you enter the advanced stage, you can gradually weaken this deliberate connection to pursue faster reaction speeds and intuition.
The Drive of “Unyielding Drive” and “Sprint Power” The more “Unyielding Drive” you invest in solving difficult problems independently, the more easily your knowledge certainty will increase. No matter how complex the problem or how long it takes, you must have the resolve to see it through. In high-pressure, timed challenges, the more you can “sprint”—overcoming distress to complete more tasks—the faster your knowledge certainty will grow.
Deep Thinking and Systematic Review The depth of your thought determines the height of your certainty. The systematic nature of your review determines the stability of your certainty. After memorizing the basic concepts, you must constantly reflect on them during application, clarifying their various permutations and boundaries. Even when you encounter a new concept that is difficult to understand at first, commit it to memory anyway. In subsequent practice, continuously try to connect new problems to it. Over time, you will naturally internalize it.
Validation Through Practice and Experimentation For empirical sciences like physics, chemistry, and engineering, hands-on experimentation is one of the best ways to increase knowledge certainty. A physics student might stagnate in theoretical study, but after personally completing the relevant experiments in a lab, abstract concepts instantly become tangible and concrete. The laws in the textbook are no longer just symbols, but touchable descriptions of the real world. The certainty this experience provides is incomparable to that from theoretical learning alone.
The Power of Osmosis For advanced learners, the increase in knowledge certainty sometimes happens effortlessly. When a person has great passion for a subject and can maintain a relaxed, joyful state of mind with high mental clarity, the internalization of knowledge occurs naturally. This is typically built upon a foundation of long-term accumulation and solid fundamentals.
Extreme Selection and Practice For subjects you find uninteresting but must master, instead of broad exposure, adopt a strategy of “Extreme Selection and Practice” or “Extreme Selection and Memorization.” Select the most central, representative examples and materials, and engage in the highest intensity of repetitive training and memorization. This method forcibly builds robust neural connections and effectively increases certainty.
Constant Self-Suggestion Throughout your learning process, constantly give yourself mental suggestions: strive for accuracy, strive for precision. Cultivate the most rigorous habits of mind. Gradually, you will feel your thinking become like a sharp blade—effortless and exact.
The Foundation of Mind and Body When you find that learning methods alone are insufficient to increase your knowledge certainty, you must look to the source: your mindset, your physical condition, and your overall state of being. The essence of learning is the ability to focus your mental and physical energy on the cognitive process. The stronger your self-confidence, the greater your “Unyielding Drive,” the calmer your mind, and the clearer your thoughts, the higher your knowledge certainty will be. Therefore, optimizing your foundational mind-body state through physical exercise, mindfulness, and a positive mindset is the ultimate path to increasing knowledge certainty.