Category: Education

On Hidden Potential

One of the Substacks I never fail to read is Range Widely by David Epstein, author of Range (my notes on his interview about the book) and The Sports Gene: Inside the Science of Extraordinary Athletic Performance.

David is a journalist by trade. His writing is well-researched. Social science research, especially the kind of pop-sci stuff that climbs the heap to find itself in airport bookstores, should require a “grain of salt” rating (G: “germane”, PG: “possibly garbage”, R: “rumored at best“). David’s process and intellectual demeanor indicate care — he resists the temptation to oversell conclusions.

Personally, I rarely read social science books — I’ll just listen to a podcast with the author if I care. The insights in such books feel like they have an asymmetrical yield — if they confirm what you already thought then the opportunity cost of reading that book is high (I’ll be lucky if I read 500 more books before I’m dead) and if the book has a ground-breaking insight it’ll almost certainly be out of fashion within a decade (“the game theory of getting published in social science” is a comically fractal idea. If you google that phrase, you’ll see why).

Anyway, David’s history of intellectual care makes him an ideal candidate to interview other social science authors about their books — critical enough to ask good questions but friendly enough that he can get the interviews in the first place.

Enough preamble…some excerpts I enjoyed from David’s Q&A with psychologist Adam Grant on his new book Hidden Potential: The Science of Achieving Greater Thing (emphasis mine):

  • Many people believe that if you’re not precocious, it’s a sign that you lack potential. But potential is not about where you start — it’s a matter of how far you’ll travel. And the latest science reveals that we shouldn’t mistake speed for aptitude. Our rate of learning is driven by motivation and opportunity, not just ability. Think of all the late bloomers who weren’t lucky enough to stumble on a passion, or to have a parent, teacher, or coach early on who recognized and developed their hidden potential.
    This doesn’t mean we should ignore “gifted” students. We need to think differently about how we nurture their potential too. Empirically, the rate of child prodigies becoming adult geniuses is surprisingly low. I suspect one of the reasons is that they learn to excel at other people’s crafts but not to develop their own. Mastering Mozart’s melodies doesn’t prepare you to write your own original symphonies. [Kris: this is exactly the point Trent Reznor made to Rick Rubin as he wrestled with his own potential]. Memorizing thousands of digits of pi does little to train your mind to come up with your own Pythagorean theorem. And the easier a new skill comes to you, the less experience you have with facing failure. This is a lesson that chess grandmaster Maurice Ashley drove home for me: the people who struggle early often build the character skills to excel later. We need to start investing in character skills sooner.
  • Because Glennie is deaf, she had to find nontraditional ways to learn, like using different parts of her body to feel vibrations that correspond to different pitches. She and her teacher were constantly trying different ways to do that, and different ways to do everything, really. As you write: “Continually varying the task and raising the bar made learning a joy.” I’ve long been fascinated by this issue of variable practice. Mixing things up constantly might seem counterintuitive, but it turns out to be better for learning.
  • You note that concert pianists who reach international acclaim by age 40 typically were not obsessed early on, and that they usually had a slow but steady increase in their commitment to music. It just made me think of the first page of Battle Hymn — in which the author promises the secrets to raising stereotypically successful children, and recounts assigning her daughter violin and soon she’s supervising five hours of deliberate practice a day. That part was excerpted in the Wall St. Journal, and it was the Journal’s most commented upon article ever! It really seeped into the public consciousness, I think. What didn’t make as much of an impression was the part later in the book where the author (to her credit) recounts her daughter turning to her and saying: “You picked it, not me,” and more or less quits. [Kris: I’m very careful riding our kids in areas that they are naturally drawn to because of such “reactance”. I don’t want to turn “their thing” into “my thing”. You have an extra gear to give for those things that you discover independently.]
  • The issue of “learning styles.” This is the very popular idea that some people learn best by listening, others by reading, others by looking, etc. Maybe someone prefers podcasts to books because they style themself an “auditory learner.” Trouble is, a mountain of research has failed to back this idea up [Kris: Veritasium calls this “the biggest myth in education”. Although I suspect the testing design for experiments that dismiss the idea might be strawmanning the contention or interpreting it too narrowly].People may indeed have a style of learning that feels most comfortable, but that doesn’t mean they’re actually learning more that way. In fact, to use a line from Range, in many cases, difficulty is not a sign that you aren’t learning, but ease is [Kris: I’ve found that many teachers I respect agree with this so it’s not as bold a statement as it might appear even if this is the first time you’ve heard that. I remind my kids — if it’s easy it’s just review, not learning. Non-superficial learning hurts. I might even go as far to say that learning and pain are nearly synonyms. To be clear, such a statement is more useful as a reminder than a universal truth. Experiential learning is an easy counterexample]. As you write: “Sometimes you even learn better in the mode that makes you the most uncomfortable, because you have to work harder at it.” I was just reading a study (“Measuring actual learning versus feeling of learning”) which showed that Harvard physics students preferred lectures from highly-rated instructors to active learning exercises. But they learned more from the latter. The main difference in the active group was that students had to try to solve problems in groups before they really knew what they were doing, and so they would discuss, generate questions, and hit dead-ends, all before seeing correct solutions. We know that forcing learners to try to generate solutions before seeing them enhances learning (the so-called “generation effect”), but it doesn’t feel great, so we may avoid it.
  • Back in December, you helped me get in touch with RA Dickey, and he was every bit as stellar of an interview as you promised. His story helps to illuminate why so many people fail to try new methods when we get stuck. It’s not so much that we’re stubborn or resistant to change. We hate the thought of giving up the gains we’ve already made. We forget that sometimes, the best way to move forward is to go back to the drawing board. [Kris: Feeling seen] If your fastball is slowing down and your career is stalling, you have nothing to lose by tinkering with the knuckleball. We shouldn’t be so afraid of failing that we fail to try.

The Midpoint From 1 to 9 is…3?

For the past 3 years, the Berkeley Chess School has done a weekly lesson in our backyard. About 15 kids attend. They are mostly 2nd and 5th graders because we know the families through our kids.

I walk home from school with all the kids on chess day. I usually throw out a math question or riddle and by now the kids just ask for them on our strolls. Lately, the questions deal with rates, percentages/fractions, exponents/roots, or some basic number play stuff (“How do you know if a number is divisible by 9?”)

Some examples:

  • Start with $100. If you earn 10% then lose 10%, how much money do you have?
  • What’s larger 3⁴ or 4³ and similar questions?
  • If you travel 5 miles in 12 minutes, how fast are you going?[I haven’t dropped this one on them: “If I drive around a one-mile track and average 30 mph for the first lap, how fast do I have to drive the second lap to average 60 mph for both laps combined?” (Solution)]
  • If you have 5 kids on your team and only 4 kids start how many possible starting lineups are there?
  • If you lose 25%, how much do you have to make to get back to even?[I like that one because it’s a useful elasticity idea. If X is the loss percentage, you need to earn back X/(1-X).

    If you are selling lemonade and you cut your price by 20%, you need to sell 25% more cups to be revenue-neutral.]

I started giving these questions because, well it’s just play. Riddles are inherently satisfying. But I’m also conscious of imparting some durable concepts. It’s not quite as deliberate as hiding the dog’s pill in the peanut butter but there’s some overlap. Honestly, the main motivation is keeping the kids who aren’t into sports engaged. There’s about 40 minutes between the kids getting to my house and the start of chess. The 2nd graders usually play soccer and the 5th graders hoop it up. A few kids aren’t into either but they gravitate to the riddles (my boys just wanna play sports and my 5th grader, Zak, with sass tells his friends “This is the stuff I deal with all the time”).

Lately, I’ve been doing more exponent stuff because I know they aren’t doing that yet in 5th grade but it’s reachable for them. Zak is taking the online Pre-Algebra I course on Art of Problem Solving which is comprised of 7 chapters. He just wrapped chapter 2 which is all about exponents so that’s been top-of-mind for coming up with the questions.

The challenge question to end the chapter was to solve for the 2 possible values of X (see below). But keep in mind, they haven’t learned how to compute square roots or any other kind of roots. You can do this without any involved computations and without roots. You can find the solution at the end of the post.

Find the 2 possible values of x:

Anyway, I didn’t give the kids that question but by this past week, they understood the basics of computing a simple exponent or taking a square root. So I took a stab at base 10 logarithms. I just explained it as the power you need to raise 10 to get to the target number.

“So if our target is 100, what do you have to raise 10 to? How about a target of 1,000?”

They had no trouble with this. So I explained how both the Richter and decibel scales were log scales that compressed a wide range into a smaller ruler. A 6 on the Richter is not twice the energy of a 3 but 1000x more energy. Every integer increase in the scale is just a higher order of magnitude.

The most pleasant thing happened. The kids that gravitated to this stuff were stoked. As it it settled in their brains they were all Keanu Reeves “Whoa, that’s so cool”.

I texted one of the parents:

Putting aside the pure joy of watching a kid unlock, exponents and logs are fundamentally important operations like adding and subtracting. Our first formal introduction to them outside a math class is usually science (exponential growth/decay) but more prosaic to this audience is the topic of investing, specifically the idea of compound growth. It’s an idea you’d love to see people internalize as young as possible.

Typically when someone (and I’ve done this too) writes about compounding they reference Einstein’s 8th Wonder of the World quote or talk about how our minds think linearly and find exponential growth unintuitive. [This was a common conversation at the start of the COVID pandemic with VCs patting themselves on the back for lateral thinking about how coefficients of virality applied to…the domain where exponential growth is usually people’s first contact with the topic. Like twisting a eulogy into a chance to talk about yourself. I’m not even mad, it’s the whole wheel of cheese].

With that in mind, I’ll leave you with an excerpt from Grant Sanderson, the mathematician behind the 3Blue1Brown YouTube channel. This is from his appearance on

Dwarkesh Patel

excellent Lunar Society Podcast:

Have you come across those studies where anthropologists interview tribes of people that are removed enough from normal society that they don’t have the level of numeracy that you or I do? But there’s some notion of counting. You have one coconut or nine coconuts like you have a sense of that. But if you ask what number is halfway between one and nine, those groups will answer three whereas you or I or people in our world would probably answer five and because we think on this very linear scale.

It’s interesting that evidently the natural way to think about things is logarithmically, which kind of makes sense. The social dynamics of as you go from solitude to a group of 10 people to a group of 100 people have roughly equal steps in increasing complexity more so than if you go from 1 to 51 to 102 and I wonder if it’s it’s the case that by adding numeracy in some senses we’ve also like lost some numeracy or lost some intuition in others, where now if you ask middle school teachers what’s a difficult topic to teacher for students to understand they’re like logarithms. But that should be deep in our bones right so somehow it got unlearned

What a cheeky observation. Gives a second entendre to the expression “natural log”.

2 ways I came up with to solve the AoPS question

Method 1:

x could also be -243 since it’s being raised to an even power.

Method 2:

Excerpts From Grant Sanderson on The Lunar Society Podcast

Dwarkesh Patel interviews Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about:

  • Whether advanced math requires AGI
  • What careers should mathematically talented students pursue
  • Why Grant plans on doing a stint as a high school teacher
  • Tips for self teaching
  • Does Godel’s incompleteness theorem actually matter
  • Why are good explanations so hard to find?

Watch on YouTube. Listen on Spotify, Apple Podcasts, or any other podcast platform. Full transcript here.

Kris: I snipped several excerpts for future reference. Emphasis mine. I cut up the excerpts as I want to remember them which means there are missing sections so I encourage you to listen to the whole episode or read the sections of transcript I’m pulling from if you want a closer look.

On the future of education 

[key ideas: reducing distance to students, educator’s role is not just explanation but more importantly “bring out knowledge” not put it in, the non-linear influence of a teacher on a student’s future, and the chaotic concept of “sensitivity to initial conditions”]

Dwarkesh Patel 0:44:44

Should the top 0.1% of educators exclusively be on the internet because it seems like a waste if you were just a college professor or a high school professor and you were teaching 50 kids a year or something. Given the greater scale available should more of them be trying to see if they can reach more people?

Grant Sanderson 0:45:01

I think it’s not a bad thing for more educators who are good at what they’re doing to put their stuff online for sure. I highly encourage that even if it’s as simple as getting someone to put a camera in the back of the classroom. I don’t think it would be a good idea to get those people out of the classroom.

If anything I think one of the best things that I could do for my career would be to put myself into more classrooms…

One of the most valuable things that you can have if you’re trying to explain stuff online is a sense of empathy for what possible viewers that are out there. The more distance that you put between yourself and them in terms of life circumstances. I’m not a college student so I don’t have the same empathy with college students. Certainly not a high school student, so I’ve lost that empathy. That distance just makes it more and more of an uphill battle to make the content good for them and I think keeping people in regular touch with just what people in the classroom actively need is necessary for them to remain as good and as sharp as they are…

The other thing I might disagree with is the idea that the reach is lower. Yes, it’s a smaller number of people but you’re with them for much, much more time and you actually have the chance of influencing their trajectory through a social connection in a way that you just don’t over Youtube.

You’re using the word education in a way that I would maybe sub out for the word explanation. You want explanations to be online but the word education derives from the same root as the word educe, to bring out, and I really like that as a bit of etymology because it reminds you that the job of an educator is not to take their knowledge and shove it into the heads of someone else the job is to bring it out. That’s very, very hard to do in a video and in fact, even if you can kind of get at it by asking intriguing questions for the most part the video is there to answer something once someone has a question.

The teacher’s job, or the educator’s job, should be to provide the environment such that you’re bringing out from your students as much as you can through inspiration through projects, through little bits of mentorship and encouragement along the way. That requires eye contact and being there in person and being the true figure in their life rather than just an abstract voice behind a screen.

Anytime I chat with mathematicians and try to get a sense for how they got into it and what got them started, so often they start by saying there was this one teacher and that teacher did something very small — like they pulled them aside and just said, “Hey. You’re really good at this. Have you considered studying more?” or they give them an interesting problem.

And the thing that takes at most 30 minutes of the teacher’s time, maybe even 30 seconds, has these completely monumental rippling effects for the life of the student they were talking to that then sets them on this whole different trajectory.

Two examples of this come to mind. One is this woman who was saying she had this moment when she got pulled aside by the teacher and he just said, “Hey, I think you’re really good at math. You should consider being a math major.” which had been completely outside of her purview at that time. That changed the way she thought about it. And then later she said she learned that he did that for a large number of people. He just pulled them and was like, “Hey, you’re really good at math.” So that’s a level of impact that you can have as a figure in their lives in a way that you can’t over screen.

Another one which was very funny. I was asking this guy why he went into the specific field that he did. It was a seemingly arbitrary thing in my mind but I guess all pure math seems to be. He said that in his first year of grad school he was sitting in this seminar and at the end of the seminar the professor, who was this old professor who he had never met him before, they didn’t have any kind of connection. He seeks this guy out and comes up and he says, “You. I have a problem for you. A good research problem that I think I think might be a good place for you to start in the next couple months” and this guy was like “Oh, okay” and he gets this research problem and he spends some months thinking about it and he comes back and then it later came to light that the professor mistook him for someone else that was someone he was supposed to be mentoring. He was just the stereotypical image of like a doddering old math professor who’s not very in tune with the people in his life that was the actual situation but nevertheless that moment of accidentally giving someone a problem completely shifted the research path for him, which if nothing else, shows you the sensitivity to initial conditions that takes place when you are a student and how the educator is is right on that nexus of sensitivity who can completely swing the fences one way or another for what you do.

For every one of those stories there’s going to be an unfortunate counterbalancing story about people who are demotivated from math. I think this was seventh grade. There was this math class that I was in and I was one of the people who was good at math and enjoyed it and would often help the people in the class understand it. I had enough ego built up to have a strong shell around things. For context, I also really liked music and there was this concert that had happened where I had a certain solo or something earlier in that week.

There was a substitute teacher one day who didn’t have any of the context and she gave some lesson and had us spend the second half of the class going over the homework for it. All of the other students in the class were very confused and I think I remember like they would come to me and I would try to offer to help them and the substitute was going around the class in these circles and basically marking off a little star for how far down the homework people were just to get a sense are they progressing. That was kind of her way of measuring how far they were. When she got to me I had done none of them because I was spending my whole time trying to help all of the others and after having written a little star next to the same problem like three different times she said to me like, “Sometimes music people just aren’t math people.” and then keeps walking on.

I was in the best possible circumstance to not let that hit hard because one, I had the moral high ground of “Hey, I’ve just been helping all these people. I understand it and I’ve been doing your job for you.” This was my little egotistical seventh grade brain. I knew that I knew the stuff. Even with all of the armor that was put up, I remember it was just this shock to my system, she says this thing and it just made me strangely teary-eyed or something.

I can only imagine if you’re in a position where you’re not confident in math and the thing that you know deep in your heart is actually you are kind of struggling with it, just a little throwaway comment like that could completely derail the whole system in terms of your relationship with the subject.

So it’s another example to illustrate the sensitivity to initial conditions. I was in a robust position and wasn’t as sensitive. I was gonna love math no matter what but you envision someone who’s a little bit more on that teetering edge and the comment, one way or another, either saying you’re good at this you should consider majoring in it or saying, “Sometimes music people aren’t math people” which isn’t even true. That was the other thing about it that niggled at my brain when she said it.

All of that is just so important for people’s development that when people talk about online education as being valuable or revolutionary or anything like that, there’s a part of me that sort of rolls my eyes because it just doesn’t get at the truth that online explanations have nothing to do with all of that important stuff that’s actually happening and at best it should be like in the service of helping that side of things where the rubber meets the road.

On explanations 

[key ideas: not everyone responds to the same explanations so explanations that scale well are difficult to conjure. There’s room for multiple approaches and ways to communicate]

Dwarkesh Patel 1:02:22

Why are good explanations so hard to find, despite how useful they are? Obviously, other than you, there’s many other cases of good explanations. But generally, it just seems like there aren’t as many as there should be. Is it just a story of economics where it’s nobody’s incentive to spend a lot of time making good explanations? Is it just a really hard skill that isn’t correlated with being able to come up with a discovery itself? Why are good explanations scarce?

Grant Sanderson 1:02:47

I think there’s maybe two explanations.

The first less important one is going to be that there’s a difference between knowing something and then remembering what it’s like not to know it. And the characteristic of a good explanation is that you’re walking someone on a path from the feeling of not understanding up to the feeling of understanding.

Earlier, you were asking about societies that lack numeracy. That’s such a hard brain state to put yourself in, like what’s it like to not even know numbers? How would you start to explain what numbers are? Maybe you should go from a bunch of concrete examples. But like the way that you think about numbers and adding things, it’s just you have to really unpack a lot before you even start there.

And I think at higher levels of abstraction, that becomes even harder because it shapes the way that you think so much that remembering what it’s like not to understand it. You’re teaching some kid algebra and the premise of like a variable. They’re like, “What is X?” It’s not necessarily anything but it’s what we’re solving for. Like, yeah, but what is it? Trying to answer “What is X?” is a weirdly hard thing because it is the premise that you’re even starting from.

The more important explanation probably is that the best explanation depends heavily on the individual who’s learning. And the perfect explanation for you often might be very different from the perfect explanation for someone else. So there’s a lot of very good domain specific explanations. Pull up in any textbook and like chapter 12 of it is probably explaining the content in there quite well, assuming that you’ve read chapters one through 11, but if you’re coming in from a cold start, it’s a little bit hard.

So the real golden egg is like, how do you construct explanations which are as generally useful as possible and generally appealing as possible? And that because you can’t assume shared context, it becomes this challenge. And I think there’s like tips and tricks along the way, but because the people that are often making explanations have a specific enough audience, it is this classroom of 30 people. Or it’s this discipline of majors who are in their third year. All the explanations from the people who are professional explainers in some sense are so targeted that maybe it’s the economic thing you’re talking about. There’s not, or at least until recently in history, there hasn’t been the need to or the incentive to come up with something that would be motivating and approachable and clear to an extremely wide variety of different backgrounds.

Putting in work with calculations

Dwarkesh Patel 1:20:44

If you’re self teaching yourself a field that involves mathematics, let’s say it’s Physics or some other thing like that, there’s problems where you have to understand how do I put this in terms of a derivative or an integral and from there, can I solve this integral? What would you recommend to somebody who is teaching themselves quantum mechanics and they figured out how to put how to get the right mathematical equation here. Is it important for their understanding to be able to go from there to getting it to the end result or can they just say well, I can just abstract that out. I understand the broader way to set up the problem in terms of the physics itself.

Grant Sanderson 1:22:00

I think where a lot of self-learners shoot themselves in the foot is by skipping calculations by thinking that that’s incidental to the core understanding. But actually, I do think you build a lot of intuition just by putting in the reps of certain calculations. Some of them maybe turn out not to be all that important and in that case, so be it, but sometimes that’s what maybe shapes your sense of where the substance of a result really came from.

I don’t know it might be something you realize like “Oh, it’s because of the square root that you get this decay.” And if you didn’t really go through the exercise, you would just come away thinking like instead of coming away thinking like such and such decays but with other circumstances, it doesn’t decay and not really understanding what was the core part of this high level result that is the thing you actually want to come out remembering.

Putting in the work with the calculations is where you solidify all of those underlying intuitions. And without the forcing function of homework, People just don’t do it. So I think that’s one thing that I learned as a big difference post college versus during college.

Post college, it’s very easy to just accidentally skip that while learning stuff and then it doesn’t sink in as well. So I think when you’re reading something, having a notebook and pencil next to you should be considered part of the actual reading process.

And if you are relying too much on reading and looking up and thinking in your head, maybe that’s going to get you something but it’s not going to be as highly leveraged as it could be.

The “failure to disrupt”

[key ideas: learning is not bottlenecked by good explanations but by social incentives. Deeply resonant. Reading between the lines — we are aspirational and good at copying others or trying to impress them, so if we know that we should provide good models for learners to emulate]

Dwarkesh Patel 1:23:39

What would be the impact of more self teaching in terms of what kinds of personalities benefit most? There’s obviously a difference in the kind of person who benefits most. In a situation where it’s a college course and everybody has to do the homework, but maybe some people are better tuned for the kind of work that’s placed there versus all this stuff is available for you on youtube and then textbooks for exercises and so on but you have to have the conscientiousness to actually go ahead and pursue it.

How do you see the distribution of who will benefit from the more modern way in which you can get whatever you want but you have to push yourself to get it.

Grant Sanderson 1:24:17

There’s a really good book that’s actually kind of relevant to some of your early questions called Failure to Disrupt that goes over the history of educational technology. It tries to answer the question of why you have these repeated cycles of people saying such and such technology that almost always is getting more explanations to more people, promises that it’ll disrupt the existing university system or disrupt the existing school system and just kind of never does.

One of the things that it highlights is how stratifying these technologies will be in that they actually are very very good for those who are already motivated or kind of already on the top in some way and they end up struggling the most just for those who are performing more poorly.

And maybe it’s because of confounding causation where the same thing that causes someone to not do poorly in the traditional system also means that they’re not going to engage as well with the plethora of tools available.

I don’t know if this answers your question, but I would reemphasize that what’s probably most important to getting people to actually learn something is not the explanation…but instead, it’s going to be the social factors. Are the five best friends you have also interested in this stuff and do they tend to push you up or they tend to pull you down when it comes to learning more things? Or do you have a reason to? There’s a job that you want to get or a domain that you want to enter where you just have to understand something or is there a personal project that you’re doing?

The existence of compelling personal projects and encouraging friend groups probably does way way more than the average quality of explanation online ever could because once you get someone motivated, they’re just they’re going to learn it and it maybe makes it a more fluid process if there’s good explanations versus bad ones and it keeps you from having some people drop out of that process,which is important.

But if you’re not motivating them into it in the first place, it doesn’t matter if you have the most world-class explanations on every possible topic out there. It’s screaming into a void effectively.

And I don’t know the best way to get more people into things. I have had a thought and this is the kind of thing that could never be done in practice but instead it’s something you would like write some kind of novel about, where if you want the perfect school, something where you can insert some students and then you want them to get the best education that you can, what you need to do is — Let’s say it’s a high school. You insert a lot of really attractive high schooler plants as actors that you get the students to develop crushes on. And then anything that you want to learn, the plant has to express a certain interest in it. They’re like, “Oh, they’re really interested in Charles Dickens.” And they express this interest and then they suggest that they would become more interested in whoever your target student is if they also read the dickens with them.

If you socially engineer the setting in that way, the effectiveness that would have to get students to actually learn stuff is probably so many miles above anything else that we could do. Nothing like that in practice could ever actually literally work but at least viewing that as this end point of “Okay, this mode of interaction would be hyper effective at education. Is there anything that kind of gets at that?”

And the kind of things that get at that would be — being cognizant of your child’s peer group or something which is something that parents very naturally do or okay, it doesn’t have to be a romantic crush, but it could be that there’s respect for the teacher. It’s someone that they genuinely respect and look up to such that when they say there’s an edification to come from reading Dickens, that actually lands in a way.

The natural extension of this:

Encourage people to mentor or teach on the side!

Grant Sanderson

I think there are two things I would want to get out of teaching in a school setting. One of them, as I was emphasizing, I think you just lose touch with what it’s like not to know stuff or what it’s like to be a student and so maintaining that kind of connection so that I don’t become duller and duller over time feels important.

The other, I would like to live in a world where more people who are savvy with STEM spend some of their time teaching. I just think that’s one of the highest leverage ways that you can think of to actually get more people to engage with math

And so I would like to encourage people to do that and call for action. Some notion of spending, maybe not your whole career, a little bit of time. In teaching, there’s not as fluid a system for doing that as going through a tour of service in certain countries where everyone spends two years in the military

Shy of having a system like that for education, there’s all these kind of ad hoc things where charter schools might have an emergency credential system to get a science teacher in. Teach for America is something out there.

There’s enough ways that someone could spend a little bit of time that’s probably not fully saturated at this point that the world would be better if more people did that

Being Stuck

This past Thursday at Back To School Night, I’m sitting in my 5th grader’s classroom chair scribbling a note on his dry-erase desk for him to see in morning. His mother is filling out a parent survey that helps the teacher get up to speed on your kid. It looks like she’s finished when she slides it over to me to answer a question she left blank — “What would you like your child to focus on this year?”

An article I read this summer immediately popped into my mind — The State of Being Stuck by math educator Ben Orlin.

The article begins:

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.

Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

Ben, like me staring at that survey question, didn’t want to waste the opportunity. He wondered…

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…before settling on this question:

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Here’s what Ben got back:

The essence of Wiles’ answer can be boiled down to just six words: “Accepting the state of being stuck.”

For Wiles, this is more than just a vague moral, an offhand suggestion. It’s the essence of his work. It’s an experience at once excruciating, joyful, and utterly unavoidable. And it’s something desperately misunderstood by the public.

“Accepting the state of being stuck”: that’s the keystone in the archway of mathematics. Without it, we’re left with nothing but a pile of fallen bricks.

Wiles began his answer, like any good mathematician, with a premise everyone can accept: “Many people have been put off mathematics,” he said. “They’ve had some adverse experience.”

It’s hard to argue with that.

“But what you find with children,” he continued, “is that they really enjoy it.”

In my experience, it’s true. Kids love games, puzzles, learning to count, playing with shapes, discovering patterns—in short, they love math.

So how does Wiles account for our alienation from mathematics, our loss of innocence?

“What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck,” Wiles said. “People don’t get used to that. They find it very stressful.”

He used another word, too: “afraid.” “Even people who are very good at mathematics sometimes find this hard to get used to. They feel they’re failing.”

But being stuck, Wiles said, isn’t failure. “It’s part of the process. It’s not something to be frightened of.”

Catch me and my teacher colleagues any afternoon, and—if you can get past the “sine” puns and fraction jokes—you’ll likely find us griping about precisely this phenomenon. Our students lack persistence. Give them a recipe, and they settle into monotonous productivity; give them an open-ended puzzle, and they panic.

Students want the Method, the panacea, the answer key. Accustomed to automaticity, they can’t accept being stuck.

…

“What I fight against most,” said Wiles, naming an unlikely enemy, “is the kind of message put out by—for example—the film Good Will Hunting.”

When it comes to math, Wiles said, people tend to believe “that there is something you’re born with, and either you have it or you don’t. But that’s not really the experience of mathematicians. We all find it difficult. It’s not that we’re any different from someone who struggles with maths problems in third grade…. We’re just prepared to handle that struggle on a much larger scale. We’ve built up resistance to those setbacks.”

If you have walked past a rack of popular non-fiction books in the past decade, you are thinking “not another lecture on grit or growth mindset please”. Ben doesn’t go there. In fact, he’s quick to affirm how we often overplay the “grit “ hand:

Recently, the currency of “grit” has fallen among teachers. It’s not that the idea lacks psychological validity. It’s more the weight of its educational connotations. Grit has become an excuse to romanticize poverty as “character-building.” It has devolved into a vague catch-all at best, and at its paradoxical worst, a reason to write kids off as lost causes.

Orlin proposes a 3rd idea:

Wiles is no educational theorist, of course, but I find that he offers a resonant and compelling third path. For him, perseverance is neither about personality (as with grit) nor belief (as with mindset).

Rather, it’s about emotion.

Fears and anxieties come to us all. You can be a nimble mathematician, a model of grit, and a fervent believer in the human potential for growth—but still, getting stuck on a math problem may leave you deflated and disheartened.

Wiles knows that the mathematician’s battle is emotional as much as intellectual. You need to quiet your fear, harness your joy, and cope effectively with the doubt we all feel when stuck on a problem.

Giles offers some counterintuitive ideas as well:

On the value of forgetfulness

“I think it’s bad to have too good a memory if you want to be a mathematician,” Wiles said. “You need to forget the way you approached [the problem] the previous time.”

It goes like this. You try one strategy on a problem. It fails. You retreat, dispirited. Later, having forgotten your bitter defeat, you try the same strategy again. Perhaps the process repeats. But eventually—again, thanks to your forgetfulness—you commit a slight error, a tiny deviation from the path you’ve tried several times. And suddenly, you succeed.

Wiles has a nifty analogy for this: it’s like a chance mutation in a strand of DNA that yields surprising evolutionary success.

“If you remember all the false, failed attempts before,” said Wiles, “you wouldn’t try. But because I have a slightly bad memory, I’ll try essentially the same thing again, and then I’ll realize I was just missing this one little thing.”

Wiles’ forgetfulness is a shield against discouragement. It neutralizes the emotions that would push him away from productive work.

Coming back to the parent survey…how did I reply?

I want Zak to build the muscle of persisting through drawn-out problems.

This skill is more valuable in a holistic, psychological sense than just being a technique. It’s hard to feel truly empowered unless you become familiar with the pattern of feeling stuck and the emotional reward of chipping your way out of it. If you find success too quickly, you’ll fear that you can’t repeat it. You’ll feel like an imposter. You’ll be imbalanced — with a bias towards protection, not growth. Coddling your ego or hating on others when you should be prepping for your next climb from a new valley.

Learning To Appreciate Learning

In the past few weeks about 5-10 people have reached out to ask me for advice in the vein of “my kid is 6 and likes math and what should I put in front of them to foster this”. They are usually looking for specific answers.

I offer a few things my kids have enjoyed (everything can be found on the blog, ie here and here) but I want to be clear — I’m no expert. I’m just like the rest of the parents who have the same goal of watching their kids’ curiosity flourish.

To kill many birds with one stone here’s the gist of my email responses:

I don’t create pressure. Let learning be a source of joy. Insight is its own reward and to train someone to appreciate that when they are young is a life-long gift because they can find stimulation in the pleasures of the mind and the mundane.

Sure, math proficiency has plenty of instrumental value in life, but appreciation and beauty is the bigger gift here (I also suspect this is an antidote to the doping that broader media does to people — if you find beauty in the evergreen you don’t need to constantly be taking drags from the current times and you’re perspective and emotional state will be better off for it. No science behind that — just my hunch).

You are already doing the single largest muscle movement –> literally giving a shit about your kids’ curiosity flourishing. Like seriously that’s 90%. The specific instances of expression — coding, writing, drawing, cooking, composing — or any other forms of creation are secondary. Creating not just consuming is the key because by being able to manipulate the world (I don’t mean manipulate in some evil sense) around you, you reinforce your agency.

When I see fear and extreme tribalism I see people retreating away from agency and frankly accepting some learned helplessness. Your role as a guardian is to shepherd a healthy sense of agency (unhealthy would be to program an overconfident narcissist).

Code and writing are symbol-manipulative domains — some will gravitate to that more than say carpentry or being a physical maker. I’d be open-minded about the specific expression and focus on nurturing the upstream creation and play impulses.

And if you got this far you exemplify an ironic phenomenon — the people who reach out looking for help/guidance/opinion/validation on their approaches are the people who don’t need to (this is not a back-handed way of saying don’t reach out btw, it’s just an observation!)

This young portal in the Moontower codex is an attempt to consolidate some specific learning stuff if interested:

🧠Moontower Brain Plug-In

Reading As A Magical Power

Something I recently started doing that might be of interest to parents:

I’m reading “Journey to the Center of the Earth” by Jules Verne to my almost 7-year-old.

Written in the 1800s, the writing style is challenging.

So I read a bit, then I “translate” it into a more natural language for him. I’ve explained to him that if he reads the books he’s able to read and I read this book to him (instead of him trying to read it himself, which he was trying to do, but I have zero confidence he’s understanding), the combination will give him “magic.” I try to create some mystique around reading because I want him to think reading gives him special powers. Because that’s a fun thing to think, of course (and we probably should think about more things in such ways because it helps us notice the joy in being alive and stuff).

One of the chapters ended in a particularly suspenseful way. And I tried to explain the concept of suspense to him (to his and his teacher’s credit, he mentioned that when they read in school, they pause to try to predict what will happen next in the story).

So with the idea of suspense established, I just asked him to come up with suspenseful sentences. I’ve never asked him to do that, and he didn’t reply with anything substantive, but that’s okay, whatever… (I did give him an example: “The boy thought he locked the door, but then he saw the knob turn,” and my son goes, “that would freak me out,” and since this was just before bed, I felt a bit guilty..oops)

Just sharing for other parents’ benefit, I think we all want to find ways to show the joy of reading and wanted to start showing him “techniques,” a word I asked Alexa to define for him. So he can identify the author’s “weapons” and so maybe one day he can use them when he writes.

Bootstrapping Agency

In Wednesday’s Munchies, I pointed you to Venkatesh Rao’s brain-expanding interview on Infinite Loops. One view I’m still marinating on is how finding a sense of meaning is not “a matter of spiritual retreats and going on soul-searching journeys and having shamans take you on ayahuasca retreats and things like that. It’s not about that at all. It’s the first time you come to a hard decision in your career or life, make the hard decision, see how good you are at making tough calls, and then keep doing that and meaning-making will take care of itself.”

To call meaning-making essential is not stepping out on a limb, unless you’re a nihilist.

Rao makes a bolder claim — looking for meaning is “intensely practical.”

A lot of people don’t get this. If you look at conversations about meaning-making in the abstract…listening to podcasters and getting radicalized, that level of conversation about the meaning crisis, it seems like a philosophical spiritual problem that should be addressed with religion and philosophy, ideas and so forth. It’s not. It’s really as simple as meaning-making is unlocked when you first learn to take courageous decisions and keep doing that, so it becomes a habit.

Connecting dots…when meaning-making is unlocked what actually changes for you?

You acquire an earned sense of agency as opposed to the illusion of agency that “tragic luck” furnishes. This requires being rugged now and again. Any rugging worth a lesson, means you took a real risk.

And I think yes, that is a learnable, teachable skill, but it’s one that the industrial environment with schooling and the paycheck world is actually anti-optimized for. It’s designed to teach you exactly the opposite of that. It’s designed to take you from an naive starting point and keep you tragically lucky for the rest of your life. And if they fail at it, you’re tossed by the wayside. That’s what the industrial world is set up to do, make you tragically lucky or throw you into the garbage heap.

Rao, coming around the bend with the baton, is arguing that our sense of agency is stunted by an institutionally enforced “narrow band of risk”. When I rummage through my feelings about education I come to a similar conclusion — the purpose of education is to bootstrap a sense of agency.

I’ll let one of my favorite education writers Matt Bateman take the baton for the last leg.

From Vocational Training For The Soul:

In the 20th century, there are two distinct rationales for education: vocational and characterological. Putting aside how well education actually does at getting you a better job or helping you become a better person or citizen, the idea is that the core of schooling should do both.

The most obvious place to look for the economic upside of an education is in the three Rs: writing, reading, and math. There are questions as to whether the specific math that students learn is optimally practical—should it instead emphasize, say, statistics, or personal finance, or maybe even spreadsheets?—literacy and numeracy are deployed throughout the economy and do indeed comprise an unambiguously useful part of education.

Literature, history, and the arts all fall under the heading of soulcraft. Even science, the practical driver of the modern world, is not that useful as you learn it in school. A small minority of students deploy their scientific knowledge in their careers, and those that do get specialized training far beyond what you get in K-12. These things are meant to prepare you for appreciation of or participation in the human project in a non-vocational way.

These divisions are very much alive today, as people struggle to find a coherent view of what our largely dysfunctional education system is supposed to accomplish. Some criticize education for not providing more economic upside, arguing for a more practical education, shorn of classical trappings. Others defend the humanistic value of education and argue that we should spend more time on non-economic upsides. This debate cuts across K-12, higher education, and even early childhood education.

Is there a way to transcend these divisions? Is there a way to get a handle on the vocational value of education that integrates its humanistic elements, rather than downplaying or siloing them?

It is commonplace today for a person to be profoundly alienated from the entire domain of work. This is not a Marxist critique about owning one’s labor, nor an aristocratic pining for a life of leisure. It is an observation that, for many people, work is a source of bitterness, not dignity. A seemingly small subset of people find meaning in work, and the rest fail to “find their passion”—a notion that is likely part of the problem—or simply resent work in a more general way.

While we still speak here and there of the value of a work ethic, the “ethic” part of this is, for us, obscure. We do not naturally see one’s personal relationship to work as a major moral issue. But it is one: the people who manage to find meaning in work are not the lucky few who land the good jobs, but the good who manage to build their souls in a certain way.

Education should offer more general value than the skills acquired on the job or in vocational training—but that general value, the soulcraft aspect of education, is not vocationally inert. It can and should nurture the beliefs and virtues associated with a life of work.

Bateman goes on to explain 4 practical ways to nurture such soulcraft. My favorite animates knowledge by linking it to actual humans. This is important (in my opinion) because without narrative disjointed ideas might as well be trivia.

  • The content of education should place more emphasis on the biographies that underlie it. There is no item of knowledge in education that is not the result of the work of some past human.

My second favorite:

  • We should allow opportunities for real work where possible. This is especially true of older adolescents, who can get jobs—from the entry-level to technical, depending on the teen’s skills and circumstances. But scaffolded opportunities can be provided for younger adolescents and elementary students to experience the reality, even the economic reality of work.

The inert child who never worked with his hands, who never had the feeling of being useful and capable of effort, who never found by experience that to live means living socially, and that to think and to create means to make use of a harmony of souls; this type of child… will become pessimistic and melancholy and will seek on the surface of vanity the compensation for a lost paradise.

And thus, a lessened man, he will appear at the gates of the university. And to ask for what? To ask for a profession that will render him capable of making his home in a society in which he is a stranger and which is indifferent to him. He will enter into a society to take part in the functioning of a civilization for which he lacks all feeling.

Maria Montessori

Homework

I used an air fryer this week. My family was proud of me.

The bar is that low. I mean look what happened that time Yinh and my MIL weren’t around:

I’m also not handy. This utter lack of domestic skills means the very sight of a Conestoga wagon gives me chills. It might as well be the trailer for Hereditary. (I also don’t watch scary movies…but I am an avid reader of their Wikipedias.)

So now that we have this family commune thing going on with my in-laws next door, I feel extra pressure to pull my weight. I really only have 2 things going for me:

  1. I enjoy making cocktails. The others enjoy drinking them. (Lately, I’ve been making mai-tais but instead of white rum, I’m using blanco tequila.)
  2. I have the patience of a cadaver. (I’m also a space cadet that will not have his boarding pass out after waiting on a long line to get to the agent — I don’t know if this is the downside to my hard-to-rile disposition but I’ve definitely annoyed my share of people in life and the worst part is this same quality makes their annoyance roll off me too easily.)

The benefit of patience is that if I try to teach something and the person can’t get it — it’s always my fault in my mind. There has to be a way. So I get the privilege of trying to help the kids with their schoolwork and can usually do it in a way that doesn’t make them snap at me when they are frustrated. Not always but I am conscious of not taking them to a place where they shut down. As any parent knows, kids put up walls and they are often only permeable to a 3rd party. (I’m not a fan of tough love unless the kid is making careless errors. Give kids credit and space and recognize that sleep helps minds consolidate. You can drill a piano scale without a sense of progress only to find that it’s easier in the morning. Patience allows breaks to do their unconscious work, but you need to trust it. Persistence and rest are a powerful combo but don’t mix well with immediacy.)

I love that moment when a kid (or anyone really) discovers they can do or understand something that felt too big. The feeling of empowerment unlocks far more than the particular lesson’s objective.

With all that said, I create lessons to challenge them. You can meet them wherever they’re at by breaking problems into smaller bites and inserting them at the point where they feel most comfortable.

I published these math word problems with guidance for how to teach your child or student.

Similar posts I’ve previously published:

This one started as a kid lesson but turned into something about portfolio risk:

I have several lessons in the queue. After doing them with my kids and their cousins I’ll write ‘em up and share.

In the meantime, there are more posts indexed here:

These are more teen/adult appropriate:

Go slow and give people credit. Many people never had someone help them see they are capable.

Now if I would just direct this advice to myself in an apron…

Sal Khan On The Finding Mastery Podcast

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

Link: https://findingmastery.net/sal-khan/

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 schoolhouse.world, 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:

THE SILVER BAR

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’

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