It has now been a bit over a month since I left academia. I’ve started blogging again. The last time that happened was in 2017—a period in time that has almost nothing in common with the present, except for it being the last time I found myself thinking hard about how to accomplish what I wanted in life. Back then, my goals were all about learning math and developing technical competence. Now, I’m trying to figure out how to build things that could never have been built before.

It is a strange experience. I no longer receive a paycheck. My days are unstructured, my evenings are spent talking to all kinds of different people. I am surrounded by a sea of openendedness, while the world at large sees clouds of uncertainty looming over the sky around them, brought about by AI. I have a lot of work to do. I can’t really afford the time to properly think, but experience has taught me that not thinking is even more costly.

The strangest part is that I am no longer bottlenecked by the number of hours in a day, only by the number of days in a week. The list of explicit tasks I must do is short in relation to the time available to get them done: progress mostly depends on how quickly I figure out the right things to do in the first place. The last time this was true, I was a teenager. Setting my career on fire in every traditional sense has given me the opportunity to become a teenager again.

A Letter to My Teenage Self

I don’t remember exactly how to be a teenager anymore. But, I do know of a few ideas I would’ve liked to tell my teenage self about, if I could. So, I’ll tell you about them too. They might or might not be useful, but they are authentic: what you read is a direct reflection of what I was thinking about at the time of writing.

That’s really rare. Someone who writes down what they actually think does not optimize for audience engagement, influencing people, or for most particular purposes. The writing they produce is therefore less effective by those metrics, and algorithms detect that—so, they show it less, and we see it less. The internet of today is defined by these dynamics. I think the world needs more of what social media does not encourage, so that’s what I’ll write.

Dear 17-year-old Alex,

It has been a half a lifetime. That’s long enough that I do not perfectly remember what I was thinking about when I was in your shoes. At the same time, there are a few things I’ve learned over the years that you should know. Let me tell you about them. I’ll group everything by topic.

Correctly Understand Reality

You are ambitious. The single most important thing an ambitious person needs to learn to do is to correctly understand reality. Every controllable consequence in life occurs downstream of the decisions you make and their quality. I know you find this to be obvious, but there’s a bunch of details here that are worth looking at carefully.

First, we should be unambiguous about what to consider correct. Correctness is fundamentally mathematical: to the strongest scientific standard known to humanity, the physical universe—down to the smallest objects we can perform experiments on—can be described in the language of mathematics. As consequence, large objects can be described by mathematics, too, at least in principle. This includes atoms, molecules, biological cells, the human brain, the country you live in, everything—again, in principle.

The challenge is that mathematical descriptions can become so complex that one cannot meaningfully say anything nontrivial about them. What is needed are approximations that accurately describe what matters, and throw away irrelevant information that takes attention away from what we are trying to understand. Obtaining these is difficult: we have no approximate descriptions for how the brain works. Approximations allow us to distinguish reality itself from our understanding of it. This understanding is correct when it matches reality.

Correctly understanding reality is difficult. Many people you’ll meet in life won’t even try, they’ll simply repeat what they have heard before, often for social, political, or economic reasons. In many cases, information is incomplete, which means you’ll need to reason about uncertainty. This is what probability—which you already find to be so compelling that you plan to dedicate your studies and career to it—allows one to do.

Using the mathematical language of probability, you can give a precise meaning to all kinds of phenomena. These include how to learn from examples, how to learn by trial and error, how to discern cause from effect, and other related concepts. You should learn how they all work as soon as possible. Once you do, you’ll be disappointed that putting these ideas into practice will involve a lot of work. You will wish you had a computer that can do it for you. Against all odds, you will soon actually get one—more on that later.

Cultural Capital

A large portion of the things you will want to do in life will involve other people. As consequence, you will need to correctly understand the factors by which other people evaluate you. These are somewhat counterintuitive, in part because of the cultural stories we tell ourselves about our society. Let’s see how.

The most important observation to make is that correctly evaluating people is very difficult. Think of job interviews: every competent candidate is optimizing their resume to improve their chances, and learning which questions will be asked at interviews. Most people won’t tell you things that make them look bad, and a small number will outright lie to make themselves look better. Since competent candidates prepare for standard interview questions, you won’t see how they perform in totally new situations that could not have been prepared for.

If you think deeply about the consequences of this observation, you’ll realize there are fundamental limits on how accurately it is possible to evaluate people under time and budget constraints. To counteract this, people will rely heavily on signals of merit—for instance, university degrees—that are easy to understand and difficult to fake. These signals effectively transfer the costs of evaluation somewhere else—in our example, from the company doing the interview, which only has a few weeks of time, to the university, which has several years.

The second most important observation is that signals of merit begin accumulating early in life, and compound over time. If you study at the world’s most competitive universities as an undergraduate, it is much easier to get into the world’s best PhD programs—both because you’ll be better-prepared, and because it will be easier for other people to verify that you’re better-prepared. To get a sense of the effect size, pick a set of university departments, and make a table of where each professor studied for both their PhD and undergraduate.

The biggest consequence of these two observations is that cultural knowledge about what you need to do to ensure that your merit is recognizable and therefore recognized is extremely valuable. This concept has a name: it’s called cultural capital, by analogy to financial capital. It is one example among many of things that are not money, but act like it—you’ll see more throughout life.

People differ in how much cultural capital they have. For example, many of your future peers will have spent their youth preparing for the international math olympiad, or for competitive programming competitions. You’d do okay—you know how to put in sustained hard work, look at the video game mods you’ve built—but neither you nor anyone who’s willing to talk to you has ever heard of those competitions. You’re a bit late to make it into those career pipelines, but there will be more—the important thing here is to realize that pipelines exist, and why.

Indeed, there’s lots you can do to prove yourself to other people. To figure out how, you need to seek advising: you want to learn from examples, not from trial and error—the latter is too slow, it has fundamental limitations of its own. Competent people who know more than you tend to be busy pursuing their own goals, and don’t have much time to advise others. And yet, I know it’s possible to get substantial support from them because I’ve seen others do it. I haven’t fully figured out how, but you can: I’ve told you what to aim for, and I am confident you’ll find a way.

You should know your competitive advantages. I can tell you one: at some point in their career, most people will decide they’re successful enough, and will shift to what is colloquially called coasting. You are never going to do that: working on something that matters is so core to your heart and soul, you won’t give it up in favor of comfort. Use that to your advantage, and continue trying more than the next guy. This alone will take you very far.

Another advantage is that you’re reflective, and not afraid to think deeply about the kind of person you want to be. In doing so, you’re decisive, and not afraid to put your plans into action. You change your mind and your behavior when doing so is called for. These traits are worth holding on to, even for uncomfortable changes, so long as they’re well-justified and actually make sense. Over time, you’ll find many of your deliberate choices in life will guide you toward the right path.

Be mindful that, the more you achieve, the more likely it is that your path will be non-standard. Cultural capital tends to consist of information about repeatable and reliable ways toward building competence and getting recognized for it—for instance, how to join a competitive university. At the same time, life is highly random: instead of following a specific repeatable path, you can have a careful look around, think a bit, and find a non-repeatable path. More on this later.

In time, cultural capital will become a central concept within your world view. It’ll one day help you recruit unusually competent people who others miss, but it’ll be a while before you get the chance to benefit from that. It’ll also inform your sense of justice, and help you see how to make the world a fairer and more competent place, both at once—meanwhile, the rest of the world will spend a lot of time arguing about the merits of trading competence for fairness, or vice versa. These arguments will often be dressed up in complex political language, but their core will amount to the above.

Capitalism is an Emergent Property, Not a Choice

Let me tell you next a few words about society itself. Very soon, many of your peers will be interested in discussing the concept of capitalism, usually in the context of pointing to its failures. There will even be a meme consisting of a bingo card where one of the cells consists of tracing the root cause of whatever problem is being discussed back to capitalism.

What is capitalism? Your peers will regularly talk about it as a choice that people collectively make that determines how we organize society. That framing is so misleading, one might as well view it as outright incorrect. The truth, to the best information I know, is that capitalism is not a changeable property of a specific society—instead, it is a universal and largely unchangeable property of all societies, and applies equally to the United States, to the Soviet Union, and to hypothetical society run by aliens from outer space. Let me explain what I mean.

Wikipedia defines capitalism to be an economic system based on the private ownership of the means of production and its use for the purpose of obtaining profit. This makes it seem like something people choose to do. Consider this: what if, in every society sophisticated enough to have an economic system with private ownership (in some potentially-non-obvious form), only entities that pursue profit will retain this ownership over time? Let me convince you that’s likely the case: the key will be to define all of the terms, for instance value, in the right way.

For our purposes, a society with an economic system will consist of a collection of abstract entities who take actions and interact with each other over time. Entities can be created and destroyed, just like companies can be registered and can go bankrupt. Entities possess a magic number which determines whether they continue to exist, and which actions they can take: the higher, the more actions are possible. The magic number changes based on the actions they and others take: it represents private ownership, but need not be money—it could instead encode prestige, or political power.

The question becomes: what actions are taken by entities that exist for a long time? Convince yourself they ought to be the actions which, on average, increase the magic number. If you agree, this means that in our abstract economic system with any form of private ownership that can be summarized using a number, entities that survive over time pursue profit. From this, you should conclude that capitalism is an inherent property of society itself—it is a consequence of evolutionary processes that take place, whether we want them or not.

It is worth asking whether this intuitive argument has a formal analog. Answering this would make for a significant mathematical undertaking, with many details. It might be that its validity depends critically on points my human-language simplification neglects. In spite of these drastic limitations, convince yourself that I have given you a much more correct frame of thinking, compared to the ones used by your peers. Almost none of them even try to relate general social and economic behavior to the mechanistic evolutionary processes that govern them.

This observation will come to significantly color your worldview. From stories told by people that lived there, you will soon consider the former Soviet Union to be just-as-capitalist as the United States in most important ways—with the key difference that, instead of the magic number mostly representing money, it will have represented proximity to Communist Party leadership. This is still a big difference—and someone with a different perspective might use it to argue the meaning of capitalism given here is non-standard—but, somehow, it’s all the same.

You’ll soon see that a large number of people around you will get this topic wrong, including ones with completely different political views. There will be left-wing and right-wing people whose ways of thinking about capitalism will be obviously contradicted by basic facts visible to them and checkable by anyone. You will conclude that many people fail to even try to be correct about what they believe when it comes to political and economic matters, including experts. You will wonder why this is the case. I wish I could tell you, but I do not fully know.

Tailwinds

The next thing I’d like to bring to your attention is how the broader environment affects on what you can do in life. I’ll use a metaphor: when birds fly, they do so within the wind. If you choose to fly against the wind, you’ll move, but not very far. In contrast, if you’ve got tailwinds behind you, you can use them to cover a great distance.

Tailwinds tend to arise from broad economic factors affecting large portions of society, not from localized circumstances. They tend to both start, and concentrate, in particular geographic areas at particular times. For example, expertise in all factors related to technology concentrates in Silicon Valley, and gives it its namesake. The world’s biggest technology companies are not located there by accident, but rather because being there makes it easier for them to get what they want done. You should read a bit about why Silicon Valley ended up in California, rather than somewhere else.

Tailwinds include many factors—geography is only one example. Before the launch of the Sputnik satellite by the Soviet Union, the United States’ scientific community was interested in studying how to build rockets. How much progress did they make? How did this rate of progress change once the government decided rocket science would be a national priority? How were the dynamics governing individual scientists’ careers different, before and after Sputnik? Spend some time thinking about this example, you will learn much from it.

I’ll conclude with this: the effect that tailwinds have on where you end up in life is unintuitively large. History is filled with people of great ambition, whose hopes turned out to be impossible to realize within the constraints around them. In deciding what direction to take your life, think deeply about the effect the broader environment around you will have. Do not forget to extrapolate from established trends, such as Moore’s Law, and be careful when assessing uncertainty—it is often larger than people may think.

Serendipity

A theme you’ll see throughout life, in different guises, is that randomness plays a significant role in what happens—one that should not be underestimated. In contrast, our explanations about the world tend to take the form of stories, where the role of sheer randomness is minimized in favor of the narrative actually making sense. Our thinking is biased to seek order within chaos. On the other hand, a deeper understanding of probability tells us that chaos itself often has order.

For instance, many of the opportunities that will make your contributions to humanity possible will not come from explicit work on your part—instead, they will come from being at the right place at the right time, in an unpredictable manner. It might seem like you cannot control this—but, to a degree, you can: for example, by choosing to live in a certain city, you expose yourself to the random opportunities of that city, as opposed to those of other cities.

You can also control the degree to which you pay attention to the opportunities around you. When you’re working on something technical, you’ll often want to focus deeply on the task at hand, because this will help you get it done. This same focus can also make it harder to see unexpected opportunities around you. Sometimes, it is better to not get the immediate task done, provided you notice those opportunities. Thus, you should keep your mind open to unexpected ways to achieve your goals, beyond what you had planned for.

This includes your broad direction of work. For example, if you’ve been working on something for a while, there are consequences to continuing to move in the same direction. By virtue of continuity, you’ll have a reasonable sense of what the results of your existing work will be. In contrast, switching to something completely different brings uncertainty. This uncertainty need not mostly consist of risks: it can sometimes bring great opportunity along with it. Do not be afraid to move quickly, but in the same breath, do not be afraid to take your time.

You will be richly rewarded for getting this right in your family life. Against all odds, you will learn early on that the typical stories society tells young men about dating and status are not true—your second half has a huge effect on your day-to-day experience, and almost no effect on how other people think of you. Thus, you should choose what’s right for you, not for others. In doing so, you should be open to meeting someone, but not be afraid to be patient and take your time. Over time, serendipity will ensure you’ll cross paths with the right person.

Devaluation of Technical Skill

You will live in extraordinarily interesting times. To describe today’s moment, from the perspective of society at large, the best words I can think of are staring into the singularity. You’ll be shocked to hear that, today, artificial general intelligence actually exists. Remember that computer I said you’d wish for? It is still new enough that its precise effects on humanity have not yet become apparent. They are being decided as we speak, and no-one appears to be in control.

This will affect you personally before it affects others. In your life, you’ll spend a lot of time learning math, because you’ll believe deeply in the style of thinking it teaches, and in the intellectual achievement of understanding a question comprehensively. Not long after you contribute what you feel is your first truly original theorem—one that is not a minor extrapolation of existing ideas—AI will solve a Millennium Problem. You’ll still be waiting on referee reports, after more than a year. In this moment, others will reach toward anger, but you will react with awe.

I don’t quite know what will make you react this way, given your mathematical ambitions will be disrupted well before AI affects most other people. Perhaps it’s because you believe in optimism, which is decision-theoretically sound, and don’t believe in bitterness. In any event, you won’t find it hard to steadily pivot your attention to new and much more important ambitions.

There will soon be a lot to do. You’ll see that AI will devalue technical skills in isolation, but won’t change the indirect benefits those same skills bring by teaching a person new ways of thinking. And you’ll need this to handle new situations that never could have been encountered before AI. The world will be facing a lot of situations like that, from every perspective imaginable—whether safety and alignment, or new opportunities to tackle previously-impossible problems. Wherever you go, your mathematical training will be there with you.

Insignificance

One of your great strengths is that, on average and in comparison with others, you’re a pretty fearless person. It is worth carefully considering the exceptions, so that you understand how fear influences you. For that, I’ll simply tell you what you fear more than anything else: insignificance. You are not even eighteen years old, but you already worry that, when you reach retirement age and have lived most of your life, none of what you did in life will have amounted to anything in particular.

The good news is that, as far as fears go, one could reasonably call this one high-functioning: it won’t actually disrupt your working or otherwise day-to-day life much. Instead, it will influence you to take out-of-distribution life choices, such as moving to a foreign country to do a PhD, with the hope that you one day return a more worldly person, with a keener pulse on society, one that will aid you later in non-obvious ways. The charitable way to view your biggest fear would therefore be to see it as a reflection of ambition.

I wish I had more concrete ways of thinking about this topic, but I don’t think I have it figured out yet. I know that I feel the same way today as you did a lifetime ago, and I don’t quite know what it would take for me to feel different. Perhaps the way to understand this on both of our parts is to wait another lifetime’s worth, and see what a future version of both of us would say about it.

Conclusion

It has taken me forever to write this letter, in part because it was not quite clear how to actually say the things I wanted to tell you about. Thinking about them has proven useful, as it has helped me understand myself better. I hope you find that there’s a good set of ideas here: they’re messy and incomplete, but I have faith in you—I think I’ve said enough, the rest you can figure out.

I wonder what you’d think of me. It has been half a lifetime. If I had to guess, I think you’d be impressed with the skills I’ve learned and frame of mind I’ve adopted, but would be disappointed with how long it took, and how many mistakes I made along the way. You would probably find it hard to figure out how many of those mistakes were unavoidable, given lack of knowledge about how life works, and, indeed, so do I. I hope this letter helps you. Good luck!

Signed,
Alex, half a lifetime later