Sal Khan On The Finding Mastery Podcast

My personal notes from Sal Khan’s interview with Michael Gervais on the Finding Mastery podcast.


How did Sal mentally manage the risk of non-venture backed entrepreneurship?

Early on in the Khan Academy journey, even when, let’s go back to 2004 2005, I started tutoring my cousin’s 2005, I started writing software for them. That’s when I got the domain name Khan Academy. And I started writing software for my cousins. And I said, “Hey, if it’s just my cousins who are using it, it’s worth doing this, it’s helping them”. But obviously, as you start writing software you’re like, but maybe people who are not my cousins could use it. But I kept trying to keep myself from getting too attached to the big ambition, just saying, hey, just put one foot in front of the other, but keep the door open to the big ambition. I didn’t want to close that door either…

Even before I had quit my job, I would show my friends, “Hey, I’ve got this hobby. I’m tutoring my cousins.” My friends, out here in Silicon Valley, their natural inclination is “why are you doing this?” And I’m like, “oh, because it’s helping my cousins.” They’d ask, “How are you going to monetize this? I don’t see the business plan. Someone else’s is doing what you’re doing.”

I’m like, no, no, no, this isn’t a business. This isn’t anything. I’m doing it because it’s helping my cousins. And hey, if it helps other people, great. So that was one form of protection.

Dealing with cynics — who do you need to convince and what evidence do you hold?

Even today, when I encounter cynics, the first thing I say is, “Sal, don’t be defensive, there might be something in what they’re saying”. You don’t want to be delusional and ignore good feedback. But at the same time, you also have to remind yourself: you don’t have to convince this person.

We always want to impress our friends and convince them that what we’re doing is a good idea. But I don’t have to convince them. That’s the first somewhat liberating thing. And then what made me not question myself too much, I said, “Okay, so what evidence do you have?” This is a friend who’s smart, I respect their opinion, but what evidence do I have?

Well, I did transform several of my cousins’ lives. I was already getting letters from people who I didn’t know around the world about how it had transformed them in some way, shape, or form or their children.

Look, my well-intentioned friend is probably trying to save me from “wasting time” or getting distracted, but they haven’t even tried it out. They just did classic MBA-type thinking of “Well, I heard some other companies are making educational videos and doing software that creates questions. You’re like the 10th person to do this, so what makes you think…”. That’s their natural, competitive analysis type of thing.

I think there’s probably a lot of people who want to do entrepreneurial things. And when they meet a friend who’s doing something entrepreneurial, part of their brain wants to help the friend and wants to be constructive for the friend, part of their brain wants to help their friend. If they think their friend is going down the wrong angle, maybe protecting them from that a little bit. But some of it is also protecting their choices. “I’ve always wanted to be an entrepreneur, but I’ve been afraid to and now my friend is doing it…maybe it’s comfortable if I convince him to stop doing it, and do what I’m doing.”

The main thing is just what just keep reminding yourself, “Why are you doing it? What gives you confidence?” And remembering “Who do you really need to convince? And who do you not really have to convince?”

Where did Sal learn to focus on evidence and focusing on who he needed to convince?

He lightly responds: Probably is a coping mechanism for a bunch of things that happen in life…I’ve been described by even some of our early board members as a “pleaser”. Like I want people to say, “Good job.” [Me: Oh man, this hits hard]

I think I realized in my life you’re never going to win trying to please everybody. Trying to convince people, getting defensive about things, you just don’t feel good about yourself. 

I’m still working on it. I have a lot of ideas. I do try to share them with people who I really respect. And when they immediately get in the devil’s advocate position or the cynical side, I do get a little defensive if I’m honest. But I I’ve been working on myself.  “Okay, I don’t have to convince them, there’s probably some truth in what they’re saying, I should process it.”

And you know, also some of it’s on me. I realized that when I get excited about an idea, I go into “sell mode” almost immediately, like “this is all the reasons why it’s good, isn’t this exciting?…” And that almost automatically puts people into that devil’s advocate position. “But what about this? What about that?” And so now when I introduce ideas, I’m going against my stereotype, where I’m showing that I’m also looking at the risks and how this could go wrong.

Half the time, the next morning, I wake up, I’m like, “Yeah, they were kind of right.” But sometimes I’m like, “No, I still have evidence that this was worth this is worth pursuing.”

How did Sal frame the decision to leave the hedge fund path to start Khan Academy?

There were some basic mechanical, left-brain considerations.

Did I save up enough money?  I was an analyst at a hedge fund, I wasn’t a hedge fund manager. So I was able to save up some money, essentially a healthy downpayment for our house in Silicon Valley. We were saving up for, you know, several hundreds of thousands of dollars not like independently wealthy money. We don’t have big expenses. My wife and I grew up quite poor so we know how to economize.  That was a mechanical thing.

Even more was the opportunity cost of the [hedge fund] career. Every year your income is accelerating. In five or six years, I could be making what my boss was making,  what could have been in the millions of dollars every year. And that’s a real big opportunity cost to give up for something that’s unproven. That’s where a little bit of the heart came in. I just told myself “Well, what is the life that you want? And the life that I want is a healthy, happy family. But I really told myself, if I had a nice 2000 square foot house, which was the house that we were renting, and we later were able to buy — a four bedroom house with you know two cars in the driveway. We’re able to go on vacations, go to restaurants every now and I’m able to support my kids through college. That’s all I want, financially, really. And if I’m able to do that then also get to work on something that, every morning, I wake up and I’m inspired to work on, I get to work on an interesting problem, and I feel like I have a sense of purpose then I consider myself the luckiest person on the planet. I’m not saying this now just to sound you know anything, that’s literally what I told myself. I’m like, if you are able to have that lifestyle, that’s a really good life. And so that liberated me a little bit from the golden handcuffs.

A lot of times when I’m making some of these decisions like even “what Khan Academy should be” I do go a little bit into what inspires me. We have one life to live. If you have a shot of being able to live your life as a protagonist in a movie, live your life as a protagonist in a science fiction book, go for it! [Me: this is the type of thinking that doesn’t show up in a spreadsheet. This is an example of how “accounting” fails us…not everything that matters can be measured and vice versa]

He fills in the details:

Even in the early days, there were a lot of VCs who reached out who wanted to write a check and Khan Academy be a for-profit, and it was tempting. But then when we start talking about monetization, and how you’re going to exit and all that I was like, “Oh, this isn’t what I want to do I want to”

Then I thought about what is the homerun is for a for-profit. And then what’s a homerun for a non-profit. A homerun for a for-profit, we all know those stories quite well. But I was also thinking, “How’s it going to change the world? And how’s that going to change me?”

And then I thought about a home run as a non-profit. I’m like, “What if Khan Academy can be the next Smithsonian, the next Oxford, or the next, whatever. In some ways, it’s bigger than all of those because even in 2009, when I was thinking about these things, it had bigger reach than some of these hundreds-of-year-old institutions. And we were, there’s no reason why we couldn’t grow another 100 fold or not 1000 fold from there. So for me, it was like, “Wow, maybe it’s worth swinging for the even higher fence.” That’s a hard thing. The head kicks in and says, “Okay, is that at all reasonable?” And as ridiculous as it sounds, it isn’t unreasonable. If you just extrapolate the growth, if you just look at what Internet technologies allow us to do, if you just think about the scale of other people on the internet, for the most part for-profits…Google scale would have seemed like science fiction 30 years ago for what it does. But it’s not. And so couldn’t Khan Academy be that same thing, but as a social institution?

Did he share this thinking with others?

Going back to our earlier, I’ve realized that there’s certain contexts where you’re this type of conversation is going to be welcome. But the conversations where I’m talking to my friend who’s talking about how you’re going to monetize this, he’s not going to be in a headspace where I’m like, Well, what do you really want out of your life? And what do I really want in my life?

And do I need his approval for me to be able to do it? Now, I did talk about this with my wife, and I kind of do need her approval because this is “how do we want to live our life”.

Healthy and unhealthy “imposter syndrome”

I think some of that impostor syndrome, I actually want to retain. I never want to forget how, like, there, there was a time not too long ago that I would pass on the organic produce. I think it lets you just appreciate the world a little bit. And we all know about hedonic adaptation and the hedonic treadmill. I don’t claim that I’m immune so I don’t want to sound like I’m some guru here. I live in Silicon Valley. We live in that same house, and a lot of our friends have now moved into houses that are multiple of the size of our house. Every now and then it’s “maybe it would be nice to have two saunas.” But I always remind myself, “well imagine their electricity bill, or like, the gardening bill or the water bill or whatever.” But, yeah, I think it’s healthy imposter syndrome.

A healthy one keeps you grounded, allows you to enjoy it a little bit. Like every now and then I get invited to meetings with people or conferences with people, where both healthy and unhealthy impostor syndrome could be at play. The healthy imposter syndrome says  “Wow, you get to meet your childhood hero, or someone that you thought you could only read books about, and you’re meeting this person, and they are interested in what you have to say, and they’re supporting Khan Academy.” That’s kind of fun. I don’t know if that’s impostor syndrome, or that’s just remembering yourself when you’re younger. And you’re like, “Wow, how is little Sal in this meeting right now? That’s kind of wild.”

The little less healthy imposter syndrome is that if that goes to an extreme, where like there’s a discussion and I’m like “Who am I to say something?”

There, I try to remind myself that everyone here is literally just a person, like everyone here. And that’s another, I guess, coping mechanism. I just treat everyone as if they’re my childhood friend. And there’s something of a self-fulfilling prophecy there as long you’re respectful. Some people who have been great supporters of Khan Academy are household names — I’m gonna treat them as my friend. And I think they appreciate that too, because so many other people treat them with such reverence, and I respect them a ton, but I get to joke around with them a little bit. And that’s how I deal with that other potential imposter syndrome.

A resonant story: college can give you a safe space to explore things you have suppressed because you grew up perhaps in a narrow place

MIT was like heaven for me. I think when you are in high school in a fairly mainstream high school, you have to suppress certain instincts. You have to suppress how much you get excited about learning certain things so you don’t get beat up, you don’t get ostracized.

Why Sal wanted to dedicate himself to education

  1. First, I’ve always enjoyed teaching. Multiple times in my life, either informally, even when I was very young, I found that I had a knack for it. In a lot of cases where a classmate might be struggling to understand what’s in a textbook or a teacher,  and I’m like, “Oh, this is how I think about it”. And my friend was like, “Oh, man, that’s so cool. Yeah, that makes all the sense in the world”. I guess I have a knack for this thing. So that kind of built confidence in my ability to do that. [Me: importance of knowing yourself in helping determine what you should be doing!]I was the president of the math club and one of the things we did was math tutoring.  We created such a legitimate program that the school then made it a formal part of the school. It made anyone who had below a certain grade in any of their math classes go to this math tutoring, that I was essentially running with a bunch of other students who are in this club. And I saw time and time again, a lot of students who were struggling, barely passing a course, or thought they hated math, if they just had the opportunity, the incentive to fill in gaps, had things explained to them the right way, a chance to practice, they were off to the races. Some of them joined the math Honor Society. A month ago, they were about to fail their algebra class, and now they’re going to math competitions with us, because they started to get excited about it. So that also gave me confidence.And that’s all about mastery learning. The opportunity, incentive to fill in any gaps to finish any unfinished learning.
  2. The other thread is I think every young person who’s even vaguely idealistic, and I think this is all young people, look at the world and say, “Oh, there’s so many problems in the world. How do you solve it?” You think about climate, you think about inequality, think about whatever you pick, you pick the issue. Conflicts, when you really keep peeling the onion, it’s just what’s going on in people’s heads. Everything else is almost just a side effect of what’s going on in people’s heads. Okay, so then we got to change what goes on inside people’s heads or improve or remodeler? Well, what does that? Education. Education is the single highest leverage point.

A quote pulled from Sal’s writing:

If you believe in trying to make the best of the finite number of years we have on this planet, while not making anyone worse think that pride and self righteousness are the cause of most conflict and negativity, and are humbled by the vastness and mystery of the universe, then I’m the same religion as you.

What is the state of education today?

The good news

If I compare the State of the Union of education to what it was 250 years ago, it’s awesome. 250 years ago, even in more literate countries, 30-40% of the of the population was functionally illiterate. Free public school, or at least a high-quality public school was not a mainstream thing as recent as even 30, 40 or 50 years ago. Because of things like segregation even in places like the US, you did not have respectable access to education. I think it’s still not perfect, and there’s still a lot of inequality but for the most literacy rates are much, much better than they were for most of human history. Even in the last 10 years, as I’ve been on this journey, things like access to technology, to the internet, to high-quality instructional materials, etc. That’s all actually gotten better, even in the last 15 years.

The bad news

Even in affluent neighborhoods or fancy prep schools, you still have a model where a lot of kids are still falling through the cracks. And those are the places where they’re not resource-constrained. Imagine in the places where they are resource constrained. I mean, there are still schools, my school in fact, which is a suburb of New Orleans which was pretty mainstream, it wasn’t a gold-plated school by any stretch of the imagination. It was a normal Louisiana public school. But I remember even when I was growing up, there were schools in New Orleans and kind of urban corridors that didn’t have air conditioning. Can you imagine not having air conditioning in New Orleans?

The disappointing news

Let’s just assume that you have all the resources…the model of education is not mastery-based. Kids are moved ahead at a fixed pace. They cover some material, they get a test, some kids get 100 on it, some kids get a 90, some kids get a 70 on it, even though that student didn’t know 30% of the material that happened to be on the test, the whole class will move on to the next concept, and then build on those gaps. And then the next concepts are going to be that much harder to learn. And then those gaps just keep accumulating. [Me: In my own tutoring I see this at the elementary level. Kids that are 2 to 3 grades behind. There’s no concept of being left back. Just push them through the system]
At some point, kids hit a wall. It hits their self-esteem, they’re not able to move any further. And this isn’t theoretical, you just look at the graduates of a fancy prep school, it’s happening. It’s definitely happening on a nationwide basis. So I think that is the biggest problem.

60% of kids who to 2-year colleges and about 30% of the kids who go to 4-year colleges (and college-bound kids are in the top half of already) exhibit giant gaps in learning, many unable to learn algebra yet — a 9th grade course. The majority of kids attending college would need to go back to middle school-level learning to fill in gaps.

On American universities

American higher education is the envy of the world. Our research is the best in the world.  American universities have very nice facilities, and they have very nice programs. So what are the problems?

  1. They’re very expensive. Partially because of the landscaping and the facilities and the programs that they have.
  2. They can be very rigid. What’s magical about four years, whether you’re gonna be a software engineer, or art historian? It’s always 4 years. Clearly no one has said “Let me just work on the stuff that you need to learn. And not just to learn to be that career, but like learn to be a human being or participate in democracy.” The opportunity cost isn’t just in dollars, although those are significant. It’s also in lost time, the fact that in the US to become a working doctor, and I observed this with my wife, and she’s not even a surgeon,  You have to keep going even as a rheumatologist. She was 32 before she was really a rheumatologist and she never took a break since kindergarten. You’re losing a lot of talent that could help serve a more diverse community because they were the ones that said, “Hey, I gotta get a job fast. I can’t sit in school until I’m 32 years old, or 35 years old to become a surgeon or a professor or whatever else.” Those are the problems that I think we need to address.

On the stress of college admissions

I actually think our system is culturally broken in a lot of ways. There’s always been a Lord of the Flies aspect. I remember reading that book in middle school, I’m like, okay, yeah, you just described the locker room or the playground — bully or be bullied. Unfortunately, it’s part of the culture and in many cases, it happens more in some of the more affluent neighborhoods, the stress and anxiety. Here in Silicon Valley, Palo Alto, I can’t afford to live in those neighborhoods that go into those high schools — they have the highest suicide rates in the country. I talk to educators there. The stress, the anxiety, the depression, there is off the charts. So that’s another thing. Talk to anyone in higher education. Roughly a third of all students are in some way dealing with some of these things. 

What is the university tuition actually buying?

Universities study everything, except some very obvious questions, like what you just asked, “What are you paying for?”You can conduct a very simple study here. Go to the upcoming Harvard graduation, and go to some kids who have some debt, “Hey, graduate, I will pay your $200,000 right now, whatever, however much debt you have, you get to keep all the knowledge you got from Harvard and all of the experiences, but you can never tell anyone that you went to Harvard University, will you take it?” I’m guessing very few people will.

On the other hand, if I were to go to a lot of people, and say, “You can pay $200,000 right now and the whole world will think that you have gone to Harvard for the rest of your life. There’s no way of proving it. You get no new knowledge.” A lot of people will take you up on that. So I think that tells you something about what people might be paying for.

I do think there are other things. Like if I offer you $200,000 but all your memories of the great conversations and friendships go away. That also would be hard for people to take. And look, I think the knowledge matters as well. But I do think the credential and the brand and the halo is a big, big, big piece of it. You absolutely can learn some of the more tangible skills at a lower cost alternative or even online.

And for the experiential, maybe the less tangible skills. You also could learn in other ways.  Some people say, “Oh, well, it’s just an important coming-of-age experience, you learn how to learn.” I don’t disagree with that. That happened to me in college. I had a great college experience. I met some of the best friends in my life, I met my wife in college. But I could imagine other coming-of-age experiences that are just as powerful. The military is one. I could imagine traveling through Europe with a cohort of students while we get jobs while we do online learning at the same time. I imagine doing internships and co-ops I’m learning, whether it’s in person or online, and getting work experience. And if I’m able to have a cohort of people my own age, that could be a great coming-of-age experience.

A not-so-great coming-of-age experience that I’ve seen happen, including people in my own family, is you have this great experience, and then you hit reality. You’re 21 years old, you’re no longer living on the well-groomed Country Club of a fancy university you attended. You have $200,000 of debt or more. You realize that in that economic seminar at the Ivy League school they treat you like you’re going to be the Federal Reserve Chairman but that’s not how the world is treating you now. You’re having trouble getting that job in economics. And if you do, it’s not paying you enough to pontificate about interest rates. We have to think a little bit more holistically outside of even just those four years.

Sal’s desire for Khan Academy

We have all the components for school in the cloud so to speak (via Khan, sister orgs and partners, through, a free online tutoring initiative) but I don’t think we’re going to be a mainstream use-case. 

I’m doing what I’m doing because I want the whole world to change. I want the people who have access to school for that school to be that much better and personalized. I want for kids not to fall through the cracks and all the associated stress and mental health issues and self-esteem issues. I also want Khan Academy and the related organizations to be like the shadow school system, the strategic education reserve, the shadow safety net, for the world, where if you don’t have school, if your school is crappy, you have, you have a safety net.

Personal resonance and reflection on Sal’s takes

  • When you take risks, cynics will be constant. Sometimes they will be right and sometimes not. But you need to focus on 2 things:
    1. Who do I actually need to convince?
    2. What evidence do I possess that says the risk is worthwhile?
  • When making a decision separate what you need from what you think you want. Then don’t be afraid to chase what inspires you (”a protagonist in your own movie”). I think of it as shedding to build.
  • Imposter syndrome can keep you grounded
  • Sal’s north star is personalized mastery learning because it increases self-esteem and well-being. It’s the maximum leverage point because our largest problems and conflicts stem from what’s in our minds. This is highly adjacent to my own “agency” argument.
  • Sal is courageous because he is trying to demonstrate that there can be a better way. He is consciously trying to be a role model through his actions and while I understand that many believe this is nudgy or righteous thinking I have argued the same point. We are suffering from a lack of healthy models and have settled into a forest of Molochian equilibriums. The “lord of the flies” broken culture around college admissions Sal uses is but a metaphor for what I see everywhere — the type of competition that is unhealthy and eats its own competitors. The people who feel on top now cannot outrun it. If it doesn’t eat them, it will eat their children.

Skynet’s Already A Better Dad Than Me

Let’s start with a math puzzle from Martin Gardner’s Entertaining Mathematical Puzzles:


A silver prospector was unable to pay his March rent in advance. He owned a bar of pure silver, 31 inches long, so he made the following arrangement with his landlady. He would cut the bar into smaller pieces. On the first day of March, he would give the lady an inch of the bar, and on each succeeding day he would add another inch to her amount of silver. She would keep this silver as security. At the end of the month, when the prospector expected to be able to pay his rent in full, she would return the pieces to him.

March has 31 days, so one way to cut the bar would be to cut it into 31 sections, each an inch long. But since it required considerable labor to cut the bar, the prospector wished to carry out his agreement with the fewest possible number of pieces. For example, he might give the lady an inch on the first day, another inch on the second day, then on the third day he could take back the two pieces and give her a solid 3- inch section.

Assuming that portions of the bar are traded back and forth in this fashion, see if you can determine the smallest number of pieces into which the prospector needs to cut his silver bar.

Don’t read further unless you want the solution.

This is the solution:

The prospector can keep his agreement by cutting his 31-inch silver bar into as few as five sections with lengths of 1, 2, 4, 8, and 16 inches.

You’ll note that you can sum to any length up to 31 with that set of bars.

Disclosure: I read this problem aloud to my kids on Wednesday night at bedtime and none of us got the answer.

The key to this problem is it can be expressed cleanly using binary or a base-2 number system instead of using the base-10 system we are used to.

Earlier that afternoon I taught Zak (9) how to count in binary. I made these charts to summarize how I explained it to him.

It’s useful to remember that when you hear “tens place” what is really meant is the [symbol occupying that space] x 10¹

  • In base-10: there’s a one’s place, tens place, hundreds place…
  • In binary: there’s a one’s place, twos place, fours place, eights place…

Once Zak understood this he could represent our family members’ ages in binary. I had him do the same thing using base-8 by following the same pattern.

  • In base-8: there’s a one’s place, eights place, sixty-fours place, five hundred and twelve place…

So representing my age of 44 in base-8 = 54 because there are 5 eights + 4 ones.

Computers do calculations in binary because electrical signals on a chip are either on or off. So representing numbers can be thought of like a morse code of “on”/”off” at light speed or something. Feel free to correct me, that’s my armchair impression.

Now a brutal coincidence.

Despite teaching binary that afternoon, I did not recognize it was the key to answering the riddle! Zak was flabbergasted by the coincidence that the solution was in “what’s that word you keep saying…binary?” after he just learned it. Baader-Meinhoff on steroids. (It was really cute that he kept shaking his head about the coincidence that the thing he just learned showed up in a random problem I chose that night. The coincidence hit him just as hard, maybe even harder, than it did me.)

The silver bars cut into 5 lengths as a binary solution:

This is all about to get better (or worse depending on what temperature you run at on the techno-optimism thermometer).

Yesterday, I started tinkering with OpenAI’s recently released ChatGPT. I found this concise description of ChatGPT:

A large language model trained by OpenAI is a machine learning model that has been trained on a large dataset of natural language text, typically using a deep learning approach. This allows the model to learn the patterns and structures of human language and to generate text that is similar in style and content to human-generated text.

You can sign-up to try it for yourself here.

This is a Twitter thread of prompts I’ve given it and its responses. Everything from a Kelly Betting problem to imagining if DMX wrote the hook for No Scrubs.

I also gave the bot a condensed version of the riddle.

Prompt: If I have a 31 inch silver bar but I need to make the minimum number of cuts so I can create a new bar any length up to 31 inches, how many cuts do I need?

It responded:

To create a bar of any length up to 31 inches, you would need to make five cuts to your silver bar. This is because the minimum number of cuts required to create a bar of any length up to a given length is equal to the log base 2 of that length, rounded up to the nearest whole number. In this case, the log base 2 of 31 is 4.8, which rounds up to 5. Therefore, you would need to make five cuts to your silver bar to create a new bar of any length up to 31 inches.

“log base 2”?! It knew it was a problem for binary.

Lacking the vision to peer around corners, my small mind can only see the 6 inches in front of my face. And I can see turning to ChatGPT over Google for many types of searches. But with the explosion of “generative AI” in the past year (GPT engines, Dall-E, Stable Diffusion or Midjourney for images), it’s clear the times they are a-changin’

A Drawer Of Curiosities

One of my deepest held beliefs is that our need for coherence is a profound source of misery. We agitate for universal theories to tie everything together. Our obsessions with gurus, religion, ideology, macro, or even astrology are symptoms. We search for meaning as if it is something that’s “out there” to be discovered. I’m not holding my breath. And I believe the quest is actively destructive when taken too seriously. When people become overly invested in any of these expeditions, they will protect their egos at any cost. It’s actually more insidious than this. They dehumanize opposition so they don’t even have to consider their plight a cost.

I just picked up Simone de Beauvoir’s book The Ethics Of Ambiguity because its description vibrates with my own feelings. I’ll report back after reading it.  (See How The Need For Coherence Drives Us Mad to see if you’d be interested in reading it.)

In the meantime, I’ll share a technique that I use to resist the seduction of coherence.

A Drawer Of Curiosities

In my notes, I keep an ever-growing list of “tensions” and “paradoxes” that I encounter from reading or experience. It is a constant reminder that every bit of advice you’ve ever heard is not universal. My buddy Jake likes to say that seat belts are the only free lunch. To which I respond, “unless the presumption of safety encourages drivers to speed or drive more recklessly”. Let’s be blunt. My response is utter ankle-biting tediousness (if you have this kind of thought, don’t make it a personality). The larger takeaway is there are paradoxes running loose everywhere and if we run around trying to corral them with some ill-conceived notion that it makes us “more right” or there are truths we can somehow own and wield, then we’ve done nothing but build intellectual totems to hubris.

Instead of trying to resolve the paradoxes, maybe just accept them. Name it to tame it, put it in a drawer, and move on. You don’t need the world to bend around your own brain to protect your ego. You can just have a big list that reminds you that the task is futile. That’s the antidote.


Just some excerpts of obvious relevance:

Why the ‘paradox mindset’ is the key to success (BBC)

  • Over a series of studies, psychologists and organizational scientists have found that people who learn to embrace, rather than reject, opposing demands show greater creativity, flexibility and productivity. The dual constraints actually enhance their performance. The researchers call this a “paradox mindset” – and there never be a better time to start cultivating it.

  • Contemplation of apparent contradictions can break down our assumptions, offering us wholly new ways of looking at the problem…study of how revolutionary thinkers had spent considerable time “actively conceiving multiple opposites or antitheses simultaneously”.

  • “Paradoxical cognition” can also help more average thinkers to solve everyday problems, and organizations to enhance their performance. In one of the early studies, Ella Miron-Spektor, associate professor of organizational behavior at INSEAD, and her research collaborators asked participants to write down three paradoxical statements. This, the participants were told, could be as banal as the idea that “sitting can be more tiring that walking”; they simply had to list any thoughts that were “seemingly contradictory but nonetheless possibly true”. She then gave them two of psychology’s standard tests of creativity. The first was the “remote association test”, which requires participants to find a common word that links three different alternatives. What links “sore, shoulder, sweat”, for example? The answer is cold – and if you get it right, you’ve been able to spot the hidden connections between diverse ideas, which is considered essential for many forms of creative thinking. [Me: Reminds me of Codenames!]

  • Although the participants’ paradoxical statements were not directly related to the task itself, their contemplation of the contradictory ideas seemed to have freed their thinking from its usual constraints, meaning that they were better able to think “outside the box” (or, in this case, inside it).

  • Questionnaire to measure the “paradox mindset”. The participants were first asked to rate statements about their willingness to embrace contradictions, such as:
    • When I consider conflicting perspectives
    • I gain a better understanding of an issue I am comfortable working on tasks that contradict each other
    • I feel uplifted when I realize that two opposites can be true

  • The participants were also asked to describe how often they experienced “resource scarcity” at work (the need to perform highly under limited time or financial resources). Their supervisors, meanwhile, had to rate their performance and innovation within the role. Sure enough, the study found that the employee’s paradox mindset had a large influence on their ability to cope with the demands. For the people who scored highly, the challenge of dealing with limited resources was energizing and inspiring, and their performance actually increased under the tension, so they came up with new and better solutions to the problems within their role. Those without the paradox mindset, in contrast, tended to crumble and struggled to maintain their performance when resources were scarce.
  • The prospect of deliberately embracing competing demands may sound arduous, but Chinese researchers have recently shown that people with this mindset also get greater satisfaction from their role. There is enjoyment, apparently, in reconciling two opposing goals – provided you have the right mindset

  • Simply note down any paradoxes you encounter – and to make a point of contemplating them before you set about solving problems. If you are stuck for ideas, you could look further into the paradoxes that inspired scientists like Einstein and Bohr. Greek philosophy is also full of paradoxical ideas that might get your creative juices flowing. Your own job may already contain many contradictory goals that could inspire paradoxical cognition. In the past, you might have assumed that you need to sacrifice one for the other – but if you want to cultivate the paradox mindset, you might spend a bit more time considering the ways you can pursue them both, simultaneously. Rather than seeing the potential conflicts as something to avoid, you can begin to view the competing demands as an opportunity for growth and a source of motivation. (And if there aren’t any external pressures, you could create your own – asking, for instance, how you could increase the efficiency and accuracy of your performance on a particular task, if only for an exercise in paradoxical thinking.)

Neural correlates of maintaining one’s political beliefs in the face of counterevidence (Nature)

  • People often discount evidence that contradicts their firmly held beliefs. However, little is known about the neural mechanisms that govern this behavior.

  • Data on any topic—from climate science to epidemiology—must first be successfully communicated and believed before it can inform personal behavior or public policy. Viewed in this light, the inability to change another person’s mind through evidence and argument, or to have one’s own mind changed in turn, stands out as a problem of great societal importance. Both human knowledge and human cooperation depend upon such feats of cognitive and emotional flexibility.

  • It is well known that people often resist changing their beliefs when directly challenged, especially when these beliefs are central to their identity. In some cases, exposure to counterevidence may even increase a person’s confidence that his or her cherished beliefs are true. Although neuroscientists have begun to study some of the social aspects of persuasion and motivated reasoning, little research is aimed directly at understanding the neural systems involved in protecting our most strongly held beliefs against counterevidence.

  • One model of belief maintenance holds that when confronted with counterevidence, people experience negative emotions borne of conflict between the perceived importance of their existing beliefs and the uncertainty created by the new information. In an effort to reduce these negative emotions, people may begin to think in ways that minimize the impact of the challenging evidence: discounting its source, forming counterarguments, socially validating their original attitude, or selectively avoiding the new information. The degree to which such rationalization occurs depends upon several factors, but the personal significance of the challenged belief appears to be crucial. Specifically, beliefs that relate to one’s social identity are likely to be more difficult to change.

  • Our results show that when people are confronted with challenges to their deeply held beliefs, they preferentially engage brain structures known to support stimulus-independent, internally directed cognition. Our data also support the role of emotion in belief persistence. Individual differences in persuasion were related to differences in activity within the insular cortex and the amygdala—structures crucial to emotion and feeling. The brain’s systems for emotion, which are purposed toward maintaining homeostatic integrity of the organism, appear also to be engaged when protecting the aspects of our mental lives with which we strongly identify, including our closely held beliefs.

Learning Is Behavioral Change: A Presentation By Alix Pasquet

Frederik Gieschen hosted a presentation by hedge fund manager Alix Pasquet.

The presentation is titled:

Learning for Analysts and Future Portfolio Managers (YouTube)

This presentation is overflowing with ideas and insights. I took notes. They are not intended to be comprehensive, but rather a filter of what stood out to me. If the topics sound interesting definitely check out the video yourself, there’s a lot of detail I’m leaving out.

Alix mentions that the presentation was inspired by Bill Gurley’s talk:

Runnin’ Down a Dream: How to Succeed and Thrive in a Career You Love (YouTube)


About Alix

  • Runs a “behavioral hedge fund” Prime Macaya that seeks to exploit uneconomic group behavior
  • Alix came from the game world specifically poker and backgammon

Key Takeaways From The Presentation

The presentation was focused on learning in the context of rising from an analyst to portfolio manager. Many of the lessons felt more universal which is what interested me. 

  • In the investment business, we are paid to learn
  • Learning is behavioral change. If your behavior hasn’t changed you haven’t learned.
    • Jim O’Shaughnessy quote emphasizes application: “Don’t look for the meaning, look for the uses”
  • Create the conditions to learn as opposed to relying on willpower.
    • There’s an emphasis on community for feedback, collaboration, filtering, and as a forcing function (ie instead of practicing public-speaking alone, join Toastmasters. I found this resonant because being forced to play guitar on stage or gives your practice more intent)

Structure of the Presentation

The first hour is focused on:

  • Problems in learning
  • Mindsets required for learning

The second hour focuses on:

  • Conditions, procedures and actions steps.

    These include specific discussions about:
    • being a good mentee
    • personal knowledge management
    • the idea of a personal lab where you can practice your learning
    • support structures
    • the role of physical exercise
    • inspectional reading
    • studying frauds and deception to “know your enemy”
    • exploiting group behavior

What Caught My Eye

Ideas That Resonated

  • Alix believes “learning is a team sport” which echoes my belief that “trading is a team sport” 

  • Problems as well as smart people and goals are useful filters for narrowing what to learn

  • The investing job needs to be about more than the money because you will compete with passionate, competitive people determined to learn and get better.

    “Many that have brain power should literally be doctors and nuclear physicists but they’re out there chasing stocks. I love what I do but I have no notion that I’m helping out the world here. We’re having fun with what we do and hopefully, we’ll make some money. One day we can help the world but this is not a business where you’re adding value to the world and if you have the intelligence and you don’t love this business go do something else.”

  • Overfitting lessons

    “Analysts don’t understand that they need to tailor their style structure processes and resources according to their own personalities and temperament. They try to replicate what others have done not realizing that these people have totally different personalities and have gone through totally different environments.

    No lesson is better than the wrong lesson. The key suggestion I would make is to involve others. Get feedback from others that will keep you intellectually honest because in the hedge fund business we have a tendency of doing this thing called “revisionist history” which frankly exists to protect our confidence but sadly it doesn’t improve our investment performance.”

    Me: Unwarranted confidence from “resulting” undermines one of the most key inputs to sound betting — calibration. Consider the Paul Slovic horse handicappers study that found  the accuracy of handicapperss’ predictions did not improve from the original 5 variables they desired as they were given more variables. Their confidence went up although their accuracy did not! The handicappers with only 5 variables were well-calibrated. They were close to 2x better than chance at predicting the winner (20% vs 10%) and they estimated their confidence as such. When they were given more variables their accuracy remained 20% but confidence grew to 30%!
  • Investing feedback is long and deceptive unlike games

    • “Futsal principle”

      “Futsal is soccer at the fraction of the size of a football team pitch. The number of players is smaller. You would think that it increases the number of strategic interactions by double but actually, it increases the number of interactions by eight to sometimes 16 times. And what that does is you’re learning at a very, very fast clip.

      And one of the patterns that we’ve seen is great investors often have gone through a futsal period in their careers. So Dan Loeb, for example, in the early 90s, he worked at Jeffries right at the moment when the Resolution Trust Corporation was selling off the problem assets of the savings and loan debacle at discounted prices in a two year period. He saw a deal every few days. And that increased the number of reps that he saw. But also, he had great customers, he had a young David Einhorn and a young David Tepper as customers. And the exposure and the reps were amazing.”
  • Like Alix, I found Mauboussin to be the bridge between trading and investing

    Measure what is incorporated in the “outside view” then work backward:

    • “PIE”: price implied expectation

    • Options implied expectation

    • Narrative/sentiment analysis
  • Imitate, Assimilate, Innovate

    Mediocre investors and business builders try to innovate first, often fail, and fall back on  imitation so they can eat. Originality starts with imitating first.

    Me: resonant just based on what I’ve read about writers. We learn to play covers before we create ourselves.
  • Importance of Mentors

    • “If you’re early on in your career and they give you a choice between a great mentor or higher pay, take the mentor every time. It’s not even close. And don’t even think about leaving that mentor until your learning curve peaks. There’s just nothing to me so invaluable in my business, but in many businesses, as great mentors. And a lot of kids are just too short-sighted in terms of going for the short-term money instead of preparing themselves for the longer term.”—Stanley Druckenmiller

      Me: reminds me of the greatest advice I received coming out of college: No matter who you work for you will be rich. The question is who do you want to work with? She knew that I knew that I would learn more at Susq and when you are 22 years old that’s what you optimize for. That’s the best way to invest in yourself. That’s when your human capital dwarfs the value of your financial capital. We are all living longer. Even at 30 I’d give the same advice. It’s a long road.
  • Community as leverage

    • Community (peers and mentors) can often have access to the context you need for an idea that might otherwise be a dead end
    • Ability to crowdsource if you have an audience (usually content is a key to having an audience in the first place so content is also a form of leverage)
    • Importance of network diversity. Belong to multiple networks which can be sorted by geography, interests, age etc

Notable Ideas

  • “Analysts do not understand that there’s a difference between analytical thinking and portfolio management thinking”

    • Bill Miller: “The difference between analytical thinking and pm thinking is you give an analyst a problem and they deconstruct it and figure out what makes a problem tick but you give a problem to a pm and his first question is how do i make money from this?”

      Me: portfolio construction and betting literature is required for analysts to be PMs.

  • Behavioral bias research is more focused on individuals, but markets are more concerned with group behavior. So there’s a “fallacy of composition. If you take 10 people that are prone to cognitive biases, their group behavior may actually be quite rational.”

    Me: a key focus should be on the wisdom and madness of crowds.

  • Learning from your own successes but others’ failures

    Surgeons learn more from their own successes than from their own failures but they learn more from the failures of others than they do from the successes of others. This was over 6500 procedures. Also my neighbor is a doctor and I spoke to him about this study and he actually made a very important comment that surgeons that had made a fatal mistake over the operating table were more likely to leave surgery because their confidence was shaken whereas a successful surgeon that had seen a surgeon have make a fatal mistake can learn better from that. It’s important to retain this as a mindset of learning from your own successes and the failures of others. Don’t get me wrong you can still learn from the successes of others but temper it. Filter it correctly. You don’t want to overindex to the successes you see in others especially since you don’t have all the context, but it might be easier to learn from somebody else’s mistake. Especially since your own mistakes get you very emotionally involved.

  • They study market participants at 4 levels to see if they are “creating opportunities they can exploit”:

    1. what are their skills?
    2. psychology?
    3. positioning?
    4. institutional quirks?
  • Data hierarchy: data —> information —> understanding —wisdom.

    • Your goals are a filter for how you travel from data to information.
    • Procedures are how you move from information to understanding.
    • The meta experience of “testing it again with your network, teaching it to somebody else, and the ability to create things gets you to wisdom”
  • Derek Sivers: “The standard pace is for chumps”

There’s no reason why it needs to take 10,000 hours. You can do it in much much less period of time if you can test it and get immediate feedback in a low-cost way than it is to be thinking about it for a long time and cramming your brain with more information.


  • “Brute intelligence can be a handicap if it leads you to believe you have figured it all out…need to have soft intangibles like integrity, grit, adaptability, flexibility, humility”.

    Me: While traders are screened for these intangibles, especially teachability/intellectual humility, another way to think of this is the importance of teams. There is a role for one-dimensional Russian super geniuses in these organizations — well captured by this quote: “The analyst’s job is to be creative everything else I can outsource to India”

  • “There’s actually no good book on portfolio management which is incredible to me. Not only that, somebody mentioned on a podcast that there’s no analytical team that analyzes what are the best portfolio management techniques”

    Me: pod/prop/and some quant shops no?

  • Alix belief that strong investors should be strong writers and that there’s a connection between these skills.

    Me: I don’t think this is true for traders. So then I wonder if Alix is overstating the case (even after allowing for exceptions) OR is trading and investing sufficiently different that my experience is not relevant. 

    Trading Vs Investing

Notable Book Recs

The entire presentation is actually organized around a reading list by topic so there are so many thoughtful book recs. That alone is worth watching for. The rationale for 2 particular book recs stood out to me:

  • The Age of The Unthinkable

    • This book “doubled the effectiveness of my judgement” and demonstrates how the world is changing rapidly and the importance of learning.

    • He gives the example: “Market structure has changed. Markets are totally different post-2008. The pipes of liquidity have changed. Prior to ‘08 we had market makers, we had prop desks. They were more prevalent. Index funds were smaller, hedge funds were smaller. Now we have no prop desks, quant funds are massive, index funds are massive, hedge funds are massive… As market participants, we’re inclined to study the past, but past markets may not be appropriate to study here because we’ve never seen a bear market with our current market structure.”

Me: this is resonant and reminds me of:

  • The Path of Least Resistance

    • Demonstrates how “structure drives behavior” and the importance of settings and environment.. consider this simple story:

      • Take two people. A very intelligent person and a total moron. You drop both in the Russian tundra in the middle of winter. The intelligent person gets a shack that can’t really handle the environment well and doesn’t have that much food. You put the moron in a shack that can handle the environment well and has enough food. Unless the intelligent person goes over there and forcibly takes it from the moron, he’s gonna die.

      • It’s about creating structures that you can fall back upon, that make you more resilient [as opposed to] being internally resilient or having inner grit. There are people that we think have this level of motivation level of grit and level of determination that’s incredible, but what we don’t see are the support structures that they’ve created in the background or exploited or frankly they were lucky.

      • An example of resilience would be to have ample living costs saved so you can think clearly as you take risk or not upgrading your lifestyle in line with your success so you can continue to take chances. In studying failure, one of the invisible patterns, or as Alix calls it “the silent killer” is investment managers raising their personal overhead:
        • It’s a “monkey on their shoulder that they have to view every single thing through and it impacts their judgment and risk-taking ability. We call it the ‘silent killer’ because we’ve seen it kill a bunch of hedge funds but the manager never talks about it as the reason they couldn’t take risks anymore.”

Another Kind Of Mean

Let’s use this section to learn a math concept.

We begin with a question:

You drive to the store and back. The store is 50 miles away. You drive 50 mph to the store and 100 mph coming back. What’s your average speed in MPH for the trip?

[Space to think about the problem]




[If you think the answer is 75 there are 2 problems worth pointing out. One of them is you have the wrong answer.]




[The other is that 75 is the obvious gut response, but since I’m asking this question, you should know that’s not the answer. If it’s not the answer that should clue you in to think harder about the question.]




[You’re trying harder, right?]




[Ok, let’s get on with this]

The answer is 66.67 MPH

If you drive 50 MPH to a store 50 miles away, then it took 60 minutes to go one way.

If you drive 100 MPH on the way back you will return home in half the time or 30 minutes.

You drove 100 miles in 1.5 hours or 66.67 MPH

Congratulations, you are on the way to learning about another type of average or mean.

You likely already know about 2 of the other so-called Pythagorean means.

  • Arithmetic mean

    Simple average. Used when trying to find a measure of central tendency in a set of values that are added together.

  • Geometric mean

    The geometric mean or geometric average is a measure of central tendency for a set of values that are multiplied together. One of the most common examples is compounding. Returns and growth rates are just fractions multiplied together. So if you have 10% growth then 25% growth you compute:

    1 x 1.10 x 1.25 = 1.375

    If you computed the arithmetic mean of the growth rates you’d get 17.5% (the average of 10% and 25%).

    The geometric mean however answers the question “what is the average growth rate I would need to multiply each period by to arrive at the final return of 1.375?”

    In this case, there are 2 periods.

    To solve we do the inverse of the multiplication by taking the root of the number of periods or 1.375^1/2 – 1 = 17.26%

    We can check that 17.26% is in fact the CAGR or compound average growth rate:

    1 x 1.1726 * 1.1726 = 1.375

    Have a cigar.

The question about speed at the beginning of the post actually calls for using a 3rd type of mean:

The harmonic mean

The harmonic mean is computed by taking the average of the reciprocals of the values, then taking the reciprocal of that number to return to the original units.

That’s wordy. Better to demonstrate the 2 steps:

  1. “Take the average of the reciprocals”

    Instead of averaging MPH, let’s average hours per mile then convert back to MPH at the end:

    50 MPH = “it takes 1/50 of an hour to go a mile” = 1/50 HPM
    100 MPH = “it takes 1/100 of an hour to go a mile” = 1/100 HPM

    The average of 1/50 HPM and 1/100 HPM = 1.5/100 HPM

  2. “Take the reciprocal of that number to return to the original units”

    Flip 1.5/100 HPM to 100/1.5 MPH. Voila, 66.67 MPH

Ok, right now you are thinking “Wtf, why is there a mean that deals with reciprocals in the first place?”

If you think about it, all means are computed with numbers that are fractions. You just assume the denominator of the numbers you are averaging is 1. That is fine when each number’s contribution to the final weight is equal, but that’s not the case with an MPH problem. You are spending 2x as much time as the lower speed as the higher speed! This pulls the average speed over the whole trip towards the lower speed. So you get a true average speed of 66.67, not the 75 that your gut gave you.

I want to pause here because you are probably a bit annoyed about this discovery. Don’t be. You have already won half the battle by realizing there is this other type of mean with the weird name “harmonic”.

The other half of the battle is knowing when to apply it. This is trickier. It relies on whether you care about the numerator or denominator of any number. And since every number has a numerator or denominator it feels like you might always want to ask if you should be using the harmonic mean.

I’ll give you a hint that will cover most practical cases. If you are presented with a whole number that is a multiple, but the thing you actually care about is a yield or rate then you should use the harmonic mean. That means you convert to the yield or rate first, find the arithmetic average which is muscle memory for you already, and then convert back to the original units.


  • When you compute the average speed for an entire trip you actually want to average hours per mile (a rate) rather than the rate expressed as a multiple (mph) before converting back to mph. Again, this is because your periods of time at each speed are not equal.
  • You can’t average P/E ratios when trying to get the average P/E for an entire portfolio. Why? Because the contribution of high P/E stocks to the average of the entire portfolio P/E is lower than for lower P/E stocks. If you average P/Es, you will systematically overestimate the portfolio’s total P/E! You need to do the math in earnings yield space (ie E/P). @econompic wrote a great post about this and it’s why I went down the harmonic mean rabbit hole in the first place:

    The Case for the Harmonic Mean P/E Calculation (3 min read)

  • Consider this example of when MPG is misleading and you actually want to think of GPM. From Percents Are Tricky:

    Which saves more fuel?

    1. Swapping a 25 mpg car for one that gets 60 mpg
    2. Swapping a 10 mpg car for one that gets 20 mpg

    [Jeopardy music…]

    You know it’s a trap, so the answer must be #2. Here’s why:

    If you travel 1,000 miles:

    1. A 25mpg car uses 40 gallons. The 60 mpg vehicle uses 16.7 gallons.
    2. A 10 mpg car uses 100 gallons. The 20 mpg vehicle uses 50 gallons

    Even though you improved the MPG efficiency of car #1 by more than 100%, we save much more fuel by replacing less efficient cars. Go for the low-hanging fruit. The illusion suggests we should switch ratings from MPG to GPM or to avoid decimals Gallons Per 1,000 Miles.

  • The Tom Brady “deflategate” controversy also created statistical illusions based on what rate they used. You want to spot anomalies by looking at fumbles per play not plays per fumble.

    Why Those Statistics About The Patriots’ Fumbles Are Mostly Junk (14 min read)

The most important takeaway is that whenever you are trying to average a rate, yield, or multiple consider

a) taking the average of the numbers you are presented with


b) doing the same computation with their reciprocals then flipping it back to the original units. That’s all it takes to compute both the arithmetic mean and the harmonic mean.

If you draw the same conclusions about the variable you care about, you’re in the clear.

Just knowing about harmonic means will put you on guard against making poor inferences from data.

For a more comprehensive but still accessible discussion of harmonic means see:

On Average, You’re Using the Wrong Average: Geometric & Harmonic Means in Data Analysis: When the Mean Doesn’t Mean What You Think it Means (20 min read)
by @dnlmc

This post is so good, that I’m not sure if I should have just linked to it and not bothered writing my own. You tell me if I was additive.

Kid’s Excel Lesson: Random Numbers

As you guys know I like to share stuff I’m doing with the kids in case you find it useful for your own teaching desires. Lately, I’ve been trying to help Zak (turned 9 last month) learn a bit of Excel. Excel is inherently useful but it’s also a bit of a coding language so it’s a soft onramp to thinking logically and computationally. We did several small Excel projects together this summer. I will IV-drip them to you over time but for today I’ll share one we did just this week.

Zak likes math in general and I often ask him to work on his workbooks (we just got both Zak and his 6-year-old bro Kanagaroo Math books. They require more creativity than Kumon-type stuff and also you can enter their international math competition in March.) Anyway, I asked Zak to “go do some workbook” and he asked if instead, I could give him a bunch of multiplication problems involving 3-digits.

Teaching moment.

Zak, how about we use Excel to generate the questions? He doesn’t know how to do that so we:

  1. Break the problem into small steps.
  2. Use the Socratic method.

If you want to replicate this with your kids, here’s a loose script.

Step 1: We need to generate 3 random numbers.

This didn’t go quite as planned. Zak went to Google and discovered on his own that he could use Excel’s RANDBETWEEN() function to generate a number between 100 and 999. I gave him a ton of praise for being resourceful. This is basic adulting really. But also, I wanted this to be more involved so I said let’s try to do it another way.

Here’s what I asked him:

What digits can exist in each of the ones, tens, and hundreds place?

The very act of asking him put him on alert. He recognized that while the ones and tens place can be 0 thru 9, the hundreds place could only be 1 thru 9. Nice work Zak.

Excel’s RAND() function generates a number between 0 and 1.

How do we make a number between 0 and 9 if we start with an Excel random number?

He realized that we need to multiply the number by 10 but I had to prompt him for a bit.

How do we get rid of the decimal?

Zak: we can round

How’s that going to work?

Zak: we want to round down (after he considered what would happen in both the round up and round down cases. You don’t want 9.4 or 9.8 to ever round up because 10 is not a valid output for our purpose).

Great. Now we get a PEDMAS lesson. Excel solves parenthesis first. With some handholding we arrive at the function for the ones and tens place:

=ROUNDDOWN(10 * RAND(), 0)

The zero was also a good lesson. Excel is not a mindreader, you need to tell it how many decimal places to go to.

But what about the hundreds place? How are you going to convert a random number between 0 and 1 into 1 thru 9?

Zak: [crickets]

Ok, what if you needed to take a random number and convert it to a 1 or 2?

Zak suggests doing what amounts to an IF-Then-Else statement.

Good. What’s another way to do that using multiply or divide?

He got stuck here and I had to play the scenario game with him.

What if we multiply by something other than 10?

And…he lost stamina. That’s ok. We can come back to it. I ultimately explained it, but I’ll ask him to reproduce it soon enough. He still won’t know how and we’ll have to go through all of this again. That’s also expected and ok. Every time we work through it, I suspect the web of thinking fibers thickens a bit, his stamina inches ahead, and most importantly he gets used to the idea that work without a satisfying end is ok. Enjoy the smaller milestone victories along the way. He’s still much further than he was when he woke up because he got to stretch a bit and exercise that little bicycle up there in a systematic way.

Just to be complete about this post, the answer is that instead of multiplying by 10, you multiply by 9 (you are trying to take a continuous range of numbers and bin it into 9 discrete numbers), but remember you must also round up this time, because we want the range to be 1 through 9 not 0 through 8.

Final answer:

=ROUNDUP(9 * RAND(), 0)

From there, just

a) concatenate the 3 digits


b) multiply each digit by its respective place (so the first number by 1, the second number by 10, and the one we generated with ROUNDUP by 100) and sum them all together.

We did both methods just to be complete.

And voila, now he can generate his own worksheet of 3-digit multiplication that’s different every time.

I will be sharing some more kid stuff in the future. A select few from the archive:

  • A Socratic Money Lesson For 2nd Graders (3 min read)
  • Hands-On Resources to Teach Kids About Business (2 min read)
  • Bohnanza Is A Great Trading & Business Game (3 min read)
  • Thoughts About Monopoly As A Teaching Tool (2 min read)

Education Ideas By Seth Godin

Dave Perell interviewed Seth Godin who has nuanced views on education.

My favorite excerpts:

On homeschooling:

Homeschooling is unavailable to many, many families because they can’t afford it. Homeschooling is really expensive because somebody needs to be home. And among families that can’t afford it, homeschooling is scary. And it’s scary because it requires accepting responsibility for one of the most important things in your entire family’s life, for which you have almost no training. And it’s also socially frightening because it is not the norm.

On the importance of public school:

Now, I am a huge believer in public school. I think we have really significant benefits from if it’s a quality education, people getting the same thing, it builds culture [Scott Young explore this idea specifically inCultural Literacy: Does Knowledge Need to Be Deep to Be Useful?]. But I also wish we could homeschool every kid from three o’clock in the afternoon until 10 o’clock at night. Because most of what we learned, most of what we believe came from what happened in our home. If you are fortunate enough to win the birthday lottery and grow up in a home that’s filled with stability and possibility and encouragement, that is a huge advantage over people who don’t have that ability. And we’ve got to figure out how to build structures and support in a remote world, in a video world, in a digital world, so that this is all much more evenly distributed. Because we’re paying for it every day.

On the outcome-orientation of school:

 I think outcome-driven is fine. I think picking the wrong outcome is wrong. Picking the wrong outcome is a mistake. Purpose of kindergarten is not college, right? And there are prizes to people who get a certain level of prestigious college education. There’s no doubt about it. But life is long. And the question is, what are we training people to do? What culture are we building? What is the point of 12 or 16 years of compulsory education if it’s not about learning and possibility and community and resilience and care and generosity and justice? I mean, if you have all of those things, why are you going to have someone who’s good at standardized tests? 

On the scalability problem of independent thought

David says:

I co-lead a summer camp for nine to 11 year olds. And one of the most surprising things is it’s based on… So just some background it’s based on design thinking and project based learning. And so we’ll have these nine-year-olds and on the first day, we’ll say you get to pick a problem that you want to research. And by the end of the week, you are going to solve the problem in the way that you see as best. And the hardest part of running the camp, isn’t helping kids solve problems. It is realizing that they have the agency to choose in the first place.


Exactly because compliance and authority scale way better than freedom and responsibility.

The presence of Moloch in our approach to education [recall Moloch as a metaphor for when competition becomes unhealthy by narrowing our values]:

What we have done in the last 50 years is leveraged everything. So, whereas in the old days of business might be able to go four or five days with no revenue because they didn’t own the bank, anything because they didn’t know the mortgage, anything. Now, if you want to compete, you need to have raised the money, to have run the ads, to have lower the price, et cetera, et cetera. So one business after another, big and small are leverage to their eyeballs. And we’ve done the same thing with education. That if other people are leaning into it, levering up, competing for scarce slots, it’s really easy for a parent to believe that balance will be punished. There’s no way to win that game against someone who’s unwilling to compromise. So what you have to do instead is play a different game. And you had to figure out what other agendas are available for my kids and my family…

If you talk to freshmen at Harvard, not one of them says they came to Harvard so they could get a job in finance. And if you talk to graduating seniors, they’ve somehow persuaded themselves that that’s exactly what they’re going to do. So what happened? Well, they’re not vocational schools in the sense that they teach you how to be an investment banker. But they are definitely labeling and finishing schools in the sense that they make it easy for investment bankers to know where to go, to get more investment bankers. The thing is that colleges that chose not to play this game got less famous. The ones that said you’re here to read great books, you’re here to explore what it means to be on the planet, you’re here to think deeply about meaning and philosophy and connection didn’t attract the same people to their placement office.

Which meant a signal went out to parents. And the signal was if you’re about to invest $200,000 or go into debt for something choose wisely and your peers will judge you for it. And so we created this capitalist driven ratchet that says money and success are the same thing. And that success means you’re a good parent. And success means you have a good kid and we’re defining that success in terms of money, but there are plenty of ways to make a living where you can be happy and make a contribution where the goal isn’t to make the most money.

On the superiority of the “flipped classroom” as pioneered by Sal Khan:

 I don’t understand why we would take this precious thing, real time, synchronization, public space, and waste it with someone reading from their notes…The reason it’s absurd is synchronization is more expensive than asynchronization. It’s absurd because you can speed things up and slow things down if you’re on your own. But mostly it’s absurd because interaction is where we learn things. So if everyone comes together, everyone might only be eight people or 80 people having all seen the lecture the night before and then actively engages in problem solving with each other, that is the way human beings have learned everything, always. This whole idea that we have to put people in a room and read something to them because it’s the best technology has to offer, there’s about 75 years out of date.

Education vs learning:

The reason that some people who are listening to this are being skeptical, is are you in the business of education or learning?  Someone who was describing how easy it was for him to slip through classes without doing anything. I was like, “But you just spent a hundred thousand dollars on these classes.” The purpose is not how little can you get, the purpose is how much, that’s learning. Education is about do I get the degree? Okay, you’re going to get the degree. But learning says, “I am eager to transform myself into someone who understands what I just read.”

Seth calls actual learning enrollment not education:

Earning enrollment is hard because from the time that kid sees the sign in kindergarten that they can’t read, it says “the road to college starts here”, they’re being reminded that enrollment doesn’t matter. And all that matters is the certificate. I don’t do online education. I do online learning. I think online education plays right into the hands of the factory mindset. If you want it to make the most efficient education system in the world where education is, do what I say, and you get a prize, it looks like solo machine. The machine is drilling, practicing somebody until they get the right answers. And it’s about regurgitation and compliance and authority to a scalable machine. Online education is going to be a disaster because we don’t need more people who are online educated. [We need online learning] Online learning is spectacular. It causes deep and permanent change and it works at scale, but it doesn’t work if you don’t have enrollment.

Opportunity to learn is cheap and abundant:

We are already seeing people who can enroll on their own. Lots of free ways for people to find the others, work together and do something. If you want to be a video editor, go find four other people and use YouTube videos to learn the technique and then challenge each other to get better at video editing, do it together. You don’t have to pay anybody anything. And the mistake we’ve made with the college industrial complex is saying the scarcity of the university, the more it costs, the more it costs, the more it’s worth. And so we have famous colleges and famous colleges charge a lot because they’re in high demand. But the thing is, once you go online, you don’t have to have scarcity because you can have an unlimited number of people take it.

So MIT has put all their courses online for free, but people still go to MIT, the institution because they’re selling a different thing, which is the place and the paper. And I think it’s important as we look at the evolution of online learning to say, if we don’t sell enrollment first and foremost, none of it’s going to work. The hardest part is getting people to trust themselves enough to enroll. And then once they’re in it with passion, the amount of learning goes through the roof.

Boundaries and the challenge of building healthy communities:

Wikipedia came from the grassroots, but there are only 5,500 people out of the millions who have edited Wikipedia, who have editing privileges without approval. Because if they didn’t do that, Wikipedia would disappear in three days. And if there wasn’t a structure and a method to keep down trolls and to eliminate vandalism, to model successful behavior, to establish cultural norms, then organic community that isn’t based on something tangible is really hard to build…Scarcity is either created by geography or by man-made structure. And in the case of the internet, there is no geography, really. So what you’re left with is what are the boundaries? And who’s enforcing them? And I think a big piece of the mess that social media has enabled is their aversion to boundaries. And I don’t think it’s paying off. I think that you don’t walk into a bank wearing a stocking over your head and expect that somebody’s going to honor your request for withdrawal. And so I think we want to find communities where people are taking responsibility and are enrolled in a similar journey.

The beautiful moment when people gain insight is a clue that it is important to create “surprise” and “delight” in the learning experience:

If there isn’t, it’s not going to work. Think about the look on a kid who’s been trying for hours to ride a bike and then they can ride a bike. Does anybody in that moment have a frown on their face? Right. No one expected it would feel like it feels. You don’t go, “Oh yeah, this is exactly what I expected.” It’s surprise and delight. And the surprise and delight comes from seeing the world differently and becoming a different, better version of yourself. And we see this in online learning all the time. We see it when people learn to program, we see it when people learn to sing, it’s that structure that lets you feel like you leveled up according to a construct that was there before you got there. People who don’t know how to ride a bike, know that there is a thing called riding a bike. And they’re imagining that there’s a level they can reach. And levels work, they’re not there to create a hierarchy. They’re there to create a chance for self achievement.

Formal and technical educations remain critically important:

 I didn’t take that many liberal arts courses in college. I was an engineer. And I want to speak up on behalf of the engineer. Because one of the things you learn, if you study engineering in your education is you have to ship work and you have to ship work that’s either right or wrong. And I think we need a blend of that and thoughtful commentary on how the world works.

Because it’s too easy to just become a critic. I think we got to be able to say, “I built this bridge and it stands up.” And I think we got to be able to say, “And the bridge needed to go live on Tuesday. And it did.” Because we live in a world that’s based on bridges and dates. But within that, I think we can learn to become the people we’d like to be.

Unlock One Another: The Right Compliment At The Right Time

This post is not science. It’s not rigorous. It is a simple belief, both self-evident and load-bearing. Itself the proof of its premise because believing it is my own generative force.

Stated as I see it:

The closest thing we have to a perpetual motion machine is inspiration.

  1. Inspiration creates its own energy for action.
  2. Action creates information.
  3. Information generates inspiration.


A finance-dork way of saying this is inspiration is the cheapest source of capital.

One of the ideas economist Tyler Cowen is recognized for comes from his short post, The high-return activity of raising others’ aspirations, where he writes:

At critical moments in time, you can raise the aspirations of other people significantly, especially when they are relatively young, simply by suggesting they do something better or more ambitious than what they might have in mind.  It costs you relatively little to do this, but the benefit to them, and to the broader world, may be enormous.

This is in fact one of the most valuable things you can do with your time and with your life.

I’m interested in education and how people learn. There’s nothing more invigorating than the moment of empowerment in a child’s eye when they realize “they can”. As a parent, my proudest moments are the goofy smiles on the boys’ faces when they found themselves able to do what they didn’t think they could. Swim their first lap, add in their head, not panic when they got stuck on a zipline (my 7-year-old was calmer than I would have been).

Learning is the receipt you get for courage.

Courage is virtue. It takes courage to see clearly. To empathize. To put aside your preconceptions. To not give into malformed ideas about yourself or others without a challenge. To face your insecurities. To step outside your comfort zone.

I’m as fallible as the next person but I try to live in a way that takes what Cowen says seriously. It’s something I try to keep top of mind especially when I can feel my patience fray. That’s when I need to recruit that belief the most. This is part of being charitable. Giving people credit for wanting to be better. Sometimes a jerk is just a jerk. But sometimes a jerk is someone who wants to be better but doesn’t know how. They are scared but don’t know it. Behind that defense mechanism is an insecure soul that once crawled on all fours, just like you. I don’t want to let go of the rope until the last second when it’s clear they want to take me over the cliff with them. Sometimes I do. I can’t live up to my own ideals.

But I and all of us must continue to try. Noah Smith, a writer and professor, explains why (emphasis mine):

I think our society has moved a huge amount in the direction of meritocracy — of being open to talent. I think we’re really good at that at this point. But I think our pursuit of meritocracy has caused us to neglect a few important things. One is ambition; the people whose talent we discover are the people who come to us, who shove their talent in our faces, because their parents instilled drive and ambition and confidence in them. But there are a lot of talented people out there whose abilities never get discovered because no one ever told them they should aim high, or because they didn’t have parents to push them, or because they simply lacked confidence. My brother-in-law grew up poor in a trailer park, no one in his family had ever been to college. But my sister instilled him with a little more ambition, and he just graduated from a top law school. Without the luck of meeting my sister, he might still be in a trailer park! So our system is so focused on setting up these tournaments for ambitious people that we fail to go out and nurture the ambition of people who have undiscovered talent...A successful society rests on a broad foundation of human capital; it does not place all its hopes on a thin sliver of genius. I see too many people in Silicon Valley — both liberals and conservatives — tacitly accept the notion that only a few people have real potential. And maybe that’s because venture-funded software is such a winner-take-all market. I don’t know. But that’s not the attitude that will bring this country a broad industrial renaissance or social revitalization.

Scientist Michael Nielsen offers an idea anyone can borrow. Nielson contends that if you give specific compliments to people instead of generic platitudes you are capable of doing far more good than you think. It kicks off a spiral of inspiration in its target. It can validate what they think they are good at, a source of energy that pays off 10-fold as they lean even harder into their gifts. And if that recipient didn’t realize they had some special gift in the first place? You just hit’em with a defibrillator. They just gasped to life.

And maybe. For the first time.

I leave you with his essay. It hit hard because my love language is compliments and since I’m not special I assume it is for many people. It’s a simple thing you can do for others. It takes being present. A dash of vulnerability. And a few words.

On Volitional Philanthropy (a short essay!)

by Michael Nielsen

T. E. Lawrence, the English soldier, diplomat and writer, possessed what one of his biographers called a capacity for enablement: he enabled others to make use of abilities they had always possessed but, until their acquaintance with him, had failed to realize. People would come into contact with Lawrence, sometimes for just a few minutes, and their lives would change, often dramatically, as they activated talents they did not know they had.

Most of us have had similar experiences. A wise friend or acquaintance will look deeply into us, and see some latent aspiration, perhaps more clearly than we do ourselves. And they will see that we are capable of taking action to achieve that aspiration, and hold up a mirror showing us that capability in crystalline form. The usual self-doubts are silenced, and we realize with conviction: “yes, I can do this”.

This is an instance of volitional philanthropy: helping expand the range of ways people can act on the world.

I am fascinated by institutions which scale up this act of volitional philanthropy.

Y Combinator is known as a startup incubator. When friends began participating in early batches, I noticed they often came back changed. Even if their company failed, they were more themselves, more confident, more capable of acting on the world. This was a gift of the program to participants [1]. And so I think of Y Combinator as volitional philanthropists.

For a year I worked as a Research Fellow at the Recurse Center. It’s a three-month long “writer’s retreat for programmers”. It’s unstructured: participants are not told what to do. Rather, they must pick projects for themselves, and structure their own path. This is challenging. But the floundering around and difficulty in picking a path is essential for growing one’s sense of choice, and of responsibility for choice. And so creating that space is, again, a form of volitional philanthropy.

There are institutions which think they’re in the volitional philanthropy game, but which are not. Many educators believe they are. In non-compulsory education that’s often true. But compulsory education is built around fundamental denials of volition: the student is denied choice about where they are, what they are doing, and who they are doing it with. With these choices denied, compulsory education shrinks and constrains a student’s sense of volition, no matter how progressive it may appear in other ways.

There is something paradoxical in the notion of helping someone develop their volition. By its nature, volition is not something which can be given; it must be taken. Nor do I think “rah-rah” encouragement helps much, since it does nothing to permanently expand the recipient’s sense of self. Rather, I suspect the key lies in a kind of listening-for-enablement, as a way of helping people discover what they perhaps do not already know is in themselves. And then explaining honestly and realistically (and with an understanding that one may be in error) what it is one sees. It is interesting to ask both how to develop that ability in ourselves, and in institutions which can scale it up.

[1] It is a median effect. I know people who start companies who become first consumed and then eventually diminished by the role. But most people I’ve known have been enlarged.

Note, by the way, that I work at Y Combinator Research, which perhaps colours my impression. On the other hand, I’ve used YC as an example of volitional philanthropy since (I think) 2010, years before I started working for YCR.

There’s Gold In Them Thar Tails: Part 1

If you were accepted to a selective college or job in the 90s, have you ever wondered if you’d get accepted in today’s environment? I wonder myself. It leaves me feeling grateful because I think the younger version of me would not have gotten into Cornell or SIG today. Not that I dwell on this too much. I take Heraclitus at his word that we do not cross the same river twice. Transporting a fixed mental impression of yourself into another era is naive (cc the self-righteous who think they’d be on the right side of history on every topic). Still, my self-deprecation has teeth. When I speak to friends with teens I hear too many stories of sterling resumes bulging with 3.9 GPAs, extracurriculars, and Varsity sport letters, being warned: “don’t bother applying to Cal”.

A close trader friend explained his approach. His daughter is a high achiever. She’s also a prolific writer. Her passion is the type all parents hope their children will be lucky enough to discover. My friend recognizes that the bar is so high to get into a top school that acceptance above that bar is a roulette wheel. With so much randomness lying above a strict filter, he de-escalates the importance of getting into an elite school. “Do what you can, but your life doesn’t depend on the whim of an admissions officer”. She will lean into getting better at what she loves wherever she lands. This approach is not just compassionate but correct. She’s thought ahead, got her umbrella, but she can’t control the weather.

My friend’s insight that acceptance above a high threshold is random is profound. And timely. I had just finished reading Rohit Krishnan’s outstanding post Spot The Outlier, and immediately sent it to my friend.

I chased down several citations in Rohit’s post to improve my understanding of this topic.

In this post, we will tie together:

  1. Why the funnels are getting narrower
  2. The trade-offs in our selection criteria
  3. The nature of the extremes: tail divergence
  4. Strategies for the extremes

We will extend the discussion in a later post with:

  1. What this means for intuition in general
  2. Applications to investing

Why Are The Funnels Getting Narrower?

The answer to this question is simple: abundance.

In college admissions, the number of candidates in aggregate grows with the population. But this isn’t the main driver behind the increased selectivity.  The chart below shows UC acceptance rates plummeting as total applications outstrip admits.

The spread between applicants and admissions has exploded. UCLA received almost 170k applications for the 2021 academic year! Cal receives over 100k applicants for about 10k spots. Your chances of getting in have cratered in the past 20 years. Applications have lapped population growth due to a familiar culprit: connectivity. It is much easier to apply to schools today. The UC system now uses a single boilerplate application for all of its campuses.

This dynamic exists everywhere. You can apply to hundreds of jobs without a postage stamp. Artists, writers, analysts, coders, designers can all contribute their work to the world in a permissionless way with as little as a smartphone. Sifting through it all necessitated the rise of algorithms — the admissions officers of our attention.

Trade-offs in Selection Criteria

There’s a trade-off between signal and variance. What if Spotify employed an extremely narrow recommendation engine indexed soley on artist? If listening to Enter Sandman only lead you to Metallica’s deepest cuts, the engine is failing to aid discovery. If it indexed by “year”, you’d get a lot more variance since it would choose across genres, but headbangers don’t want to listen to Color Me Badd.  This prediction fails to delight the user.

Algorithms are smarter than my cardboard examples but the tension remains. Our solutions to one problem excarbates another. Rohit describes the dilemma:

The solution to the problem of discovery is better selection, which is the second problem. Discovery problems demand you do something different, change your strategy, to fight to be amongst those who get seen.

There’s plenty of low-hanging fruit to find recommendations that reside between Color Me Badd and St. Anger. But once it’s picked, we are still left with a vast universe of possible songs for the recommendation engine to choose from.

Selection problems reinforce the fact that what we can measure and what we want to measure are two different things, and they diverge once you get past the easy quadrant.

In other words, it’s easy enough to rule out B students, but we still need to make tens of thousands of coinflip-like decisions between the remaining A students. Are even stricter exams an effective way narrow an unwieldy number of similar candidates? Since in many cases predictors poorly map to the target, the answer is probably no. Imagine taking it to the extreme and setting the cutoff to the lowest SAT score that would satisfy Cal’s expected enrollment. Say that’s 1400. This feels wrong for good reasons (and this is not even touching the hot stove topic of “fairness”). Our metrics are simply imperfect proxies for who we want to admit. In mathy language we can say, the best person at Y (our target variable) is not likely to come from the best candidates we screened if the screening criteria, X, is an imperfect correlate of success(Y).

The cost of this imperfect correlation is a loss of diversity or variance. Rohit articulates the true goal of selection criteria (emphasis mine):

Since no exam perfectly captures the necessary qualities of the work, you end up over-indexing on some qualities to the detriment of others. For most selection processes the idea isn’t to get those that perfectly fit the criteria as much as a good selection of people from amongst whom a great candidate can emerge.

This is even true in sports. Imagine you have a high NBA draft pick. A great professional must endure 82 games (plus a long playoff season), fame, money, and most importantly, a sustained level of unprecedented competition. Until the pros, they were kids. Big fish in small ponds. If you are selecting for an NBA player with narrow metrics, even beyond the well-understood requisite screens for talent, then those metrics are likely to be a poor guide to how the player will handle such an outlier life. The criteria will become more squishy as you try to parse the right tail of the distribution.

In the heart of the population distribution, the contribution to signal of increasing selectivity is worth the loss of variance. We can safely rule out B students for Cal and D3 basketball players for the NBA.  But as we get closer to elite performers, at what point should our metrics give way to discretion? Rohit provides a hint:

When the correlation between the variable measured and outcome desired isn’t a hundred percent, the point at which the variance starts outweighing the mean error is where dragons lie!

Nature Of The Extremes: Tail Divergence

To appreciate why the signal of our predictive metrics become random at the extreme right tail we start with these intuitive observations via LessWrong:

Extreme outliers of a given predictor are seldom similarly extreme outliers on the outcome it predicts, and vice versa. Although 6’7″ is very tall, it lies within a couple of standard deviations of the median US adult male height – there are many thousands of US men taller than the average NBA player, yet are not in the NBA. Although elite tennis players have very fast serves, if you look at the players serving the fastest serves ever recorded, they aren’t the very best players of their time. It is harder to look at the IQ case due to test ceilings, but again there seems to be some divergence near the top: the very highest earners tendto be very smart, but their intelligence is not in step with their income (their cognitive ability is around +3 to +4 SD above the mean, yet their wealth is much higher than this).

The trend seems to be that even when two factors are correlated, their tails diverge: the fastest servers are good tennis players, but not the very best (and the very best players serve fast, but not the very fastest); the very richest tend to be smart, but not the very smartest (and vice versa). 

The post uses simple scatterplots to demonstrate. Here are 2 self-explanatory charts. 

LessWrong contines: Given a correlation, the envelope of the distribution should form some sort of ellipse, narrower as the correlation goes stronger, and more circular as it gets weaker.

If we zoom into the far corners of the ellipse, we see ‘divergence of the tails’: as the ellipse doesn’t sharpen to a point, there are bulges where the maximum x and y values lie with sub-maximal y and x values respectively:

Say X is SAT score and Y is college GPA. We shoudn’t expect that the person with highest SATs will earn the highest GPA. SAT is an imperfect correlate of GPA. LessWrong’s interpretation is not surprising:

The fact that a correlation is less than 1 implies that other things matter to an outcome of interest. Although being tall matters for being good at basketball, strength, agility, hand-eye-coordination matter as well (to name but a few). The same applies to other outcomes where multiple factors play a role: being smart helps in getting rich, but so does being hard working, being lucky, and so on.

Pushing this even further, if we zoom in on the extreme of a distribution we may find correlations invert! This scatterplot via shows a positive correlation over the full sample (pink) but a negative correlation for a slice (blue). 

This is known as Berkson’s Paradox and can appear when you measure a correlation over a “restricted range” of a distribution (for example, if we restrict our sample to the best 20 basketball players in the world we might find that height is negatively correlated to skill if the best players were mostly point guards).

[I’ve written about Berkson’s Paradox here. Always be wary of someone trying to show a correlation from a cherry-picked range of a distribution. Once you internalize this you will see it everywhere! I’d be charitable to the perpetrator. I suspect it’s usually careless thinking rather than a nefarious attempt to persuade.]

Strategies For The Extremes

In 1849, assayor Dr. M. F. Stephenson shouted ‘There’s gold in them thar hills’ from the steps of the Lumpkin County Courthouse in a desperate bid to keep the miners in Georgia from heading west to chase riches in California. We know there’s gold in the tails of distributions but our standard filters are unfit to sift for them. 

Let’s pause to take inventory of what we know. 

  1. As the number of candidates or choices increases we demand stricter criteria to keep the field to a manageable size.
  2. At some cutoff, in the extreme of a distribution, selection metrics can lead to random or even misleading predictions. 1

    I’ll add a third point to what we have already established:

  3. Evolution in nature works by applying competitve pressures to a diverse population to stimulate adaptation (a form of learning). Diversity is more than a social buzzword. It’s an essential input to progress. Rohit implicitly acknowledges the dangers of inbreeding when he warns against putting folks through a selection process that reflexively molds them into rule-following perfectionists rather than those who are willing to take risks to create something new.

With these premises in place we can theorize strategies for both the selector and the selectee to improve the match between a system’s desired output (the definition of success depends on the context) and its inputs (the criteria the selector uses to filter). 

Selector Strategies

We can continue to rely on conventional metrics to filter the meat of the distribution for a pool of candidates. As we get into the tails, our adherence and reverance for measures should be put aside in favor of increasing diversity and variance. Remember the output of an overly strict filter in the tail is arbitrary anyway. Instead we can be deliberate about the randomness we let seep into selections to maximize the upside of our optionality. 

Rohit summarizes the philosophy:

Change our thinking from a selection mindset (hire the best 5%) to a curation mindset (give more people a chance, to get to the best 5%).

Practically speaking this means selectors must widen the top of the funnel then…enforce the higher variance strategy of hire-and-train.

Rohit furnishes examples:

  • Tyler Cowen’s strategy of identifying unconventional talent and placing small but influential bets on the candidates. This is easier to say than do but Tony Kulesa finds some hints in Cowen’s template. 
  • The Marine Corps famously funnels wide electing not to focus so much on the incoming qualifications, but rather look at recruiting a large class and banking on attrition to select the right few.
  • Investment banks and consulting firms hire a large group of generically smart associates, and let attrition decide who is best suited to stick around.

David Epstein, author of Range and The Sports Gene, has spent the past decade studying the development of talent in sports and beyond. He echoes these strategies:

One practice we’ve often come back to: not forcing selection earlier than necessary. People develop at different speeds, so keep the participation funnel wide, with as many access points as possible, for as long as possible. I think that’s a pretty good principle in general, not just for sports.

I’ll add 2 meta observations to these strategies:

  1. The silent implication is the upside of matching the right talent to the right role is potentially massive. If you were hiring someone to bag groceries the payoff to finding the fastest bagger on the planet is capped. An efficient checkout process is not the bottleneck to a supermarket’s profits. There’s a predictable ceiling to optimizing it to the microsecond. That’s not the case with roles in the above examples. 

  2. Increasing adoption of these strategies requires thoughtful “accounting” design. High stakes busts, whether they are first round draft picks or 10x engineers, are expensive in time and money for the employer and candidate. If we introduce more of a curation mindset, cast wider nets and hire more employees, we need to understand that the direct costs of doing that should be weighed against the opaque and deferred costs of taking a full-size position in expensive employees from the outset.

    Accrual accounting is an attempt match a business’ economic mechanics to meaningful reports of stocks and flows so we extract insights that lead to better bets. Fully internalized, we must recognize that some amount of churn is expected as “breakage”. Lost option premiums need to be charged against the options that have paid off 100x. If an organization fails to design its incentive and accounting structures in accordance with curation/optionality thinking it will be unable to maintain its discipline to the strategy.  

Selectee Strategies

For the selectee trying to maximise their own potential there are strategies which exploit the divergence in the tails. 

To understand, we first recognize, that in any complicated domain, the effort to become the best is not linear. You could devote a few years to becoming an 80th or 90 percentile golfer or chess player. But in your lifetime you wouldn’t become Tiger or Magnus. The rewards to effort decay exponentially after a certain point. Anyone who has lifted weights knows you can spend a year progressing rapidly, only to hit a plateau that lasts just as long. 

The folk wisdom of the 80/20 rule captures this succintly: 80% of the reward comes from 20% of the effort, and the remaining 20% of the reward requires 80% effort. The exact numbers don’t matter. Divorced from contexts, it’s more of a guideline. 

This is the invisible foundation of Marc Andreesen and Scott Adam’s career advice to level up your skills in multiple domains. Say coding and public speaking or writing plus math. If it’s exponentially easier to get to the 90th percentile than the 99th then consider the arithmetic2.

a) If you are in the 99th percentile you are 1 in 100. 

b) If you are top 10% in 2 different (technically uncorrelated) domains then you are also 1 in 100 because 10% x 10% = 1%

It’s exponentially easier to achieve the second scenario because of the effort scaling function. 

If this feels too stifling you can simply follow your curiosity. In Why History’s Greatest Innovators Optimized for Interesting, Taylor Pearson summarizes the work of Juergen Schmidhuber which contends that curiousity is the desire to make sense of, or compress, information in such a way that we make it more beautiful or useful in its newly ordered form. If learning (or as I prefer to say – adapting) is downstream from curiousity we should optimize for interesting

Lawrence Yeo unknowingly takes the baton in True Learning Is Done With Agency, with his practical advice. He tells us to truly learn we must:

decouple an interest from its practical value. Instead of embarking on something with an end goal in mind, you do it for its own sake. You don’t learn because of the career path it’ll open up, but because you often wonder about the topic at hand.

…understand that a pursuit truly driven by curiosity will inevitably lend itself to practical value anyway. The internet has massively widened the scope of possible careers, and it rewards those who exercise agency in what they pursue.


Rohit’s essay anchored Part 1 of this series. I can’t do better than let his words linger before moving on to Part 2.
If measurement is too strict, we lose out on variance.

If we lose out on variance, we miss out on what actually impacts outcomes.

If we miss what actually impacts outcomes, we think we’re in a rut.

But we might not be.

Once you’ve weeded out the clear “no”s, then it’s better to bet on variance rather than trying to ascertain the true mean through imprecise means.

We should at least recognize that our problems might be stemming from selection efforts. We should probably lower our bars at the margin and rely on actual performance [as opposed to proxies for performance] to select for the best. And face up to the fact that maybe we need lower retention and higher experimentation.

Looking Ahead

In Part 2, we will explore what divergence in the tails can tell us about about life and investing. 


Lessons From Susquehanna

Trading is just decision-making under uncertainty. I suspect that the most advanced thinking on reasoning about risk/reward comes from areas where the stakes are high and there are many reps. Military, medicine, markets.

I got my professional start out of college at SIG (Susquehanna Investment Group). They were and remain one of the largest trading firms globally. In the derivatives world, their training program is legendary.

While I only spent 2000-2008 at SIG, I continued to work with SIG alum until I left trading a year ago. My writing is deeply influenced by my career and the thinking I absorbed from SIG’s education and its culture.

Shane Parrish of The Knowledge Project recently interviewed long-time SIG director Todd Simkin. Todd has a hand in many of SIG’s functions including trading, education, recruiting and determining compensation (option traders negotiating comp with option traders would make an amazing YT channel btw…bonus season is a steady brigade of Moroccan bazaar tactics and brinksmanship).

The institutional knowledge leaking from the interview is hard to come by. SIG is famously secretive which should give you a hint about Todd’s lessons: they are hard enough to implement that there’s little risk in sharing them. The infrastructure and know-how to teach people to make good decisions is a high leverage activity. It is a competitive advantage and it is expensive (before going to SIG’s boot camp in Bala Cynwyd, PA for 3 months we signed 3-year non-compete agreements so they could protect their investments in us).

I did a write-up of the interview dotted with my own commentary. I refactored the lessons into 3 broad categories: decision-making, education, communication. The 3 are deeply intertwined. Only after listening to this interview did I appreciate just how deliberate SIG’s leaders were about education. The interview left me feeling somehow hacked and grateful.

SIG’s influences on me are self-apparent. But I want to highlight imprints that were not obvious until I heard Todd explain their dogma. For example, my own beliefs about education being “socio-cultural” is something I picked up by osmosis. The way I talk to my kids is reminiscent of how I communicate at work (minus the occasional f-bomb lobbed at an anthropomorphized futures ladder). As I listened I was thinking, “wait a minute, is that where I got that from”?

It’s hard to separate SIG’s influence from the lessons anyone would pick up from surviving any high-rep trading career. Still, the lessons from the interview are evergreen and conveniently encapsulated.

Here’s what to expect:

On Decision-Making

  • Why SIG’s approach to markets starts with humility and Bayesian thinking: update hard!
  • Trading is not about opinions or theses. It’s about finding disconfirming propositions. See what that means.
  • How to minimize confirmation bias and “resulting”.
  • Tribalism as a short-circuit in an otherwise useful shortcut. The tension between heuristics and “first principles”.
  • Addressing a paradox — knowledge of cognitive bias doesn’t inoculate you from it.
  • Todd was put on the spot to name the single most important variable to making better decisions. He doesn’t even hesitate. It has to do with the next section.


  • Truth-finding is the raw material needed to make better decisions. Creating a culture of truth-finding requires a deep appreciation of how to communicate. How does SIG foster such a culture? What does constructive communication look like? Unconstructive communication is subtle and dangerous because it can actually look like constructive communication. Find out the difference.
  • What is “reflective listening”? Why does it sound stupid? Why does it actually work? (This will be a familiar topic to anyone who has read Chris Voss’ negotiation manual Never Split The Difference).
  • The power of “how do you feel about that?”. When my wife listened to that part she told me “It sounds just like you”.
  • The principle of “charity” in both life and trading and why it’s the base of the negotiation pyramid.
  • An amazing example of “modeling behavior” — the story of Todd’s dad when he tried to quit lacrosse.


  • How SIG’s training class is organized
  • SIG’s education philosophy: Traders are made, not born. What they look for in recruits and why.
  • SIG’s application of Lev Vygotsky’s idea that all learning is “socio-cultural”. What that means and the emphasis on modeling behavior.
  • When teaching, a master needs to find a student’s “zone of proximal development” so they can provide suitable “scaffolding”. By using the Socratic method, a teacher can zero in on where the student’s boundaries are. This idea even extends into their interview process.


  • Todd was on Jeopardy (won once and lost once). The conversation he had with SIG co-founder Jeff Yass before and after his competition is comically revealing of SIG’s culture.
  • Todd’s experience with depression and emphasis on mental health.

✍️My Commentary on Todd Simkin’s Interview On The Knowledge Project (31 min read)

If you prefer to skip directly to the interview:

🎤 Todd Simkin – Making Better Decisions (The Knowledge Project)

I tend to believe that the most advanced thinking on risk-taking in markets comes from trading firms operating at scale betting their own money. There is plenty of cross-pollination between prop firms and traditional bank trading desks as well. Many of these firms have training programs to form a solid basis for decision-making.

You can find a list of prop trading firms here:

📜 Listing of Proprietary Trading Firms (

Their websites tend to be sparse but if you are looking for a rigorous foundation in markets it would be hard to find a better education than spending some time at one of these shops.

Fair warning:

Like college admissions, I expect it’s harder to get into these firms than when I graduated. The business has a brutally high attrition rate as well. If any of that deters you, you likely saved yourself from a career that wasn’t going to work for you anyway.

You can see SIG’s gaming blog for a glimpse into what they find fun.

🔖Raise Your Game (Link)

One last personal note.

I am grateful for everything I learned at SIG and from the brilliant people I was able to work alongside throughout my career.

But I’ve written before about how I “overlearned” some lessons. This wasn’t SIG’s fault so much as me being dense. Trading and investing are sufficiently similar that you can port your thinking directly from trading to investing. But they are different enough to screw with how you map concepts from one to the other.

This is especially true for derivatives traders. Derivs folk will tend to start with a much stronger prior of market efficiency. It’s partly an expression of SIG’s humility credo and partly reinforced by the daily grind of the job. Everything they trade is on its way to being arbed with respect to underlying securities. Arb pricing is always relative. It does not share the same undiversifiable or systematic risk premium that the underlying has.

This leaves derivatives traders blind to underlying risk premiums. That is not their business. That’s the business of investors.

I’ve written before about how my narrow understanding of derivatives hindered me in the domain of investing.

✍️ How I Misapplied My Trader Mindset To Investing (14 min read)