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)

Jason Zweig On Writing

Jason Zweig of the WSJ wrote a 3-part series on writing.

I took notes for myself.

On Getting Better

Making your writing better is tantamount to declaring war on yourself.

I’m often asked what the most important quality is to be a columnist for a major publication.

I always answer: “Self-loathing.”

I don’t loathe myself as a person, at least not most of the time. But I loathe myself as a writer, because I should and I must: because I know, to the marrow of my bones, that nothing I’ve ever written or ever will write can capture the subtle, confounding, infinite complexity and contradictions of reality. To be a writer is to recognize that you will always be overmastered and defeated by whatever topic you choose: The richness of life always beggars anyone who tries to wrap it in words.

As Nathaniel Hawthorne wrote in his notebooks, “When we see how little we can express, it is a wonder that any man ever takes up a pen a second time.” The great playwright and novelist and Samuel Beckett wasn’t joking when he defined writing as “disimproving the silence.”

Coaching and constant practice can minimize and manage the problem, but never quite eliminate it. As Mark Twain said, “You can straighten a worm, but the crook is in him and only waiting.”

You have no right to act affronted when someone asks you to cut your writing as if the request were some sort of selfish demand. You’re the one who’s being selfish, by refusing to make your readers’ lives easier. And, above all, you’re hurting yourself, as selfish people always do: The point of cutting your writing isn’t to make it shorter. The point of cutting it is to make it better.

Cutting your writing is the surest way to find its weaknesses; it is only when you take a knife to what you wrote that you can find out whether any of it is even alive.

How To Get Better (Link)

  1. Cut your writing

    Now, cut hard and deep.  The biggest mistake developing writers make is to try cutting a few words here and a handful there.  But you aren’t doing cosmetic surgery on beautiful moviestars in Beverly Hills; you are doing amputations.  The tools you need aren’t microscopes and miniaturized scalpels.  You need to start with a chain saw. It sounds harder and scarier than it is.  Read as fast as you can.  Read in big gulps, a paragraph at a time.  Identify the weakest paragraph and delete it.  Delete the next weakest, and the one after that. If you can’t find any paragraphs to cut, you’re kidding yourself.  The best solution I know of is to become exhausted: Go run 10 miles, or stay up an hour past your bedtime, or get up an hour earlier in the morning than usual.  Now, while you’re exhausted, read what you wrote.  The weak links should leap out at you. Next, find the weakest remaining sentence, and kill that.  If you can’t find one, take any sentence at random and delete it. Ask yourself: Do I miss it? Answer honestly.  Your piece might be better without it.  Or maybe you can replace the deleted sentence with something shorter and sharper.  Put it back only if its absence creates a black hole.  Keep searching for sentences to kill.

    • Kill adverbs. They are a crutch for weak verbs.

      Now, kill all the adverbs.  It’s not that I really dislike adverbs; I hate them. When you use the right verb — notice how, in the previous sentence, I replaced that wimpy “really dislike” with the militant “hate”? — you don’t need the fake emphasis of “really,” or most other adverbs either.  Get rid of them: Slaughter every single “actually,” “very,” “really,” “truly,” “clearly,” “certainly,” and the entire kennel-full of these weasel words.  The typical writer can cut a piece by 5% just by exterminating every adverb

    Finally, set it aside for a day, or longer if you have the luxury of time.  Don’t touch what you wrote.  Don’t look at it or even think about it.  Let it rest, and get some rest yourself.  You’re about to embark on the hardest leg of the journey to becoming a better writer.

  2. Re-writing

The essence of rewriting is destruction. Journalists and other professional writers almost always call it “killing my darlings.” Cutting is bloody, but rewriting is what hurts, because it requires brutal self-examination. Rewriting also hurts more than cutting because, after you already put all that work into striving for perfection, now you have to scan everything you did with a cold, alien, objective eye that focuses on finding every imperfection. If you can’t find any, you are writing, but you are not a writer.

If you wrote it in Microsoft Word, copy-and-paste it into Google Docs, or vice versa. If you printed it out, then read it on a computer screen. If you wrote it on your computer, then read it on a printout. Change the font or the color. Do whatever it takes to help you see it as someone else’s work, or as no one’s work.

Specific Techniques (From Part1 and Part2)

  • Good writing flashes between the concrete and the abstract
    • bounce between the particular and the general; it uses specific details and images to ignite our feelings and open our minds to the wider world.

  • Write something else when you have writer’s block:
    • it’s okay to drop a piece of writing when you can’t seem to make headway on it.  Use the extra time you’ve just created to write something else instead, so you can still work on polishing your craft even when you aren’t working on the piece of writing you most want to do.  Writer’s block doesn’t mean you can’t write anything; it just means you can’t write the one thing you’ve been working on.  If you switch to something easier, you will probably write better; that should help you get unstuck, enabling you to turn back to the harder writing with more freedom and openness.

  • Momentum

    • Just talk it out onto the page, without overthinking. Once you pop the cork out of the bottle, keep pouring as fast and as long as you can. Do not — I repeat, do not — revise or edit the sentences you’ve already written. Keep rolling forward, and don’t look back at what you’ve done, or you will lose your momentum…If you lose your momentum and get stuck again, step away and come back. Go to the bathroom; go to the gym; go for a walk; go get lunch. Try again — where you left off, not where you started.

    • Picking up a thread: If you’re writing something long and making good progress, but you won’t have time to finish it until tomorrow, stop in midstream. You can even stop in the middle of a sentence. Go do any old thing that gets your mind off your writing. Pick it up the next day; it will be easier to resume where you left off if you stopped right in the middle of a great idea that you know how to see through to completion.

  • How to practice

    • Write more: always writing mindfully — developing good mental hygiene by never being sloppy or lazy, whether you’re tossing off an email, putting together an office memo, or writing a note inside a birthday card. If you want to become a better writer, there’s no such thing as being off-duty. Treat every opportunity to write anything as a chance to improve. Challenge yourself to avoid lazy language and phrases that feel effortless.
    • Read more: When you find writers you love, read everything they’ve written. I continually ask myself: How did he do that? Why did she make this choice here?  What makes this work so well?

  • Don’t write with a passive styleIf you ever find yourself typing that something “…will have an effect on…” or “…had an impact on…,” it isn’t your writing that’s passive.  It’s you!  How dare you pretend that you are providing any information by telling your reader that something will have an “impact” or an “effect” on something else?  Nearly everything in the universe has an effect or an impact on other things!  Delete that passive crud and tell us what will happen: It “…will devastate…” or “…will rejuvenate…” or “…will eradicate…” or “…will repair…” without  resorting to the pallid abstractions of “impact” or “effect” or “result.”

    Consider this:

    There is a growing number of people who find themselves using smart phones to track whether their friendships are healthy.

    Let’s pick that apart.  It’s passive in at least three ways.

    “There is a growing number of people who…” means nothing more, and nothing less, than “I have no idea how many people…”

      1. The “there is a” is unnecessary.  It’s one of the most common, and annoying, crutches of passive language.  “There is a reason for the shortfall in wheat production:…”  Well, duh!  Instead, say: “Wheat production fell short because….”  (Note how, when you do this, the clunky noun string “the shortfall in” naturally turns into a simple verb structure: “fell short.”)  Once you develop the habit of recognizing “there is” as passive language that serves no purpose, you will be able to look at “There was somebody at the door” and automatically edit it to “Somebody was at the door.

      2. Zweig’s Law of Passive Language: Writers resort to passive wording when they are actively trying to hide something. The thing they are trying to hide is usually their ignorance or the flimsiness of an idea
      3. Why are these people with the smartphones “finding themselves”? They’re not in an ashram or a hippie commune. They are, unfortunately, in the hands of a writer who is piling up verbiage like balsa wood to try covering the hollowness of the premise.
  • Writing better is all about paying attention to the smallest details. 

    If you don’t treat each word with exquisite care, you can’t improve….Are you letting verbs do their work, or are you treating them as if they can’t move without crutches and canes?

    Most people handle words as if they were pennies: light, cheap, dispensable.  Instead, I want you to handle them as if they were manhole covers or 45-pound weights in the gym.  Think before you pick them up.  Look before you put them down.  Make sure you choose the right one and put it in the right place.  Words shouldn’t be cheap to you and interchangeable.  They should be dear to you and fit-for-purpose.

    As for me, I estimate that I’ve written about 425,000 words for The Wall Street Journal over the past decade.  It wouldn’t surprise me if at least 20,000 of them were wasted —

    — Hey!  I meant, “It wouldn’t surprise me if I wasted at least 20,000 words.”

    All you can do is try to purge all the passive wording from your writing. You will fail and fail and fail again. I’ve been failing at it my entire life. But trying to expunge every instance of passive language from every sentence will make your writing far better than it is — no matter how good it already may be.

  • Cliches and idioms are lazy but that’s not all

    One of the biggest mistakes an aspiring writer can make is to assume that you can easily avoid perpetrating clichés if only you steer clear of obviously proverbial language. That’s much too narrow a view! A cliché is any wording that springs automatically to mind and types itself, as if it has kidnapped your hands, but that falls apart at the slightest touch:

    “incredible”(“I was there, and I’ve never witnessed anything like it.  But, rather than use vivid language to show you, I’ll just tell you.  Maybe if you read a few more paragraphs, I’ll finally get around to making you feel what I felt.”)

    “interesting”(“Trust me: You do want to read about this thing I’m describing, although I can’t be bothered yet to explain why.”)

    “a serious crisis”(if a crisis isn’t serious, what is it?)

    “in a very real sense”(What would “a partly real sense” be? So the “very” adds nothing. Delete it! How does “in a real sense” differ from “in a sense”? Delete it! Now that you’re left with only “in a sense,” which sense? You don’t know, do you? Go back to the drawing board. Figure out what you mean, and say that.)

    “on a weekly basis”(“weekly”)

    “despite the fact that”(“although”)

    “in a state of anxiety”(“anxious”)

    “the reasons are three-fold”(“the three reasons are…”)

    “a disaster of epic / catastrophic / historic proportions”(And what would those proportions be: a mile wide and 10 feet tall? If you’re trying to say “it will go down in history,” what makes you so sure?  Show, don’t tell: How bad is the damage?  Give us numbers or imagery, not a lame reference to “proportions.”)

    “unmitigated gall”(What might “mitigated gall” be?)

    “mounting concerns / mounting pressure / mounting evidence”(Everything seems to be “mounting” nowadays; if you grew up around farm animals, as I did, the thought of using that term in serious prose would make you burst out laughing)

    “He disappeared under mysterious circumstances.”(“He disappeared mysteriously” or “No one knows how or why he disappeared.”)

    “The weather forecast calls for rainy conditions.”(“It will probably rain.”)

    “The car dealership is holding a sales event.”(“The car dealership is holding a sale.”)

    “That’s how innovation occurs in the social-media space.”(“That’s how innovation occurs in social media.”)

    “He’s argumentative by nature.”(“He’s argumentative.”)

    “The company’s clout is such that…”(“The company has so much clout that…”)

    “The crime was a terrible one.”(“The crime was terrible.”)

    “in some ways” / “in certain aspects”(Which ways or aspects might those be?)

    “The groups are similar with respect to their income and net worth.”(“The groups have similar income and net worth.”)

    “in terms of”(“in”)

    “…is at this point in time…”(“…is…”)

    “…is currently…”(“…is…”)

    “…is now…”(“…is…”)

As the great Viennese journalist Karl Kraus wrote, “The closer one looks at a word, the farther away it moves.”  Your goal should be to treat every word you write as an alien object: You should be able to look at it and say, What is that doing here? Why did I use that word instead of a better one? What am I trying to say here? How can I get to where I’m going if I use such stale and lifeless words?

You want to slash passive language out of your writing just as a tropical explorer blazing a trail hacks through the underbrush with a machete.

The more intensely I write, the more often I mutter under my breath, Get out of my way.  I’m talking to myself, and I’m talking to all the junk words that aren’t mine: Get out of my way!

Tips For Writing A Book (Link)

  • Be creative

Ask yourself, what’s the craziest, wackiest way I can possibly think of to make this point? Cartoons, diagrams, Rube Goldberg illustrations, graphs and charts, music, movies, paintings — make everything grist for your mill. Mind you, you don’t have to use all these sources in the final product, but they may help spark ideas for you that will help you turn abstract ideas into concrete words in a way no one else has thought of.

  • Use your eyes and ears.

Too many people write books entirely from the isolation of an office or a den at home. Get out in the field: travel, talk to people, explore, turn over the rocks. When I did my neuroeconomics book, I went to labs and had my brain scanned about a half-dozen times. The more you can get other places and other people’s voices and your own physical experiences into the project, the less it will seem like another generic advice book. Criticizing mutual funds? Well, go visit Fidelity (or you name it) and describe a day in the life of a stockpicker. Skeptical about day trading? Parachute into a brokerage office or trading floor and tell the reader what you found. Keep an open mind, and be honest with yourself: You might well find the exact opposite of what you expected. The best way to thrill your readers is to tell them things that surprised you. The same advice applies to any topic, not just finance.

  • It’s your book.

    You can write whatever you want, however you want to write it. Ask yourself: What are the three/five/ten/X things I most wish that I understood that I don’t?

    Go answer those questions.

    bove all, figure out what would make the project as fun and interesting as possible for you.  Write the book for yourself, and readers will follow.

Educational Ideas Inspired By Seymour Papert’s Constructionism

From wikipedia:

Seymour Aubrey Papert (/ˈpæpərt/; 29 February 1928 – 31 July 2016) was a South African-born American mathematician, computer scientist, and educator, who spent most of his career teaching and researching at MIT.[2][3][4] He was one of the pioneers of artificial intelligence, and of the constructionist movement in education.[5] He was co-inventor, with Wally Feurzeig and Cynthia Solomon, of the Logo programming language.


Below is a collection of insights from Papert’s “constructionist” educational ideas:


From Greg Wilson’s Teaching Tech Together by Ced Chin

  • Wilson asserts that the way you teach novices is to help them construct the right mental models, so they have somewhere to put your facts…Wilson uses the word ‘construct’ because he is most influenced by Seymour Papert’s work on knowledge acquisition. Papert’s claim is that humans learn by ‘construction’ — that is, we build knowledge in an iterative, cumulative way, replacing old, flawed mental models with newer ones, or stacking concepts on top of what we already know.


  • it explains why you must generate lots of examples and explanations until it clicks — and what clicks for one person may be different from what clicks for another.


  • Knowledge is a guided walk as the teacher gently nudges the student based on whatever models the student currently holds in their heads.


  • Because novice learners build knowledge based on what they already know, it is very common for them to construct a mistaken mental model as they begin to progress in their learning. Good teachers watch out for this and clear it out; one important way they do this is to use formative assessments (formative here means ‘to form’, or ‘to shape’ the learning) to diagnose mistaken mental models.


  • The education system should be reformed to encourage facilitation, not recitation. For instance, if a learner is made to move through a series of formative examples that are designed to subtly shape his or her understanding, this learner will develop intuition far quicker and more enjoyably than if he or she was given a mathematical equation in a lecture (and expected to develop intuition from that equation). The former practice teaches through knowledge acquisition; the latter practice stems from the belief that insight can be passed along wholesale. The sad truth is that the majority of our education systems teach in the latter manner;


  • Expertise, then, is a densely connected graph of facts. We should note that expertise comes not from the facts that are known (a competent practitioner may add many more facts to their mental model of the domain but not see an increase in expertise) — instead, expertise comes from how densely these facts are interconnected. And that interconnectedness comes from reflection and practice.

From You Can’t Teach What They Aren’t Ready To Know by Ced Chin

  • A key corollary of Papert’s critique of modern education is that by learning academic’s formal representations of knowledge, students come to hate learning. Papert believed that learning to memorize and compute F=ma, completely divorced from its meaning in the world and in a person’s life, essentially requires teachers to lie to children about its relevance. He lamented that teachers around the world must regularly argue, “This formula is important and valuable to you,” when teachers know it is not, and don’t even believe it is personally valuable to them. Papert believed that this deception erodes the relationship between teachers and children, and ultimately erodes the trust and respect of educational institutions. This stems from Papert’s ideas — basically, if you can only guide a ready mind, then you can’t hope to communicate insight or mental models just like that.


  • This idea — that you can’t communicate insight by explaining — has haunted me ever since.


  • [Me: this is the importance of scaffolding customized to the individual]


  • because all knowledge is constructed, the best way to teach would be to give a student a series of progressive exercises designed to correct their existing mental models. Explanations and formalisations come after  the student has developed an intuitive understanding of the concept; the teacher’s job is merely to facilitate the development of that insight — before giving the student tools to communicate it, such as mathematical notation. A knowledge-construction approach to teaching would involve the student experiencing a series of such questions, making guesses and mistakes as they slowly built up an intuition for how volume relates to weight and density. Then, as a final step, the teacher introduces the technical notation that captures this relationship, allowing the intuition to be externalised and made manipulatable.


  • Notice how different this approach is from teaching p=m/V first, and then asking the student to construct this intuition on their own. (Cue the references to ‘conceptual wall bashing’ — as I used to do). Papert asserts that this format of teaching is exactly backwards, and it creates an artificial selection process for those who are masochistic enough, or persistent enough, to acquire that intuition for themselves.


  • Papert’s vision of teachers was therefore not as someone “presenting” knowledge and guiding their “acquisition” toward it, but as someone understanding a child’s prior knowledge, intuitively understanding the opportunities to build on top of that knowledge in a manner that results in a deeper understanding of a concept.


  • [this also explains why some books hit at the right time and others will not. And also why re-reading books is a good idea. Heraclitus: No man ever steps in the same river twice, for it’s not the same river and he’s not the same man.]

  • Papert’s big idea explains why the Socratic method works as a teaching methodology. By eschewing explanations and relying on repeated questioning, a teacher may quickly learn the map of a student’s existing understanding, and better guide them to the insight that is the goal of their conversation.
    • the Socratic method (and therefore Papert’s approach) works wonderfully for “know-what” (facts) and “know-why” (science). But it begins to fail the further we move away from such explicit forms of knowledge, towards embodied or tacit knowledge. This is the ‘technê ’ I’ve mentioned so often on Commonplace — the idea that certain types of knowledge cannot be easily expressed through words, and may only be learnt through practice or apprenticeship.


  • Prescription: But that means that when it comes to technê — a form of knowledge that can only be learnt through practice or apprenticeship — Papert’s idea becomes a limiting factor. If you can only learn what you are ready for, then you cannot learn from experts without practice of your own. I wager that the mutterings of people like Dalio, Buffett and Munger are of limited use when you remain at the bottom levels of their respective skillsets. Technê is by definition knowledge that is difficult to codify and explain; their mutterings will therefore only be useful to people of a certain level of expertise. This implies that you shouldn’t waste time looking for insight in codified mental models written down by second-rate bloggers (myself included). It implies that you should do as Buffett did when he went straight to Benjamin Graham at age 19: read only from expert practitioners, put things into practice, and if possible, find those practitioners directly and learn from them.

From Mindstorms: what did Papert argue and what does it mean for learning and education? by Amy J Ko

  • Computing is necessary to make powerful representations personal and concrete.

    To Papert, personal computers were therefore the perfect medium in which to engage students with powerful representations:

    “Before computers there were very few good points of contact between what is most fundamental and engaging in mathematics and anything firmly planted in everyday life. But the computer —mathematics speak being in the midst of the everyday life of the home, school, and workplace — is able to provide such links. The challenge to education is to find ways to exploit them.” — Papert, Mindstorms (Chapter 2)

    But it wasn’t just computers that Papert viewed as necessary for realizing his vision. It was also computing, and in particular, concrete expressions of systematic procedures, which we now call algorithms. Papert viewed algorithms as descriptions of action in the world and a means for reflecting on action. By encouraging children to write down algorithms as part of their learning, he believed we might help them learn to better reflect concretely on their ideas, accelerating their construction of knowledge.

    Because of the power of algorithms, Papert lamented that schools taught so much about numbers but so little about procedures:

    “In our culture number is richly represented, systematic procedure is poorly represented” — Papert, Mindstorms (Chapter 7)

    He imagined a world in which children learned just as much about algorithmic thinking as they did about numerical thinking, evening coining the widely used phrase “computational thinking,” in the hopes that thinking like a computer, combined with more powerful representations for making that thinking explicit, would be a path to better learning of all subjects.

  • Education should be facilitation, not recitation

    Some of the biggest critics of Papert’s ideas were teachers themselves: they could not comprehend a world without curriculum, pedagogy, learning objectives, and assessments.

    Papert responded with a vision of education as facilitating bricolage, which is the construction new things out of what is available, namely, the knowledge a child has available:

    “But ‘teaching without curriculum‘ does not mean spontaneous, free-form classrooms or simply “leaving the child alone.” It means supporting children as they build their own intellectual structures with materials drawn from the surrounding culture. In this model, educational intervention means changing the culture, planting new constructive elements in it and eliminating noxious ones. This is a more ambitious undertaking than introducing a curriculum change…” — Papert, Mindstorms (Chapter 1)

    Papert’s vision of teachers was therefore not as someone “presenting” knowledge and guiding their “acquisition” toward it, but as someone understanding a child’s prior knowledge, intuitively understanding the opportunities to build on top of that knowledge in a manner that results in a deeper understanding of a concept.

  • Making learning culturally relevant

    Thus we are brought back to seeing the necessity for the educator to be an anthropologist. Educational innovators must be aware that in order to be successful they must be sensitive to what is happening in the surrounding culture and use dynamic cultural trends as a medium to carry their educational interventions.” — Papert, Mindstorms (Chapter 8)

    This demanded that teachers and education researchers be more than just experts on a subject: it demanded that they be experts on the social worlds in which their children live, so they could make culturally meaningful representations of ideas.

  • Practical problem

    Where will the powerful representations come from?

    When describing his vision, Papert worried a lot about where all of the powerful representations like Logo’s turtle would come from:

    “…the essential remaining problem in regard to the future of computers and education: the problem of the supply of people who will develop these [powerful representations]. The problem goes much deeper than a mere short supply of such people… there is a role but no place for them. In current professional definitions physicists think about how to do physics, educators think about how to teach it. There is no recognized place for people whose research is really physics, but physics oriented in directions that will be educationally meaningful.”—Papert, Mindstorms (Chapter 8)

    Here, Papert is essentially concerned about what institutions would support the work of physics education researchers, as they weren’t likely to be recognized as either physicists or education researchers. While this problem has been overcome in some domains (by coincidence, math and physics education are quite mature and have found homes in education, math, and physics), it remains a major issue for most other areas of education. It’s a particular issue for my doctoral students who study computing education: will they join CS departments or Education departments or rejected by both?

  • Amy Ko’s concerns

Papert’s ideas demand breaking the fundamental assumption of school, that children of similar ages learn similar things. It’s hard to imagine an educational institution that would actually realize Papert’s ideas about learning without violating this constraint, allowing children to follow their interests, learn different things at different paces.

I do believe that this would be an ideal context for learning, but I don’t buy that it’s feasible. Teachers would have to be virtuosos of many domains and representations, and would have to scale the facilitation of so many diverse student interests. That’s a lot of teacher training and a lot of research to build new representations.

From Edith Ackermann’s Piaget’s Constructivism, Papert’s Constructionism:
What’s the difference? (Link)

  • Piaget & Papert: Similar Goals, Different Means

    Piaget and Papert are both constructivists in that they view children as the

    builders of their own cognitive tools, as well as of their external realities. For
    them, knowledge and the world are both constructed and constantly reconstructed
    through personal experience. Each gains existence and form through the
    construction of the other. Knowledge is not merely a commodity to be
    transmitted, encoded, retained, and re-applied, but a personal experience to be
    constructed. Similarily, the world is not just sitting out there waiting to be to be
    uncovered, but gets progressively shaped and transformed through the child’s, or
    the scientist’s, personal experience.

    Piaget and Papert are also both developmentalists in that they share an
    incremental view of knowledge construction. The common objective is to
    highlight the processes by which people outgrow their current views of the world,
    and construct deeper understandings about themselves and their environment. In
    their empirical investigations, Piaget and Papert both study the conditions under
    which learners are likely to maintain or change their theories of a given
    phenomenon through interacting with it during a significant period of time.

    Despite these important convergences, the approaches of the two thinkers
    nonetheless differ. Understanding these differences requires a clarification of
    what each thinker means by intelligence, and of how he chooses to study it.
    In appearance, both Piaget and Papert define intelligence as adaptation, or
    the ability to maintain a balance between stability and change, closure and
    openess, continuity and diversity, or, in Piaget’s words, between assimilation and accommodation. And both see psychological theories as attempts to model how people handle such difficult balances. At a deeper level, however, the difference is that Piaget’s interest was mainly in the construction of internal stability (la conservation et la reorganisation des acquis), whereas Papert is more interested in the dynamics of change (la decouverte de nouveaute).

    Allow me to elaborate:

    Piaget’s theory relates how children become progressively detached from the world of concrete objects and local contingencies, gradually becoming able to mentally manipulate symbolic objects within a realm of hypothetical worlds. He studied children’s increasing ability to extract rules from empirical regularities and to build cognitive invariants. He emphasized the importance of such cognitive invariants as means of interpreting and organizing the world. One could say that Piaget’s interest was in the assimilation pole. His theory emphasizes all those things needed to maintain the internal structure and organization of the cognitive system. [Me: Moving from the experiential to the formal or  abstract where in service of consistency]. And what Piaget describes particularly well is  precisely this internal structure and organization of knowledge at different levels of development.

    Papert’s emphasis lies almost at the opposite pole. His contribution is to remind us that intelligence should be defined and studied in-situ; alas, that being intelligent means being situated, connected, and sensitive to variations in the environment. In contrast to Piaget, Papert draws our attention to the fact that “diving into” situations rather than looking at them from a distance, that connectedness rather than separation, are powerful means of gaining understanding. Becoming one with the phenomenon under study is, in his view, a key to learning. It’s main function is to put empathy at the service of intelligence.

    To conclude, Papert’s research focuses on how knowledge is formed and transformed within specific contexts, shaped and expressed through different media, and processed in different people’s minds. While Piaget liked to describe the genesis of internal mental stability in terms of successive plateaus of equilibrium, Papert is interested in the dynamics of change. He stresses the fragility of thought during transitional periods. He is concerned with how different people think once their convictions break down, once alternative views
    sink in, once adjusting, stretching, and expanding their current view of the world becomes necessary. [Me: this seems critically important today] Papert always points toward this  fragility, contextuality, and flexibility of knowledge under construction.

    Last but not least, the type of “children” that Piaget and Papert depict in their theories are different and much in tune with the researchers’ personal styles and scientific interests. Note that all researchers ‘construct” their own idealized child. Piaget’s “child,” often referred to as an epistemic subject, is a representative of the most common way of thinking at a given level of development. And the “common way of thinking” that Piaget captures in his descriptions is that of a young scientist whose purpose is to impose stability and order over an everchanging physical world. I like to think of Piaget’s child as a young Robinson  Crusoe in the conquest of an unpopulated yet naturally rich island. Robinson’s conquest is solitary yet extremely exciting since the explorer himself is an innerdriven, very curious, and independent character. The ultimate goal of his adventure is not the exploration as such, but the joy of stepping back and being able to build maps and other useful tools in order to better master and control the territory under exploration.

    Papert’s “child,” on the other hand, is more relational and likes to get in tune with others and with situations. S/he resembles what Sherry Turkle describes as a “soft” master (Turkle, 1984). Like Piaget’s Robinson, s/he enjoys discovering novelties, yet unlike him, s/he likes to remain in touch with situations (people and things) for the very sake of feeling at one with them. Like Robinson, s/he learns from personal experience rather than from being told. Unlike him, s/he enjoys gaining understanding from singular cases, rather than  extracting and applying general rules. S/he likes to be engaged in situations and not step back from them. S/he might be better at pointing at what s/he understands while still in context, than at telling what s/he experienced in retrospect.

    Integrating the views:

    Along with Piaget, I view separateness through progressive decentration as a necessary step toward reaching deeper understanding. Distancing oneself from a situation does not necessarily entail disengaging, but may constitute a necessary step toward relating even more intimately and sensitively to people and things. In any situation, it would seem, there are moments when we need to project part of our experience outwards, to detach from it, to encapsulate it, and then reengage with it. This view of separateness can be seen as a provisory means of gaining closer relatedness and understanding. It does not preclude the value of being embedded in one’s own experience.

    On the other hand, Papert’s view that diving into unknown situations, at the cost of experiencing a momentary sense of loss, is also a crucial part of learning. Only when a learner has actually traveled through a world, by adopting different perspectives, or putting on different “glasses,” can a dialogue begin between local and initially incompatible experiences.

    To conclude, both “dwelling in” and “stepping back” are equally important in getting such a cognitive dance going. How could people learn from their experience as long as they  are totally immersed in it. There comes a time when one needs to translate the experience into a description or a model. Once built, the model gains a life of its own, and can be addressed as if it were “not me.” From then on, a new cycle can begin, because as soon as the dialog gets started (between me and my artifact), the stage is set for new and deeper connectedness and understanding.

    In his book, The Evolving Self, Kegan elaborates on the notion that becoming embedded and emerging from embeddedness are both needed to achieve deeper understandings of oneself and others. To Kegan, human development is a lifelong attempt on the part of the subject to resolve the tension between getting embedded and emerging from embeddedness (Kegan, 1982). In a similar way, I think of cognitive growth as a lifelong attempt on the part of the subject to form and constantly reform some kind of balance between closeness and separation, openness and closure, mobility and stability, change and invariance.

Meatspace Wordle

I discovered Wordle last week while looking over a friend’s shoulder. I showed the word on Twitter.

Like a drunk orc hobbling out of its winter cave. Clueless.

Luckily, I nipped the ratio in the bud quickly by deleting the Tweet when others informed me of my spoiling ways (thanks Tina!).

I had avoided the game for a long time because I didn’t want to take drugs. But the one-word-a-day design is built-in chastity so I gave myself permission.

Its cryptography aspect reminded me of Mastermind (described in my older post Fun Ways To Teach Your Kids Encryption), but having it be a word game is a seductive mix of Scrabble + logic.

Meatspace Wordle

Use pen and paper to play Wordle with your kids. Take turns giving words vs solving the puzzle. You can do this anywhere and use the number of guesses as the basis for a scoring system.

For advanced players, consider a quadratic scoring system (ie make your score proportion to the inverse square of how many guesses it take…4 guesses is worth 1/16 of a point, 3 guesses is 1/9, 2 is 1/4 and so on). This might disincentivize the algorithmic approach and optimize for trying to guess the word earlier. I haven’t thought about it hard enough, but it would be an interesting problem to compute just how steep the scoring system’s decay function would need to be to justify the informed guess approach.

Snapshot of Freddie de Boer’s Education Views

The New Yorker summarized Freddie de Boer’s book Cult of Smart by saying he  “argues that the education-reform movement has been trammelled by its willful ignorance of genetic variation.”

I’m a regular reader of DeBoer’s writing and found his post You Don’t Get to Withdraw “Your Share” of Public Expenditures, Doofus to conveniently encapsulate many of his views on education. I have a lot of respect for deBoer’s thinking and research so I jotted down some of these views. All bold is mine.

Despite arguments to the contrary the US education system is quite competent

Many detractors of public spending on education claim some version of “but the schools are doing such a bad job.” Longtime readers will know how little I think of that claim. American public schools are not, in fact, uniquely or especially bad; our median student does alright, given that they consistently rank in the middle of OECD nations in international comparisons and the OECD no doubt performs far better than the international average. (Don’t get me started on Chinese educational data, or the inherent unfairness of including Hong Kong, Macau, and Singapore, city-states that are simply not good comparisons.) Plus we look better in Trends in International Mathematics and Science Study (TIMMS) than in the PISA, from where I’m sitting. (Play with the data viz tools there, they’re great.) Our top 5% or 1% are competitive with any nation on Earth, and we frequently win international STEM competitions. Please enjoy looking over the American kids absolutely whipping everybody’s ass in the International Chemistry Olympiad, for one example. Or the International Math Olympiad, where we won outright in 2015, 2016, and 2018, and tied with China for first place in 2019.

The problem is not at the top nor, I would argue, in the middle.

Where is the problem in education?

The trouble is that we’re dragged down by a relatively small number of students that perform so terribly that they drag down our averages. That is indeed a problem, but it’s not primarily (or even secondarily, really) an educational problem. Rather it’s a complex and multivariate social problem that can’t be solved at the school level. Given the amount of money, energy, and manpower this country exerts on public education, whether defined in aggregate or per pupil, we should be able to confidently say that if there were any silver bullets available we would have killed all the werewolves by now. Unfortunately wonkism rules in this domain and core to the wonkist philosophy is that every problem has a policy solution.

How about teachers?

Our teachers deserve little of the blame (and, for consistency’s sake, the praise) for our current situation, as student-side factors dominate school-side factors in determining student quantitative outcomes. I’m not going to go through the paces of that particular claim here; I’ve written on this topic extensively and immediately above is a one-stop shop for my general take on the macro educational situation in this country. But for shorthand we might consider that the vast majority of American educational inequality exists within schools, not between them, making it very odd to blame schools for inequality. (For such blame to make sense, we would have to believe that schools are deliberately withholding the better education from the low-achieving students and hoarding it for the high-achieving, when in fact most schools do everything in their power to improve performance among their worst students, given how intense the pressure from above is to do so.) We could also look at serial failures of touted prescriptions like charter schools or vouchers, a world in which districts that are still referred to as “miracles” house tons of schools with terrible performance, where programs hailed as transformative turn out to be disastrous, and where the randomization tools that are so essential for equal access and effective research operate as a black box with little or no consistency or oversight. Like I said, I’ve made the case at length before.

The students themselves matter more than the schools or teachers in determining outcomes

I’m not the only one who says that the individual student is more important than the teacher or school for determining outcomes. There is grudging but growing understanding of this reality in the policy world. For example, RAND Education, which is very much in line with the broader neoliberal education reform movement, has estimated that student-side factors are four to eight times more responsible for student outcomes than school-side factors (The Rand report that included this estimation has been “superseded” and the specific numbers have been removed from the new report, in favor of perfectly vague language about the “many factors” which influence outcomes, which is pretty common for this world – inconvenient realities get whitewashed away. Luckily for us, I got the old report.).

This should be common sense, it seems to me, and more and more people are willing to admit to it, but there’s still profound resistance to this idea, as a) there’s a large educational profiteering industry in this country and b) too many people are still addicted to Stand and Deliver-style romanticism about education, the cheery notion that all any student needs is a passionate teacher.

The determinism is not rosy, but it’s closer to reality than many want us to believe

Here’s the thing, folks: wherever your kid goes, there they’ll be. If they’re particularly talented, they’re very likely to perform well regardless of school. If they’re particularly untalented, they’re very likely to perform poorly regardless of school. Many studies that involve randomly assigning students to schools perceived to be of differing quality find no school effects, which is counterintuitive only if you assume every brain is the same. There are no magical institutions anywhere in the world where you can take a kid who is not naturally inclined to be a genius and turn them into a genius. If such a place existed, this would be a profoundly different world. 

Why a policy of diverting funding away from poorly performing schools misses the point and is basically unjustified

The case for “school choice” is not remotely strong enough to overwhelm the basic social contract that dictates public expenditure. Even many of the most ardent ed reformers will now concede, after several decades of yelling “no excuses!” and then making constant excuses for charter schools and vouchers, that neither of those programs provide fast, reliable, or scalable improvements. In many cases, students in such situations perform worse. Are the rest of us really obligated to divert precious public funds into institutions that do not operate under public control when the case for the superiority of those institutions is so thin and so contested?