Paul Graham is the founder of YC, and the leader and friend of Ultraman, the father of ChatGPT.When I was a kid, one of my big misconceptions about the world was that the degree to which performance pays off was super-linear.During his time at YC, he coached 9,000 founders and led YC from 0 to 1. For details, see "Counseling 9,000 founders, the world's largest business incubator boss has 8 scriptures".
As a businessman, Graham was a Silicon Valley thinker and prolific evangelist, and the author of the best-selling book "Hackers and Painters."
In a recent article titled "Super Linear," Graham breaks down the impact of exponential growth on entrepreneurship and life. This also explains why YC is so focused on the growth rate of its incubators.
The following is the original text (translated by chatgpt):
Teachers and coaches implicitly tell us that returns are linear. "You get as much as you give," I've heard it countless times, "you get as much as you get." "They have good intentions, but that's rarely true. If your product is only half as good as your competitors, you won't get half the customers. You'll have no customers, and then your business will go out of business.
In business, the payoff for performance is ultra-linear, and that's obviously true. Some people see this as a flaw in capitalism, which will no longer be true if we change the rules. But the super-linear return of performance is a feature of the world, not a product of the rules we invented. We see the same pattern in fame, power, military victories, knowledge, and even benefits to humanity. In all these ways, the rich get richer. [1]
You can't understand the world if you don't understand the concept of super-linear returns. If you are ambitious, you should definitely understand this because it will be the wave of your surfing.
You might think that there are a lot of different scenarios where there are hyperlinear returns, but as far as I can tell, they boil down to two fundamental reasons: exponential growth and thresholds.
The most obvious example of a super-linear return is when you're engaged in something that can grow exponentially. For example, cultivating bacterial cultures. When they start growing, they grow exponentially. But cultivating them is tricky. This means that the difference in results between skilled and unskilled is very large.
Start-ups can also grow exponentially, and we see the same pattern there. Some businesses have managed to achieve high growth rates. Most don't. As a result, you'll get qualitatively different results: companies with high growth rates tend to become extremely valuable, while companies with low growth rates may not even survive.
Y Combinator encourages founders to focus on growth rates rather than absolute numbers. This prevents them from getting frustrated in the early stages, when the absolute numbers are still low. It also helps them decide what they should focus on:You can use the growth rate as a guide to tell you how to grow your company. But the main advantage is that by focusing on the growth rate, you tend to get something that grows exponentially.
YC doesn't explicitly tell founders that the growth rate is "what you give, you get", but that's not too far from the truth. If the growth rate is proportional to performance, then the return on performance p over time t will be proportional to p t.
Even after thinking about this for decades, I find this statement still shocking.
Whenever you do well depends on how well you have done before, you get exponential growth. But neither our DNA nor our Xi are ready for this. No one thinks exponential growth is natural;Every child is amazed when they first hear the story of asking the king to give a grain of rice on the first day and double it every day thereafter.
Natural phenomena that we do not understand, we develop Xi to deal with, but we have few Xi habits for exponential growth, because this has been rare in human history. In principle, herding should be one of them: the more animals you have, the more offspring they will have. But in reality, the limiting factor is pasture land, which is not planned to grow exponentially.
Or more precisely, there is no universally applicable plan. There is indeed a way to exponentially grow one's territory: through conquest. The more territory you control, the stronger your army will be, and the easier it will be to conquer new territories. That's why history is full of empires. But few people created or managed empires, and their experiences had little impact on Xi. The Emperor is a distant and terrifying figure, not a lesson that one can use in one's own life.
Probably the most common case of exponential growth in the pre-industrial era is learning. The more you know, the easier it will be to learn something Xi new. As a result, then, as now, there were people who were far more knowledgeable than others in certain topics. But this has little effect on Xi. Although empires of ideas can overlap and therefore have more emperors, in the pre-industrial era this type of empire had little practical effect. [2]
This has changed over the centuries. Now the Emperor of Ideas can design bombs to defeat the Emperor of the Territory. But this phenomenon is still very new, and we have not yet fully absorbed it. Even a small number of participants realized that they were benefiting from exponential growth or asked what they could learn from other instances.
Another ** of super-linear returns is embodied in the "winner takes all" expression. In sports, the relationship between performance and return is a ladder function: whether they perform much better or slightly better, the winning team gets a win. [3]
However, the ** of the ladder function is not the competition itself. Rather, there is a threshold in the results. You don't need competition to get these. Even if you are the only participant, like proving a theorem or hitting a target, there can be thresholds.
In cases where there is only one super-linear return**, there is often another as well. Crossing the threshold leads to exponential growth: the side that wins the battle usually loses less, which makes them more likely to win in the future. And exponential growth helps you cross the threshold: in a market with network effects, companies that grow fast enough can exclude potential competitors.
Fame is an interesting example of combining two types of ultra-linear returns**. Fame grows exponentially because existing followers bring you new followers. But the fundamental reason it's so concentrated is the threshold: there are only so many places on the A-list in the minds of the average person.
Learning Xi is probably the most important case of combining two types of ultra-linear returns**. Knowledge grows exponentially, but there are thresholds in it. For example, learn to ride a bike. Some of these thresholds are similar to mechanical tools: once you learn to read, you'll be able to learn Xi anything else faster. But the most important thresholds are those that represent new discoveries. Knowledge seems to be fractal, meaning that if you push the boundaries of knowledge in a certain field, you will sometimes find a whole new field. If you do, you'll have the opportunity to study all the new findings in it first. Newton, Duller, and Darwin all did this.
So, is there a general rule for looking for a super-linear return situation?One of the most obvious is to look for jobs that can be compounded.
Work can be compounded in two ways. It can be compounded directly, meaning that doing well in one cycle will lead you to do better in the next. This happens, for example, when you're building infrastructure, or growing your audience or brand. Or work can be compounded by educating you, because learning Xi is compounding. This second scenario is interesting because when it happens, you may feel like you're not doing a good job. You may not have achieved your immediate goals. But if you learn a lot, then you still get exponential growth.
This is one of the reasons why Silicon Valley is so tolerant of failure. Silicon Valley people are not blindly tolerant of failure. If you learn from your failures, they will continue to bet on you. But if you do, you're actually a good investment: maybe your company isn't growing the way you'd like, but you've grown on your own and should end up paying dividends.
In fact, forms of exponential growth that do not include Xi are so often intertwined with Xi that we should probably treat this as the rule rather than the exception. This gives rise to another heuristic principle: always Xi. If you're not Xi, you're probably not on the path to super-linear returns.
But don't over-optimize what you're learning Xi. Don't limit yourself to learning only Xi things that are known to be valuable. You are Xi;You're not sure what will be valuable yet, and if you're too strict, you'll cut out the outliers.
What about the ladder function?Are there useful heuristics like "look for thresholds" or "look for competition" as well?Here the situation is more complicated. The presence of a threshold does not guarantee that the game is worth playing. If you play a round of Russian roulette, you will definitely come across a threshold, but in the best case you are no better. "Look for competition"Equally useless;What if the reward isn't worth the competition?Exponential growth fast enough guarantees the shape and size of the return curve – because if the growth is fast enough, it will become large even if it is insignificant at first – but the threshold only guarantees the shape. [4]
The principle of utilizing thresholds must include a test to ensure that the game is worth playing. Here's a rule of thumb: if you come across something mediocre but still popular, it might be a good idea to replace it. For example, if a company makes a product that people don't like but still buy, they might buy it if you make a better replacement. [5]
It would be nice to find a way to find a promising intellectual threshold. Is there a way to know which problems have completely new areas behind them?I doubt we'll be able to ** this exactly, but this reward is so valuable that even slightly better than the random ** * We can somehow ** a research question is unlikely to lead to new discoveries: when it seems legitimate but boring. And the questions that do lead to new discoveries often seem very mysterious, but may not be relevant. (If they're both mysterious and obviously important, they'll be famously unsolved mysteries that have been studied by a lot of people.) So one heuristic principle here is to be driven by curiosity, not careerism – to give your curiosity free run rather than doing what you're supposed to do.
The prospect of super-linear returns for performance is exciting news for ambitious people. Here's the good news: in this space, things are expanding in both directions. You can earn super-linear returns with a greater variety of work, and the returns themselves are growing.
There are two reasons for this, although they are so closely connected that they are more like one and a half reasons: technological advances, and the reduction of organizational importance.
Fifty years ago, being part of an organization was almost a must to work on ambitious projects. That's the only way you get the resources you need, the only way to have colleagues, and the only way to get distribution. So in 1970, your prestige was in most cases the prestige of the organization you belonged to. Prestige is an accurate tool because if you're not part of an organization, you're unlikely to achieve much. There are a few exceptions, most notably artists and writers, who work alone with inexpensive tools and own their own brands. But even they are subject to organizing to reach audiences. [6]
A world dominated by organizations reduces variation in performance returns. But the world has eroded significantly in my lifetime. Now, more people can have the freedom that 20th-century artists and writers have. There are a lot of ambitious projects that don't require much initial capital, and there are also a lot of new ways to learn Xi, make money, find colleagues, and reach audiences.
There are still a lot of old worlds, but the pace of change is dramatic by historical standards. Especially considering how big the stakes are. It's hard to imagine a more fundamental change than a change in performance returns.
Without the damping effect of the mechanism, the result would be even more changeable. This doesn't mean that everyone will be better off: those who do well will do better, but those who don't do well will be worse. This is an important point to keep in mind. Exposing yourself to ultra-linear returns isn't for everyone. Most people would be better off being part of a pool. So, who should go after super-linear returns?There are two groups of ambitious people: those who know they are so good that their net gains are higher in a highly changing world, and those who are especially young people who can take the risk of trying to find out. [7]
The shift from institutions is not just a massive outflow of their existing residents. Many of the new winners will be the ones they will never let in the door. Thus, the democratization of opportunity will be bigger and more real than any modest version of the interior that the institutions themselves might concoct.
Not everyone is happy with this great act to unleash ambitions. It threatens some vested interests and contradicts some ideologies. [8] But if you're an ambitious individual, that's good news for you. How should you take advantage of it?
The most obvious way to leverage performance to deliver super-linear returns is to do extraordinarily good work. At the far end of the curve, incremental effort is cost-effective. What's more, there's less competition at the far end – not just because it's difficult to do it very well, but because people find the prospect so prohibitive that few try it. This means that it is not only cost-effective to do extraordinary work, but even to try to do it.
There are many variables that affect the quality of your work, and if you want to be an anomaly, you need to get almost all of these variables right. For example, in order to do it particularly well, you have to be interested in it. Diligence alone is not enough. So, in a world with super-linear returns, it's more valuable to know what you're interested in and find ways to do it. [9] It is equally important to choose a job that is appropriate for your current situation. For example, if there is a job that inherently requires a huge investment of time and energy, it will be increasingly rewarding to do it when you are young and do not yet have children.
There are many tricks to making great work. It's not just a matter of effort. I'm going to use a text to try to give a square **.
Choose a job that you are naturally suited for and deeply interested in. Develop the Xi of working on your own projects;As long as you feel they're ambitious enough, it doesn't matter what they are. Work as hard as you can, and eventually this will take you to the cutting edge of knowledge. These look smooth, but up close they are full of gaps. Pay attention and explore these gaps, and if you're lucky, one of them will expand into a whole new realm. Take the risk you can tolerate;If you don't fail once in a while, you're probably being too conservative. Find the best colleagues. Develop good taste and Xi from the best examples. Be honest, especially to yourself. Exercise, eat well, sleep well, and avoid more dangerous medications. In doubt, follow your curiosity. It never lies, and it knows more about things to deserve attention than you do. [10]
Of course, there's one more thing you need: luck. Luck is always a factor, but it's even more important when you're working independently rather than as part of an organization. While there are some valid adages about luck being ready to meet opportunities and so on, there is also a part of true serendipity that you can't do anything to change. The solution is multiple attempts. This is another reason why you should start your adventure early.
Science is probably the best example of a superlinear return. It has exponential growth, in the form of learning Xi, plus the threshold of extreme performance – literally the limit of knowledge.
The result is a scientifically discovered level of inequality that makes wealth inequality appear moderate in even the most stratified societies. Newton's discoveries were probably greater than all of his contemporaries combined. [11]
This may seem obvious, but it's best to make it clear. Super-linear returns mean inequality. The steeper the return curve, the greater the variation in the outcome.
In fact, the relationship between superlinear returns and inequality is so strong that it gives rise to another heuristic principle for finding this type of work: looking for areas where a few big winners perform better than everyone else. The type of work that everyone performs roughly the same is unlikely to have a super-linear return.
What are the areas where a handful of big winners are performing better than everyone else?Here are some obvious examples: sports, politics, art, acting, directing, writing, math, science, entrepreneurship, and investing. In sports, this phenomenon is caused by externally imposed thresholds;You only need to be a few percentage points faster to win every game. In politics, the growth of power was much like in the time of emperors. In some other areas, including politics, where success is largely driven by fame, it has its own super-linear growth**. But when we exclude the influence of sports, politics and fame, a striking pattern emerges: the rest of the list is exactly the same, the areas where you have to think for yourself to succeed – your ideas must not only be right, but also original. [12]
In science, this is obvious. You can't make a statement to repeat what someone else has already said. But the same applies to the field of investment. The belief that a company will perform well is only useful if most other investors don't;If everyone thinks that this company is going to do well, then its share price already reflects this, there is no room to make money.
What else can we learn from these areas?In all of these areas, you have to put in the initial effort. The super-linear returns may seem small at first. You'd think that at this rate, I'll never get there. But because at the far end, the reward curve rises dramatically, it's worth taking extraordinary steps to get there.
In the startup world, this principle is known as "doing something that is not scalable". If you put ridiculous attention into your tiny initial customer base, ideally, you'll trigger exponential growth through word of mouth. But this principle applies to anything that grows exponentially. For example, Xi. When you first start learning Xi something, you feel lost. But it's worth the initial effort to gain a foothold because the more you learn, the easier it becomes.
There's a more subtle lesson in the list of areas with super-linear returns: don't equate work with a job. For most of the 20th century, the two were the same for almost everyone, and as a result, we inherited a Xi that equated productivity with having a job. Even now, for most people, the phrase "your job" means their profession. But for writers, artists, or scientists, it refers to something they are currently researching or creating. For such people, their job is something that they carry from one job to another, if they don't have a job at all. It may be done for the employer, but it's part of their portfolio.
Entering a field where a handful of big winners outperform everyone else is a daunting prospect. Some people do it on purpose, but you don't need to. If you're gifted enough, and your curiosity is far enough away, you'll end up in one of these areas. Your curiosity doesn't interest you in boring questions, and interesting questions tend to create domains with super-linear payoffs, if they're not already a part of them.
The realm of super-linear returns is by no means static. In fact, the most extreme rewards come from scaling it. So, while both ambition and curiosity can get you into this field, curiosity can be the more powerful of the two. Ambition tends to make you climb existing peaks, but if you tightly wrap around a problem that's interesting enough, it might grow into a mountain below you.
There is a limit to the difference between effort, performance, and reward, because in fact they are not clearly distinguished. What counts as a reward for one person may be a manifestation for another. But while the boundaries of these concepts are blurred, they are not without meaning. I wrote about them as precisely as possible, but without crossing the line.
1] From a performance perspective, evolution itself is probably the most prevalent example of superlinear returns. But it's hard for us to resonate because we're not the beneficiaries;We are rewarded.
2] Of course, before the Industrial Revolution, knowledge did have practical effects. The development of agriculture has completely changed human life. But this change is the result of extensive, incremental technological improvements, not the findings of a few particularly learned people.
3] Mathematically, it is incorrect to describe a ladder function as superlinear, but a ladder function from zero works like a hyperlinear function when describing the reward curve for the efforts of rational actors. If it starts from zero, then the part before the ladder is below any linear growth return, and the part after the ladder must be higher than the return required at that point, otherwise no one will bother.
4] Finding competition can be a good heuristic because it is an incentive for some people. It also guides promising issues to a certain extent, because it shows that others see them as promising. But this is a sign of a very imperfection: often there is a large group of people chasing a problem, only to be overtaken by another person who works silently.
5] Not always, though. You have to be careful with this rule. When something is popular despite its mediocrity, there is usually a hidden reason. Perhaps it is monopolies or regulations that make competition difficult. Maybe it's because the customer is in bad taste, or the program they choose to buy is flawed. There are a lot of banal things that exist for such reasons.
6] In my twenties, I wanted to be an artist and even go to art school to learn Xi painting. Mainly because I love art, but a non-small part of my motivation comes from the fact that artists seem to be least at the mercy of organization.
7] In principle, everyone is getting super-linear returns. Learning Xi is cumulative, and everyone is learning Xi in their lives. But in reality, very few people push this daily learning Xi to the point where the return curve becomes very steep.
8] It's not clear what exactly an advocate of "fairness" means. There also seems to be disagreements between them. But whatever they mean, it can be the opposite of a world in which an institution's ability to control outcomes is diminished, and a few outperform others.
The concept came at a moment when the world was turning in the opposite direction, which may seem like bad luck, but I don't think it's a coincidence. I think one of the reasons it's emerging now is because its adherents feel threatened by the growing difference in performance.
9] Corollary: Parents who force their children to take up a prestigious job like medicine, even though they have no interest in it, will do them more harm than in the past.
10] The original version of this text was the first draft of How to Make a Great Work. As soon as I finished writing it, I realized that this was a more important topic than super-linear returns, so I paused the current article to expand this text into its own. Because I rewrote it based on that after I finished How to Make a Great Work, the original version barely survived.
11] Before the Industrial Revolution, people who became rich usually did what emperors did: controlling a certain resource made them stronger, and thus able to control more. Now it can do like a scientist, by discovering or building something unique and valuable. Most people who have become wealthy use a mixture of old and new methods, but in the most advanced economies, this proportion has skewed significantly in favor of discovery in the last half-century alone.
12] If independent thinking is one of the biggest drivers of inequality, it's not surprising that people with traditional thinking don't like it. But it's not just because they don't want others to have what they can't. Traditional-minded people simply can't imagine what it would be like to have a novel idea. So, when they encounter a big difference in performance, they feel that this phenomenon is unnatural, and they think that it must be due to cheating or some kind of bad external influence.
References: 1] Superlinear returns: