1.1 Neurons and Signal Transmission#

Note: If you find this difficult to understand, feel free to skip it. Section 1.1 basically explains the most basic neural mechanisms. Theoretically, you can go straight to section 1.2.

If you zoom in on that image of neurons, you’ll find that it looks very much like a tree:

• Dendrites (canopy): Responsible for receiving information from other neurons.
• Axon (trunk): Responsible for transmitting information within a neuron; it is a long output cable.
• Axon terminal (root): The structure responsible for sending information to the next neuron.

When a neuron is activated, it generates a weak electrical signal that travels rapidly along the long axon (the trunk) to its terminal. The terminal connects to the next neuron, and the process repeats until the last neuron—which then produces an action or secretes a hormone.

However, the connection between two neurons is not seamless. If we magnify the connection (as shown in the image below), we can see a tiny gap in the middle, which we call a “synapse”.

The electrical signal doesn’t travel directly to the next neuron; instead, it’s converted into a chemical signal and transmitted to the next neuron. The next neuron then converts the chemical signal back into an electrical signal. These chemical signals are called neurotransmitters, and they determine whether the electrical potential transmitted to the next neuron is positive or negative, and the strength of the signal. The entire process occurring in the synapse can be roughly divided into the following four steps:

1. Vesicle storage: In the axon terminals of upstream neurons, neurotransmitters are neatly encased in vesicles, awaiting commands.
2. Signal release: When an electrical signal is received, these vesicles move to the edge and release the encapsulated neurotransmitters into the synaptic cleft.
3. Precise matching (receptors): These chemical messengers swim across the interneuronal space, but that’s not the end. Specific receptors grow on the dendritic surfaces of downstream neurons. Neurotransmitters must attach precisely to these receptors, like a key into a lock, opening a channel for free positive or negative ions to enter the next neuron. Only when a match is successful and ions successfully enter will the next neuron be activated and generate a new electrical signal.
4. Cleaning up the battlefield (enzymes): After the signal transmission is completed, the excess neurotransmitters must be cleared or recycled. Specialized enzymes will work together to process these neurotransmitters that have completed their tasks.

By combining the conduction within neurons and between synapses, we can roughly construct a “brain,” but this brain currently only mechanically transmits signals, showing no signs of plasticity. In this case, our brains may never develop intelligence—what enables intelligence in the brain is the reshaping of these connections, possessing the physical ability to change its strength according to usage frequency—this is neuroplasticity.

1.2 Neuroplasticity#

It’s time to understand neuroplasticity, which occurs at any stage of life, and that this plasticity is not one-way (or not always beneficial). Sometimes you shape the wrong circuit, and sometimes you cut off neurons that you don’t use.

When you first try to learn a new concept (like memorizing an unfamiliar word), a specific neuron A sends a signal to neuron B. Initially, this pathway is unfamiliar and inefficient; signal transmission is fraught with resistance, and there may be very few connections. However, as you repeatedly repeat the word, neuron A repeatedly and frequently activates neuron B. This continuous repetition leads to changes in the related activated neurons. Specifically:

• Myelination: Strengthening existing connections. Neuronal axons are wrapped layer by layer with a lipid-rich substance called myelin. This substance can significantly increase the speed of electrical signal conduction in neurons.
• New synapses: establishing new connections. The dendrites of neurons branch and grow, producing new dendritic spines. These newly formed tentacles explore their surroundings, seeking other axons and establishing entirely new connections that have never existed before.
• Neurogenesis: the formation of new neurons. The germinal layer of the brain generates entirely new neurons through stem cell differentiation.

Ultimately, the brain optimizes into an extremely efficient network, constantly reinforcing the skills you use daily, making you increasingly proficient in them. Examples include social skills and motor skills. Of course, the brain also forgets. The other side of neuroplasticity is synaptic pruning—meaning unused skills are gradually forgotten. Infancy and adolescence are marked by continuous and efficient synaptic pruning, a process that slows down in adulthood. However, the brain continues to optimize this network formed during adolescence, an optimization that continues until death.

Regarding neuroplasticity, there is a frequently cited example—taxi drivers, whose hippocampal systems are enlarged due to memory maps:

Taxi drivers rely on cognitive spatial maps for their livelihood, and a prominent study showed that London taxi drivers had larger hippocampal areas in this region. Furthermore, a follow-up study compared hippocampal imaging before and after years of grueling work and preparation for the London taxi driver ‘s license exam (described by the New York Times as the world’s toughest exam). After this process, the hippocampus enlarged—but only those who passed the exam did.

1.3 Sensitivity - The Best Window for Learning#

We’ve observed that children learn languages ​​incredibly quickly, while the brain struggles to absorb new information as adults. This isn’t limited to language; children demonstrate remarkable learning abilities in almost every area. Many adults regret not having learned more at the right time. This is indeed true. While our neurons change with our daily actions, these adjustments are ultimately subtle. In many brain regions, plasticity reaches its peak only within a limited timeframe, known as a “sensitive period.” This period is activated and peaks in early childhood, gradually diminishing with age. For example, sensory areas experience increased plasticity around 1-2 years of age, followed by a gradual decline. The longest and latest sensitive period occurs in the frontal cortex, an area that begins developing during puberty and continues until around age 20.

One of the best examples to explain sensitive periods comes from our mastery of the sounds of our native language—every child is born with the ability to quickly distinguish all the phonemes of any language. Regardless of where they are born or their genetic background, they only need to immerse themselves in a language environment for a few months (whether it’s monolingual, bilingual, or even trilingual) for their hearing to adapt to the phonological system of the surrounding languages. Adults, on the other hand, can hardly do this. For example, most Chinese people end up speaking Chinglish their entire lives; Japanese speakers who live in English-speaking countries their whole lives will not be able to distinguish the sounds of R and L; and people from some countries will be unable to pronounce the retroflex consonants of Indian languages. Compared to children, an adult will need to expend tremendous effort to regain the ability to distinguish the sounds of a foreign language.

The examples above demonstrate the importance of sensitive periods. However, the very reason a period is sensitive is because, although the corresponding learning ability may diminish after the sensitive period, it doesn’t disappear, and the degree of diminishment varies from person to person . We also see many people who missed the critical period but still learned English through considerable effort.

For example, experiments have shown that later-stage training can still rebuild language mastery (though it’s not as easy as during the sensitive period). In this study, they trained Japanese listeners to recognize the R and L sounds in English. The results showed that three months after completing perceptual training, the Japanese trainees maintained good performance on the perceptual recognition task. Furthermore, native English-speaking American listeners conducted perceptual assessments of the Japanese trainees’ speech output before and after training, as well as during a three- month follow-up period. The results indicated that the trainees maintained long-term improvement in the overall quality, recognizability, and intelligibility of their English /r/-/l/ pronunciations.

1.4 Nutrition, Exercise and Sleep#

It is certain that significant neural remodeling occurs during learning. However, any remodeling requires a certain amount of time, inevitably accompanied by high energy consumption. Such high energy consumption necessitates ample nutrition and high-quality rest, which are essentially the foundation of diet, sleep, and exercise. Yet, modern people generally neglect these factors—thus sowing the seeds of a long-term hidden danger.

Let’s first discuss the often-overlooked nutrients, which are essential for a developing brain. One such substance that has been severely neglected is Omega-3 (derived from olive oil, seafood, etc.) – a 2013 paper studied it .

• Omega-3 is an essential unsaturated fatty acid. Unfortunately, mammals cannot synthesize it themselves and must obtain it from food or supplements.
• They are involved in a variety of physiological processes and have been reported to potentially help protect neurons in neurological diseases, such as aging or damaged neurons and Alzheimer’s disease. Their effects on cognitive and behavioral function, as well as on a variety of neurological and psychiatric disorders, have also been confirmed.

What’s relatively easy to replenish are the nutrients we lack, but modern people not only face nutritional deficiencies but also the problem of excessive nutrient intake. The modern food industry leads to our excessive consumption of sugar and fat. A 2002 research paper indicated that a high-fat, refined-sugar diet reduces brain-derived neurotrophic factor (BDNF), neuronal plasticity, and learning ability in the hippocampus.

Not only are we severely imbalanced in our nutrition, but we also suffer from a serious lack of daily physical activity—a significant factor affecting neuroplasticity. A 2014 paper specifically investigated this point .

• Exercise has a positive impact on cognitive function and can increase the level of brain-derived neurotrophic factor (BDNF), an important neurotrophic factor.
• Physical exercise is closely associated with a reduction in various physical and mental illnesses. Extensive evidence suggests that physical exercise not only reduces the incidence of cardiovascular disease, colon cancer, breast cancer, and obesity, but also lowers the incidence of diseases such as Alzheimer’s disease, depression, and anxiety.
• Multiple cross-sectional and longitudinal studies have confirmed the association between being overweight and poor academic performance. Aerobic capacity is also associated with cognitive ability and academic achievement.

Finally, regarding sleep research, although there is a serious imbalance in diet and exercise, at least sleep is necessary, but the quality of sleep is hard to describe—which is also a huge problem. Here is a paper from 2014 and 2022, which mentions 7 [ 8 ]:

• Sleep is considered to play an essential role in brain plasticity.
• Sufficient blood flow to the brain provides oxygen to active neurons and removes metabolic waste, thereby promoting neuroplasticity.
• Sleep duration also affects the process of voluntary neural plasticity, as evidenced by the effects of sleep deprivation on task-related cerebral blood flow and cognitive function.

1.5 Summary#

Learning alters neural networks: a pathway is repeatedly activated, increasing synaptic efficiency, accelerating myelination and transmission, and even leading to new dendritic spines and connections; conversely, pathways that are not used for a long time are weakened or even disappear during “synaptic pruning.” This remodeling continues throughout life, but there are “sensitive periods” in different brain regions. However, adults do not lose their learning ability; they simply usually require higher-quality training, more repetition, and longer consolidation periods. Finally, neural remodeling is an energy-intensive and time-consuming biological process that requires us to provide a favorable environment for it.

4.1 Chunking and Long-Term Models Help Experts “Remember More”#

There is a classic case study in this field—it was discovered that chess masters can often memorize complex piece positions at a glance, while novices often cannot. In the early 1970s, researchers began studying this to understand how chess grandmasters could remember piece positions so accurately.

Researchers posed a simple question: Do chess grandmasters recall the position of every single piece, or do they actually only remember the overall board position and treat the individual pieces as part of a larger whole? They conducted a simple yet effective experiment. They set up two chessboards and tested national-level chess players (i.e., chess grandmasters), intermediate-level players, and beginners. On one board, a real game was played; on the other, pieces were simply arranged in a more haphazard manner.

When a chess grandmaster sees a real chess game, after five minutes of study, they can remember the positions of about two-thirds of the pieces, while a novice can only remember about four. When they see a board with randomly placed pieces, both intermediate and advanced players (novices are still at a disadvantage) can only remember the positions of two or three pieces. At this point, the advantage of experienced players disappears. For a grandmaster, upon seeing a real chess game, the brain quickly invokes prior models for prediction. The positions of the pieces seen highly match the brain’s predictions. Therefore, the brain doesn’t need to record the coordinates of every piece; it only needs to record the information “this is a variant of the Sicilian Defense” and then perform a little deduction. 24

A similar experiment can be conducted again now. Since everyone reading this article is a master of Chinese, please try to remember:

• There are many people among them, but I am not one of them.

Take a few seconds to look at these words, then close your eyes and try to recall the order in which they are written.

This task is not easy. Although you are very familiar with these Chinese characters, their random arrangement and lack of grammatical structure and semantic connections make it impossible to predict the next piece of information. Therefore, you often only remember two or three, or even get completely confused. Of course, some people might try to use a trick, such as making up a homonym or a mnemonic—which is certainly effective, but you definitely won’t find the previous line of characters easy to remember. The next set of materials is the opposite; you can probably remember them easily in a few seconds.

Now please look at another set of materials:

• We are studying the working mechanisms of human memory.

This time, even with significantly more words, you’ll find yourself able to repeat it almost entirely. This is because when your brain reads “we,” it automatically predicts, based on grammatical conventions, that it might be followed by “is” or “thinks.” When your eyes see “is,” the visual input perfectly matches the prediction, and your brain hardly needs to expend any energy processing it. However, in the first example, you could only struggle to remember individual words.

Based on the above experiments, we found that the difference between chess masters and novices lies not in working memory capacity, but in the fact that masters possess a large number of “chess board diagrams” in their long-term memory. Masters can automatically integrate the positions of multiple pieces into a few meaningful memory units, thus making more complex predictions. Novices cannot do this. However, when faced with a chaotic chessboard, their performance is almost identical, much like how we Chinese experts try to memorize our first set of material. Therefore, we can conclude that the prerequisite for predicting complex things is building a large number of “chunks” (i.e., predictive models) in memory. The essence of chunking is compressing a large amount of uncertainty into a simple predictive unit, thereby greatly reducing the computational power required for the brain to process prediction biases in real time.

4.2 Sources of cognitive load#

If you feel mentally overloaded (“brain-burning”) when performing complex deductions, this means in neuroscience that your brain is processing excessive predictive bias. We can think of cognitive load as the systemic resources the brain consumes to eliminate “unexpected” and “uncertain” events.

So, where does cognitive load come from? Researchers have categorized these loads into two aspects based on their sources:

• External loads—ineffective biases caused by noise interference. These have nothing to do with what you’re learning; they’re purely related to the way the material is arranged and the level of annotation. For example, a classical Chinese text, but with annotations for every single word in every paragraph and color illustrations, makes what was originally a simple article complex. Or a product manual with too many technical terms (like asking why I need to know the materials science names; just tell me what it does, like “this is number 1,” not “expansion screw”). Dealing with these meaningless prediction biases wastes valuable mental energy.
• Intrinsic load—the necessary bias required for model reconstruction. For example, 2. 2 ​ It’s harder than $1+1$ because 2 2 ​ The concepts involved (irrational numbers, square roots) haven’t yet formed a complete predictive model in your brain. You need to mobilize resources to understand them; this predictive bias caused by “new knowledge” is an inevitable part of learning.

Okay, now:

Therefore, we can conclude that when external load (ineffective information presentation) takes up too much space, the space left for internal load (understanding the core logic) becomes smaller. This is why, even if we are of normal intelligence, we feel like our “brain can’t work” when faced with poorly formatted and verbose textbooks.

In the next two sections, we will explore how to reduce external load by “optimizing presentation” and how to deal with internal load by “deconstructing information”.

4.3 Reduce external load - eliminate redundancy#

External load is generally related to the way learning materials are presented. Often we feel that something that could be explained in one sentence is stretched out in eight or ten sentences in textbooks, leaving us feeling like we don’t understand it at all after reading it. Here’s a 1993 study on elementary school students’ origami tasks that effectively explored the influence of related factors on cognitive load. 25

The first experiment tested folding a circular piece of paper into an isosceles triangle. In this task, they assigned different cognitive materials to groups A and B:

• Group A (Illustrated Group): Provides only self-explanatory illustrations, accompanied by a very small number of arrows and words.

• Group B (Redundant Group): Same diagram, but with full text description.

During the testing phase, the illustrated group significantly outperformed the redundant group. Subsequent experiments further confirmed that using images alone was far superior to “image + text” or “plain text”.

Therefore, we can conclude that when images are sufficient to illustrate a point, additional textual descriptions may become a distraction.

Of course, subsequent experiments in the paper further illustrate the inverse benefits of redundant information on comprehension tasks. The first experiment on this was the effect of multiple views—one group of students only saw the front view, while the other group was asked to see the back view of the origami in addition to the front view. The results showed that the group without the back view completed the task in a significantly shorter time during the test.

Another experiment differentiated the placement of instructions. In one group, the instruction booklet was placed on the left, and the paper slip on the right. Students had to constantly switch their gaze between the two. In the other group, the instructions (lines, arrows, numbers) were printed directly on the paper slip to be folded. The results showed that the group with the embedded instructions significantly outperformed the other groups in both the learning and testing phases.

This experiment allows us to be almost 100% certain that external load exists, and the way materials are presented affects the degree of load. When an image can already enable the brain to accurately predict the next action, additional textual descriptions become interference signals. The brain is forced to divert its attention to process the text, trying to figure out “Is this text saying something else?”, only to find that the text and the image are saying the same thing. This process of repeated verification generates unnecessary costs in handling prediction bias.

Of course, the subjects of the above experiment were primary school students, which might be overlooked by us adults. Let’s now look at another research case in online anatomy education. A quasi-experimental study at the Iranian University of Medical Sciences (IUMS) involving 104 basic medical students further validated this physical logic. 26

Researchers divided students into an intervention group and a control group, both receiving instruction in digestive system anatomy on the same Big Blue Button platform. The intervention group’s teaching materials were optimized strictly according to cognitive load theory, eliminating unnecessary colors, lines, noise, and irrelevant content from the screen. Auditory and visual channels were simultaneously engaged, redundant and repetitive text was avoided, and images were used in conjunction with verbal explanations. Data analysis showed no significant difference in academic engagement between the two groups before the intervention. However, after the intervention, the group following cognitive load theory showed a significant improvement in academic engagement scores.

This demonstrates that even in highly complex fields, reducing external burdens remains highly beneficial for learning materials. By optimizing presentation methods (such as reducing redundancy and integrating text and graphics), we can eliminate prediction biases irrelevant to the learning objectives, allowing the brain to focus all its computational power on building the core model.

4.4 Reduce Internal Load - Divide Complexity#

The inherent complexity of knowledge is something we cannot eliminate. For example, when faced with a complex concept like Python’s For loop, if you try to understand variables, sequences, indentation, and iteration logic all at once, your brain will instantly face a massive and utter failure in prediction—because there are too many unknown variables, causing the old model to completely fail and making no effective predictions. Therefore, what we need is to learn step by step, first forming chunks and then learning the whole. We need to first understand what an iterator is before looking at what a For loop is; the corresponding method is called—segmenting material.

A 2024 paper investigated the impact of segmented material in English language teaching. 27 It suggests that the most effective weapon against high-load material is “segmentation.” The study found that breaking down highly concentrated PPT slides (integrated groups) into 10-page, more dispersed PPT slides (segmented groups) significantly improved learning outcomes. The paper also analyzed the logic behind segmenting knowledge points, arguing that segmentation separates these points, giving working memory a chunking opportunity to memorize information, allowing the brain to remember less information simultaneously when completing the current unit. Secondly, segmenting material into small fragments allows us to learn the names and characteristics of individual symbols first, and then their interaction logic, when faced with extremely complex systems. This helps control the magnitude of prediction bias.

Next, let’s take learning Python’s for loop as an example. An inefficient way to divide it is to first talk about variables, then lists, then syntax, and finally the loop logic. Although it seems to be separated, learners still need to call all the information at the same time when they actually write code, and the difficulty of prediction has not decreased compared to the previous approach.

A more reasonable way to divide the data is by using cognitive units as boundaries:

Phase 1 (Building Sequence Intuition): Only print(1) , print(2) , print(3) are shown, and then for x in [1,2,3] is introduced.

• Prediction goal: To help the brain build a simple model of “Oh, this thing automatically helps me count.”
• Load status: Only corrects for prediction bias regarding “repetition”.

Phase Two (Introducing Variable Placeholders): Demonstrating that for x and for y have the same effect.

• Prediction objective: Update the model – “The original name is not important; it is just a code name.”
• Load status: Only corrects prediction bias regarding “symbol naming”.

Phase 3 (Syntax and Indentation): Finally, we will explain the rules of colons and indentation.

1
for i in range(5):
2
    print(i)

Prediction objective: Refined model – “Only indented code will be looped.”

The essence of segmenting material is to avoid exposing the brain to too many prediction biases simultaneously. We break down a large bias into multiple smaller biases. At each step, the brain only needs to process a small unexpected event and update the model a tiny bit.

4.5 Summary#

The so-called “complexity” simply stems from your brain’s lack of a corresponding prior model, causing predictions to completely fail, and working memory to be overwhelmed by massive prediction biases. What we need to do is reduce noise interference by optimizing the presentation (reducing external load) and guide the brain to gradually correct the model by breaking it down into chunks (reducing internal load). When you can subconsciously and naturally predict the next line of code or the next step in a math problem, you have successfully created a complex yet accurate predictive model.

5.1 Starting Point - Error Detection#

Before discussing the two types of learning, it’s necessary to address the prerequisites for learning. A common misconception is that people learn simply by making mistakes. The opposite is true—the vast majority of errors are systematically ignored by the brain. As mentioned earlier in section 3.4, regarding the conditions for model updates, we only begin to learn when we encounter prediction errors with significant subjective costs. Note the word “subjective”—it varies from person to person and is influenced by various environmental factors. Therefore, how we notice errors is also worth discussing.

Of course, this isn’t something people pay attention to, and schools never teach you this. Most students passively discover their mistakes during their daily learning process. For example, the path we take in learning mathematics—first learning addition, subtraction, multiplication, and division, then moving on to more complex coordinate systems and calculus, etc. As long as you follow this path, you will naturally discover mistakes and learn new knowledge. This path doesn’t require us to actively discover mistakes; we will naturally pay attention to these mistakes because of exams.

So, what about outside of school?

Generally, in the real world without “syllabi” and “standard answers,” the brain not only doesn’t actively seek out errors, but instead activates a defense mechanism called “confirmation bias.” When reality doesn’t match our internal models, the brain tends to distort perception to maintain the old model rather than overturn it. For example, a tennis beginner might attribute a missed shot to “too much wind” or “a bad racket,” rather than “my hitting motion model is wrong.” This mechanism protects our confidence but hinders learning. 28

Besides automatically maintaining old models, real-world errors are often difficult to trace back to their origins. For example, in today’s society, results are frequently delayed; a mistake made today may only lead to consequences six months later. The causal chain is too long, making it difficult for the brain to attribute errors to specific models. Furthermore, multiple causes may lead to a single effect, and we often struggle to grasp the key points, such as deteriorating relationships, work setbacks, or learning stagnation—these signals don’t provide clear answers like math problems.

To address these issues, here are some simple methods.

First, let’s address confirmation bias. It’s important to clarify that a 1990 study found that confirmation bias is generally caused by our emotions, with a slight added layer of blockage (the brain tends towards laziness). The solution is simple—maintain a belief that “I might be wrong” and “I love truth more than my teacher.” The next time you face a mistake, this reduces emotional blockage because you anticipate being wrong, reducing the intense need to protect your self-esteem or sense of security. It also provides a stronger motivation to seek truth, helping you combat your brain’s laziness. 28

Furthermore, we need to proactively gather information from the outside world. This mainly involves understanding the key conclusions of important disciplines, and even proactively delving into the progress of certain disciplines—these conclusions are often correct and can even overturn conventional wisdom. Essentially, each of these can help you uncover errors (just as this article’s foundation—the brain is a predictive machine)—and by understanding these conclusions, you can ensure your predictive models cover most of the necessary scenarios.

There doesn’t seem to be much research available on methods for detecting errors, so this article only presents two simple approaches, one of which is based on experience. More information may be available in the future, at which point I will update this article on error detection methods.

5.2 Imitation - The Lowest Cost of Learning#

In 99% of cases, when you face a difficult problem, you’re not the first person in history to solve it. When you don’t know why an apple falls to the ground, Newton has already provided the formula; when you don’t know how to cook, a recipe has already validated the steps. In these moments, the brain doesn’t need to reinvent the wheel; it only needs to perform one of the most efficient operations—model transfer.

This is known as “social learning” in neuroscience and evolutionary psychology. It refers to the rapid acquisition of existing skills and concepts through observation, imitation of others, or acquisition of knowledge from culture. Michael Tomasello aptly describes this mechanism as the “cultural ratchet effect”—each generation doesn’t have to start from scratch with trial and error; we, like a ratchet, lock in the wisdom of our predecessors, thus freeing up our energy to explore higher realms. 29

The neural mechanisms of social learning have received substantial research support. Scientists have discovered that the mirror neuron system provides the neural basis for imitative learning: when we observe others performing an action, the neurons in the brain associated with that action are activated in the same way as when we perform it ourselves. This “mental simulation” allows us to experience the behavior of others at a neural level without having to practice it ourselves, making it easier to replicate. Mirror neurons were first discovered in the 1990s by Italian neuroscientist Rizzolati and others, demonstrating the brain’s “empathic” reproduction function of others’ experiences. In terms of social learning theory, psychologist Albert Bandura proposed as early as the 20th century that humans can learn new behaviors by observing others (the famous Bobo doll experiment verified that children imitate aggressive behavior through observation). Bandura’s observational learning theory emphasizes that in many cases, learning does not require direct rewards or punishments; the demonstration of a role model is sufficient for the observer to learn the behavior.

The general steps of socialization learning include:

• The old model is considered wrong (as discussed in 5.1), and possible new model theories are sought.

• Learning new theories to quickly eliminate large amounts of structural errors

• The residual error of the learned new model is finely corrected through feedback.

• Solidify a stable new model during time and sleep.

Furthermore, it’s important to note that if the new theory found in this step is overly complex, please refer back to Chapter Four—at this point, we need to break down complex knowledge into simpler pieces, just like how a semester’s worth of material is divided into weeks, and then studied progressively in rounds. Ultimately, this will allow you to master the new theory.

The steps at this point are roughly as follows:

• The old model is considered wrong (as discussed in 5.1), and possible new model theories are sought.

• Learning the new theory block 1 allows for the rapid elimination of numerous structural errors.

• The residual error of the learned new model is finely corrected through feedback.

• Solidify a stable new model during time and sleep.

• Learn the new theory block 2 to quickly eliminate a large number of structural errors.

• The residual error of the learned new model is finely corrected through feedback.

• Solidify a stable new model during time and sleep.

• Learning New Theory Block 3

• ……

Next, we will discuss how to conduct social learning efficiently.

5.3 Methods for finding credible new theories#

Students don’t need to find new theories; they just need to read the textbooks.

It’s actually very simple, and everyone knows this method: find academic papers. Here, we’ll simply rank the credibility of the information sources:

Generally speaking, books, high-quality papers, systematic meta-analysis of papers, and academic guides are the most reliable sources; there is basically no need to look at any other information sources.

For example, if you want to study whether intermittent fasting is effective, first search for “Intermittent fasting meta-analysis” . Read the reviews to see what they say; this can help you avoid being misled by a few extreme experiments. Then search for relevant highly cited papers, or whether there are any systematic books (the books must contain a large number of cited papers, not just the author rambling on).

Of course, I don’t intend to condemn all science popularization creators here. Some creators do achieve highly credible updates, such as Veritasium—the most typical characteristic of which is that they include academic paper citations at the end of the article/introduction or video ending. This greatly increases the credibility of their work, and often includes their own statistical analysis.

Another point to note is that the “most reliable source” varies slightly across different fields, for example:

• Mathematics/Logic: Peer-reviewed paper + formal proof
• Medicine/Public Health: Systematic reviews/guidelines are generally more valuable than single papers.
• Economics/Social Sciences/Psychology: Identification strategies, reproducibility, and external validity are particularly critical (psychology has a well-known reproducibility crisis, namely, the discovery that some psychological experiments cannot be reproduced).
• Engineering/Computer Science: Reproducible experiments, standards, benchmarks, and open-source implementations are very important.
• Pseudoscience: Don’t believe it! If someone says that astrology can predict the future, they are definitely just trying to make money off you.

5.4 Imitation - Rapidly Eliminating Large Amounts of Errors#

Once you’ve successfully identified a new theory to learn, what should you do? Generally, we can master a concept with a suitable workload in a short time, except for a few minor flaws. This section focuses on how to quickly grasp the general content of a theoretical model, thereby gaining a certain level of application ability.

5.5 Imitation - Fine Correction of Residual Errors#

After quickly eliminating a large number of errors, we need to correct the small errors that we can’t perceive even after repeated readings. —Yes, repeated readings will inevitably cause us to overlook some things, and these overlooked things may manifest in exam scores.

5.6 Imitation-Consolidation#

We may remember the theory in the short term, but we will inevitably forget it gradually. Therefore, to remember it for a long time, we must repeatedly retrieve it in the future.

5.7 Imitation - Summary#

This chapter redefines “learning” as a more engineered process: continuously optimizing internal models. First, errors are identified; then, correct structures are transferred through imitation; attention and deep processing improve comprehension efficiency; testing, interleaving, and feedback refine the process; and finally, interval retrieval and sleep solidify the knowledge. We are fortunate to live within the accumulated wisdom of human civilization. Most of the time, we don’t need to “reinvent the wheel” from scratch; instead, we can efficiently transfer the wisdom of our predecessors through social learning (imitation).

Final review cards:#