And maybe most importantly, how might we keep what works in Direct Instruction while elevating it, so that education becomes an adventure?

Tomorrow, we’ll be exploring these questions (and more!) in our Substack Live event, as we tackle the third episode of Sold a Story, “The Forgotten Experiment.”

Sunday, November 8
2pm Eastern / 11am Pacific / Your local time
Click here to join the live discussion

It’s free for all subscribers (paid and unpaid alike). You don’t have to have listened to the episode beforehand — I’ll bring you up to speed, and we’ll puzzle through the ideas together.

Again, bring your questions, objections, and half-baked hypotheses! You can engage in the chat, or simply nod along while you wash your dishes.1

If you missed our previous discussions, you can watch the recording of our responses to the first episode, and to the second one. But they’re optional — tomorrow’s discussion stands on its own.

Hope to see you there!

Join the live discussion

Hey, all! We’re back with another letter and another question from Elias Venn, as a perk for paid subscribers. (You can find my response to his first letter here.) Any questions and such for me to consider in my response, drop ’em in the comments.

Look out for our plan to Eganize computer science in next week’s letter, available to all subscribers!

-Brandon

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Hey, all! Last month in Letter to a Homeschooler #1, I explained how to anchor an Egan education in one or more daily practices. Today, as a treat for paid subscribers, I’m sharing the first letter I received from Elias Venn.

There’s nothing load-bearing here—you can find all that in my response—but you’ll learn more about my eccentric correspondent.

And look out for more questions and answers about Egan homeschooling in the coming weeks!

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It went quite well — the folk who showed up were top-notch — so we’re going to do another one this Sunday to discuss the second episode:

Sunday, November 1
2pm Eastern / 11am Pacific
See exactly what time that is where you live1

This one will be free for all subscribers — you don’t need to pay or register or anything like that. To join (I’m told, I’m new at this) open this substack at the start time above, and click on the live video. (Make sure you’re signed into your Substack account.)

Imaginary Interlocutor: Brandon, what’s this all about, now?

A spicy confession: I loved, loved, loved the first season of the Sold a Story podcast. It took the phonics/whole language fight — the closest thing the education world has to WWI-style trench warfare! — and won it.2 It brought the science of reading to a huge audience, and helped change the way reading is taught in schools.

Now Sold a Story is back for a second season, and they’re championing Direct Instruction.

Direct Instruction (“DI” to its friends and lovers) is a highly structured teaching method that uses carefully scripted, systematically sequenced lessons, built around lots of student responses and immediate corrections. To call it “controversial” would be… underselling the controversy a bit. I’ve heard it called things like “soulless” and “authoritarian”.

I’ve had a complicated relationship with it myself.

When I first heard about DI, I thought it was straight-up evil. I was working in a progressivist school at the time. In graduate school, when I came across evidence that goshdarnit it works — specifically, that it was effective for kids in situations where better forms of education routinely failed — I thought that, maybe, maybe, it could be a method of last resort, but goodness knows that I wouldn’t want to teach it.

Then, a few months ago, Alessandro pointed out that Science is WEIRD, ah, is direct instruction, just reimagined through the tools of Egan education:

• clear learning objectives → compelling riddles

• examples and non-examples → surprising contrasts

• (and perhaps much more?)

So now I don’t know what I think about DI. Is it evil? Is it amazing? Is my teaching — and the teaching that we’re helping other people around the world do — a type of it? (Would its practitioners think so? Would its opponents?)

And are there ways that Egan education can make DI (1) more attractive to teachers and parents, or (2) measurably better?

To explore these, I’m listening to this new season of Sold a Story and responding to each episode. And to make this more fun, I’m doing these responses live on video on Substack Live.

Like I said, the recording above is my response to the first episode of season 2, “It’s Not Just Reading”. I strongly recommend listening to the episode before watching the recording. It’s only about 20 minutes long, and you can listen to it on the web, or in whatever podcast player you use. And whatever you think about the topic, the episode is well-produced (see how many of Egan’s tools you can spot!) and a treat to listen to.

Enjoy! And if you’d like, come to the next one. You can listen, argue back, or ask questions. (There’s a chat feature for this.) Or just watch me puzzle through this!

Hope to see you (or at least your chats) there!

Get more from Brandon Hendrickson in the Substack app

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A spicy confession: I loved, loved, loved the first season of the Sold a Story podcast. It took the phonics/whole language fight — the closest thing the education world has to WWI-style trench warfare — and won it.1 It brought the science of reading to a huge audience, and helped change the way reading is taught in schools.

Now Sold is Story is back for a…

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Hey, all! In my never-ending quest to actually write this blog (in this, a period of helping people actually create what we’re talking about), I’ve decided to try something new. I’ve lately been exchanging letters about Egan education with a fellow homeschool dad. Our correspondence has actually become quite voluminous, and he’s given me permission to share both my responses and his letters (well, most of them).

His name is Elias, and he’s told me it’s okay if I publicly describe him as “eccentric”, and also “very, very eccentric”. He said it’s on-brand for him, which honestly is a strange expression to hear from a person who’s living with his wife and three kids in an abandoned Pentecostal church in the woods. (Also, he mostly sends me hand-written letters, some written with what appears to be . . . quill?)

I’ll be sharing these mostly in order. In this one, we talk about what one practice might be the anchor of an Egan homeschooling education. Elias writes:

The wireframes were working for us, but I’m missing so many of the pieces, and you have gone radio silent—WHY?!—on the whole process. So I have to know: will this project be left unfinished?

Hullo, Elias!

I apologize profusely for — goodness, it feels overwrought to say “abandoning you in your hour of need”, but I’ve gotten other emails from people who were counting on my series of “Egan education practices”. (One of them actually pulled his kids out of school because he thought he could depend on them!)

But here’s what I’ll do: answer your questions, and put them up on the blog for everyone to see. I’m hopeful that corresponding might make these easier for me to write.

And can you perhaps start back in with the thing that I need most: a reference point. We four homeschoolers (I’m counting myself) have so many different projects in process. I think we need a moment of convergence—an anchor in our day, a foundational practice that can be adjusted for each of us—that we can use to chart our progress and to reassure and remind ourselves that we are proceeding according to Egan’s principles. That’s my first question.

Hmm — I’m hearing you say that you’re looking for one daily practice that can be the linchpin of an Egan education. If that’s right, I suppose I could suggest a number of things.

The Big Spiral History course that we’re making is (1) fully Eganized, (2) simple, (3) easy, (4) quick, and (5) a long list of other adjectives that basically mean “simple, easy, and quick”. So, that could be helpful! And like I’ve said elsewhere, history (particularly when welded to Big History) is the glue that binds everything together. It connects everything that we teach and learn into the big story of life, the universe, and everything.

And if that doesn’t float your boat, you could make the geography curriculum (the one that I wrote up earlier this year) the anchor. Geography is such low-hanging fruit for Eganization — every place is filled with wonder, and the books that we suggested there (especially the Atlas Obscura guides) make it so easy to tap into that wonder. And geography is the handmaiden of history.

But — but! — if you want something more general, can I suggest something very different — the Memory Box?

I’ve written a bit about the Memory Box on the blog, but I don’t think that I’ve expressed how central we see it being for Egan education.

So, in short: every day, take a few minutes to reflect, and then write down one meaningful thing that you learned.

We can Eganize this simple process further, though, by making it a ritual.

Note that I didn’t say “make a habit of it”. My favorite college professor — Dr. Karen Bruhn, whose PhD was in Religious Studies — once asked us what’s the difference between a “ritual” and a “habit”. I’ve been reflecting on that for decades now, and I think the answer is “the experience of meaning”. We don’t want the Memory Box to be an automatic practice—we want it be rich with meaning.

So, some ideas for how to ritualize the Memory Box:

1. Keep to one time of day and one spot in your home.

2. Dim the lights, and then add in a special light — a candle,1 a lantern, or a particular lamp.

3. Put on some “reflection-inducing” music — Arvo Pärt’s “Spiegel im Spiegel” or Bach’s “Aria” from the Goldberg Variations wouldn’t be a terrible place to start. (Note that these also gently time-bracket the exercise.)

4. Repeat the words that prompt it. I’m thinking of something histrionic like “All that we’ve learned today will be forgotten; what do you want to save from the fire?” This, of course, can evolve (as good rituals do).

Most importantly, limit yourself to one card.

(And then, just in case you don’t remember, review these in spaced repetitions! I’ve sketched out one method of doing so that’s also ritual-heavy… at the low, low cost of being moon-based and kinda eccentric. But I guess that’s “on-brand” for you?)

A fun wrinkle here: the first time I met Kieran Egan, I presented him with two ideas. The second was Big Spiral History, to which he reacted very positively. The first, though, was spaced-repetition flashcards (specifically, Anki), to which he reacted very . . . politely.

“Ah yes”, I recall him saying, “Hermann Ebbinghaus’s work. I believe I once taught about that when I was roped into teaching psychology of education.”

(Reading his memoir, I later discovered that Kieran had a rather low view of educational psychology. Teaching that course, in fact, was the spark that led him to conclude that a confusion of educational psychology with curriculum theory was a slice of what’s wrong with education, but that’s a different story.)

But I think Kieran was wrong about this one, and for an interesting reason: I think in spaced-repetition he was only seeing the “remembering”, and missing the “forgetting”.

Yeah, I’m not being clear. How can I put this better?

Egan’s philosophy of education, as you wrote, is a sprawling complex of complexes. It’s hard work to beat it into forms that can be used easily without losing the philosophy’s power. There are “ways of understanding” and “tools” and “narrativization” and other things besides. But the beating heart of the whole philosophy is meaning-making.

On one level, any kind of memory is meaningful, because our memories are part of our selves. This is literally true: a memory is a linking of neurons, a literal adding of glutamate receptors in a synapse. Every time you forget something, you’re losing part of yourself. You’re being erased a little bit every hour of the day. (And can you tell that Alzheimer’s runs in my family? I have frequent occasions to meditate on forgetting.) To retain a memory is to secure a bit of ourselves.

But there’s another level to it: choosing what to remember — what to enter into our spaced-repetition system — is an opportunity to reflect on what’s meaningful to us. That gives it extra meaning! And then the repetitions of that piece of information (over the next days and weeks and years) are chances to deepen and extend its meaning, and to connect it up with the other meaningful things we’ve learned.

Meaning, meaning, meaning. Not bad for an activity that takes something like 10 minutes a day.

There’s more to the letter — we go into talking about how to teach reading — but that’s a good place to stop for a blog post. If you’re new here, you might enjoy these two earlier posts about spaced repetition:

The Lost Tools of Learning

Forgetting Curve Box

1. A problem…

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2 years ago · 8 likes · 3 comments

The Lost Tools of Learning

Spaced Repetition Everywhere

Note: It’s been a summer! you’ll find an announcement (or two) at the end of this post…

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a year ago · 11 likes · 7 comments

You can sign up for it right now at schoolsforhumans.com/history. We have a rather practical Q&A about it there. Here, I want to talk about the big ideas behind it. (I’d also like your help in committing a murder… but I’ll hold that to the end.)

Imaginary Interlocutor: Back in spring, you blogged about the elementary, middle, and high school history curriculum you’re building. Is this the same thing?

It’s the first stage of that, but with some big changes.

First, it’s for all ages. The original plan was to make it primarily for elementary schoolers, but we’ve designed these to include a wider age range: elementary schoolers ages 8 and up, younger kids with some parental help, and adults. You don’t even need to be a teacher or homeschooler to do it. (We’re excited about this, because we can make this for whole families.)

Second, we’re making it easy. This is in response to all the people who gave us diverse feedback like “this is hard” and “why is this so hard?” and “you know most of us don’t have history degrees, right?” We’ve chosen the 144 stories ourselves, and are scripting each of them as a quick, compelling performance. (We’re excited about this, because we can make the stories accessible.)

Third, we’re making it go fast. Originally, we suggested that people do one story a week over four years. We realized that while this might be perfect in a school context, in any other context, it was too slow.Who has the ability to commit to anything for four years? At the rate of four stories a week, we can cover everything in a single year. (We’re excited about this, because we can make the experience compact.)

I.I.: Is this basically just a bunch of stories?

Honestly, if that was all this was, it’d actually still be an achievement — so many history curriculums don’t seem to know what a “story” is. But the small stories become part of the big picture of life, the universe, and everything as they enter your living timeline. You won’t just hear the stories, you’ll plant them in your head, where all sorts of great stuff can grow.

I.I.: Why 144?

There are about 180 days in a school year, but we’re only creating videos for the first four days of the week, and ⅘ of 180 is 144. (There are other considerations, but they’re too geeky for a respectable post to have in its main text.1)

I.I.: What are the odds that my family actually remembers all these stories, long-term?

Pretty high, because we’ve built the entire course around how human memory actually works —

• stories: everything is a short, evocative story

• vivid images: for each story, you’ll get a printable icon — a small square picture

• locations: you’ll put up the icons onto your walls in chronological order to make a living timeline

• songs: at the end of the year, you’ll turn your whole timeline into a song

And, well, of course, repetition: throughout the year you’ll float through your living timeline (in your mind) to remember the order of the stories. You’ll also play little games to connect stories that are related to each other.

I’ve taken lots of fascinating history courses from which I’ve later forgotten nearly everything. We’re hell-bent on saving you from this fate. Our goal is to help you effect a sort of intellectual transformation for your household — we want this to be the start of you seeing everything in terms of history. (And of falling in love with history to boot.)

I.I.: Must we put up these icons? They sound clutter-y.

We’re making them small, but in any case they’re optional — your family could jump straight to imagining the images inside your heads. You will want, however, to put up tiny stickers whose 🔴 rainbow 🟠 colors 🟡 help 🟢 you 🔵 recall 🟣 different 🩷 eras.2

I.I.: How can I know that these stories will be any good?

We’re working with the actor and dramaturg Emma Baker to script and perform these stories in ways that bring out the human experiences inside them. Keep reading to see our process for it. We’re working on the first examples; once those are done, you won’t have to take our word for it.

I.I.: How much does it cost?

We’re investing a lot of resources into making this, but we’re selling access to the entire year — which is to say, 144 stories from across all history — at $144. (That’s actually in the realm of what a lot of homeschooling families pay for a year of history.)

I.I.: What are these 144 stories?

They’re a diverse set — horrible rulers, brilliant activists, pirates, the first stars, Vikings, cruel explorers, massacre upon massacre, religious reformers, dinosaurs… There’s a lot of old favorites in there:

• Ann Frank (🩷 space 19, dot 5)

• Judas Maccabee’s Rebellion (🟢 space 7, dot 4)

• Joan of Arc (🔵 space 10, dot 4)

And there are some gems you might not be familiar with. Have you heard about Potosí, the mountain of misery (🟣 space 11, dot 5)? How about the princess–priestess Enheduanna, the earliest known named author (🟡 space 5, dot 3)?

You can see them all here, along with a one-sentence description of each:

See all 144 stories

I.I.: How’d you pick them?

With fear and trembling and a bucket to collect all our sweat.

Foolishly, I had thought choosing the stories was going to be easy! After all, I’ve been preparing for this my entire adult life: I have a bachelor’s in history. I have a half-wall of history books in my home. I developed this very idea into my master’s thesis, which I presented at a history conference.3 I figured that because it’s impossible to get a “perfect” list of history stories, we could embrace imperfection. I guessed we’d hash this out in a couple days.

That was months ago. To oversimplify a painful and convoluted process, we knew each story needed to work on three levels:

1. a vivid, simple story (🧙‍♂️MYTHIC understanding)

2. a window into one of history’s huge, complex narratives (🦹‍♂️ROMANTIC understanding)

3. a cage where students could have an idea fight (👩‍🔬PHILOSOPHIC understanding)4

So we set about winnowing through the famous stories from world history to find the ones that worked as each. Let’s start with the 🧙‍♂️MYTHIC.

I.I.: How do you know these events will be mythically engaging?

Well, we made sure to put in historical figures that already live in the imaginations of most people: think mummies, ninjas, pirates, cavemen, and knights. But beyond that, we made sure that everything we chose is rich in the stuff that makes any story great.

We start by putting the agony back in protagonist — we center the story on a person who needs something. This desire should be one of the big binaries of human struggle: say, poverty/wealth, oppression/equality, destruction/salvation, or ignorance/insight. And by the end of the story, something needs to have happened — the world and the protagonist should be changed in some way.

I.I.: That sounds like a template: does that mean that the stories will sound repetitive?

Oh no. These stories are richly detailed, and crafted capture 144 very different historical moments. But we’re going to further diversify these by telling them in different genres: the rise of Caesar Augustus can be scripted as a thriller; Equiano’s account of being kidnapped may become true crime. Confucius’ attempt to remake his world can be political intrigue; the story of Fūma Kotarō is easy to tell as a heist. We’re considering a famous 20th century story for gothic horror (see if you can guess it in the comments). We think that one will be a murder mystery.

This all makes sure that these stories work on the 🧙‍♂️MYTHIC level. How they work on the 🦹‍♂️ROMANTIC level is something that flows from a very different question…

I.I.: Are these stories important?

Very much so! Remember that this is Big Spiral History: we’re creating our whole history curriculum to revisit the same stories again and again.

The thrust of this first cycle is to stack up simple stories to make a timeline of Big History. The thrust of the second cycle will be to see how these simple stories weave together into the many complex narratives that make a popular history of the world. A simple way of thinking about that is to ask, “what would a history teacher say are the most important things in all of history?”

I.I.: Oy… what are the most important things in all of history?

While there isn’t any single agreed-upon list, there are quite a few attempts. We decided to see where they overlapped. We (and here I of course mean “an LLM”) identified nine of these lists. They included sources like Encyclopedia Britannica, the International Baccalaureate history syllabus, the World History Encyclopedia’s timeline, and UCLA’s ambitious World History for Us All. We found nine such lists, compared them, and gave each a score. Some topics (e.g. the 2008 financial crisis) only scored a 5/9. Others (e.g. the Holocaust) scored a full 9/9.

We took all the topics that scored at least a 7/9, and ran them through a special list — Wikipedia’s Vital Articles. It’s essentially a crowd-sourced canon of the world’s most important topics. It comes in tiers:

• Level 1: the 10 most important subjects

• Level 2: the 100 most important subjects

• Level 3: the 1,000

• Level 4: the 10,000

• Level 5: the 50,000

We found that while there were historical topics in the first two levels, none could be made into a 🧙‍♂️MYTHIC story. (Level 1, for example, has “human history”, and Level 2 has “prehistory”, “ancient history”, “post-classical history”, and so on. Good stuff, important stuff — but not 🧙‍♂️MYTHIC stuff.)

Level 3 was where we hit pay dirt. It featured 27 of the stories we were already considering; we decided that, come hell or high water, we were going to include those. Level 4 featured 41 more stories and Level 5 had 17 more; we decided to shoot for including most of those.

Some took some ingenuity — we knew we needed to include the Black Death (it scored a 9/9 and was a Vital Article level 3), so we tied it to the story of the Muslim philosopher Ibn Khaldun’s watching his teachers and parents die (🔵 space 10, dot 4). We needed to include a window to the mass migration of Europeans in the late 1800s, so we chose the arrival of Emma Goldman in New York City (🩷 space 18, dot 4).

In the end, we’re quite happy with how many of “the most important things” we were able to include in our 144 stories. Most of the chapters you’d find in a history textbook — topics like “the seven cradles of civilization”, the Renaissance and Reformation, the Industrial Revolution, the decolonization movement — have anchors in our list.

But again, nothing’s perfect. You can take a look at the concordance document here, and use it to berate us on what we’ve missed.

I.I.: You call this “Year 1”. What’s “Year 2”?

Big Spiral History is just getting started.

Before long, we’re going to throw ourselves into creating the 🦹‍♂️ROMANTIC and 👩‍🔬PHILOSOPHIC cycles of world history. (To get a glimpse of what we think that’ll look like, see my posts on middle school and high school history… though you can expect those to evolve quite a lot.)

Before that, we’re planning to create some 🧙‍♂️MYTHIC, national history add-ons to Year 1. In the U.S., at least, most homeschoolers are required to study American history, and we believe this model can be an amazing way to do it. At the same time we do this, we’d like to start working with people to develop some other national histories, too.

But even before that, in the 2027–28 school year we’ll fine-tune what we’re making this year, and turn it into a respectable consumer-oriented product. You can get it now, in its untamed, wild pilot year now!

Anyhoo, this all flows from a 🦹‍♂️ROMANTIC view of history. What we do for the 👩‍🔬PHILOSOPHIC level is something that flows from a very different question…

I.I.: What attention did you give to gender? To race? To religion? To class?

Well: lots. To show it off, we need to take a look at our 👩‍🔬PHILOSOPHIC cycle, which we will eventually build for high schoolers. It’ll be a baptism into the (many) theories that intellectuals use to make sense of how human society ticks. This means that we’ll center it on the tools of 👩‍🔬BIG QUESTIONS, 👩‍🔬GENERAL THEORIES, and 👩‍🔬IDEA FIGHTS.

But this is a bigger topic than I can answer here. Look forward to a follow-up in a later post.

I.I.: I believe you said you’d like help murdering someone?

If you count through the 144 stories carefully, you’ll find that there aren’t actually one hundred forty-four of them — there are one hundred forty-five.

We’ve already worked danged hard to whittle these down. Everything in the current list is either so important or such a great stand-alone story that we can’t imagine denying it.

We need to knock out another one, but we can’t bear to choose which… so we’d like you to do the dirty deed for us!

On Sunday, August 30, at 6pm Eastern / 3pm Pacific, I’ll hold a live meeting for paid subscribers. In it, I’ll give you a behind-the-scenes look at the list of stories, and tell you some things that excite me about it. I’ll answer any questions you have (including rude ones that start with “How dare you not include…”). You can come with any suggestions you have about which story to kill. To start, here are some that we’re considering giving the ax:

• rice cultivation in Hemudu (space 4, dot 5)

• Ötzi the Iceman… dies (space 5, dot 2)

• Hannibal crosses the Alps (space 7, dot 3)

• Gutenberg invents the printing press (space 10, dot 5)

• the Haitian Revolution (space 16, dot 5)

• Princess Isabel ends slavery in Brazil (space 18, dot 4)

• creation of the State of Israel (space 19, dot 5)

• Rachel Carson writes Silent Spring (space 20, dot 2)

• Tim Berners-Lee gives away the World Wide Web (space 20, dot 5)

• the January 6 Capitol attack (space 21, dot 3)

I’ll lead us in a conversation about the ways each story is load-bearing (sometimes in unexpected ways). By the end of the hour, we’ll have decided which story to kill, and we’ll have arrived at the sensible, excellent, magical number of 144.

Here’s the link —

In the meantime, you can AMA about Big Spiral History, Year 1 in the comments, and you can sign up for it here.

Thanks for being a paid subscriber! With this, you gain access to the 10-session series of “Egan homeschooling” workshops I did in the summer of 2025. After the first, big-idea workshop, each shows how you can use Egan’s paradigm to revolutionize a particular academic subject:

1. A new way to see education

2. Geography & history

3. The sciences

4. Problem-solving & ari…

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A while back, Scott Alexander wrote that he gets pitched on schemes to solve debate:

Astral Codex Ten

Your Attempt To Solve Debate Will Not Work

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7 months ago · 490 likes · 393 comments · Scott Alexander

These attempts, he said, are “well-intentioned, sophisticated, and doomed.” The problem is that they misunderstand why internet debates are so terrible — it’s not logical fallacies, false facts, or bad argument structure. Rather, he argued, it’s because

1. real disagreements are intractably messy, and

2. few people actually want to put in the frustrating, painful work of revamping beliefs.

So, he writes, it seems next-to-impossible to organize a community around this.

I suppose this is an awkward way to begin a “Scott is wrong” post, but: I think this is substantially right! But I see a way forward in what he wrote — a way to radically improve the practice of debating people on the internet so that people regularly (semi-regularly?) change their minds.

I don’t have any expertise in formal debate, but my hobbies include befriending young-Earth creationists, arguing with my fellow evolutionists on Reddit, interviewing flat-Earthers, and hosting dinners that bridge political divides. And over the last decade, I’ve been tinkering with new approaches to public debated that actually help the audience change their minds. At the moment, I’m part of a team that’s just finished putting on a series of debates over the Shroud of Turin — the purported burial cloth of Christ, and modern Catholic relic par excellence — and I think we’ve found the seeds of something that might work.

We can’t yet claim to have a scalable model, but if I had to describe our “minimum viable product”, it’s this: (1) pick a juicy topic that a community really cares about, (2) get a pair of people to fight each other publicly, (3) identify a bigger enemy against which they can fight alongside each other, and (4) use Bayes to keep score.

My hunch is that these tactics overcome Scott’s objections — in fact, his critique obliquely points to them. I’ll take them in turn.

1. Pick a juicy topic

Our team came together over the Shroud of Turin.

Imaginary Interlocutor: You’ll forgive my ignorance of Catholic relic-lore, but: what’s that?

The Shroud of Turin is a medieval con — or at least this is the mainstream scholarly view. It’s a forgery of the burial cloth of Jesus; it was fabricated in the 1300s and displayed in a small French church to attract pilgrims and their money.

To me (as you’ll see), the evidence for this seems overwhelming. But famously, the cloth has an eerie, faded image on it:

…which honestly does have some interesting properties! It doesn’t, for example, seem to have been painted or printed onto the cloth. The coloration is thin and superficial — less than a thousandth of a millimeter thick — and seems to be caused by a chemical change in the linen’s fibers. Intriguingly, many skeptics grant that it encodes three-dimensional information: that is, the darker areas of the image seem to correlate with how close they would be to a 3D body.

Attempts by skeptics to recreate this image haven’t come particularly close to succeeding: a recent, well-publicized, $1 million contest to replicate the details of the Shroud didn’t even find any entrants.

That’s the skeptical take. The other interpretation is that this is the burial cloth of Jesus himself, whose resurrection created the image. This is forcibly argued by an international community of researchers calling themselves “sindonologists”, from the Greek sindon, “shroud” (hence the colloquial term “shroudie”).

My friend Georges (pronounced just like “George”, it’s French) is a dyed-in-the-wool shroudie, and has taken the other side in these debates.

Imaginary Interlocutor: Why do you care about this? Of all the truly important things in the world that we need to spend time discussing, why waste time on a medieval Catholic relic?

Is this the moment I should point out that ACX has been slowly morphing into the Internet’s central node for diving into Catholic lore? But I think that this debate would have happened without our community’s interesting turn.

One is negative. I’ve encountered forms of traditionalist Catholicism that were catastrophically wrong about history (especially Jewish history) in ways that seemed not just embarrassing, but dangerous.1 My time with fundamentalists taught me that big-belief systems often loosen when people start to question a concrete claim.

On the positive side, I have a crush on Catholicism! I think classical Catholic schooling contains real insights into what a re-humanized education can look like, and I actively support that community. I want to help my Catholic friends become better acquainted with the riches in their tradition — and the Shroud of Turin feels like cruft. As an open-minded agnostic (who spends far too much time thinking about religion), I want to steer Catholics to the best arguments their faith has to offer.

But there are two objective reasons I think the Shroud is a great topic on which to re-invent debate: (1) lots of people care about it, but (2) no one needs it to be true.

The Shroud is having a cultural moment. Joe Rogan has talked about it, it made the Today Show, and it seems to be trending in skeptical debunking circles. It’s even spread into some Protestant apologetics — long thought to be a safe space from “Papist relics”.

And I think this is key for anyone looking to “solve debate”. Scott wrote:

The hardest problem for any social technology is getting users: We’ve talked about this before for dating apps. And if it’s that hard to lure people in with the promise of sex, it’s probably even harder to lure them in with the promise of logical accuracy.

Like dating, arguments require two compatible people. That means your app is useless until it has a big enough population that, whenever someone wants to argue, there will be a compatible person willing to take the other side of that argument in a reasonable amount of time. That’s hard to bootstrap.

Dating apps can only work because they promise passion. Anyone hoping to “solve” debate would do well to recognize that, and start with communities who are already passionately debating a specific topic.

Of course, we don’t lack for topics that people are passionate about! But I suspect there’s a second, somewhat-opposite reason the Shroud is a great topic — it’s not a hard identity marker, like (say) the resurrection of Christ. While lots of Christians can get really charged up about the Shroud, no one is required to believe in it to stay in their community. Most Protestant pastors I know are disdainful of it, but even the Vatican keeps some distance from it: Catholics are permitted to venerate the Shroud, but the Church refuses to officially deem it authentic.

That’s to say, the Shroud is ideal because people care about it deeply, but almost nobody needs it to be true.

2. Find two fighters to gin up the drama

The biggest weakness in the proposals Scott describes is that they seem to mistake humans for Vulcans. He wrote:

The simplest “solve debate” proposal is the argument map. Some technology helps people decompose arguments into premises and conclusions, then lets skeptics point out where the premises are wrong, or where the conclusion doesn’t follow from the premise.

To “solve” debate, we need to more fully humanize it — and that means taking human nature seriously, warts and all. People usually say we want to be rational. We say we want to know the truth. And to some extent, we do! But most of the time, what we really want to see is a fight. We want to see our champion triumph over the enemy. We want to see them humiliated.

We realized that to re-invent debate, we needed to play up the “fight” part to get people to come to the event in the first place. So we played it like a mashup of a boxing match and the Roman Colosseum. We advertised with this image:

Our moderator kicked off the evening by bellowing LET’S GET READY TO RUUUUUUUMBLE! which would have been inexcusably cheesy except by God he pulled it off. At various points we put the crowd in the position of Caesar, giving us a thumbs up/down to judge how convincing they were finding us.2

The point, for all of this, is to find ways to gin up those passions that are implicit in the debate topic. People want to think, but they need to feel.

Imaginary Interlocutor: I can’t help but notice that you’re betraying all the norms the rationalist community has built up over the years. Politics is the mind-killer — have you not heard?

Bayes is coming, don’t worry! But to sell the methods of rationality to people, they need to feel the need for them. In our next step, we’ll help them feel it — but before that, they need to be able to feel something, anything, at all. Starting with analytic, logico-deductive tools is a self-own. Be more Kirk.

3. Find a bigger enemy to fight together

Having built up the enmity between the debaters, we now need to find a way to pull them together to seek truth — and we need to get the audience to root for it.

I.I.: This is when you embrace your inner Vulcan nature and choose peace?

Heck no — this is when we find a bigger enemy.

This is, of course, one of the classic moves in storytelling. Who allied the Elves, Dwarves, and Men? Sauron. Who reunited Iron Man and Captain America? Thanos. Who got the Starks and the Targaryens to stop killing each other? The White Walkers. (There’s a long TV Tropes page on this.) This works in storytelling because it pulls on some of our deep evolutionary and cultural strings — social psychologists call these “superordinate goals”, which is a particularly bloodless way of saying “a big baddie”.

To capitalize on this, we just need to find something that almost everyone on every side of every debate hates.

Thank God for the dumpster fire that is contemporary civil dialogue!

It’s of course fashionable to hate on the things that drive the terrible state of our dialogue: social media, polarizing politics, and culture-war pundits. We leaned into that. We even took potshots at the institutions of “formal debate” that we see: it’s our observation that both sides of audiences often leave a debate more confident of what they believed when they came in.3 This sucks! We defined our events as the opposite of those: we were there to have a real conversation, where we’d help each other steelman our positions.

At every point we could, we flipped the audience’s expectations of our being against one another. Not only did we avoid complaining about the bad actors on each other’s side — we took pains to call out the bad actors and bad arguments on our own side.

I.I.: After ramping up the fighty-ness before, it seems hard to pull off being friends now.

Indeed, which is why it’s so important that Georges and I are already good friends. For five years, we’ve been getting together to walk around town and argue about our respective religious views — and he’s an excellent sparring partner. He has a classical Catholic seminary education, a Ph.D. from Yale, and an open mind. He’s assiduously honest and fair, telling me when I’ve changed his mind about things. Our families have eaten dinner together. I like him heaps.

I.I.: How’s that hopey changey stuff working out for ya?

It’s working great! After the first debate, some members of the audience (ones who had come in very confident of our opinions) expressed that they had become less confident. One guy came up to thank me, saying that he had believed in the Shroud before — and still believed in it now — but that I had given him a lot to think about.

I.I.: But then is the fight fake? Is this just kayfabe?

No, not at all! Georges and I really disagree about the Shroud of Turin (and Catholicism, Christianity, and theism). We drive each other a little crazy. And the topic really does matter to us: if I become more convinced that it’s true, I’ll become more open to other supernatural claims; if he becomes more convinced it’s not, he’ll become less willing to give credence to “scientific” claims in his faith community.

I.I.: I’m having a hard time reconciling these. Are you really trying to beat him, or not?

I want to beat Georges so badly — and, of course, he wants to do the same to me. And, of course, I want to help him do it. “That which can be destroyed by the truth, should be”, and all that. Of all the people I know, Georges is one of my best hopes for someone who can radically change my mind. I want to win about as much as I want to lose.

Our whole relationship is an adversarial collaboration. If we can use this peculiar friendship of ours to help other people become more rational, that’s a cool silver lining.

4. Use Bayes to keep score

I’ve been experimenting with many different formats for public debate over fifteen years; I’m happy to say that they’ve (mostly) succeeded at demonstrating how to argue honestly and civilly and to keep a scout mindset. What those formats lacked, however, was a method to regularly change people’s minds.

For this project, then, I decided to make it overtly, cringefully Bayesian — to boldly Bayes where no one has dared to Bayes before!

I.I.: I see — this is a guest post for ACX, so you think that this needs to be about Bayes’s Theorem! How sweetly autistic of you. You get that all the Bayes worship is a half-joke in the rationalist community, right?

I’ve become convinced that rapid, quantifiable updates are what all debates are lacking.

Without them, it’s almost impossible to pin your opponent down. Even when they concede something, they can go back to arguing like it didn’t matter. Words let you move in an infinite number of directions; numbers force you to go up or down.

Worse, without them, it’s easy for even an airtight argument to be overcome by anecdotes. Humans are vibe-based creatures: we reason in stories and images. Whoever can get the best impression into an audience’s heads usually wins. Bayesian reasoning forces people to cut through all this and be clear about how what they’re saying matters.

On the positive side, rapid quantitative updates provide an excuse to externalize and simplify our thinking. As Scott noted in his post, real arguments are messy (“‘Debate’”, he wrote, “almost never corresponds to mappable arguments”), and yet working memory is limited. We need lots of data to seriously change our minds, and that data can be fit together in an infinity of different ways. It really helps to write out the evidences systematically. (This is especially true when the debaters are bringing in pieces of evidence that the audience has never heard of before.)

But best of all, rapid quantifiable updates gin up the drama of the fight, because they let each person make small wins against the other. When confronted with a good point in the midst of the debate, you can reward that by changing the number you were planning to give — it won’t cause you to lose the debate, and will prove to the audience that you’re honest and trustworthy.

This, actually, led to my favorite moment in our two debate events so far. To describe it, I need to first show the specifics of how we used Bayes to argue about the Shroud in particular. (If you find your heart strangely warmed by neither relic lore nor radiocarbon dating, you may want to skip to #5 below.)

Our specific arguments

Before we fought on stage, we fought over coffee so many times. By the end of this process, we each picked our three strongest evidences for or against Shroud’s authenticity.

My three evidences:

1. the Shroud was carbon dated by three labs; each reported that the linen was made in the 1300s

2. the face on the Shroud looks like how medieval artists were depicting Jesus — a narrow face and a long beard

3. the whole image is front-facing: if it had been created by a blast of radiation (as is often hypothesized by Shroudies), the sides of the body would have colored the cloth as well

Georges’ three:

4. the many modern attempts to re-create the image have failed; we still don’t have a good hypothesis for how a medieval craftsman could have done it

5. stories of a cloth miraculously featuring the face of Jesus date back to the 500s at least

6. the bloodstains on the Shroud match with 80% accuracy with the bloodstains on a wholly separate Catholic relic, the Face Cloth of Oviedo

During our pre-debate coffees, we came up with our own set of updates for each of these. To do that, of course, we had to pull from our butts estimate the chances that each of these evidences would be true in both the world in which the Shroud is Jesus’ burial cloth, and the world in which the Shroud isn’t.4

And then we had LLMs do all the hard work! Here’s how we prompted them:

I was shocked by how well GPT and Claude did at this — not just running the numbers correctly, but in calling out reasoning errors we were making (like double-counting evidence) and suggesting numbers that more sensibly matched our models.

I.I.: What were your priors for the Shroud?

We talked a lot about this. We intuited that it would be good for the audience if we came in with a compromise prior — we didn’t want to lose people at the beginning — and I was happy with making it high. We chose 10%.

I.I.: That’s ludicrously high. Surely 10% of other Jesus-related relics haven’t been proven to be authentic.

Indeed — yet honestly, when we repeat this in the future for an audience new to Bayes’ theorem, we’re tempted to just ignore the prior, and let it implicitly be set to 50%. The more we’ve done this, the more we’re convinced that what matters most is helping the audience come along on this ride, and priors are a cognitive hurdle.

I.I.: What numbers did you end up with?

In each of these, I strove to be as generous as possible to the other side. I do have some regrets, though. The technical ones (about my numbers for #45, and my use of the × and ÷ symbols6) I’ll put in footnotes. The more important ones were rhetorical.

First, I made a big deal to the audience as to how almost every piece of evidence should cause us to update in one direction or another — even if only a tiny bit! — and yet for #5, I didn’t update at all. While I don’t think that the story of the Face Cloth of Oviedo is much evidence in favor of the Shroud’s authenticity, I can acknowledge that if there were no story at all about an eerie image of Jesus on a cloth for the thirteen centuries before the Shroud came into the historical record, that would be a significant mark against its authenticity — so that story should tilt me upwards, even if only 51/50 (instead of the 50/50 I gave). That was a missed opportunity to display my openness to the Shroudies in the audience.

Second, I also didn’t update on #6. The reason for this is simple: I’m not yet sure how meaningful this fact is. We brought this evidence into the conversation only a week before the first debate, and I didn’t yet have time to research it. If there really is (as Shroudies say) a statistically staggering correspondence between the bloodstains on the Shroud and the Face Cloth, then this could tilt my final confidence impressively toward Georges’ position. But entering this as a non-update meant that I looked like I was disregarding the evidence entirely — it would probably have been better to put “???” in instead.

I.I.: Any other regrets here?

Yes — I realize now that we shouldn’t have presented these numbers all at once to the audience. It would have been far easier to follow (and far more dramatic to watch!) to see the numbers appear as we debated each piece of evidence in turn.

I.I.: Enough navel-gazing — what numbers did Georges give?

From this, you can see that we’re actually more-or-less aligned on #2, #3, #4, and #5. (This is another great benefit of using Bayes to fight: it helps you cut to the evidences that would actually change your and your opponent’s minds.) It’s only #1 and #6 that really make the difference — which brings me back to my favorite moment of the debates so far.

The best moment of the debate

We decided to focus our second debate on evidence #1, the carbon dating. The debate itself left much to be desired. Whereas the first event was scripted to be fast-paced, in the second we allowed ourselves to go long in our explanations. Much less compelling drama — we’ll be going back to the original model for our next debate. But all the factors I’ve been talking about in this post allowed for something truly rare to happen: Georges updated live on stage.

Shroudies proffer many possible explanations as to why the 1988 carbon dating tests (done concurrently by three separate labs) returned a date in the 1300s.7 They range from fanciful (neutron flux from the Resurrection) to boring-sounding-but-demonstrably-untenable (soot contamination from a fire in 1532).

Georges sees all of these as hopeless, and advocates for what I think is the only defensible possibility: the segment of the Shroud that was snipped out and tested wasn’t originally part of the Shroud, but a patch added in the 1300s. Now, I think there are many reasons to think this quite improbable, but on stage I pointed out an oddity: even if we were positive the snipped sample was from a patch, what are the odds that the patch was from the precise century mainstream historians say the Shroud was fabricated in?

There’ve been 20 centuries since Jesus, I pointed out. The chance that the patch was made in the 1300s would then have a ceiling of just 1 in 20 — 5%.

On the spot, Georges agreed, and flipped that number to 5%. This dropped his overall confidence from 98% to 90%.

To me, this is strong evidence we’re breaking exciting ground with debate. (I have hopes that, eventually, I can move that number down from 5% to 1%, which would drop his final number from 90% to 68% — making him less a Shroudie than a Shruggie.)

5. Against civility

I.I.: This sounds a lot like the wave of “civil conversations” that came around 2017. You know those didn’t work, right?

While I can understand how what I’m proposing might be mistaken for a “civil conversation”, I think that, in the ways that matter, it’s the opposite.

The deepest goal of a “civil conversation” is to show that it’s possible to disagree with someone without hating them. And that’s good! But that means that, in practice, “civil conversations” usually end up being compromises between the poles of honesty and kindness.

The deepest goal of this kind of conversation is to actually change people’s minds, which means bringing together both radical honesty and radical kindness.

I.I.: Isn’t that a mixed message?

No — it’s what’s at the core of every great friendship. We shouldn’t forget that when we argue with someone online about something important, we’re asking them to do something that feels dangerous: open up their own beliefs for public attack. If you want to change the mind of somebody online, step zero isn’t to avoid being mean or nasty, it’s to open up your own beliefs. To get the other side to be vulnerable, you have to become vulnerable yourself. There’s no other way around this.

This vulnerability is hard. It’s perhaps impossible for most people to do with strangers. And so, to power it, we need something stronger. As the good book says:

In the moment when I truly understand my enemy, understand him well enough to defeat him, then in that very moment I also love him.

I think it’s impossible to really understand somebody, what they want, what they believe, and not love them the way they love themselves. And then, in that very moment when I love them… I destroy them.

Which is all to say: yup, I think the secret ingredient in solving debate is love.

Love means truly wanting the best for someone. I don’t just enjoy Georges’ company, I want to help him deepen his Catholicism — and from my perspective, the Shroud is a distraction from the deeper, truer threads of his tradition. Meanwhile, he wants me to experience the joy of his religion. And we both love the truth, and want to change our opinions to match it, even if that’s painful.

Love sounds trite, but Scott’s written about how love may have powered the spread of Christianity. It sounds sentimental, but I’m becoming convinced it’s an acid that can dissolve untruths. It’s the opposite of dunking on your opponents. I will acknowledge that a dunk, done at the highest levels, is a work of art,8 but I suspect that the ultimate effect of most dunks is to harden the beliefs of the people being dunked on. Dunking shows contempt, and the idiosyncrasies of monkey evolution make it almost impossible to adopt the beliefs of anyone who’s shown us contempt.

Love is the opposite of contempt. And yet — as the work of Orson Scott Card reminds us — it can be the more dangerous weapon.

6. But could it scale?

Scott’s right that debate can’t be solved by anything as simple as argument maps or tidy fallacy labels. I nurse a hope that it could be solved by teams of people who can be more Kirk, more Spock, and more Ender — more human.

That’s hard to scale. But it seems worthwhile to imagine what it might look like if someone tried. What would it take?

Create a specific model

My team held these debates locally, which had the advantage of being cheap, but the disadvantage of a limited audience (in each of our three events, we averaged 20 audience members). Since being face-to-face seems crucial for this sort of trusted debate, we suspect that putting up video podcasts on a YouTube channel might be ideal.

Pick an important topic

I wrote above that, to scale, the first adopters of any new method of debate should come from particular communities who are already passionate about a weird topic, and disagree strongly with each other. Some possible topics might be:

• the effects of AI on the environment

• the wisdom (or not) of effective altruism

• prediction markets

• geoengineering

• AI personhood

• animal welfare

• renewable energy

• NIMBY/YIMBY stuff

Bond with great people

It would take teams of talented people to pull this off. Some specific roles:

• a pair of fighters (to fight)

• a moderator (to run the debates with both flair and fairness)

• a debate coach (to give the fighters feedback on arguing without showing contempt)

• a graphic designer and a video editor (to turn the raw video into something professional)

• a marketer (to get an audience)

• a researcher (to see if this actually works, and conduct experiments in making it work better)

Find a #%@*! name

I’ve spent far too long thinking about this, and have yet to come up with anything resembling a great name for this sort of debate. “Bayesian Brouhahas”? “Anti-debates”? I invite (beg!) any ideas in the comments.

This is all to say, that with the right kind of support, I think that maybe — possibly! — debate could be “solved”. I think we could cultivate debates like this inside many topics that matter. I think that we begin to move the needle toward productive debates that actually change people’s minds.

The odds, of course, seem against it. As Scott pointed out:

This hasn’t worked in two thousand years of arguing

But consider the potential payoff. History seems to be careening toward something like total epistemic closure: groups living in their watertight fictions, trained by their beliefs to feel even the mildest rebuke as an existential threat. The chance to “solve” debate seems to be worthy of some serious attempts.

Note: I’ll be at Less Online next week, where I’ll be doing a break-out group about how debate might be “solved”. Fingers crossed, I’ll be joining Ross Richey (the original creator of the fantastic Astral Codex Ten podcast, and the author of the Substack We Are Not Saved) to do an example round of the format I’m sketching out here. I’d love to connect there with anyone who’s interested in all of this. Also, the comments!

Two notes on doing (and teaching) Bayes

In these debates, I needed to explain Bayesian reasoning to our lay audience — a bunch of Shroud-curious folks who included everyone from Mayo Clinic research scientists to high-school dropouts.

While working on these debates, I was called upon to explain to our lay audience what the hell “Bayesian reasoning” is. To do this, I drew from a post I wrote last year — 

Astral Codex Ten

Bayes For Everyone

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a year ago · 241 likes · 199 comments · Scott Alexander

I stand by everything in that post, except

1. it hid the most important point about Bayesian reasoning in an implication near the end, and

2. it didn’t actually teach Bayesian reasoning.

I’d like to share my screw-ups in explaining Bayes for anyone in the community who’s called upon to teach this topic.

Screw-up #1: Get clear on the social use of Bayes (Don’t do Bayes alone)

I wrote:

Drawing little rectangles is a great way to see where you disagree with somebody. You think aliens have infiltrated the world’s governments? Cool! Let’s talk priors, and see where we draw our vertical lines. You think you saw a ghost, and now it’s rocked your worldview? Let’s talk about how strongly we should update from personal experience. Get a napkin — let’s draw some cute boxes.

This, I think, is actually the deepest value of teaching kids Bayes: it’s a way to get them to converse with people whose views they think are stupid. And it’s only through actually doing that that we have any chance of helping people become rational.

I see now that this isn’t nearly strong enough. Three summers of doing Bayesian reasoning with kids has taught me to say this plainer:

Screw-up #2: Don’t assume the fundamental move of Bayes is intuitive (Hop in a cardboard box)

Also in that post, I created a toy example of Bayes’ boxes, involving math teachers, NFL quarterbacks, and a perfectly-spiraled football. And it was fine… except that it didn’t actually teach the counterintuitive, essential move of Bayesian reasoning: quantifying belief.

This (so far as I understand it) is the thing that divided the Bayesians from the Frequentists in the mid-20th-century. And the move to doing it well requires a leap of imagination that (I can now report!) strikes many people as deeply weird, and sometimes even morally icky: you have to imagine you’re in a world where the other side is actually correct.

The best way that I’ve found to do this is to embrace the absurdity of it all, and invite people to fly with you in a cardboard box to another world:

If anyone has any other tips as to how to explain Bayesian reasoning to a lay audience, or any critiques of this, I’d love to hear ‘em. And if you’d like to watch the debates, they can be seen here.

Astral Codex Ten

Your Attempt To Solve Debate Will Not Work

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6 months ago · 314 likes · 309 comments · Scott Alexander

— and I’d very much benefit from your thoughts on it.

If you haven’t read it already, you’ll probably want to go ahead and do so — it’s just a seven-minute read. But in a nutshell, here’s what I see Scott as saying:

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Where does our math come from?

Around 600 BCE there was an explosion in ancient Greece, and we’ve been trying to re-create it ever since.

Last week we talked about the roots of Greek math: wandering Babylonian priests sharing riddles around campfires. But how did we get from those riddles to modern math? The answer, according to the historian of mathematics Reviel Netz, is the quest for glory.1

Take a look at the first distinctively Greek math problem we’ve found record of —

What’s the area of the yellow moon? If it helps to give numbers to the triangle’s sides, call them “1”. Peer at it for ten seconds. (Hint: the moon is formed by drawing arcs — the moon’s “inner” curve is a quarter-circle centered on the green triangle’s right angle, and its “outer” curve is a different half-circle centered on that big black dot.)

This is the famous Lune of Hippocrates.2 Before this, clever people could do a fine job figuring out the area of a shape made of straight lines, but no one could figure out how to do it with one made of curves.

Until Hippocrates. He constructed this, and showed that the moon’s area and the triangle’s are exactly the same. His proof is short and elegant. Netz explains it well:

…you start out not assuming anything… but a few sentences later, you have been, epistemologically speaking, punched in the gut. You cannot speak back, you are doubled over by the force of the proof. You must stare at Hippocrates and admit: yes, you won. You are right. The [lune] is equal to the triangle.

– Why the Ancient Greeks Matter: The Problematic Miracle That Was Greece

We need to understand that mathematical proofs began as provocative artworks — think something like Picasso’s Guernica or the opening to Beethoven’s Fifth Symphony or the ending of Planet of the Apes. This shock of delight became the dragon that all future mathematicians would chase for more than two thousand years. Netz again:

From this knockout there is no turning back and mathematics, henceforth, would be the science of amazing proofs.

What happened? How’d Hippocrates pull this off? What made the Greeks special?

Old-school racists, of course, had a simple answer to this: it was in their DNA. Greeks were just smarter than everyone else; their intellectual victory was inevitable. Alas, the subsequent history of Greece doesn’t give us any confidence in this — after it was conquered by the Romans, its creative intensity dampened.3

A better answer comes in looking at the particular moment in which this explosion sat. In this blog, we’ve made a big deal of two factors:

• the first easily-usable alphabet was invented in Greece; this allowed common people to share their ideas farther, and across time (see Origins of the Alphabet°)

• the particular place the Greek miracle began — the islands off of Turkey — was a hotspot for trade; anyone living there could see that there was no one “natural” way for humans to live (see Other Alphabets°)

Netz adds a third observation: the nearby empires were centrally-run bureaucracies. Rulers ruled, and subjects obeyed. Because of the mountainous island geography of Greece, its people were broken up into small city-states that ran themselves. Societies were relatively egalitarian. In these cities, status came from the ability to persuade other people. In these cultures (Athens above all) if you could say something new and interesting, people would celebrate you. You’d have clout and the chance to exercise power.

It’s in this context that “the author” gets invented. Stories and poems had existed for eons, of course — but they were anonymous or semi-anonymous. Suddenly, we get individual philosophers and poets who made a name for themselves through outrageous utterances.

You could achieve personal glory through your ability to compose a poem, to wax philosophic, and — suddenly — to prove a surprising mathematical truth.

Imaginary Interlocutor: This history is fun and all, but what does this have to do with middle school?

Because the origin of math tells us a lot about what we struggle with now. Why don’t we regularly see genius in contemporary math classrooms? Maybe because we’ve re-created Sumerian classrooms:

An educational traditionalist might tell you we need to double down on this. (This seems short-sighted.) A progressivist might say we need to liberate kids from this and restore humanity’s native love of numbers. (This seems blind to humanity’s long indifference toward math.)

An Egan-head, however, might ask how humanity became obsessed with mathematics in the first place. That runs through (1) riddles & puzzles, into which (2) a quest for glory is injected.

We began the first in elementary school. And middle school seems a good time to start doing the second.

I.I.: Could a “quest for glory” backfire?

Indeed — we’re playing with psychological fire here. I’ll address that at the end of this post.

So what does glory look like in middle school math? Four things: mysterious messages, complex games, joke-telling contests, and impossible puzzles.

🧵PUZZLES, Practice A: Mysterious Messages°

In elementary school, we delivered kids Mysterious Messages° in a rather simple way — “oh look, here’s a sealed envelope”. Now in middle school this continues, but the mystery merges with history.

In short, continue giving encoded messages, and helping kids solve them. Obviously, keep making the ciphers more elaborate, but also start finding ways to power them with a lust for glory.

I.I.: How elaborate are you thinking?

In elementary school, we want to start with super-simple ciphers like Caesar shift…

and Atbash…

You can combine these in various ways, of course. But these ciphers are weak: as soon as you figure out one or two letters, you’ve broken the whole code. So in middle school, we can move to straight-up monoalphabetic substitution…

This is much harder to solve. You can’t brute-force it (at least not without a computer, or a lot of willpower). The way to solve it is to analyze letter frequencies: if the letter “Q” comes up a lot, see if it makes sense for it to be an “E” or a “T” or an “A”.

I.I.: And how can you fuel this with a lust for glory?

A few routes. (And a clever Cipher Master — someone we’ll need to find to help us develop this curriculum! — could come up with more.)

First, we can tell the stories of the 🦹‍♂️HEROES of cryptography. Among them:

• Alan Turing, whose brilliance may have shortened the life of Nazi Germany by years (and who was rewarded by his government with chemical castration)

• Thomas Phelippes, whose cleverness decrypting the letters of Mary, Queen of Scots led to Mary’s beheading

• Elizebeth Smith Friedman, who dismantled networks of rum-runners in Prohibition and exposed Nazi spy rings in South America

We can also hold 🦹‍♂️CONTESTS to see which teens can crack a new code the fastest. And we can invite them to encipher a message that no one can crack! Emulating the famous Kryptos monument outside the CIA, these teenage works can be hung up on the wall as a challenge to anyone who comes inside.

🧵PUZZLES, Practice B: Board Games°

Last week, I wrote about how board games in elementary school can power analytical thinking. And now, as with Mysterious Messages°, as these continue, they should get more complex, and be charged with more glory.

I.I.: In what ways should the games get more complex?

Obviously, we should add on more complicated games. If elementary schoolers played Checkers and Carcassonne, middle schoolers can move to Hive and Settlers of Catan.

But we can also increase the complexity by playing old games in new ways. What would happen if you changed one rule of Connect Four, and let players remove one of their discs at the bottom of a column instead of adding a new one to the top?

When playing an old game, you can institute a meta-rule: whoever wins must invent a new rule for the game and write it down inside the game box. Try the rule out — how does it change the way the whole game works?

I.I.: And glory?

Learn about the greatest players of the games you love. The 🦹‍♂️LORE of chess masters is so famous that even those of us who don’t play recognize some grandmasters, but did you know that there’s a GOAT of Checkers and a GOAT of Scrabble?

Getting good at a game, too, feels cooler when you understand some of the history of where the game comes from — it helps you imaginatively enter into the tradition. So look up some of the 🦹‍♂️HUMANIZING KNOWLEDGE of the games that you’re playing.

🧵PUZZLES, Practice C: Jokes°

In our elementary school puzzles post, I argued that we should hone analytical reasoning through helping kids learn and create jokes — especially ones that play with words.

These should continue, and we should increasingly move into jokes that engage satire.

I.I.: Why satire?

Alessandro suggests that different modes of comedy develop from different ways of understanding:

SOMATIC (🤸‍♀️): slapstick
MYTHIC (🧙‍♂️): basic wordplay
ROMANTIC (🦹‍♂️): satire (plus refined wordplay — puns)
PHILOSOPHIC (👩‍🔬) / IRONIC (😏): paradoxes & irony

To satirize, you have to understand the complexities of how humans interact with each other.

I.I.: How can we do satire with kids?

Satire needs to be about something — so the best place in the curriculum to actually do this is literature and music. After reading a classic story (or listening to a great song), teens can make a parody of it. (For more on this, see an earlier post, Playing Inside Stories°.)

And let’s not kid ourselves about how naturally mocking something comes to most middle schoolers! One way to honor them is to channel this (frequently destructive, consistently irritating) trait into something useful.

Throughout all of this, look for opportunities to hold joke-telling 🦹‍♂️ CONTESTS.

Historically, many cultures have used contests as a way to focus attention on glory-worthy skills. You can imagine contests being made for satire (“write a parody of the Gettysburg Address”) or for wordplay (“this afternoon, we’ll have a 5-minute pun contest on the topic of the isosceles triangles”).

🧵PUZZLES, Practice D: Strange Math°

In elementary school, we introduced a smattering of classic mathematical puzzles — one every week or so. We hooked kids with a 🧙‍♂️SIMPLE STORY to pull them into 🧙‍♂️PLAYING with the things… and then put them away!

Now, we bring those puzzles back out again, one at a time, and use 🦹‍♂️COMPLEX STORIES to root them in the actual history of the world, and then push kids to exploring 🦹‍♂️LIMITS and 🦹‍♂️EXTREMES.

Let’s take the Tower of Hanoi as our example again.

Phase 1: 💥 Orient

Before, we introduced the Tower with the simple fantasy first told by the puzzle’s creator, the French mathematician Édouard Lucas. Now, we can tell his story:

Phase 2: ⚠️ Complicate

Teens have tackled the Tower of Hanoi years before, and you may want to start by just letting them play with it. But soon, challenge them —

• how quickly can you, personally, physically, solve the puzzle?

• how few moves can you solve it in?

• what if you vary the number of discs?

Phase 3: 🐛 Transform

Here, you might just want to set them loose on Lucas’s original problem — how long would it take you to move all 64 discs from one pole to another?

I.I.: How would they solve that?

If you’d like, you can give them a hint — is there a pattern to how many moves it would take to solve the puzzle for different numbers of discs?

• 1 disc → 1 move (duh)

• 2 discs → 3 moves

• 3 discs → 7 moves

• 4 discs → 15 moves (see above)

What’s the pattern? With every new disc, you double the number of moves, plus one. If the teens know exponents, you can give them this as a hint:

Using that insight, how long would it take you to solve Lucas’s original problem, with 64 discs? How long would it take you to solve the 32-disc version in the photograph above?4

The usual thing we do with the 🐛Transform step is to make something — here, teens could write/draw an explanation of how they got to the answer.

Well, if they got the answer. This stuff is hard! And remember that the purpose of these 🧵PUZZLES is to sit outside the mainstream math curriculum and be delight-inducing add-ins.

Phase 4: 🪢 Integrate

Afterwards, prompt teens to reflect on what they learned, and what they’re wondering about now. (This is true whether they’ve solved the problem or not.)

I.I.: I asked this last week, but I’ll ask it again: where would I get a collection of puzzles like this?

We’ll eventually want a Puzzle Master who can make a collection of these. If you have a recommendation for one, feel free to put it in the comments… but know that we’ll be revisiting these in high school, where these same problems will take on a new purpose.

In the meantime, I’ll again recommend Dylan Kane’s wonderful post on his choice of such puzzles, which he dubs “glimpses” (as in, “glimpses into the wonderful math that didn’t happen to fall into the K–12 scope and sequence”). And Dylan, thanks for your help in thinking through this practice!

But is this bad?

I.I.: I believe you that this sort of “quest for glory” was how an obsessive love for mathematics was originally sparked. But I worry — is it necessary now? Couldn’t this sort of egoistic love of the self have downsides? Is math worth making our kids into a**holes?

I have two answers, neither of which is complete.

First, insofar as the story I told at the top is true, I think that we’d be fools to ignore this possible source of math love. That said, yeah, we should go in with our eyes open.

Second, I wonder if there are different ways to channel this. In her book The Mattering Instinct, the philosopher and novelist Rebecca Newberger Goldstein argues that people can be grouped by the four “mattering projects” we put at the centers of our lives:

1. competitors (who seek to beat others)

2. heroic strivers (who seek to achieve something great)

3. transcenders (who seek to connect with something larger than themselves)

4. socializers (who seek to connect with other people)

Greek mathematics was born by embracing #1 and #2. The third — transcendence — is touched upon by the “sense of magic” that we’re building all our math on, starting in elementary school, and will get even more attention in high school.

So I’m actually feeling okay about how our approach treats most people. It’s the fourth category — the quest for socialization — that I’m not sure how to address in the math curriculum. Maybe a little of this is done by Making Friends with Numbers° and Number Extremes°? Perhaps more of this could be done through communal struggle — so that figuring out math is a way to help the people on your team?

I’d love your thoughts in the comments.

Next up: A quixotic goal

Again, we suspect that there might be one more remarkable thing to chase in middle school math: Fermi estimates and Bayesian reasoning. Look for it in our next post.

And inspiration for this post came from Dan & Katherine Cook at Math for Love, who introduced me to the Julia Robinson Math Festivals. All I can say is, if someone ever asks you to spend three hours in a gymnasium pushing artfully weird math puzzles at middle schoolers, say yes.

© 2026 losttools.org. CC BY 4.0

Since this was written in 1623, the life of the mind hasn’t been the same.

Before Galileo, there were two streams of mathematics. The first saw numbers as mystical objects with hidden meanings — the “magic” of numbers that we wrote of last week. The second saw numbers as a means to the end of measuring stuff. Galileo fused these streams. He realized that math can subdue reality not because (per the Greeks) whole numbers were special, but because the universe is spun not out of words or stories but out of ratios.

We want middle schoolers to feel this shift. While in elementary school we helped kids fall in love with numbers for their own sake, now we want to invite them into the project of using numbers to wrestle the blooming, buzzing confusion of the world into neat models that let us understand it.

Imaginary Interlocutor: This sounds… romantic, and not entirely practical.

It’s a high goal, to be sure. To meet it, we need to plug into the energies unleashed by ROMANTIC (🦹‍♂️) understanding as kids grow up. Hank Green — who understands more-or-less everything! — understands adolescence, too:

There’s something in all of us, something that blooms in adolescence and never leaves… and it’s just… want. And the most amazing tool that anyone in the world can have is the ability to control and direct that want.

– A Beautifully Foolish Endeavor

This “want” can take many forms — fame, excellence, a longing to matter. Any attempt to rehumanize education has to provide ways to channel this.

Just as in elementary school, our middle school math curriculum will follow three threads:

1. 🧵 LESSONS, where we push against our own limits,

2. 🧵 PUZZLES, where we complicate the extra-curricular math we saw before and discover a hidden simplicity, and

3. 🧵 QUIXOTIC GOALS, where we use all of this to do something crazy: Fermi estimates and Bayesian reasoning.

Middle school math thread 1: 🧵DAILY LESSONS

In which we get to feel our boundaries, and poke through them

🧵LESSONS, Practice A: Daily Ladders°

As in elementary school, so in middle school we’ll ground ourselves in a pre-existing math curriculum. I introduced JUMP Math last week; it’ll continue apace.

🧵LESSONS, Practice B: Boss Problems°

These, too, continue more or less the same, though of course with higher levels of math. If anything, you can make these bigger and brasher to fit the mood of self-overcoming. (See our explanation of Boss Problems° in elementary school for more.)

🧵LESSONS, Practice C: Number Extremes°

Here, we’ve got some bigger changes. In elementary school, we spent some time Making Friends with Numbers°. In middle school, we keep this going — but our numbers increasingly get wilder.

It turns out that the world is big. To describe it with numbers, we’re gonna need some very big numbers. At first glance, this is no problem at all — numbers increase endlessly. But practically, we have no innate ways to differentiate big numbers from one another. To most adults, “a quadrillion” and “a quintillion” sound more-or-less the same, even though one is a thousand times bigger. (And you’ll remember if I say “sexillion” only because it makes you snicker.)

The difficulty of understanding big numbers has famously led to some very bad decisions:

One immediate goal is to create a vivid mental image for the “illions” — when you think of a million, you could think of (to pick just one thing that I learned watching Reading Rainbow) the number of goldfish bowls it would take to hold a whale. A cube of a billion Go Pro’s would crush a Target store.

I.I.: Oh yeah, I think one of my teachers did this with our class, once.

Indeed, picturing large numbers isn’t unknown in school. (Here’s a particularly excellent example.) What’s missing, we think, is treating it as an essential part of the curriculum. Time should be devoted to coming up with a 🧙‍♂️VIVID MENTAL IMAGE of each “illion”, and then they should be remembered and used throughout the rest of math, and the other subjects, too.

I.I.: What about big numbers that are less than, like, a million?

It’d be nice to have mental images for other “big” numbers —

• hundreds (100, 200, 300…)

• thousands (1,000;1 2,000; 3,000…)

• ten thousands (10,000; 20,000; 30,000…)

• hundred thousands (you get the idea)

If you’d like to help out, throw some in the comments below! My recommendation is just that these all be (1) countable objects rather than measurements, and (2) vividly memorable.

I.I.: What about numbers that are much higher than the “illions”? Are those really necessary?

Practical usefulness is only one goal in learning these numbers: the other part is the sheer mind-boggle that comes from contemplating such 🦹‍♂️EXTREMES in quantity.

How big is a googol, really? How can we feel it? How about a googolplex? And did you know that there are named, meaningful numbers that make a googol look like taking a whizz in the ocean?2

I.I.: Hasn’t this already been covered in your post Masters of Measurementº?

Masters of Measurement° works with units — meters, kilometers, megameters, gigaliters, and so forth. This practice is just about countable numbers, which is a prerequisite for understanding those. (You can’t really understand what a “teraliter” is without feeling how big a “trillion” is.) Look for both of these to become part of the first of middle school’s 🧵QUIXOTIC GOALS, Fermi Estimates.

I.I.: How can I do this, now?

Simply extend the notebook (or cards) you made to Make Friends with Numbers° in elementary school to include these extreme numbers.

🧵LESSONS, Practice D: Origin Stories of Math°

In elementary school, we made sure to tell the 🧙‍♂️SIMPLE STORIES behind the symbols of math. A challenge was that many of the details have been lost. (Am I the only one who’s bothered by the fact that we don’t really know where the ÷ symbol comes from?)

In middle school, of course, the math that students learn becomes more complex — functions, rates, rational numbers, and so forth. The silver lining here is that these tend to have been developed more recently, often by specific people whose stories we know.

Historically, these people are often odd. The Pythagoreans worshipped integers, refused to eat beans, and murdered one of their members when he discovered irrational numbers. René Descartes believed he discovered the seat of the soul, did most of his work in bed, and invented his “Cartesian coordinate system” while watching a fly wander the ceiling. The decimal number system was introduced to Europe by a pope who built a hydraulic organ along with — according to rumor — a mechanical head which would answer any question he asked it.3

Again, these people are odd. Our job, pedagogically, is to make them into 🦹‍♂️HEROES who wrested fire from the gods.

I.I.: But how true should we make these stories? (I note that the thing about Pythagoreans murdering the guy who discovered irrationals is a legend told centuries afterwards.)

In general, of course, we should strive to be truthful. In our history classes, that’s especially important. But we can’t forget that one of the reasons for these origin stories is to induct kids into the 🦹‍♂️LORE of math. A safe compromise would be to be quick to include the mythical stories, but to name them as such. (The book The Cult of Pythagoras: Math and Myths is, sigh, a particularly solid debunker of some of my favorite stories.)

I.I.: Can we really spend the time in math to tell stories?

I have two answers to this; one is happy, the other is angry. First, the happy answer: because we’ve made a memory palace in elementary school history, we’re able to tell a memorable math story in just a few sentences. That is, we’ve already helped kids understand what life was like at many different locations & times; now, all it takes to set a math story in ancient Greece is to say, “the Pythagoreans lived in ancient Greece”.

Now, the other answer. I don’t know how to say this clearly enough:

With apologies to Steve Jobs, learning can be so much broader once we discover one simple fact: that everything we call “math” was made up by people who were no smarter than us. Well, okay, a good number of them were geniuses — but none of the formulas or algorithms that students struggle to learn was obvious to the person who first figured it out. It was an achievement. It felt like stealing fire from the gods. To master it while knowing its origin is to teleport through time back into their skin, and to become a hero, if only for a moment.

This is part of what we mean when we talk about “re-humanizing math”.

🧵LESSONS, Practice E: The Deep Practice Book°

In elementary school, we introduced the practice The Return of the Bosses° — on Fridays, pull out the Boss Problems° that bedeviled you, and take another pass at them. This was mostly intended to solve the problem of memory by bringing some light spaced repetition into the math curriculum.

In middle school, we’re going to deepen this with a “Deep Practice Book” (hereafter “DPB”). I wrote quite a lot about this in one of my favorite posts:

In a nutshell, it’s a notebook built on deliberate practice.

I.I.: Wait, in that post, didn’t you say that a DPB was “doomed to fall into a pit and crash and burn when it enters the classroom”?

Yes, because it’s built on deliberate practice. Deliberate practice sucks. It’s hard and boring and painful. It demands repetition and attention, the willingness to veer into error and correct it again and again with the stubbornness of a saint. It’s singularly unglamorous. Everyone hates it. Throughout the history of education, every single attempt to force deliberate attention on an unwilling subject has backfired.

I.I.: Why are we talking about this, then?

Because it is the one best way to grow skill. But in order for it to work, you need to want to grow skill.

I.I.: And how are we cultivating a “want” for math?

In short, everything I wrote in the last three posts, on elementary school math. But we can summarize those in two pieces:

1. practices that help you fall in love with the math itself, and

2. practices that help you develop a taste for getting stumped by hard problems.

In adolescence, all this can be multiplied by the joy of 🦹‍♂️SELF-OVERCOMING… something that teenagers often have in spades. (This is why we didn’t introduce DPBs in elementary school — and for many students, the DPB should be held back until high school.)

Here’s a reminder of what it can look like:

If you’re interested, go ahead and re-read that essay. To capitalize on 🦹‍♂️SELF-OVERCOMING in the middle-school years, you might want to focus on the “How’d it go?” section on the front page, in which students record how difficult the problem was for them:

• I = impossible

• H = hard

• M = medium

• E = easy

• A = automatic

All in all, a DPB can become a mathematical dojo — a place to go, be knocked onto your back, and get up stronger (and hopefully wiser).

Next up: Puzzles in middle school math

Hopefully, you’re getting a glimpse of the personal transformations that we’re trying to make happen through math. I wrote last week about how the “magic” of math can only really be brought out when we take math seriously — and help kids take it seriously, too. People pushed back on that! Alessandro and I will be recording a conversation soon with the redoubtable Michelle Scharfe, creator of Minimalist Math (and of researchparent.com) who thinks all my talk about “seriousness” is me trying to look edgy and cool towards traditionalists. Maybe she’s right!

In any case, I think that in middle school, the payoff of “seriousness” is greater. There’s a desire in teens to transcend boundaries and embody 🦹‍♂️HEROISM. But as any Marvel character can tell you, being a hero sucks.

Do you want to be a hero?

Look forward to seeing how this can be done with less pain and more joy in our next thread: 🧵PUZZLES.

© 2026 losttools.org. CC BY 4.0

I’m teaching two week-long online camps this summer designed, in rather different ways, to fix that. They train the instinct for truth, and make the truth feel real.

This Sunday I’ll be doing an open house to help parents know if this is for their kids; you can sign up below.

Believe it (or Not): UFOs

Monday June 1 – Thursday June 4, 2026
Morning & afternoon sessions open
See the webpage

What’s it about?

On the surface, UFOs. What’s going on with those weird objects Navy pilots keep seeing? But beneath that, it’s about how to know what’s true. What does good evidence for aliens actually look like?

This is the third in our series of “Believe it (or Not)” summer courses, which train kids in the subtle art of Bayesian reasoning. (I wrote a bit about this on Astral Codex Ten last year; this year’s class will go much further.) If you sign up, you’ll get the recordings from last year’s topic (Sea Monsters) for free.

A Dinosaur a Day

Monday June 15 – Thursday June 18, 2026
Morning & afternoon sessions open
See the webpage

What’s it about?

To say that I was “dinosaur obsessed” as a kid probably undersells it. Dinosaurs were my window into the adult world, and especially the world of science…

…and dang it, they really are a great window. While, as a science teacher, I bring a little bit of dinosaurs into everything that I do, up to now I’ve avoided teaching a “dinosaur” class, because where would you even start?

I think I’ve figured it out. Our goal, here, will be to (1) look at some of the most thrilling recent discoveries in paleontology, and (2) try to imaginatively bring them back to life. Expect all of the Egan tools that we talk about on this blog to make an appearance.

The open house

These classes aren’t what they seem on the surface, but I think I can more clearly give a taste in the our open house. If you’ve got a kid (ages 8–15 is our sweet spot) who you think this might be good for, feel free to attend our Zoom webinar open house this weekend:

3pm Eastern / 12 noon Pacific
Sunday, April 12

Sign up for the open house

Sign up for a course

By the end of elementary school, every kid should be able to perform feats of mental arithmetic that others might call “freaky”.

This is our last post on elementary math. If we play our cards right, the two threads before — 🧵DAILY LESSONS and 🧵PUZZLES — should help kids cultivate both (1) a proficiency at math and (2) an affection for it.

Having put all this together, Alessandro and I thought: maybe that's enough! But then we asked ourselves: what if we wanted to go deeper? What could we do with this appreciation for the magic of numbers that our students will have? We concluded that we wanted kids to have them bring the power of numbers inside themselves.

To do this, we propose having a third thread of math: 🧵QUIXOTIC GOALS. In elementary school, this means fantastic feats of mental math.

Hold onto your butts; this is about to get strange. And we admit that while we’re in love with it, it might not be right for every kid. As you read this, ask yourself whether it seems approachable for your son or daughter (or, if you’re a teacher, your students), and register your hot take in the comments.

We could push this back to middle school… though that would mean that middle school’s 🧵QUIXOTIC GOAL of Fermi estimates and Bayesian fights would be pushed back to high school, and high school’s 🧵QUIXOTIC GOAL of Philosophy of math would disappear in a puff of smoke. So there’s a trade-off there, too.

Let’s dive into this one.

To state this clearly, by the end of fourth grade, our goal is to have helped our students calculate impressive sums, differences, products, and quotients without a calculator or pencil.

I.I.: This feels — what’s the word? — “stupid”. No, “abhorrent”. No, “evil”! (Help me out here, I’m no good with words.)

If this is forced on students, yes, all three of those are true. Our goal is to create the conditions so that (1) building these skills is straightforward, and (2) the kids want to do it (or at least don’t fight against it).

The trick to cultivate desire is to tap into kids’ sense of 🦹‍♂️THE HEROIC, and to show them what the human mind can do.

I.I.: I see by that emoji that “the heroic” comes from ROMANTIC (🦹‍♂️) understanding. Usually you associate that with middle school. Isn’t elementary a bit early for this?

Possibly — and if this isn’t right for your kid or class, then by all means hold this back until middle school. But we suspect there’s enough of a desire for heroism in little kids that we can start building this now. (And for what it’s worth, Egan was keen to emphasize that we don’t suddenly switch from one way of understanding to another as we grow, and that the seeds of each are with us at every age.)

I.I.: If I want to do this, how can I tap into this hunger for the heroic?

Show your kids that the human mind is amazing, and that with the proper practice individuals can achieve amazing things. Introduce them to quick videos of young kids performing freaky feats of mental math. Tell them that to learn this they don’t have to be naturally gifted at math, but that learning it will make them something akin to being gifted.

🧵MENTAL MATH, Practice A: Counting Rhymes°

We’ll start utterly simple. As stated above, our native 🧙‍♂️NUMBER SENSE sucks at numbers above three or four. But of course we want kids to learn to count! While they’re still young, we can teach kids various 🧙‍♂️RHYMES to lock patterns into their memories.

But this goes further than “one, two, buckle my shoe” — we can also use this for skip-counting to prepare the way for mental multiplication.

For more on this, see my earlier post Counting Rhymes°.

🧵MENTAL MATH, Practice B: 9-bead Abacus°

A basic abacus is an OG computer, but people mostly use them as rather chintzy home decor. If you remove just one bead from any 10-bead abacus, you make obvious its true power: each row is a “place” in the base-10 numbering system, and every configuration of an abacus literally displays a number.

To be fair, it’s actually pretty hard to remove the beads on a store-bought abacus; easier is to paint the left-most bead black and use it to “carry”. For more on this, see my earlier post Basic Abacus°.

🧵MENTAL MATH, Practice C: Finger Math°

Your fingers are mightier than they seem. If you know how to use them, they can give the answers to impressive calculations, and there are hints that using them is cognitively privileged — that it recruits extra parts of the brain.

We’ll teach this to prepare the way for the next type of abacus, which follows the patterns of finger math suspiciously closely. For more, see Finger Math°.

🧵MENTAL MATH, Practice D: 5-bead Abacus°

This is a finger calculator, but better — a tool for people who want to do arithmetic quickly and accurately and actually understand what’s happening. It’s the penultimate step before being able to do truly fantastic feats of mental math —

(Watch the fingers of the first kid fly.) For more on this, see Bead Computers°.

🧵MENTAL MATH, Practice E: The Grammar of Numbers°

Throughout, unveil the patterns that keep popping up when we do arithmetic. As always, start with the simple classics:

When you multiply by 10, the answer is always the original number with a “0” on the end:

• 4 × 10 = 40

• 5 × 10 = 50

When you multiply a one-digit number by 11, the answer is always the original number written twice:

• 4 × 11 = 44

• 7 × 11 = 77

I.I.: But this isn’t new. Everyone learns these.

Exactly! The dominant curriculum introduces these bits of mental math — and then drops them. All we’re suggesting is that we keep going. So make it slightly more complex by going to two-digit numbers:

When you multiply a two-digit number by 11, the answer will always have three digits. The first and last will stay the same; in the middle will be a new number… which will be their sum!

• 42 × 11 = 462 (6 is the sum of 4 and 2)

• 27 × 11 = 297 (9 is the sum of 2 and 7)

Whenever those two digits sum to 10 or more, the pattern continues — but you carry the “1”:

• 49 × 11 = 539 (13 is the sum of 4 and 9)

• 28 × 11 = 308 (10 is the sum of 2 and 8)

From there, it’s not too hard to move to numbers that are many digits long:

When you multiply a super-long number by 11, the answer will always have one more digit than before. The first and last will stay the same, but each number in the middle will be the sum of the pairs of adjacent digits:

• 1,234 × 11 = 13,574 (3 is the sum of 1 and 2…)

• 1,002,005,009 × 11 = 11,022,055,099 (1 is the sum of 1 and 0…)

I.I.: But where would you get the basic building blocks of the curriculum?

Like I wrote before,

a well-made math curriculum is a complex machine, and people have invested their lives into making good ones. Rather than trying to invent our own, we’ll build on someone else’s.

That’s true here, too. Thankfully, the world abounds in mental math curriculums. If you’ve gone through one that you’d like to recommend (or to caution us away from) — or if you’d like to explore the options for us — let us know in the comments. (For the moment, I’ll assume Arthur Benjamin’s Secrets of Mental Math.)

Once that’s chosen, we can Eganize the heck out of it, starting with the concept ladders and boss problems we use in the 🧵DAILY LESSONS.

And then, perhaps, we can go further. More than anything else we teach in elementary school, this has the potential to really seem like arcane magic. So lean into that: treat these tricks as ancient 🧙‍♂️MYSTERIES. By 🧙‍♂️FINDING PATTERNS, kids can unveil them, and add their power to themselves. (In truth, this can be done in all the practices in this thread.)

Why mental math?

This deserves to be answered squarely. Imaginary Interlocutor, take it away!

I.I.: Who cares about this? Why is this worth anything? Haven’t you heard of calculators? This is old school to the point of parody; even mathematicians don’t learn to do mental math anymore. You’re letting your cottagecore aesthetics push out your common sense.

Four reasons, perhaps.

1. It makes all math easier

Arithmetic is, practically speaking, part of all the math we do in school; any middle schooler who still struggles with

will bang their head against the table when they see

The easier that we can make addition, subtraction, multiplication, and division, the more we can free students from pain.

2. It makes everyday math possible

If arithmetic is automatic for you, you’ll actually use it in everyday life. If it’s not, you won’t.

I.I.: “Everyday math” is a lie concocted by textbook companies to sell curriculum. No one actually uses math in real life.

If by “everyday math” you mean contrived word problems, you might be right:

But elementary school math pops up constantly — adjusting a recipe, comparing prices, estimating times, and so forth. And when arithmetic is really easy, then all sorts of opportunities open up.

I.I.: But surely not enough opportunities to justify all this work.

Ordinarily, you might be right. But see if you still think so after you read the 🧵QUIXOTIC GOAL for middle school — Fermi estimates.

3. It turns elementary math into real intellectual food

It’s easy, I think, for a certain type of “math person” to look down their nose at arithmetic as “mere calculation”. Best (they think) to master it quickly and move on to the good stuff.

But arithmetic, understood properly, is as heady as anything in math.

To understand why, for example, the “11 trick” above works, you need to build a mental model of how numbers split and recombine across place values. That means that you need to have a deep appreciation for how our base 10 system works, which means that you need to understand how any base system can work.1

4. It makes you a wizard

Deep in our hearts, all of us want to be accosted by an 8-foot tall bearded man who proclaims, Yer a wizard, Harry!2 Like I said before, mental math is one of most direct routes into wizardry for young kids.

When we first learn to add, it’s effortful, and we get frustrated by screwing up. In normal schools, we move past that, and can (with some focus, and perhaps a pencil) get the answers right without too much suffering. We enter, that is, into tool-aided fluency.

But few people take the next logical step, and progress to automaticity.

And automaticity can feel amazing. There’s an ecstasy to it that’s difficult to put into words, but I’ll try it: you stop being a thing that’s doing math, and become the place where the math is happening. You feel that there’s great power swirling inside you, and finally you have a way to focus it.

And this, in the end, is why we think that every kid should have the opportunity to learn mental math. Alessandro and I get that this sounds strange. But what’s truly strange to us is that we do 90% of the work to learn math… and then stop before the last 10%, where it would become something truly powerful.

Next up: Middle school

We’d love to get your radically honest thoughts below; we’ll try to answer everything. In any case, we’ve now laid out what we’re going to do with math in elementary school, and are ready to turn to middle school.

Oh, that reminds me of a question — I’ve been trying an experiment of publishing each thread separately. How do you like it?

© 2026 losttools.org. CC BY 4.0

As promised, Alessandro and I got together to discuss Rebecca Newberger Goldstein’s new book The Mattering Instinct: How Our Deepest Longing Drives us and Divides Us. It’s good! And, we think, it has huge ramifications for how we think about education.

We talk about how the book’s ideas can help us understand where progressivist & traditionalist education go wrong, and how we can explain Egan education as a bridge between them. Along the way, we find that the book also elucidates how competition (done in a particular way) can make schools better, and how Hogwarts should have really structured its houses.

Maybe we’ll make this viewable to everyone at some point! For the time being, if you’d like to see it, just become a paid subscriber. (And throw any questions into the comments!)

00:00 Introduction to the Mattering Instinct
01:36 The Role of Education in Finding Meaning
06:39 Connecting Mattering with Egan's Educational Philosophy
11:58 Teaching Strategies for Mattering in Education
18:58 The Dialectic of Progressivism and Traditionalism
25:46 Re-enchanting the Curriculum
30:34 The Importance of Wonder in Education
36:32 Tools for Engaging Students in Learning
47:51 Emotional Engagement and the Quest to Matter
50:32 The Essence of Mattering
56:11 Exploring Mattering Projects
01:01:47 The Role of Competition in Education
01:10:01 Noble Competition and Its Educational Value
01:19:55 The Complexity of Mattering in Education

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In our last blueprint post, I laid out how we’re planning to rehumanize the boring part of the elementary school math curriculum: daily lessons. Today, I want to limn out the obviously exciting part that we’re putting in: puzzles.

Elementary math thread 2: 🧵PUZZLES

It’s one of those niggling facts of history that the brilliant minds who created the discipline of math… had no standardized math curriculum to learn it from themselves.

It’s not that these people (and I’m talking about the Greeks1) were somehow more brilliant than their neighbors — the centuries before and after their Golden Age show they were average. As the historian of math Reviel Netz points out, they were lucky enough to live at a cultural moment where a few ingredients came together. One of those was that they were the heirs of the mathematics of the Babylonians:

The Babylonians were masters of numbers…. the training of Mesopotamian bureaucrats was always geared toward the needs of the state.

But what the state needs, above all, is legitimacy, meaning, symbolism. What ancient masters of knowledge were doing, above all, was looking for signs…. The world was a web of signs, point to each other and ultimately shining light… on the big questions of the state: the rivers, the kings, the outcome of war.

– Reviel Netz, Why the Ancient Greeks Matter: The Problematic Miracle that was Greece

The Babylonians taught by puzzles that would look familiar to anyone who’s taken algebra: “the area of a square and the length of its side, taken together, equals three-fourths: what is the length of the side?”. What changed, though, is the context in which the Greeks heard the puzzles. While, for the Babylonians, they had been sets of problems encountered in classrooms for nose-grinding scribes-in-training…

…for Greeks, these were presented as “nice puzzles”:

The school exercises were, among other things, nice puzzles. Maybe we need to imagine caravans with merchants from different lands, camped for the night, sharing tales and riddles. They did not know it but those mathematical riddles could well have been their most precious cargo. From such small events, knowledge gets transferred.

By encountering these problems as tasty treats in themselves, some Greeks began to savor mathematics.

This isn’t the only ingredient in the Greek invention of systematic mathematics. (We’ll explore another ingredient in our post on middle school math.) But it is an important one — so 🧵PUZZLES will be a second thread in our math curriculum, one that will extend the magic of math outside the mainstream curriculum.

🧵PUZZLES, Practice A: Mysterious Messages°

There’s something satisfying about cracking a code. Enciphered messages will appear in our classrooms, and we’ll drop hints as to how kids might be able to unravel the 🧙‍♂️MYSTERIES.

They’ll start simply (e.g. A = 1, B = 2…) and very, very slowly become harder. Eventually, they’ll lead kids into thinking about their native language (e.g. English) from a mathematical perspective — what letters are most common? Which two-and-three-letter combinations are most common?

For more on this, see my previous post Mysterious Messages°.

🧵PUZZLES, Practice B: Board Games°

Turn-based 🧙‍♂️GAMES are already ripe with analytical thinking. And while there are some overtly mathematical games that are actually enjoyable to play — Prime Climb is probably everyone’s favorite here — in truth, any game that features strategy is inherently math in disguise.

Think Connect Four or Carcassonne. Think Hive or Risk. Heck, think Tic Tac Toe — they all reward seeing (and exploiting) patterns. In middle school, we’ll talk about how to make them more deeply mathematical while also making them more fun. But for that to work, the kids first need to enjoy the games, so we’ll start this early.

🧵PUZZLES, Practice C: Jokes°

A 🧙‍♂️JOKE is perhaps the most immediately-rewarding type of reasoning. Each is a tiny house of screwy logic;2 “getting” the punchline requires making a new sense of how the pieces fit together.

I.I.: It feels faintly ridiculous to put this into the “math” curriculum, though.

Which means there’s a lot of low-hanging fruit here! We want to have kids read jokes, practice telling them, and even make their own. In elementary school, our focus will be on wordplay — puns, knock-knock jokes, lightbulb jokes, and so on.

I.I.: I’m not sure I could take a whole classroom of joke-spouting children.

Indeed, it’s hard to be a teacher. But the payoff is worth it; as Egan writes:

Stimulating each child to become a jokester is fundamental to the later development of logical thinking.

– Kieran Egan, Primary Understanding

And we want kids who are logical — and who know how to bend logic. For more on this, check out my earlier post, Telling Jokes°.

🧵PUZZLES, Practice D: Strange Math°

There are so many branches of mathematics that never darken the doorway of an elementary school. Some barely enter into K–12 education at all — think topology, game theory, and so on. Each branch of math has its classic riddles, stories, and games.

Among math geeks many of these are famous, and you probably already know of some of them already — the Tower of Hanoi, the grains of rice on a chessboard, Zeno’s paradoxes, a young Carl Friedrich Gauss adding all the numbers from 1 to 100 in his head, and so on. These survive because they’re fun!

Our goal is to collect perhaps a hundred of these, and to bring them into the classroom once a week. We’ll be engaging them in a manner inspired by the people who champion “Thinking Classrooms”, and then perhaps find ways to turn up the drama by triggering 🧙‍♂️EMOTIONAL BINARIES and ramping up the 🧙‍♂️FANTASY.

And a good way to do that, of course, is to narrativize the puzzle. Let’s take the Tower of Hanoi as an example.

Phase 1: 💥 Orient

Our first step, as always, is to help kids feel something. The Tower of Hanoi started as a silly story told by a 19th century mathematician. We can modify his version a little as we tell it:

In a land far, far away, there is a tower. On the top of this tower are three diamond needles. And on the first needle, when the world was young, priests stacked 64 disks of pure gold, each one slightly smaller than the one beneath it, forming a perfect cone.

The priests were charged with a sacred duty: move the entire stack of golden disks to the third needle. They only had to follow two rules:

1. they could only move one disk at a time, and

2. they could never place a larger disk on top of a smaller one.

When they complete their duty, the world will come to an end.

How long will that take?

Phase 2: ⚠️ Complicate

Now it’s time for the kids to get hands-on. Give them a little version of the tower (you can make one, or buy one for $10), and challenge them to move any size of stack (four is fine; three or even two is fine to begin) from one needle to the other following the rules. Then, of course, have them add more disks. How many can they manage?

Phase 3: 🐛 Transform

Here, we want them to produce something that shows their understanding of the specific pattern for solving a certain number of disks, or (better) the general pattern for solving any number of disks.

I.I.: And what should they produce?

For this, they could, say, write a letter, teach it to a friend, draw a diagram, or shoot an explainer for YouTube. (Across their education, elementary schoolers should be experimenting with many types of production, so just make sure they’re getting a smattering of everything.)

Phase 4: 🪢 Integrate

As usual, it’s good to “close the book” on this, and prompt the kids to reflect on what they did — what they discovered, what surprised them, what they learned about themselves, whatever. This needn’t take more than a couple minutes.

And then the puzzle can be put away for a few years… until we return to it in middle school.

Imaginary Interlocutor: Where would I get a collection of math problems like this?

Start with this post:

Five Twelve Thirteen

Glimpses

I love learning math. One element of math I love is exploration: figuring out something new and feeling the rush of realization…

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a year ago · 25 likes · 5 comments · Dylan Kane

It’s written by the invariably insightful and preternaturally pleasant Dylan Kane, who was generous in spending a couple hours talking through this practice with me. I suddenly realize that I’ve somehow never formally recommended his Substack. Fixed!

Next up: A quixotic goal

If we do our job well (and the stars are aligned), the four practices above will help most kids fall in love with math. This is, obviously, a ridiculous goal to swing for — but then, why else get out of bed in the morning? In any case, any sensible person would say that, having achieved it, we should move onto other topics. (Geography! Writing! Cooking!)

We, however, suspect that there could be one more remarkable thing to pursue in elementary school math: stupendous feats of mental math. Look for it in our next post.

(Inspiration for this post came from Dan & Katherine Cook at Math for Love, who introduced me to the Julia Robinson Math Festivals. All I can say is, if someone ever asks you to spend three hours in a gymnasium pushing artfully weird math puzzles at middle schoolers, say yes.)

© 2026 losttools.org. CC BY 4.0

Arithmetic — which we make students spend years studying — is an enchanted thing, but to most students, it’s presented as cold. Because of that, most of them grow up not caring about math; they put up with it only because school demands it of them. Immediately upon graduating, most of them put it out of their minds, only fitfully recalling the things that are routinely required for life.

This is a tragedy. It squanders human potential, and shows that we don’t value students’ time or effort. To solve this, educational Traditionalism and Progressivism have each had their own suggestions:

Though if you had to distill what the core of mathematics is, they might say…

We can’t dismiss this fight — important values are at stake; everyone reading this has Opinions. But I want to suggest that while this war rages on, some of the things that matter most are being ignored: the magic of numbers, the power of numbers to wrestle reality into submission, and the possibility that numbers can help us peek into ultimate reality itself.

Imaginary Interlocutor: Slow down; that’s some pretty heady stuff there.

A sign we’re not wasting our time! Each of those will become, in turn, the north star of the three cycles of our curriculum, starting in elementary school (grades 1–4) with “the magic of numbers”.

Through each of those cycles, our math curriculum will follow three threads:

1. 🧵 LESSONS, where we build a wee bit of magic into the foundation of math,

2. 🧵 PUZZLES, where we go wild with that magic in other kinds of math, and

3. 🧵 QUIXOTIC GOALS, where we use all of this to do something crazy (in elementary school: mental math).

Let’s get started. (A note that I’m trying something new today — instead of giving all three of those threads in one post, I’m going to give them one post each. My hope is to make these easier to read. After the third one, I’d love your feedback as to how this is working.)

Elementary math thread 1: 🧵LESSONS

In which we secure math-magic through rather rigorous daily practice.

Parents depend on a school’s elementary math curriculum to keep their kids at (or above) grade level — so anyone wanting to do something new with math needs to first show kids won't fall behind.

The first task of any exciting new math curriculum, then, must be don’t screw this up. Think of this thread as being the serious, risk-averse side of the curriculum.

I.I.: This sounds like the opposite of “enchanted”.

No — “serious” needn’t rule out “magical”. As professional illusionists (and debunkers) know, the real experience of magic comes through diligent work.1

🧵LESSONS, Practice A: Daily Ladders° 

A well-made math curriculum is a complex machine, and people have invested their lives into making good ones. Rather than trying to invent our own, we’ll build on someone else’s.

I.I.: Which curriculum will you build on?

If you’re a homeschooler, whatever works for your kid is great. If you’re a teacher, we can help you utilize whatever curriculum you’re obligated to use.

But as we get to recommend curriculums to new schools, our answer is going to be JUMP Math, which (along with geodes, cats, and the first Jurassic Park movie) is one of the world’s few perfect things.

I.I.: I’ve never heard of that one before! What makes it so good?

It’s built on one singular idea — they call it “guided discovery” or “incremental mastery”; I call it Concept Ladders°. In brief: it teaches big new hard ideas through tiny steps by taking kids through those steps (rather than separating the teaching from the doing).

It’s the brainchild of the playwright-turned-mathematician2 John Mighton, who discovered a method of teaching math that could help more-or-less any student build skill quickly.

Say a student can’t figure out:

0.80 + 0.04 = ?

The temptation for a teacher is explain with words. But in math, words suck! Much better to build on our innate ability of 🤸‍♀️SPOTTING PATTERNS. So instead of explaining, write a simpler question:

0.80 + 0.01 = ?

If that’s too hard, ask a simpler one:

0.8 + 0.1 = ?

If that’s still too hard, then ask a simpler one:

8 + 1 = ?

Let’s call this “stepping down the ladder”. Once you find something related that students can do, start stepping up:

8 + 0.1 = ?

8 + 0.2 = ?

8.0 + 0.2 = ?

The goal in choosing these is to keep the student mental state where the answers come with only a moment of thinking — that magical area between “boredom” and “kicking chairs”. (Educational nerds like to call this “the zone of proximal development”. It’s similar to the experience of “flow”.)

Keep climbing that ladder!

8.1 + 0.1 = ?

0.8 + 0.1 = ?

0.80 + 0.1 = ?

Keeping students in this state is the genius of JUMP’s teacher training program; they’ve built their whole K–8 curriculum around the idea of making this easy.

0.80 + 0.01 = ?

0.80 + 0.02 = ?

0.80 + 0.04 = ?

…and that problem, if you recall, is the original problem the student couldn’t solve.

And this is the magic of daily math ladders — you hit your head against something that seems too complex for you, and then you come back, and realize it’s simple. JUMP makes it easy to make this routine. To make kids care, we need to show that this isn’t merely true for adding decimals, but is also true for fractions, percents, long division, and everything in math. Mighton points out that this, in fact, was proven by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica: all mathematics is decomposable. It’s all one long ladder. There aren’t any gaps.

This is the magic that we want to help kids feel.

I.I.: I’m a bit confused — is JUMP Math part of educational progressivism, or educational traditionalism?

It blends both in the most remarkable way. Unlike old-school traditionalism, it doesn’t spend much time telling kids how to solve problems; instead, it tucks the teaching into the problem-solving itself. And unlike old-school progressivism, it doesn’t give kids much creative room to find their own ways to solve problems; instead, it shepherds them through efficient, powerful methods.

To me, it’s the best of both worlds: it respects kids as agents who need to make sense of things themselves, but doesn’t assume that they have god-like powers to re-invent the corpus of math on their own.

But maybe this isn’t your kid! If JUMP doesn’t float your boat, there are certainly other curriculums that people love. (In our Egan homeschooling group, Beast Academy comes up a lot, as does Minimalist Math and Math Academy.) If your curiosity is piqued by JUMP Math, Zach Groshell’s interview with John Mighton is a great place to start, as are these pieces (1, 2) in The New York Times.

🧵LESSONS, Practice B: Boss Problems°

There’s a problem with doing ladder lessons as a class — kids who already know how to do the problems will be bored. (This is, of course, a problem with teaching anything in a classroom.)

We can solve this elegantly: before teaching each day’s lesson, write down a couple of ludicrously hard problems that kids will be able to do only if they understand the lesson perfectly. Give kids a couple minutes to read the problem, to ask questions about it, and to try it.

Invite any students who get it right to skip right to doing their homework.

For the math lesson above, such a problem might look like this:

I.I.: Is that actually “ludicrously hard”?

For you it may look easy — but it’ll make many a fourth grader’s eyes bug out. Which is precisely what’s important for a good Boss Problem — it should look hard, but not actually require any cleverness beyond what they’ll learn in the lesson.

And this is the magic of Boss Problems: you take the drama that we talked about above and crank it up to 11. You lead them into experiencing defeat; then you help them experience success. Problems that seemed impossible suddenly seem obvious.

JUMP’s genius is that it makes math easy. Boss Problems’ genius is that they make math hard.

Showing these Boss Problems to kids at the start of a lesson has a huge benefit: now the lesson has purpose. They want to beat that sucker, and understanding the lesson is the key to doing it. (Again and again, I’ve seen kids’ eyes go wide in the middle of teaching, and then see them jump up and run to the wall to try out an idea that’s just come to them.)

We can make the lessons matter even more by repeating this on a larger level: write a special set of Boss Problems on colored paper at the start of a new unit (about once a month). These should presage what they might learn — I based them on the problems in the unit’s final test, but then made them look even harder.

If you’d like to learn more about this, take a look at my old post, Boss Questions°.

🧵LESSONS, Practice C: Making Friends with Numbers°

It’s important to recognize how uneasily numbers fit inside our heads. Until recently, most languages didn’t even have names for anything in the double-digits. Our 🤸‍♀️NATIVE NUMBER SENSE is paltry. As Kieran Egan quips:

“Our number system is about as good as that of a blackbird’s, but less good than that of some species of wasps.”

Egan, Primary Understanding: Education in Early Childhood

I.I.: This sounds like the excuse of someone who’s not going to expect much of their students.

No, the opposite: understanding our innate weaknesses is the first step toward overcoming them.

I.I.: And how can we overcome them?

For a hint, we can look to where math came from historically: numerology.

I.I.: I feel my finger reaching for the “unsubscribe” button…

Throughout many cultures, before numbers were technical things to compute with, they held mystical significance. We suspect that this was load-bearing. In China, odd numbers were yang, and even numbers yin. Across the Near East, 7 was a “heavenly” number — seven planets, seven heavens, seven days of the week. The Pythagoreans swore oaths on the number 10.

I.I.: Oh glory. Are you planning to impose some sort of spirituality on kids?

Nothing like that. All you want is to show how each number has meaning outside itself, and to do that all you need to do is collect links that each has to things in the natural and human worlds. For example:

• 1 star in the solar system and eye on a Cyclops

• 2 arms, ears, nostrils, pinky toes, and so forth on most animals

• 3 primary colors

• 4 cardinal directions

• 5 fingers on a hand

• 6 legs on every insect

• 7 planets (classically)

• 8 arms of an octopus, legs of a spider

• 9 Muses

• 10 fingers, toes

• 11 players on a soccer team

• 12 months in a year, signs in the zodiac, tribes in ancient Israel, hours on a clock face

To keep this collection, you may want a special notebook or cards from 1–100 hanging on a wall. At the top, write the number lightly, and in pencil.

Use the paper to write down links. For the single-digit numbers, you can also sketch in a little history of where our numeral came from — easily found on each number’s Wikipedia page:

After you find two or three links for a number, it's time to 🤸‍♀️PERSONIFY it. Ask what the number feels like to you. What color does it seem to want to be? What font feels right to write it in?

When numbers have feelings, people pay attention to them.

🧵LESSONS, Practice D: Origins Stories of Math°

Now that we’ve made an emotional connection with numbers, let’s turn to the other squiggles we face in math: symbols like +, –, ×, ÷, and =, and the written numerals themselves.

Unlike the numbers, these don’t describe things in the natural world — they’re conventions created by some now-dead person (often a very quirky one) who was trying to solve a problem.

Historians have figured out where all these come from. All we need to do is to turn them into 🧙‍♂️SIMPLE STORIES, and slip them into our math lessons.

Let's turn back to that initial problem:

0.87 + 0.04 = ?

Squiggles, squiggles, squiggles.

Why is “plus” written as a tiny cross, and “equals” as two straight lines? What’s up with the decimal point? Heck, what’s up with decimal values — why is the “8” in “0.87” ten times bigger than the “7”?

I.I.: That’s a lot of questions, and I don’t want to bog down a lesson.

Three responses to that. First, this can be solved by teaching these stories early, just as kids are learning each of the concepts. That is, when they’re learning addition, they should hear why we use the “+” symbol.

Second, these don’t take much time to learn: a few sentences suffice:

• “+” is a lazy way to write the word “and” in Latin — “et”

• “3” is just three horizontal lines, swooped together

• “÷” was invented by a Swiss professor in the 1600s and we still don’t know why he chose it… but it’s interesting that it looks a lot like a tiny picture of a fraction

But I can’t say the third part emphatically enough: math is stories, too. To do math isn’t just to arbitrarily manipulate random squiggles: it’s (also) to step into a millennia-long tradition. When we forget this, we alienate students from what we’re asking them to do. (No wonder so many people hate math!) When we remember this, we re-humanize the discipline, and make it easier for normies to fall in love with math.

If you’d like to see more about this, take a look at my earlier post, Origin Stories°.

🧵LESSONS, Practice E: The Return of the Bosses°

So much of math that’s learned gets forgotten. This is especially true of the hardest problems that kids struggle with, which is tragic: having put in the work, they’re what students most deserve to remember!

A simple fix: instead of throwing away the Boss Problems, hold onto them. Put them in a box. Each Friday, as you sip your tea and review your Memory Box, pull out one to see if it still stumps them. If it does, great — you created these to be really hard, and this one is a good fit for the kid! Savor that feeling of confusion, and write down more questions on the front of the paper.

Hard problems can become friends, too.

(In middle school, we’ll go deeper into this with our Deep Practice Books°.)

Next up: Puzzles

If we do our job right, the five practices above will make it easy for students to not hate math, even as they stay at (or above) their grade level. But our bigger task is to help them fall in love with math. That’s what the next thread — 🧵PUZZLES — is for.

Be prepared for things to get strange, and delightful. In the meantime, ask questions below.

© 2026 losttools.org. CC BY 4.0

We’ll have up a special paid-subscribers-only post with our recording, and you’ll be able to comment! We plan to put it up in two weeks — Thursday, April 2. So if you’d like to grab a copy, there’s time.

Imaginary Interlocutor: Is this a book about education?

It proposes to give a new foundation to human flourishing, so… yes.

Its bold claim is that the need to matter isn’t just one feeling among others, it’s a biological imperative that spools out of our evolutionary history. Among the questions that I want to raise with Alessandro:

• is helping people matter the goal of education?

• is the hunger to matter the über-tool of teaching?

• how does this look different across different academic subjects?

• how does this look different across different ages?

If you haven’t read any of her books before, you should know that she’s a philosopher and novelist: when she addresses a topic, it is addressed. Her works cut to the core of whatever she’s talking about, and this is no exception. If you’re interested in what it means to matter, this book has insights for you.

You can get a taste of this book in her interview with :

Persuasion

Rebecca Goldstein on Why Humans Need to Matter

Rebecca Goldstein is a philosopher and novelist. Her latest book is The Mattering Instinct: How Our Deepest Longing Drives Us and Divides Us…

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10 months ago · 6 likes · Yascha Mounk

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