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Simple Formula

First, there is a simple formula, similar to Newton's second law: Force = Mass × Acceleration.

If there were such a wealth formula in the investment field, making money would be simple. But don't forget that capital markets are often zero-sum games, or even negative-sum games. Easy money, like the moon in the water or flowers in the mirror, is just a beautiful illusion.

Table Formula

Edward Thorp is the most famous gambler in America and later became the father of quantitative hedge funds. The winning strategy he proposed for blackjack is based on a table of about 10×30, which corresponds to different calling, doubling, and splitting strategies based on various combinations of the dealer's card and the player's cards.

This book tells his story. He was originally a math PhD in college but became fascinated with casino strategies. He wrote his algorithm as a mathematical paper titled "The Winning Strategy for Blackjack" (later published as the bestseller "Beat the Dealer," which sold over a million copies, and American casinos changed their rules because of the book's influence). Thorp wanted to publish this research in the prestigious Proceedings of the National Academy of Sciences, but only articles recommended by members of the National Academy of Sciences could be selected for this journal. Among the mathematicians at MIT, there was only one member of the National Academy of Sciences, the famous Claude Shannon. It was a cold afternoon in November 1960. Before Thorp entered the room, the secretary reminded him that Shannon could only spare a few minutes to talk to him because Shannon wouldn't spend time on topics he wasn't interested in. Unexpectedly, the renowned mathematician was pulled into Thorp's research and not only agreed to help but also agreed to collaborate on building a roulette prediction machine for research.

Later, while researching the distribution of gambling funds at Bell Labs, managed by Shannon, a physicist named Kelly invented a mathematical gambling system that helped them solve this problem. Kelly's gambling system is known as the "Kelly Criterion," which can be applied to any form of favorable gambling activity to maximize returns.

The Kelly Criterion is a mathematical formula used to determine how to optimally allocate funds among multiple investment or gambling opportunities to maximize long-term capital growth. It helps investors or gamblers determine the best betting proportion in each decision by considering the probability of winning, the odds, and the capital situation, thus avoiding over-speculation and preventing excessive conservatism.

The Formula of the Kelly Criterion#

The basic formula of the Kelly Criterion is:

[
f^* = \frac{bp - q}{b}
]

Where:

• ( f^* ) is the suggested proportion of funds to bet (i.e., the percentage of capital).
• ( b ) is the odds, i.e., the return won for each unit bet (for example, odds of 3 mean that for every unit bet, 3 units will be won).
• ( p ) is the probability of winning.
• ( q ) is the probability of losing, i.e., ( q = 1 - p ).

Explanation#

• ( f^ )* represents the proportion of capital that should be bet.
• If ( f^ )* is a positive number, it indicates that one should invest or bet according to this proportion.
• If ( f^ )* is a negative number, it means that one should not invest or bet.
• The Kelly Criterion aims to maximize long-term capital growth rather than short-term returns.

Advantages of the Kelly Criterion#

1. Maximization of Long-Term Returns: The Kelly Criterion avoids excessive gambling or overly conservative investment behavior by appropriately allocating funds.
2. Avoiding Bankruptcy: Theoretically, investing or gambling according to the Kelly Criterion can prevent capital depletion, as it avoids excessive risk.
3. Self-Adjusting: The Kelly Criterion automatically adjusts fund allocation based on different probabilities and odds, allowing it to respond to various investment environments.

Disadvantages of the Kelly Criterion#

1. Difficulty in Accurately Estimating Probabilities: In practice, investors may find it challenging to accurately estimate winning probabilities and odds.
2. Short-Term Volatility Risk: Although the Kelly Criterion maximizes returns in the long term, it may experience significant volatility in the short term, requiring investors to have strong psychological resilience.
3. Complexity: For inexperienced investors, applying the Kelly Criterion may lead to misunderstandings, especially in situations involving multiple variables and uncertainties.

Practical Applications#

In fields such as stock markets, cryptocurrencies, foreign exchange, and sports betting, the Kelly Criterion is used to determine the proportion of funds to invest in each trade or bet. For example:

• If you estimate that a particular stock has a 60% probability of rising with odds of 2 (i.e., for every unit invested, 2 units will be returned), the Kelly Criterion tells you that the proportion of funds to invest should be:

[
f^* = \frac{2 \times 0.6 - 0.4}{2} = 0.4
]

That is, you should invest 40% of your capital.

Variants: Fractional Kelly#

Some investors choose to use a fractional form of the Kelly Criterion (such as half-Kelly) to reduce volatility. For example, if the full Kelly Criterion suggests investing 40% of capital, using half-Kelly would mean investing 20% of capital to reduce potential volatility and risk.

Summary#

The Kelly Criterion is a powerful fund management tool, especially suitable for long-term investments and high-frequency trading scenarios. It maximizes long-term capital growth through reasonable fund allocation. However, caution must be exercised in practical applications to ensure accurate estimation of relevant probabilities and odds, while also being psychologically prepared to endure potential short-term fluctuations.

Therefore, the key to the success of planning lies in confidentiality. Shannon told Thorp that an analysis showed that in the U.S., any two people could potentially be connected through three degrees of friendship [he was referring to the research of Ithiel de Sola Pool, a political scientist at MIT in the 1950s, rather than the more famous research of Harvard psychologist Stanley Milgram in 1967, who discovered the "six degrees of separation" theory]. Shannon worried that the secret might have already leaked, perhaps from the initial discussion at UCLA. Some nodes in the social network could connect MIT scientists and Las Vegas casino owners to a gambler's downfall.

Shannon had another layer of concern. Even with a mathematical probability advantage, it is easy to lose money.

Professional gamblers must have an edge in "money management." This is a tricky yet crucial matter: how to maximize returns from favorable gambling opportunities. You might be the world's greatest poker player, backgammon player, or outcome predictor, but if you cannot manage your money, you will eventually go bankrupt. The sad truth is that almost every gambler ultimately faces bankruptcy.

The "Gambler's Ruin" graph (Figure 1-1) typically refers to a chart that describes the gradual losses of a gambler due to over-investment over a long gambling process. Such charts are generally used to vividly represent a gambler's journey from initial capital to eventual bankruptcy, reflecting the "negative expected value" characteristic of gambling.

The "Gambler's Ruin" phenomenon can be understood in the following aspects:

1. Capital Decline: The chart usually shows that over time, the gambler's capital gradually declines until bankruptcy occurs. Even if there are victories or profits in the short term, the gambler's capital will eventually be exhausted in the long run.

2. Volatility and Trends: The gambler's capital curve typically exhibits significant fluctuations, reflecting the unpredictable outcomes of gambling. Even if there are victories in the short term, due to the negative expected value of gambling, bankruptcy will ultimately occur in the long run.

3. Negative Expected Value of Gambling: This chart essentially reveals the probability and return structure of gambling games. In most cases, the rules of gambling are set to ensure that the casino (or game provider) profits in the long run, thus gamblers cannot avoid losses in long-term participation.

Specifically, the key characteristics of the Gambler's Ruin graph may include:

• Initial Capital: The chart typically shows the amount of funds the gambler starts with.
• Random Fluctuations: Indicates that the gambler will occasionally experience fluctuations or short-term victories during the gambling process.
• Gradual Decline: Over time, the funds will gradually decline, indicating the loss trend of long-term gambling.
• Bankruptcy Point: At the end of the chart, the gambler's capital ultimately reaches zero.

Such graphs are often used in gambling theory and risk management research to remind people of the rational understanding of gambling and to avoid over-investment or blindly pursuing short-term gains.

This is not advice that most gamblers want to hear, as it does not fundamentally solve the bankruptcy problem. You still need a money management system to manage your gambling funds, as it is all too easy to lose all your money.

The most famous betting systems are the "Martingale System" and the "Reverse Martingale" or "Paroli System." In these systems, gamblers will keep doubling their bets until they win.
The "Martingale System" and the "Reverse Martingale" or "Paroli System" are classic betting systems widely used in gambling, especially in casino games like roulette. These strategies aim to minimize losses or achieve profits through specific betting patterns. Here’s a brief explanation of the two systems:

1. Martingale System#

The Martingale System is a doubling betting strategy most commonly used in games with binary outcomes, such as roulette or baccarat. The basic principle is: every time a player loses a round, they double their bet for the next round until they eventually win.

• How it Works: Suppose you start by betting 1 unit. If you lose, you bet 2 units in the next round; if you continue to lose, you bet 4 units, 8 units, 16 units, and so on.
• Goal: Once you win, you will recover all previous losses and gain a profit equal to your initial bet.

Advantages:

• Once you win, you can recover all previous losses and earn a small profit.

Disadvantages:

• Requires a very high bankroll, as consecutive losses can quickly escalate the required bet size.
• Betting limits in gambling games may restrict the effectiveness of this strategy, preventing players from continuing to double their bets.
• Long streaks of consecutive losses can lead to significant losses.

2. Reverse Martingale (Paroli System)#

The Reverse Martingale System, also known as the Paroli System, is the inverse variant of the Martingale strategy. Its basic idea is to increase the bet when you win and keep the initial bet amount when you lose. This method tends to allow players to maximize profits during winning streaks while limiting losses during losing streaks.

• How it Works: Suppose you start by betting 1 unit. If you win, you increase your bet to 2 units, then 4 units, and so on; if you lose, you revert to the initial bet of 1 unit.
• Goal: By increasing the bet during winning streaks, you maximize profits while limiting losses by maintaining the initial bet during losing streaks.

Advantages:

• Compared to the Martingale System, it carries less risk, as it does not rapidly increase bet sizes.
• It can yield higher returns during winning streaks, but if losing streaks occur, it protects the principal better.

Disadvantages:

• If there are no long winning streaks, profits may be limited.

• It may be challenging to achieve substantial profits if there are prolonged periods without winning streaks.

• The Martingale System focuses on doubling bets to recover losses, suitable for those with sufficient funds who can withstand long losing streaks, but it carries relatively high risk.

• The Reverse Martingale System is more conservative, emphasizing gradually increasing bets during winning streaks to maximize profits while better protecting the principal during losing streaks.

Both methods have their pros and cons, and players should choose which system to use based on their risk tolerance and financial situation. It is also important to note that these betting strategies do not change the inherent probabilities of the games or the house edge; in the long run, the house always has the advantage.

The Kelly Formula (Kelly Criterion) is often used by gamblers and investors as a fund management strategy in different contexts to maximize long-term capital growth. Its mathematical expression is:

[ G_{\text{max}} = \frac{b}{p} - \frac{1 - p}{p} ]

Where:

• ( G_{\text{max}} ) represents the proportion of funds that should be bet (or invested);
• ( b ) represents the odds (i.e., how much return you can get from each unit bet);
• ( p ) represents the probability of winning.

The core idea is to calculate an optimal betting proportion based on the ratio of risk to return, thereby maximizing long-term returns across multiple bets or investments while avoiding risks associated with over-betting or under-betting.

Comparing the Kelly Formula to Einstein's famous equation ( E = mc^2 ), one could say that the significance and elegance of the Kelly Formula in the fields of investment and gambling are akin to the status of ( E = mc^2 ) in physics. Both reveal a profound, simple yet powerful principle. The Kelly Formula provides a mathematical method for optimizing decision-making, while ( E = mc^2 ) describes the direct equivalence between mass and energy. Both can be seen as exquisite, concise, and effective foundational formulas in their respective fields.

In summary, the Kelly Formula is indeed as concise and far-reaching as Einstein's ( E = mc^2 ), capable of producing profound impacts in practice.

The St. Petersburg Paradox is a famous paradox in probability theory, proposed by mathematician Daniel Bernoulli in the 18th century, aimed at discussing human decision-making behavior in the face of risk and uncertainty. The story of this paradox is based on a gambling game and reveals the gap between classical expected utility theory and actual human behavior.

The Story of the St. Petersburg Paradox#

Imagine a gambling game where there is a fair coin (i.e., the probability of heads and tails is each 50%). The rules of the game are as follows:

1. You pay a certain fee to participate in the game.
2. At the start of the game, the coin is tossed. If it lands heads, the game ends, and the player wins $1.
3. If it lands tails, the coin is tossed again. If heads appears again, the game ends, and the player wins $2.
4. If tails appears again, the coin is tossed again. If heads appears, the player wins $4.
5. The game continues until heads appears for the first time.

Thus, the player could win the following amounts:

• 1st toss heads: $1
• 2nd toss heads: $2
• 3rd toss heads: $4
• 4th toss heads: $8
• … and so on.

Calculation of Expected Earnings#

From a probability perspective, the player may end the game on the nth toss when heads appears. If the game ends on the nth toss, the player will win $2^{(n-1)}. Let's calculate the expected earnings of this game.

The expected earnings (E) of this game can be obtained by calculating the product of each outcome's earnings and its probability. The probability of tossing the coin until the nth toss is ( \frac{1}{2^n} ), thus the expected earnings are:

[
E = \sum_{n=1}^{\infty} \frac{1}{2^n} \cdot 2^{n-1}
]
[
E = \sum_{n=1}^{\infty} \frac{1}{2}
]
This sum is infinite because each term is ( \frac{1}{2} ), and such an infinite sum is clearly infinite.

The Emergence of the Paradox#

According to the above calculation, the expected earnings of the St. Petersburg gambling game are infinite. However, in reality, most people would not be willing to pay a large amount to participate in this game. In other words, although mathematically the expected earnings of the game are infinite, people are not willing to invest large sums to participate, which creates the paradox.

Resolving the Paradox#

Bernoulli resolved this paradox by introducing the concept of "utility." He argued that people do not make decisions solely based on the quantity of money but rather based on "utility"—the actual value of money to them. When the amount of money becomes large, the additional money contributes less to people's utility (for example, gaining $100 may have a larger utility difference than gaining $1, but the difference is smaller than the difference between $1000 and $100). Therefore, Bernoulli proposed using a logarithmic function to describe the diminishing effect of utility, which can explain why people would not be willing to pay an infinitely high price to participate in this game.

Conclusion#

The St. Petersburg Paradox reveals the discrepancy between rational economic models (especially expected value theory) and actual human behavior. It prompted later economists and decision theorists to explore concepts such as irrational behavior, risk preference, and utility functions in human decision-making, becoming an important starting point for behavioral economics.

The Kelly Criterion and the Markowitz Criterion are two classic financial theories. Although both involve making trade-offs between risk and return, their starting points, application scenarios, and core ideas differ. Here is a comparative illustration to help understand the differences between the two criteria:

Key Comparison Summary:#

• The Kelly Criterion focuses on maximizing long-term growth of wealth by optimizing the investment proportion of a single asset, suitable for frequent trading environments (such as gambling, futures markets, etc.). It assumes unlimited fund allocation and provides a mathematical formula to guide fund distribution in balancing risk and return.
• The Markowitz Criterion emphasizes constructing a diversified investment portfolio to minimize overall risk and find an optimal balance between risk and return, suitable for long-term asset allocation.

From an intuitive understanding perspective, the Kelly Criterion is a "dynamic bet optimization" strategy, while the Markowitz Criterion is a "risk control" method for multi-asset portfolios.

The Kelly Criterion is a mathematical formula used to determine the optimal betting proportion in gambling or investing to maximize long-term capital growth. Its basic idea is to calculate the optimal amount to bet based on the current probability of winning and the odds. The core formula of the Kelly Criterion is:

[
f^* = \frac{p \cdot b - q}{b}
]

Where:

• ( f^* ) is the optimal betting proportion;
• ( p ) is the probability of winning;
• ( b ) is the odds (the return you can get from each unit bet);
• ( q = 1 - p ) is the probability of losing.

Analogy of the Kelly Criterion with a Pinball Machine#

The Kelly Criterion can be likened to a pinball machine, which is often used to visualize and understand its behavior.

1. How a Pinball Machine Works:
   In a pinball machine, the ball bounces around various obstacles, ultimately determining whether the ball enters a reward zone or falls off. Each time a player launches the ball, its path is uncertain and can change.

2. Role of the Kelly Criterion:
   Just like the ball's path in a pinball machine, the Kelly Criterion is also a "probability game." Players decide how much to bet each time based on their current funds and potential returns. Different betting decisions (size of the bets) are akin to different path choices in the pinball machine. The Kelly Criterion attempts to optimize each bet (or each ball launch) to favor long-term returns.

Key Points of the Analogy:#

• Probability and Risk Control: The core of the Kelly Criterion is to make decisions based on the ratio of risk to return, just as players try to control the ball's path in the pinball machine.
• Long-Term Optimization: Each investment's result may not be ideal, but in the long run, through reasonable betting proportions, long-term capital growth can be achieved, similar to the cumulative results of multiple rounds in the pinball machine.
• Feedback Mechanism: Just as each bounce of the ball affects subsequent outcomes in the pinball machine, the Kelly Criterion adjusts its strategy based on the results of previous bets to ensure better future returns.

Through this analogy, we can more easily understand the dynamic nature of the Kelly Criterion and its goal of optimizing bets.

The core of this question is the application of the Kelly gambler's strategy and how to maximize capital growth in gambling while avoiding bankruptcy in extreme situations. In this question, we face a "tail event," which refers to an occurrence of a probability event that is more extreme than expected. Here is a detailed analysis of this issue:

1. Background and Assumptions#

• Kelly Gambler's Strategy: The core idea of the Kelly gambler's strategy is to determine the proportion of funds to bet based on known winning probabilities and odds. The goal is to maximize long-term capital growth while avoiding bankruptcy in adverse situations.
• Coin Tossing: Typically, coin tossing is fair, meaning there is a 50% probability of heads and a 50% probability of tails. However, in this case, we have a 55% probability of heads. The problem is set in a scenario where the result of one toss is 45% heads.

2. Why Does a "Tail Event" Occur?#

A "tail event" refers to an unusual occurrence at the tail end of a probability distribution. Here, we originally expected a 55% probability of heads, but the actual result is only 45%. This deviation from expectation is what is referred to as a "tail event," meaning an uncommon and extreme outcome has occurred.

In the Kelly gambler's model, such deviations often lead to prediction failures because they break the assumptions of the model (for example, the expected winning probability is not realized). However, the Kelly strategy itself does not suggest putting all funds into each round; instead, it recommends a reasonable betting proportion based on probabilities.

3. How Does the Kelly Gambler Respond?#

The Kelly gambler determines the betting distribution based on known probabilities and odds. Suppose the Kelly gambler knows the probability and odds of each coin toss; they would calculate the betting proportion using the following formula:

[
f^* = \frac{bp - q}{b}
]

• ( f^* ) is the proportion of funds to bet.
• ( b ) is the odds.
• ( p ) is the winning probability (in this problem, it is 55%).
• ( q ) is the losing probability (1 - p).

According to this formula, if the Kelly gambler's goal is to maximize long-term capital growth, even when facing a "tail event," they will adjust their betting proportion based on the winning probability. If the winning probability does not meet expectations, they will also adjust their betting amounts to ensure they do not lose all their funds due to a single event.

4. How to Keep Funds Safe?#

Even in unfavorable situations, the Kelly gambler's strategy can still safeguard funds. For example, if the result of the coin toss is 45% heads, this means the Kelly gambler will only lose a portion of their funds, not all:

• Suppose in each round of betting, the Kelly gambler only bets a portion of their total funds rather than all. Even if they lose some bets, their total capital remains sufficient to support the next round of betting, and by continuing to apply the Kelly strategy, they can maintain profitability in the long run.
• In this case, the Kelly gambler can retain most of their funds even after experiencing an unfavorable result, for instance, preserving at least 90% of their capital.

The advantage of the Kelly gambler's strategy is that even when encountering "tail events" or probability deviations, it can still avoid complete bankruptcy. The Kelly gambler ensures that the size of each bet adapts to the current odds and winning probabilities through reasonable fund allocation, thus maintaining long-term growth of capital.

In summary, the Kelly gambler will not go bankrupt after one coin toss; they avoid the risks posed by "tail events" through a scientific betting strategy, ensuring that they can at least preserve most of their funds. This strategy is designed to ensure that, in the long run, capital can continue to grow, even if they occasionally experience unfavorable gambling results.

Seeing Probability Theory is an innovative mathematical education platform that makes abstract mathematical concepts visible and understandable through engaging interactive visual demonstrations, helping you grasp the core ideas of probability statistics and deeply understand classic probability theory knowledge such as the law of large numbers, Bayes' theorem, and the Kelly formula.

The Endowment Effect refers to the phenomenon where people greatly overestimate the value of an item once they own it, and this phenomenon is very important in behavioral economics.

Concept Explanation

The Endowment Effect is a theory proposed by Richard Thaler in 1980. It describes a cognitive bias where people tend to overestimate the value of items they own simply because they belong to them. This effect corresponds to the theory of "loss aversion," which states that people fear losses much more than they anticipate gains.

Phenomenon Performance

• Overestimating Owned Items: People often believe that the items they own are worth more than they actually are.
• Transaction Inertia: Due to the fear of losing what they already have, people are reluctant to give up their current assets, leading to difficulties in transactions.
• Price Differences Between Selling and Buying: When buying and selling the same item, sellers often ask for a price higher than what buyers are willing to pay, leading to reduced market efficiency.

Influencing Factors

• Loss Aversion: The aversion to losing something is greater than the pleasure of gaining an equally valued item.
• Sense of Ownership: Actually owning something changes the evaluation of its value, making it difficult to give it up.
• Personal Preferences: Different individuals exhibit varying strengths of the Endowment Effect, but generally, this effect is evident in decision-making.

Morey gathered his employees together and listed some biases he believed could influence judgment on the whiteboard: the Endowment Effect, confirmation bias, etc. There is also a psychological phenomenon known as the "current effect"—when making decisions, people tend to underestimate future developments, believing that the present is better than what will come later. In Morey's view, the "hindsight effect" refers to how people, upon seeing the results, easily appear to have anticipated everything. Data models help mitigate these quirky thoughts. However, by 2012, Morey's model seemed to be approaching its limits in processing information used to evaluate players for the Rockets. "Every year we study what data to delete and what to add," Morey said, "but its performance is becoming increasingly unsatisfactory."

Managing a professional team is nothing like Morey imagined as a child. He now feels as if he has to cruelly dismantle a complex alarm clock to check where it has gone wrong, only to find that an important part of the clock is embedded in his brain.

When players are playing, it is easy to form instant impressions and then look for evidence based on those impressions. He has heard that this situation is called "confirmation bias." People are always reluctant to see things they do not want to see and are eager to see things they are happy to see.

Confirmation Bias refers to the tendency of people to seek, interpret, and remember information that is consistent with their existing beliefs or hypotheses while ignoring or undervaluing contradictory information. This bias can lead to increasingly entrenched viewpoints, reducing openness to new evidence.

For example:

Suppose a person firmly believes that "left-handed people are smarter than right-handed people." This person may pay special attention to cases where left-handed individuals achieve success or perform well while ignoring equally outstanding right-handed individuals. For instance, when they hear about a famous left-handed scientist or artist, they may view this as support for their belief; when they hear about the success stories of right-handed individuals, they may attribute it to other factors rather than considering it as a contradiction to their viewpoint.

This bias can cause this person to gradually strengthen their belief that left-handed individuals are smarter while being unwilling to accept data or facts that contradict it.

Regardless of the biases others may carry when selecting amateur players, Morey always pays attention because he is constantly trying to validate these biases.

According to Roy Baumeister, culture is a biological game of humanity, so from an evolutionary perspective, those who can keep pace with the ever-changing social lifestyles (i.e., culture) are more likely to be favored in choices, and human nature has been shaped in this slow evolutionary process. Therefore, for Baumeister, the progress of brain research will not be replaced but will instead promote research in human behavior. He is concerned that the widespread neglect of interpersonal relationships in brain science research will distort our correct understanding of human nature.

When unavoidable contradictions arise in social life, law becomes the basic means of resolving conflicts. Baumeister has also studied the concepts closely related to morality, such as sin, self-control, choice, and free will. According to Yale University psychologist Paul Bloom, morality is an innate human trait, and the value judgment of good and bad is deeply rooted in our marrow. Bloom's research shows that infants in cribs and toddlers can already understand the goodwill and malice in others' behaviors; they exhibit tendencies to encourage goodwill and punish malice; they will take action to help those in distress; they will experience emotions such as guilt, shame, pride, and righteous indignation.

Harvard University's cognitive neuroscientist and philosopher Joshua Greene believes that our most serious social problems today, such as war, terrorism, and environmental destruction, stem from people's use of outdated moral views from the Stone Age to address the complex issues of modern life. Our brains deceive us into thinking we are addressing problems from a moral high ground, while in fact, the outcomes often contradict our intentions. Moral superiority blinds our brains, preventing it from considering moral values that we are not inherently equipped with.

Research by Jonathan Haidt, a psychologist at the University of Virginia, suggests that morality is a social product based on five or more innate basic "psychological" components, including harm, fear, group loyalty, authority, and purity. Educated liberals tend to consider the first two aspects, while more conservative, religious, or lower-status individuals often consider all five aspects.

As neuroscientist Sam Harris has said, the impotence of science in explaining interpretation, morality, and values is precisely why religious beliefs flourish. It is because rational debate and scientific inquiry are weak in the realm of interpretation and moral issues that many seek explanations from religious dogmatism and supernatural doctrines, leading to sectarian disputes. The stronger the skepticism towards science, the more pronounced the divide between science and religion becomes, and the more they seem to be at odds with each other.

A significant amount of work by Joshua Knobe, an experimental philosopher, focuses on the phenomenon of excessive moral judgment in people's lives—making intuitive moral judgments about many non-moral issues, such as speculating on intentions and inferring causality. It is often said that the best way to study how people think is to treat them as objective research subjects, just like experimental subjects in scientific research paradigms. However, Knobe's perspective differs; he believes that the way people view the world is always influenced by moral judgments, and moral bias is ubiquitous. Knobe's most controversial and well-known contribution is the "Knobe Effect," also known as the "side effect effect."

The "Knobe Effect" refers to the phenomenon where the influence and reputation of a person or team significantly increase after they receive a Nobel Prize. This effect is reflected not only in the academic reputation of the laureates but also positively impacts funding support, subsequent research, and public attention in that field.

Disgust is considered an emotion that plays a crucial role in many moral evaluations. Research by David Pizarro, a psychologist at Cornell University, indicates that political leanings are increasingly intertwined with heightened experiences of disgust (measured using the "disgust sensitivity scale" created by Jonathan Haidt and his colleagues).

Jonathan Haidt (1)

As the first speaker, I would like to thank the Edge Foundation for bringing us to such a beautiful place and gathering us together. I have been looking forward to having a conversation with each of you.

Recently, I attended a conference focused on research in moral development. During the conference, a moral psychologist who clearly supported Kohlberg's theory (2) stood up and said, "Moral psychology is in decline." At that moment, I thought, well, perhaps things are not going well in your "house," but other places in this "city" are thriving. We are witnessing a golden age.

In this "city," the area I reside in is called social psychology, and it is becoming increasingly interesting with the influx of many newcomers. I don't have to walk far to find cognitive neuroscientists, primatologists, developmental psychologists, experimental philosophers, and economists. I mentioned that we are in a golden age, where the theory of racial fusion that Edward Wilson (3) passionately advocated in 1975 is becoming a reality. We are witnessing an era of knowledge integration.

Today, we still have many differing opinions on various issues, but I believe we have reached a consensus on many viewpoints. We all agree that moral research must involve evolution and culture. You need to understand chimpanzees, bonobos, human infants, and psychopaths, and explore the distinctions among these subjects. You need to study the brain and mind and ultimately integrate these insights.

For this conference, I hope everyone present can speak freely and find common ground while respecting differences. For those watching this conference online, I hope they can be inspired by our enthusiasm and optimism while maintaining sufficient rationality.

When I was a graduate student in Philadelphia, I had a peculiar experience at a restaurant. One day, I was walking on Chestnut Street and suddenly saw a restaurant called "True Taste." I thought to myself, "What is the true taste?" So I walked into the restaurant and looked for a menu. The menu was divided into four sections, labeled "Brown Sugar," "Honey," "Syrup," and "Saccharin." I was completely baffled by the menu, so I approached a waiter and asked, "What's going on? Don't you serve food here?"

It turned out that the waiter I asked was the owner of the restaurant, and he was the only staff member in the entire place. He explained that this was a restaurant selling sweeteners. There was only one like it in the world, with no branches. I could taste various sweeteners from 32 countries in his restaurant. He also told me that his professional background was not in the food industry, and he had never worked in any restaurant before, but he had a PhD in biology and had worked at the Monell Chemical Senses Center in Philadelphia.

The owner discovered in his research that among all five taste sensations (sweet, sour, salty, bitter, umami) that humans perceive, the experience of sweetness most strongly stimulates the secretion of dopamine. Therefore, he believed that sweetness is the "true taste," the taste stimulus we crave the most. He thought repeatedly and inferred that the most effective way to maximize the pleasure per calorie consumed in his restaurant was to focus on stimulating sweet taste receptors. This was his motivation for running that restaurant.

I asked him, "So how's business?" He replied, "Terrible. But at least I'm doing better than that chemist who opened a savory restaurant at the end of the street."

Well, I want to say that this story is, of course, fictional. I just wanted to use a vivid analogy to illustrate my feelings while reading moral philosophy and certain moral psychology papers recently. The connotation of morality is very rich and complex, and discussions about it often require considering multiple levels and facing countless contradictions. However, many authors of papers reduce it to single-factor propositions, falling into the cliché of discussing maximizing social welfare. This is akin to the sugar I mentioned in my story. Sometimes, people also discuss justice and the corresponding fairness and rights. This is like the chemist at the end of the street. So, according to these papers, the only two restaurants we can choose from are either the utilitarian fast-food joint or the deontological restaurant, with no other options.

For difficult topics like morality, we always need some metaphors and analogies. A few years ago, Mark Hauser and John Mikhail used language to draw an analogy for morality. I think this is a very appropriate metaphor that reflects many characteristics of morality. Personally, I believe that morality and language share similarities in that the intention behind a behavior can differ when the same behavior produces consequences.

However, once the definition of morality is further expanded, I find that using perception as an analogy for morality can be more enlightening and explanatory. I am not saying that using language as an analogy for morality is wrong or flawed. I just suggest that we try a different analogy, using perception to compare with morality.

Imagine vision, touch, and taste; for these three senses, our bodies are equipped with corresponding receptors. For instance, there are four different cells on our retina to perceive different frequencies of light. On our skin, we have three types of receptor cells for sensing temperature, pressure, and tissue damage, which is pain. On our tongue, we have the five taste receptors mentioned above.

Among these three senses, I believe taste is the closest and richest analogy for morality.

First, the relationship between taste and behavior is very straightforward. A taste is either good or bad. Good tastes, including sweetness and umami, as well as appropriately salty flavors, stimulate our desire for "more." They seem to say, "This is really good." In contrast, sour and bitter tastes seem to say, "Yuck, stay away."

Second, the metaphor of taste aligns well with people's moral intuitions; we often unconsciously use taste to describe moral feelings in our daily lives. We might describe someone's behavior as "tasteless" or "disgusting." When we see others crossing moral boundaries, our expressions often mirror those of tasting something unpleasant.

Third, every culture has its unique culinary flavors and ways to please taste receptors. The metaphor of taste captures the universality of morality. Just as moral thought has its taste receptors, preferences for flavors depend on different cultural characteristics. Each culture draws from local resources, learning from predecessors, and excites moral receptors in its unique way.

Finally, the use of taste as a metaphor for morality has a long history. Over 2300 years ago, Mencius in China said, "Thus, the joy of reason and righteousness delights my heart, just as the joy of food delights my mouth." David Hume also liked this saying, and I will return to it later.

So, my goal in this dialogue is to illustrate some important similarities between moral psychology and taste psychology. I want to reiterate that I do not oppose comparing morality to language; I just think that using taste as a metaphor is also very appropriate. Looking at morality from different perspectives may yield different conclusions.

Some may know that I am one of the founders of Moral Foundations Theory. This theory proposes that moral judgments originate from a small segment of the audience in society, who are the taste receptors of moral awareness. I will explore this theory again as my speech draws to a close.

Before returning to the topic of taste receptors and moral foundations, I want to discuss two important cautionary examples. I want to mention two papers published in Behavioral and Brain Sciences, which benefited from Paul Bloom's keen eye as an editor. I believe these two papers are significant, and their abstracts deserve to be posted on the walls of psychology departments across the country, much like the "food choking first aid guide" you see in restaurants. In some states in the U.S., laws require restaurants to post these guides on their walls.

The first paper is titled "The Weirdest People in the World," authored by Joe Henrich, Steve Heine, and Ara Norenzayan. This paper was first published on an electronic bulletin board (BBS). The authors argue that psychology is the most "American" field among all disciplines, with as much as 70% of the papers cited in mainstream psychology journals coming from Americans. In contrast, this figure is only 37% in the field of chemistry. This issue is quite serious because psychology is a science closely related to culture, while chemistry is not.

The authors attempted to collect and organize all the papers they could access that explored the comparison between industrialized societies and small-scale societies. They found that even in some low-level perceptual processing and spatial cognitive abilities, people living in industrialized societies appeared different.

Morality is like the matrix in "The Matrix"; it is a mutually agreed illusion. If we only interact with people within the same matrix, then undoubtedly, united in our common cause, we can find conclusions that all members within this matrix agree upon and refute the values of members from other matrices.

I believe that Mercier and Sperber's paper is a typical example of Humean views, representing the moral inference perspective under Humeanism. Hume has a famous saying: "Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them." When Hume passed away in 1776, he left us a series of solid foundational theories, which he and his contemporaries referred to as "moral science."

The subtitle of my speech today is "Using Taste to Compare Moral Psychology: A Relay with Hume." I have listed some characteristics related to Hume at the bottom of my written materials, which provide references for continuing the study of Hume's theories.

Hume was a leader of Enlightenment thought. First, he was a naturalist, meaning he believed that morality is a natural component of the natural world, so studying morality is studying humanity itself, rather than burying oneself in scriptures or studying a priori logic. Moral psychology allows us to step outside, and so does moral science. Therefore, I placed naturalism, or naturalists, at the top of this list as the first of seven characteristics.

Second, Hume was a nativist. He never met Darwin, so he was unaware of the concept of evolution. But if he had the opportunity, he would likely strongly agree with Darwin and his theory of evolution. Hume believed that morality is like aesthetics; both "are established on the unique foundation of this particular species, human beings."

Third, Hume was also a sentimentalist. He believed that the greatest threat to the foundation of human morality comes from the diversity of moral sentiments. You can see Hume's emphasis on emotions in another quote I selected. He said, "Morality is not a vague abstract thing; it is a unique manifestation of each person's emotions and tastes, just as we perceive and prefer sweetness and bitterness, warmth and coldness. Therefore, moral concepts should not be viewed alongside thoughts but should be regarded as akin to taste or emotions."

Thus, I briefly summarize the main arguments of this theory. The Moral Foundations Theory proposes that the most important five pairs of "taste" receptors of human emotions are: Care/Harm, Fairness/Cheating, Loyalty/Betrayal, Authority/Subversion, and Purity/Degradation. Moral sentiment is like taste, produced by the different ways these five basic moral foundations are harmonized.

In other words, these are the five elements that best serve as the foundation of moral sentiments. Our moral foundations are certainly not limited to these five pairs; in fact, they are much more than that. The perceptual abilities, language abilities, and others developed by humans over a long evolutionary process are the foundations that shape moral concepts. However, I hope the theory we propose serves as a good starting point and acts as a catalyst. The metaphor used in this theory aligns with Hume's analogy for morality, which is taste.

In conclusion, I believe we should take up the baton from Hume. Compared to Hume's time, we have countless new insights in psychology, biological evolution, and neuroscience. If Hume could live today and spend a few years catching up on the literature, he would likely agree with what I am saying: he is a naturalist, a nativist, an intuitionist, a pluralist, and a non-reductionist.

For those inclined to agree with nativism, I want to say a few more words because I think this is important. For those who claim that "evolution is the innate ability of biology," you might want to refer to some constructivist perspectives. As long as they complement emergentism, I personally can fully accept reductionism. Reductionists excel at seeking the essence of things, but they still need to reassemble these essences from the ground up, returning to the heights of institutions and cultures. What I mean is that it is necessary to consider incorporating various localized factors. There is a saying in cultural psychology: "Culture and psychology promote each other." As you know, psychologists specialize in psychology. We still do not know what gears manipulate changes in the mind, but there are indeed these gears turning, adapting under different ecological and economic conditions. Above us is a psychological level higher than the self; below us is a reductionist or neuroscientific level lower than the self, and we need to pay attention to both levels and our connections with them.

Now, finally, we come to the last point. We must be very cautious about biases. I believe morality should generally be viewed as a collective phenomenon, at least regarding its origins. Essentially, the role of morality is to unite us against other groups with differing moral cognitions.

As I mentioned earlier, almost everyone engaged in research in our field is, to some extent, a rebellious "outlaw." We easily misinterpret others' moral views that differ from our own. If we were judges in a courtroom, people like us would have to be dismissed. However, as scholars, we do not do this; when studying moral views in foreign cultures, we must be very cautious, empathizing and trying to view the beliefs and values contained in foreign cultures with a self-consistent perspective. Because the significance of their existence is similar to ours, both starting from the desire to make their societies more humane and prosperous.

This is the entirety of my speech, and it is what I believe moral science should look like in the 21st century. Of course, the content of this speech comes entirely from my rational inference ability, and I am well aware that the only reason for my inference ability is to find evidence to support my argument. Therefore, I want to thank you in advance for the arguments you will soon present that contradict my views, and I appreciate your help in combating my confirmation bias.

Clarity is a biological means of humanity. It connects every individual in society through information sharing, labor distribution, responsibility allocation, and other means. It is a new and better way to connect us, and it indeed works effectively. Civilization is our primary means of addressing survival and reproduction issues, and its effects are evident. The uniqueness of human nature is also reflected in human social life.

So, after all this, what does it have to do with morality? Yes, just as I quoted McIntyre earlier, the essence of morality is not to redeem individuals or promote individual fulfillment; rather, it is a series of rules that help many people live together. Since civilization is born from interactions and cooperation between people, such as the need for trust and consensus, the role of morality is to maintain the operation of civilization.

Nature and civilization are complementary to some extent, but conflicts and contradictions between the two still exist. Fundamentally, nature endows us with selfish characteristics. The brain is selfish; perhaps we should say genes are selfish. But in any case, human nature carries selfishness, while civilization requires people to overcome this characteristic as much as possible because you must cooperate with others, suppress your shortsighted and selfish impulses, and consider things from a longer-term, self-interested perspective. To ensure the normal operation of social civilization, you need to keep your promises, follow the rules of first-come-first-served, pay taxes, and even send your children to the battlefield, risking their lives. These actions contradict human nature, but they are often praised by morality, as they encourage people to restrain their selfish impulses and direct everything toward maintaining the normal operation of the social system. In the long run, this can benefit every individual in society.

Morality works this way, and so does law. We have not yet explored law in detail, but in regulating human behavior, law and morality share many similarities. Both establish many similar rules in advance to guide self-interest to serve the entire social system, ensuring that society can operate efficiently. However, there is a key and significant difference between law and morality: the degree of enforcement. People follow moral norms in life because they are concerned about their reputation, and personal reputation is built on long-term social relationships. If you deceive your neighbor living next door, they will remember this for the rest of their lives, and others will hear about it, which will severely damage your long-term interests, ultimately leading to negative consequences for yourself.

As society develops and grows, the social structure becomes more complex, and interactions between strangers become more frequent. It becomes easy to deceive a stranger you may never meet again and get away with it, at which point the law must step in to take over the role of morality. Regardless, we cannot overlook the interpersonal interaction perspective when studying morality. Exploring morality requires considering the relationships between people. Morality can regulate interpersonal behavior to promote cooperation between individuals and the normal operation of society.

Now, let us look at which human characteristics can help individuals overcome selfish impulses and think about the collective and society as a whole. Among all these characteristics, I believe the most important is self-regulation. I think one reason I was invited to speak here is that I have previously researched self-regulation and self-control. The essence of self-regulation is to abandon one thought and instead focus on doing another thing, which is usually more necessary, whether for one's long-term interests or for the collective's welfare.

This is why we refer to self-control as the muscle of morality. I want to break this term down and discuss it piece by piece. First is morality. Self-control is moral because its purpose is to make you do moral things, sometimes even requiring you to sacrifice yourself for others. So if you want to list terms related to moral sentiment, whether the seven deadly sins, the Ten Commandments, or various virtues, they all fall within the realm of self-control. You can view self-control as the center of these concepts; its failure leads to the sins of gluttony, wrath, greed, and so on. They are all the results of insufficient self-control. Therefore, various virtues can also be seen as successful examples of self-control. This is the part of self-control related to "morality" within the "muscle of morality." Self-control is the guarantee of good virtues, and virtues can benefit a collective, even if sometimes this requires sacrificing short-term personal interests.

The "muscle" metaphor also comes from our experimental research and has no relation to the aforementioned virtue level. In our laboratory, we found that self-control cannot be output indefinitely; it can also be exhausted. Just like muscles, self-control can become fatigued. In more than one experiment, we found that when people engage in tasks that require self-control and then immediately enter another task that requires different demands, their performance often worsens. Their self-control, like muscles, becomes fatigued after use. Self-control is a limited ability that can be depleted.

The muscle metaphor has other apt aspects. If you exercise self-control daily, it becomes stronger. I do not want to hear people say, "Well, since self-control is a limited ability, I never want to squander or waste it anywhere." No, no, no; on the contrary, you need to use self-control regularly; daily practice is what makes it stronger and better able to cope with the challenges at hand.

When people overuse a particular muscle, leading to muscle fatigue, or in other words, when self-control is completely depleted, we refer to this situation as ego depletion. In this case, without the protection of self-control, people's behavior begins to deviate from the moral track. We find that when self-control is low and the source of moral power is exhausted, people become more proactive in infringing on the interests of others.

Free will is another topic that sparks endless debate. People have a fervent obsession with this concept, and I can only keep my distance from it. Before you want to express your views on free will, I want to clarify my understanding of free will theory. In my theory, free will is not a supernatural, causeless phenomenon. What causes subjects in experiments to make their own choices and maintain rationality? I believe it is a reflection of the realities of human society. In our society, rational restraint, virtuous deeds, and good decisions are all related to free will. Whether the spirit of free will is manifested depends on our understanding and definition of it; I do not know how many people are aware of this spirit.

An example is the dictator game (16), where the rules of the dictator game are actually simpler than those of the ultimatum game. My approach is to randomly recruit two people, one of whom, the experimental subject, is very lucky. He will receive a sum of money, say $100. He can decide how much to share with the other person, and he can choose to give anywhere from $0 to $100. The other person will never know who decided how much to give him, and the entire process is strictly anonymous.

From a self-interested perspective, the experimental subject should keep all the money for himself. However, you will find that people are indeed willing to share. On average, subjects will give about 30% of the money to others. Some give nothing, while others give half, and some even give away most of the money. They are surprisingly generous. Ernst Fehr and Simon Gachter recently repeated this experiment with children as subjects, designing a very simple ultimatum game. Two children each received two candies; they could keep both or give one to the other, even though they did not know each other.

Seven or eight-year-old children typically choose to share the candy they have, while younger children almost always choose to keep both candies for themselves. If we have generosity towards strangers, this sentiment should have emerged later. Now I want to say that the standard ultimatum game is not perfect; it places two conflicting desires in opposition. A child may have impulses to demonstrate fairness, kindness, and justice, which lead them to want to share their candy. However, children also love candy, so they may desire to keep both candies for themselves. We pit these two desires against each other, and the results of the experiment may simply indicate that at that moment, the craving for candy overpowers their impulse to be generous.

Fehr and Gachter conducted more in-depth research on this. They had children make a choice between two options: one was to receive an extra piece of candy and then share it with others, and the other was to receive an extra piece of candy without giving it to others. In this case, from a consequentialist perspective, the previous worries disappear. Without the opposition of the two desires, children can be good without incurring a loss. However, the experiment found that for children under seven or eight years old, the two choices seemed indistinguishable. The probability of giving or not giving was roughly 50%, and younger children did not care. They were not thinking about hoarding candy from others; whether they kept the candy or shared it, they did not feel anything.

Such results are not surprising and may even be better than we expected. The mainstream trend of human nature development is to respond to strangers, such as people living in other tribes. Jared Diamond detailed his experiences in a tribe in Papua New Guinea. He pointed out that for those in the tribe, leaving their own tribe and entering another tribe is tantamount to seeking death. Other scholars have also found deep hostility between tribes in the ways they refer to companions and members of other tribes. For example, the term used to refer to tribe members often means "human" or "people"; while terms used to refer to others may only mean "someone," much like in the TV series "Lost." Sometimes, terms used to describe others between tribes are also used to refer to "prey" or "food."

So, since the goodness of human nature, at least the goodness recognized by us, contradicts the moral views inherent in our nature, which has almost nothing to do with goodness, how did we bridge the gap between the two? How did our nature become so friendly?

Note that I am focusing on our goodwill towards strangers here, but we can also use these experiments to explore other moral issues, such as the origins of new moral perspectives, why slavery is wrong, and why we should not have gender or racial discrimination.

These are profound topics. Regarding the origins of human goodness, I will conclude with two equally compelling theories.

The first theory centers on the increasing interdependence between people. Interdependence is a theme in several books by Robert Wright, and Peter Singer and Steven Pinker have also discussed it. The main point of the interdependence theory can be summarized as follows: when you interact with others, interdependence arises; when your quality of life improves due to contact and mutual care with others, and the relationship is a non-zero-sum relationship, you become concerned about the fate of others.

The essence of this goodness in human nature is self-interest. Robert Wright once said in an interview, "One of the reasons I don't want Japan to be bombed is that the little truck I drive is a Nissan." Clearly, having a favorable commercial relationship with Japan is the reason for his goodwill.

A paper published by Henrich and colleagues in Science a few months ago serves as evidence for this viewpoint. Henrich and others studied 15 countries, having people from these countries participate in a series of economic games. They found significant regional differences in people's friendliness towards strangers, so they turned to analyze the factors determining this friendliness. One of the findings was that capitalist societies make people friendlier towards strangers, indicating a strong correlation between immersion in market-oriented societies and people's friendliness towards strangers, possibly because when you live in a market-oriented society, you frequently need to interact with strangers for long-term benefits, even if these people are neither family nor friends. The second factor is religion, especially Christianity or Islam. Believing in religion can make people friendlier, possibly because religion, as a larger social organization, promotes communication between people and strangers.

The second theory explaining the goodness of human nature posits the power of storytelling. One of the impacts of fictional works and the news industry is that they shorten the distance between strangers and us. Through them, you can get to know people who were originally unrelated to you as if they were your relatives or neighbors, making it easier for us to empathize with strangers. However, according to Martha Nussbaum and others, novels and news not only allow us to empathize with individuals but can even evoke empathy for groups of people.

Let us review the moral evolution in America. I believe the most significant moral change in American society over the past 50 to 100 years has been the change in attitudes of white people towards black people. The most important change in the past decade has been the shift in attitudes of traditionally heterosexual individuals towards the LGBTQ+ community. I believe the forces driving these two changes are not philosophical debates, religious doctrines, or legal regulations, but rather fictional works and imagination. This power brings the plight of marginalized groups to the attention of others, allowing them to gain sympathy. Personally, I believe one of the most important forces driving moral change in America is sitcoms. As a conclusion, what I want to discuss may relate to many people present, which is the role of rational thinking in morality. Rational thinking seems contradictory. On the one hand, social psychologists have long discovered that people are often indifferent to rational thinking. The views I am discussing regarding slavery and homosexuality are my own and not influenced by anyone. On the other hand, we all know that certain rational viewpoints have strongly influenced people. A recent example is the deep impact of Peter Singer's views on the treatment of non-human animals on the world.

Similar to the views proposed by Jonathan Haidt, I believe one logical way to break this contradiction is to acknowledge that rational inferences can indeed change us, but their influence is indirect and mediated by emotions. If so, it suggests a very valuable line of research: how humans acquire new moral concepts and how they get others to accept these new concepts.

I present three points.

• First, humans are friendly, and there are many interesting behaviors in humans.

• Second, humans have evolved a powerful capacity to perceive morality, and the friendliness of humans can largely be explained by this capacity for moral perception. The connotation of moral perception is far richer than some empiricists believe.

• Third, innate moral perception is not enough; the factors that ensure we achieve those proud accomplishments go far beyond evolutionary forces, including human civilization, wisdom, and imagination.

The motivations that support our moral beliefs are not to obliterate our rational thinking ability; rather, their role is to guide the direction of inferences. Driven by motivations, we use skills and energy to seek evidence that supports our beliefs. This phenomenon may exist in most social value judgments, but I think it is precisely because of the strong suggestive effect that it appears particularly interesting and subtle in the realm of moral judgments.

Humans are born with all parameters related to language set to their default unconfigured state, waiting for the environment to serve as the "trigger" for parameter settings. This view is very appealing. As Steven Pinker has said, this is akin to humans having an instinct for learning language, with the environment merely serving to trigger and shape this instinct. In the Pinker-Chomsky doctrine, the environment is the trigger and the shaper of language. However, beyond that, the environment seems to have no greater utility for the inherent linguistic abilities of humans, and I gradually realize that this may not be the case. The terms "language parameters" and "language as an instinct" are very attractive, but I still find some basic features of language that do not seem to be inherently possessed by people.

According to Chomsky, a prominent feature of human language is its ability to generate "infinite" grammar from a limited brain. The "infinite" that Chomsky refers to not only pertains to the meanings humans can express but also to the number of sentences we can produce and the upper limit on the length of each sentence. Chomsky points out that the tool that endows human language with infinite creativity is recursion: a phrase can serve as a component of another similar type of phrase. For example, when I say "John's brother's house," the first word is "house," which appears in another noun phrase "brother's house," and then this noun phrase appears in another noun phrase "John's brother's house." Through this recursion, language can express many meanings, which is an interesting characteristic of human language.

So, what if a language lacks recursion? What difference does it make whether it is recursive or not? First, a non-recursive language is not an infinite language but becomes a finite language with a limited number of sentences. This means you can find a sentence in this language that is the so-called "longest sentence in this language." This sounds strange, but if you think about chess, you may suddenly understand, because the number of possible moves in chess is also finite. Chess is a game with many variable patterns that has been played for centuries, and people are still innovating on the moves, enjoying it endlessly. Chess may not be a great example because the variables are so numerous that you completely lose the sense of its finiteness.

If a language becomes a finite language due to the absence of recursion, it does not mean that the users of that language are a bunch of freaks, nor does it mean that the language cannot meet the rich communication needs of its users. However, if the living environment intentionally limits the number of topics you can discuss, and this limitation arises not only from the narrowness of the environment's experiences but also from explicit value orientations in the local culture that teach people not to discuss things they have not seen, meaning only to discuss immediate experiences and not to talk about anything they have not witnessed or heard from eyewitnesses, then what you can say becomes very limited. If all these conditions are met, then this language is likely to be a finite language, but that does not necessarily mean it is a barren language; it could still be a fairly rich language. The finiteness and richness of a language are not necessarily mutually exclusive; if it is finite yet rich, you need to confirm whether it truly lacks recursion.

In fact, you need not worry that a certain part of your laptop will do bad things or try to do things that the system does not want it to do. They are like slaves with very clear task descriptions. They need to be fed every day without worrying about where the energy comes from. They have no ambitions and only complete the tasks they are asked to do; although they do it beautifully, they know almost nothing about the tasks. The power you see in computers comes from these thoughtless machine slaves, but your brain is not like that.

The brain is made up of neurons. I now think of them as cells within cells, like cells within a prison. Imagine that each neuron in our brain, every cell in our body (not to mention symbionts) is a direct descendant of eukaryotic cells, and these eukaryotic cells have been self-sustaining and self-perpetuating for a billion years. They have survived through self-sustenance.

They must know a vast number of methods, possess many functions, and have self-protective abilities to realize these functions. When they aggregate into multicellular organisms, they will give up some of the functions they previously had. In fact, they are like tamed beings, becoming part of a larger, more centralized system. I believe this is true for everything. You need not worry about your muscle cells rebelling or going awry; if it does happen, we would call it cancer. But in the brain, I feel (this is a very superficial thought of mine) that this may only occur in certain species, such as humans; and it may only happen in areas of the brain that are noticeably more unstable, like the cortex. In fact, there are some small switches in genes that can make our neurons wild, just like you can make sheep or pigs aggressive; neurons can quickly regain this wild instinct.

Decision-making is often shaped into what I consider a quick and economical heuristic. For example, deciding which job to accept may lead to disproportionately significant consequences for the decision-maker. A new job may offer you a higher salary and better prestige, but it may also make your children sad because they do not want to leave and lose their friends. Some economists may think that everything has the same common denominator, but others may not feel that way. A person may ultimately make a decision based on a single factor.

We make decisions based on limited rationality, rather than being shaped by an omniscient deity with infinite rationality. However, limited rationality is not deterministic. For instance, some economists study the constraints or limitations that influence the decision-making process. This research is called "optimization under constraints," and Nobel Prizes have been awarded multiple times to researchers in this field. From this perspective on limited rationality, you will realize that an organism has neither infinite resources nor infinite time. So, given these constraints, what is the optimal solution?

There is also a group of people who study not the constraints in the environment but the constraints in thinking, including psychologists and behavioral economists. They find that people often consider only limited information and sometimes make decisions based on just one or two criteria. However, these researchers do not analyze the impact of the environment on decision-making. They believe that the primary reason people make poor decisions is due to biases, errors, and misunderstandings, and they focus on the limitations in thinking.

All these concepts do not reflect the advantages of human thinking; these limitations of thinking are not unrelated to environmental limitations; these two limitations are intertwined. Herbert Simon made a brilliant analogy with scissors: one side represents cognition, while the other side represents the structure of the environment or the task. Only by seeing both sides can we understand human behavior.

Evolutionary thinking provides us with a useful framework to pose interesting questions that are often overlooked. For example, when observing a certain heuristic thinking, that is, when people make decisions based on one factor while ignoring all other aspects, I would certainly ask in what environmental structures this heuristic thinking works and in which environmental structures it does not. This question pertains to ecological principles and the adaptability of heuristics, and it is very different from what we see in social psychology when studying cognitive illusions and judgment decisions. In those studies, any behavior indicating that people have ignored information or used only one or two pieces of information is defined as bias. This approach is non-constructive, meaning it does not connect thinking with the environment.

Heuristic thinking refers to a way of thinking that simplifies the problem-solving process through experience, intuition, or rules. It is often used to solve complex or highly uncertain problems and to make quick decisions under incomplete information or time constraints. Heuristic methods do not guarantee optimal solutions but can effectively find "good enough" solutions, especially when facing complex and uncertain problems.

Heuristic thinking is commonly seen in the following situations:

1. Rule of Thumb: Using past experiences to quickly judge a problem. For example, when faced with a similar problem, one can choose a feasible solution based on past experiences without starting from scratch each time.

2. Simplifying Problems: When facing complex problems, simplifying, narrowing the scope, or ignoring unimportant information reduces the difficulty of decision-making.

3. Intuitive Judgment: Relying on quick intuition or feelings rather than systematically analyzing all details. For example, when shopping, one might intuitively choose what they think is the most suitable product without comparing all options one by one.

4. Trial-and-Error Method: Trying some seemingly effective solutions, providing quick feedback, and adjusting strategies rather than seeking a best solution from the start.

Heuristic thinking is widely applied in psychology, computer science (such as heuristic search in artificial intelligence), decision theory, behavioral economics, and other fields. While it can improve efficiency, it may also lead to systematic biases or errors.

Common Types of Heuristic Thinking#

1. Availability Heuristic: Making judgments based on information that is easily retrievable from memory. For example, we may overestimate the probability of an event occurring because we recently heard of similar events.

2. Representativeness Heuristic: Judging based on the similarity of an event or object to a typical example. For instance, when encountering a person in a suit, one might assume they are a businessperson while ignoring other possible identities.

3. Anchoring Effect: Over-relying on the initial information when making decisions. For example, in negotiations, the first price proposed often influences the final price agreed upon.

4. Contextual Heuristic: Making quick decisions based on specific contexts or frames. For example, in emergencies, people may make riskier decisions than usual.

Advantages and Disadvantages of Heuristic Thinking#

Advantages:#

• Quick and Efficient: Able to make decisions quickly in time-sensitive or information-limited situations.
• Saves Cognitive Resources: Simplifying problems reduces the cognitive load on the brain.
• Applicable to Complex Problems: Can find reasonable solutions when it is impossible to analyze all options completely.

Disadvantages:#

• May Lead to Biases and Errors: Because heuristic thinking is based on simplified assumptions, it may overlook important details, leading to inaccurate decisions.
• Over-Reliance on Experience: Heuristic methods are often based on past experiences, but in novel or changing situations, these experiences may not apply.

In summary, heuristic thinking is a very practical tool, especially when facing complex, uncertain, or time-pressured problems. However, in critical decision-making or situations requiring high precision, heuristic methods may need to be combined with other more systematic analytical approaches.

The future of cognitive science is an important direction to understand that human thought is embedded in the environment, but many psychologists and economists do not think so. In many psychological theories about thinking, there may be various theories related to cognitive operations and motivations. However, there is almost no constructive thinking about how a certain cognitive strategy or emotion affects us and what problems they can solve. One of my points is that we need to understand not only how cognitive heuristics work and in what environments it is wise to use them, but also how emotions play a role in our judgments. We have experienced a kind of liberation in recent years. Many works by Antonio Damasio and others illustrate that emotions are crucial to cognitive function, rather than merely distracting, diverting attention, or misleading. In fact, emotions can achieve things that some cognitive strategies cannot, but we know very little about how they work.

For a simple example, imagine a "homo economicus" seeking a partner, trying to find a woman to marry. According to standard theory, the "homo economicus" must identify all possible candidates and the potential outcomes of marrying each of them. He would also study the probabilities of