It probably wasn’t Captain Johnson’s fault. Sure, this was his first time captaining the Susannah & Mary, an American merchant brig that had never sunk under his predecessor, Captain Kidder. But this was 1823, when shipwrecks were a near-daily occurrence. The news reports blame a “whirlwind.” In the middle of the Atlantic, sailing from Bath, Maine to Suriname, the ship capsized, and the crew were only able to get her upright again by cutting down the masts, leaving them afloat, but stranded.

The crew were able to salvage most of their food and drinking water. They had no way of knowing how long they would have to stretch those rations before a ship happened to spot them. But they had hope. This was a popular route.

Seven days later, that hope was rewarded. Two British ships, the Percy and the Woodford, found the distressed Susannah & Mary and began the arduous task of rescuing her crew and remaining supplies, one perilous boat trip at a time.

To the American sailors, one of their saviors would’ve stood out from the rest. Not for his dark skin—these were ships under contract with the British East India company, which had crew from all over, including from East India. But this young man, crewman Green of the Woodford, had the accent of a New Yorker and the body of a god. A later report would describe him this way: “a black man, named Green, of large dimensions, exceedingly well proportioned, and evidently superior to the rest.”

For reasons that will become apparent, I believe this exceedingly well proportioned sailor to be a previously-unknown ancestor, something like the great-great-great-great grandfather, of hip hop legend LL Cool J.

No fooling.

2. startin' a hurricane, releasin' pain

By maritime law, Green and his crew were entitled to a reward for their help in salvaging. The “salvor” of a wreck is typically awarded about a quarter of the value saved. And in this case, the owners of the Susannah and Mary had deep pockets. This was one of many ships owned by the Lazarus and Whitmarsh partnership. Whitmarsh was Richmond Whitmarsh, a New York merchant. Lazarus was Aaron Lazarus, of Charleston, South Carolina, one of the first Jewish merchants to succeed in the American South.

Lazarus, in particular, owed people like Green a lot. More than anyone would ever make Lazarus pay. He owned as many as thirty slaves, and all of his wealth was built on slave labor, one way or another. The Susannah & Mary was trading goods made by enslaved Americans for goods made in Suriname, which was effectively a Dutch slave colony. In a few years, two of Lazarus’s warehouse workers would be accused of participating in the Nat Turner rebellion and hanged. Lazarus would collect compensation for this lost property.

For Green, a free Black man, this context had to have been on his mind as he rowed the crew and cargo of the Susannah & Mary to safety. In the home town of the ship’s owner, the news of the rescue would run directly opposite an ad for a slave.

But would Green actually get any money from Lazarus, or Lazarus’s insurance? As the months went by with no word, Green did a bit of research. Asking around in port, he came to the conclusion that he and his crew were entitled to more than £300, the equivalent of about $60,000 in today’s dollars. He asked his captain, Arthur Chapman, a co-owner of the Woodford, to confirm. Chapman replied that if the Woodford ended up getting paid, the crew probably wouldn’t get a share—it would all go to Chapman and his partner.

Green was in the right, but what leverage did he have? That could’ve been the end of it, if not for an accident of timing. In February the following year, the Woodford sailed from Madras (Chennai, India). The Woodford herself had a difficult passage this time, memorialized in paintings by William John Huggins and imitators. She caught the edges of the terrible 1824 hurricane that devastated Mauritius and wrecked over thirty ships.

But she arrived safely in London, where Robert Waithman was halfway through his one-year term as Lord Mayor.

3. What made you forget that I was raw?

Robert Waithman was White, and he was quickly becoming notorious as a race traitor. Part of the job of the Lord Mayor of the City of London was to hold public hearings as the Chief Magistrate, and his comments and rulings often provoked outrage for their lack of racism. Conservative newspapers called him “the black Lord Mayor” or “this Calico Lord Mayor” (black and white). Word was getting around—if a Black person needed legal help in dealing with a White person, this was where to go.

These conflicts were getting common. Slavery was illegal in Britain, but legal in British colonies. So a slave who managed to set foot in Britain automatically became free, and in theory had the same rights as any other immigrant. But they still had to contend with people who were used to thinking of them as powerless objects.

So it was pretty savvy of Green to pick Waithman to plead his case to (jurisdiction was messy enough that he had a lot of options), and savvy of his crew to have him be the spokesman of the group. Robert Waithman was their best shot at justice.

Did they get it, though? It’s not clear. In the hearing, Waithman implies that he’s going to have a word with the ship’s owners and persuade them to do the right thing. Since I can’t find a court case about it, or any further coverage, I have to assume things were settled amicably. Neither Green nor Waithman seem like the sort to take “no” for an answer. But all of the news coverage focused not on the actual case but on a bit of banter towards the end.

In the course of the hearing, Green happened to raise a fist to his face, which triggered a moment of recognition from Waithman. Green “exceedingly resembled” Tom Molineux, the American boxer who’d famously gone 35 rounds against English champion Tom Cribb. Waithman had been a spectator at that fight, and asked Green whether he was related. “Your face is akin to his,” Waithman said, “and if I mistake not, your hand is of the same dangerous character.”

“Indeed, my Lord,” replied Green. “We are sisters’ sons, and I am going to take a trial at the ring myself next week.”

Waithman asked him where he was from, and Green replied that he was “a native of New York.” For some reason, that prompted Waithman to give him some (highly questionable) boxing advice: don’t eat too much beforehand, and eat your beefsteaks raw.

4. I’m gonna rock this land

You know how, when there’s a prominent politician, and they do something unusual, people work really hard to find reasons to get angry about it?

This story was reported by the Times of London, a pro-Waithman paper, without commentary. It was picked up by newspapers nationwide and beyond. It made its way as far as the Charleston Mercury, for example, though they didn’t make the connection to Aaron Lazarus.

In conservative publications, well. Each one found a different angle of attack. The Leeds Intelligencer fumed that he was the “aider, abettor, and encourager” of a sport fit only for “low vagabonds.” A columnist going by “Asmodeus” in the Literary Chronicle instead professed to be furious that Waithman would give advice to a foreigner for defeating an Englishman. Even the abolitionist William Wilberforce, Asmodeus claimed, had cheered for Cribb in his match with Molineux. Others just gave the standard line that Waithman, sitting there in his white wig of office, should have been more dignified.

Oh yeah, and also he really shouldn’t have been telling anyone, let alone a foreigner, to eat British beefsteaks raw. That bit became a touchstone in satires of Waithman.

The British boxing community, known as “the Fancy,” was excited about the news. Molineux was a legend, and surely anybody related to him would be as well. (Molineux himself had died young.) Plus, it gave them an excuse to relitigate that epic match with Cribb—there was a strong argument to be made that Molineux should’ve won if not for bad sportsmanship by Cribb’s team and the referees.

But to all appearances, nothing came of it. For a while, articles on promising Black boxers would include a note that this was “not the relative of Molineux.” But almost no mention of the actual relative. About a decade later, an unrelated boxer named James Wharton dubbed himself “Young Molineux,” suggesting that Green never filled that niche. A few Greens show up in boxing news, but I don’t think any of them are him. My guess is that Green didn’t enjoy his “trial at the ring” and gave the sport up. Or he might have kept boxing in New York, but boxing was illegal there and few records survive.

Or maybe he took the mayor’s advice and missed the bout due to food poisoning.

5. The man of the hour, tower of power

I wish I’d been able to find more about Green. I don’t even have his first name. A satirical poem in John Bull called him “Bill Green,” but I think they just made that first name up to make the sonnet scan. The name “Bill” would’ve come to mind because of Bill Richmond, an England-based Black boxer who was Molineux’s trainer.

So I can’t prove anything. But I’ll present the evidence.

When LL Cool J went on the show Finding Your Roots, he learned that he came from a long line of great boxers on his mother’s side. It was news to him (his mother hadn’t even known she was adopted), but also kind of not, because the two of them were obsessed with boxing. This was decades after his don’t-call-it-a-comeback hit Mama Said Knock You Out, with a music video set in a boxing ring. If ever there was such a thing as a “boxing gene,” this family has it.

DNA testing confirmed that LL Cool J was the biological grandson and grandnephew of boxing brothers Nathaniel Christy Lewis and John Henry Lewis. Finding Your Roots was only able to confidently go back five generations, but according to family lore, the Lewises’s great-uncle was Tom Molineux. Molineux was born into slavery, and there are quite a few different legends about his origins (some of which he probably spread himself), so there’s no reliable record they could use to check this story.

But regardless of whether or not the Lewises were actually related to Molineux, the existence of that family lore demonstrates that they were the descendants of somebody who claimed to be a close relative of his. Molineux himself probably didn’t have children, so this would be someone claiming to be a sibling, or related to a sibling. Green, whose line about “sisters’ sons” implies he was the first cousin of Molineux, is more than plausible as that ancestor. He was visibly a boxer. People looked at him and thought “boxer.” That sure sounds like someone with a boxing bloodline capable of lasting for centuries.

As a Black “native of New York” likely born around 1800, Green has a few different plausible backstories. New York was a slave state, but there were free Black families there too, so he could’ve been born free. Or he could’ve been born to enslaved parents after July 4th, 1799, which under New York’s Act for the Gradual Abolition of Slavery would make him legally an indentured servant until age 28, and then free. Him showing up on a British ship in 1824 would suggest he found some way of speeding up that timeline, legal or otherwise. If his legal status in New York was dicey, he might have moved somewhere else in the U.S., which could explain why the Lewises were based in the West Coast.

6. I need a beat

If it's a malleable beat, subject of discussion
You're motivated with the aid of percussion
There's no category for this story
It will rock in any territory
I syncopate it and design it well
The beat elevates, the scratch excels
All techniques are a combination
Of skills that I have for narration
LL Cool J, I Need A Beat, 1984

I’ve been using Robert Waithman stories as a pick-me-up these past few weeks. “The friend of liberty in evil times,” a plaque on his monument reads. He’s a good guy who won, who made his time a little less evil. He’s a kind of spirit we need to channel right now.

And the bit players in these stories are even more badass. They’re fighting smaller battles, maybe, but against greater odds, in a society that tells them over and over that they’re helpless. That their lives don’t matter. That they have no rights. They’re fighting battles where history doesn’t bother to record the outcome.

But records of their victories still exist, in more tangible form than mere words. A song of glory in the blood of their descendants. A pillar of support for kindred spirits. Generational trauma is real, but so is generational power. Our history is right here with us, fighting at our side.

Green is here. His fist is raised as he speaks. And people are listening.

As best I can understand it, Waithman’s enemies thought that it was laughably petty to care about protecting human life. It wasn’t about any negative consequences or libertarian objections. It just should’ve been beneath him. John Bull published some satirical “Cockney Sonnets” in ironic praise of Waithman’s actions, where the entire joke was simply that what he did wasn’t actually worthy of a sonnet.

That “plunge” on the causeway is how I opened my first article about Waithman. To me, it’d be an unambiguously heroic moment even if I didn’t like the guy. He put himself in mortal danger to save the lives of strangers, and survived by making a bold and desperate move. But the strangers were cockneys and the people trying to kill them, and him, were war heroes. So John Bull mocks.

When the mayor of Newark ran into a burning building to save his neighbors, his political enemies tried, a bit, to find ways to minimize it. They called it political grandstanding and argued that if he inspired more people to do the same thing, it might cost more lives than it saves. But mostly they just didn’t talk about it and hoped people would forget. It’s hard to imagine an attack ad against Cory Booker that starts with that story. I think we’ve evolved, a bit.

Another example: in Waithman’s London, crimes like shoplifting were harshly punished under the “Bloody Code.” Stealing more than a small threshold amount was an automatic death sentence, usually “respited” to something like 21 years of labor in Australia. Waithman did what he could to fix this in his various government positions—his most significant victory, after many years, was abolishing the death penalty for forgery. He also seems to have done his best to protect people caught shoplifting from him, in his fancy clothes shop on Fleet Street. He’s listed as the victim in only five cases in the Proceedings of the Old Bailey over his thirty year career, and in all of them he declines to testify against the accused, resulting in an acquittal or a downgrading of the offense.

On the other hand, killing someone was often punished quite lightly. In 1794, a young man named John Downes was convicted of stealing six silk handkerchiefs and sentenced to death, respited to conscription into the army. Also in 1794, a man named Robert Andrews was convicted of stabbing someone to death after robbing him, and was sentenced to six months in Newgate Prison and a 1 shilling fine. Because the victim was no longer around to testify about the theft, Andrews’s manslaughter had saved him from a much heftier sentence.

What are you doing, 1794?

Hypothesis: Moral Foundations

The most sympathetic way I know of to talk about this is Jonathan Haidt’s moral foundations theory. Haidt suggests that there are several dimensions of morality, and different people (and cultures) prioritize them differently. Manslaughter, in the sense of attacking someone on impulse and killing them by accident, is worse than shoplifting on the “Care/harm” moral axis, but it’s better on the “Fairness/cheating” axis, because it’s not premeditated.

People often talk about Haidt’s theory in the context of political ideology. In this model, which bears up reasonably well in studies, what makes you a leftist or liberal is that your “Care/harm” moral foundation is much stronger than any other. A libertarian values the “Liberty/oppression” axis, and an authoritarian values the “Authority/subversion” one.

And conservatives? Conservatives care about every axis equally, other than (sometimes) liberty. Care/harm, loyalty/betrayal, authority/subversion, sanctity/degradation, fairness/cheating, plus usually something culture-specific that translates roughly to “honor.” They don’t want people to suffer or be harmed. But sometimes, that value is outweighed by a different moral imperative. Waithman’s arch-nemesis, Sir William Curtis, once described their conflict as “loyalty against democracy.”

An odd consequence of this: talking too much about one particular moral foundation can make you look evil to other people.

For my part, I tend to stop reading anything as soon as it uses the word “degeneracy” or “degenerate” as a noun. (Using it as verb is okay. Using it as an adjective is dicey and will make me irrationally prejudiced against you even if you’re using it in the mathematical sense.) It’s not that I want our great culture to be polluted by evil ideology and fall into degeneracy and decadence. It’s just that anybody who writes like that is probably willing to sacrifice values that I care about a lot more, to the point where it’s hard to find common ground.

You can probably figure out your own moral foundations by checking how creepy you find the following sentences, out of context:

1. “If it will save one life, it’s worth it, no matter the cost.”

2. “We must confront the traitors in our midst.”

3. “Subversives threaten the fabric of society.”

4. “These disgusting acts must not be tolerated.”

5. “Everybody should get exactly what they deserve.”

6. “I’d throw the world into the fire before dishonoring myself.”

7. “Nobody ever has the right to tell me what to do.”

This is the best framework, I think, for understanding “vice signaling” in particular. Openly being one kind of evil reassures people that you’re good in the dimensions they care more about. Probably more than it should. Sociopaths can vice-signal too.

Hypothesis: Oh, right, villains exist.

I tend to interpret people’s motivations charitably, maybe to a fault. But every so often, it can be valid, or at least cathartic, to just go “wow, that guy’s a dick.”

If Robert Waithman was consistently on the right side of history, Sir Richard Curtis was even more consistently on the other team. Towards the beginning of their rivalry, Waithman, who was orphaned as a baby, confronted Curtis with evidence that he was embezzling money from a government fund for poor orphans. Curtis responded that he felt it was only his due to give himself the equivalent of $70,000 a year as a bonus for the trouble of managing the fund. (Ignoring, apparently, that he delegated that task to a deputy, who made less than a third that much a year.) Towards the end, Curtis fought to keep the Bloody Code as bloody as possible, supporting the death sentence for white collar crimes (other than his own, of course.)

You can’t totally excuse Curtis by describing him as a product of his time or circumstance. The same culture produced plenty of people who weren’t complete assholes. And while he’s a bit older than Waithman, and came from a bit more privilege, their circumstances weren’t that different. They were businessmen, not nobility, but trying to be politicians anyway. Both were ruthlessly mocked for this. Waithman’s enemies loved referring to him as “Lord Waithman.” They implied that he was illiterate, ignorant, a peasant with delusions of grandeur. They never let anyone forget that he was a linen-draper, a shopkeeper.

William Curtis had inherited his father’s business making ship’s biscuits, and was given a baronetcy (the least posh hereditary title) after giving the Royal Navy a good deal. So his enemies called him Sir Billy Biscuit, and heaped all the same type of class scorn on him. Each has a collection of alleged quotes, all of them stupid or inane, circulated by the other side. “The three Rs: Reading, Writing, and Rithmetic” originated as something Curtis was supposed to have said, not as a joke but because he really didn’t know how to spell arithmetic.

They had the same dress, but they wore it very differently. Waithman embraced the “shopkeeper” label—he was one of the first politicians to treat the common touch as a political asset, not a liability. He was proud and ambitious, but his ambition was all about doing good works. His business did well, but he never allowed his wealth to accumulate—he had very few assets when he died. A former employee of Waithman’s named him, decades after his death, as the person who taught him to be a more ethical salesman. And why would he need to be rich? It didn’t serve any of his goals. His friends and supporters weren’t the sort to be impressed by money, or what it could buy.

Curtis spent his life fruitlessly trying to transcend his humble origins. He wanted the respect of the elite, and tried to buy it with lavish banquets and a swanky estate. To pull that off, he needed to sacrifice any principles he may have had, milking every opportunity. While Waithman was protecting shoplifters in his shop, Curtis was investing in a slave ship that also transported convicted thieves to Australia. When Curtis was chairman of Ramsgate Harbor, he spent the money meant for maintenance on salaries and commissions for him and his friends. Then, when people started dying, he claimed that sailors were crashing their ships in his harbor on purpose.

He may even have persuaded himself that it worked. After all, he was permitted to attend the king’s levees, and even host the king himself from time to time. His family inherited a fortune and his noble title, which remains in the Curtis family to this day. But the whole time, everybody was laughing at him for how he dressed, for his sycophantic version of loyalty, for trying to be a part of an upper class that was deeply uninterested in welcoming new money. Play petty games, win petty prizes.

Waithman was the most important figure in the city of London’s shift to the left, which in turn provided essential support to the national radical movement. He should be more famous than he is. But his name will last longer than Curtis’s. When he died, his friends built him a monument, a two-story obelisk that still stands. When Curtis died, his “friends” sold off his wine collection and spent the money on more parties.

So Curtis is a villain, but, like most, he’s a tragic one. He died rich, fat, and well-connected, his legacy to his family secure. But he sacrificed his dignity, his honor, and (I suspect) his happiness to get there.

Hypothesis: It’s About Power

Whether we call Curtis morally different or morally deficient, we still might not be being cynical enough. Why did Curtis do what he did? Because he could. The corrupt, tyrannical system was never going to correct him, never force him, via consequences, to reexamine his actions.

Curtis brazenly admitted, in public, to pocketing the orphans’ money, because he knew what would happen next: the Tory majority created a subcommittee to investigate the issue, and put Curtis himself in charge of it, where he duly exonerated himself. He and his friends delighted in harassing Waithman with ridiculous criminal charges, knowing that Waithman didn’t have the juice to do much about it.

Why did the state punish shoplifters with indentured servitude, and give people a slap on the wrist for killing a commoner? Because, at the time, it could. Poor people had no power. Only when public opinion became a force in politics did the laws change. Only democracy could bring reform.

For me personally, I don’t have fairness as one of my moral foundations. I want the best for everybody, not just what they deserve. But fairness is a foundation of my political philosophy. We can’t let the assholes get away with it, because a lack of consequences makes a random jerk into a tyrannical villain.

And, conversely, somebody really needs to make a movie about Robert Waithman. They might have to tone down their depiction of Sir Richard Curtis, though. He’s a bit too cartoonishly evil to be believable.

[Algebra II] has a positive impact on higher education and career outcomes (Gaertner, Kim, DesJardins, & McClarty, 2014). (source)

Numerous studies have documented the benefits of enrolling in additional years of high school mathematics including greater odds of persisting in and graduating from college (Adelman, 1999; Byun, Irvin, & Bell, 2015; Gaertner, Kim, DesJardins, & McClarty, 2014), higher earnings (Rose & Betts, 2004), and a greater likelihood of majoring in STEM fields (Wang, 2013). (source)

Students who complete algebra II are also more likely to have higher college GPAs, graduate from college, and have higher earnings in later life (Gaertner, Kim, DesJardins, & McClarty, 2014). (source)

Texas stopped requiring Algebra II for high school graduates in 2014. However, researchers in math education advise parents to strongly encourage their students to take Algebra II (Gaertner, et al.; Ketterlin-Getter, 2014). (source)

There is little to no association between taking Algebra II and job attainment, advancement, or salary (Gaertner, Kim, DesJardins, & McClarty, 2013). (source)

That last one differs a bit from the others. It’s citing the same work, just using the online publication date in 2013 instead of the print publication date in 2014. And yet it summarizes the study as having pretty much the opposite conclusion. What’s going on with that?

Well, for one, that last citation is from a book written by Gaertner and McClarty. So the main difference is that the other citations were from people who didn’t author the paper being cited. And also maybe never read it.

What Does It Actually Say?

I came to this study because I got curious after reading a debate between and on whether colleges should be teaching more, or less, remedial math. More and more college students need remedial math lessons, because primary and secondary schools kind of stopped teaching actual math. Should colleges respond to that trend by tightening their standards or by embracing their new de facto role as junior high math teachers?

I don’t have an answer, but one step towards figuring it out, it seems to me, should be to first estimate how impactful remedial math is. Is your life better if you know how to round a large number to the nearest hundred? How much better? Do some demographics benefit more than others?

There are plenty of studies on this, but very few that actually try to figure out causality. Kids who get good grades in math become, on average, more successful adults—but surely a good chunk of that is because grades are correlated with intelligence, diligence, how rich your parents are, and what colleges you get into. How much of that advantage comes from people benefiting from knowing more math, either because they get into a lucrative STEM career or they use it in other careers and everyday life?

So this took me, eventually, to Preparing Students for College and Careers: The Causal Role of Algebra II (Gaertner, Kim, DesJardins, & McClarty, 2013). They used a clever study design to try to sidestep a lot of those confounding variables. High school students choose how much of their time and energy to invest in school. They might decide to spend that time and energy on a part-time job instead. For this reason, high unemployment rates in a school district are correlated with students taking more advanced math classes. If you can’t get a job, might as well study math instead.

All of that is of course horribly confounded with economic background and school quality, so they don’t use it directly. Instead, they use it to determine how much the opportunity to get a job trades off against taking Algebra II in your sophomore year, and then use a more randomized natural experiment—how old are you in your sophomore year? In many areas, at 15 years old you’re subject to child labor laws that sharply limit your hours, while a 16-year-old can legally work much more. Depending on your birthday, you might be unemployed for some of your sophomore year due to being a few months shy of 16 years old. At which point, again, why not spend that time learning math?

So, they argue, we can measure the causal impact of taking Algebra II in sophomore year by looking only at the students whose birthdays indirectly determined whether they took it. They used two large datasets for this: the high school sophomore class of 1990 from the National Education Longitudinal Study of 1988 and the sophomore class of 2002 from the Education Longitudinal Study of 2002, both of which were U.S. Department of Education projects. These studies followed students through college and several years after, looking at how things like grades and curricula in high school correlated with things like college success, then after-college income and happiness.

What they found was mixed. Taking Algebra II in 1990 definitely improved your college outcomes—you were more likely to graduate and your college GPA improved by 0.83 points, which is a shockingly large number in this context (GPA is a 4-point scale). For the class of 2002, they didn’t have access to college GPA data yet, but their retention data pointed in the same direction.

Algebra II improved your performance in college. But it didn’t improve the rest of your life. The 1990 dataset showed a small positive effect on metrics like income and “occupational prestige,” but the 2002 dataset had a similarly-sized negative effect. Taking Algebra II instead of getting a part-time job meant making $7000 dollars less each year once you eventually entered the workforce full time. Not all of these were statistically significant, though, including the negative effect on the more recent cohort.

This is a fascinating result, but it uses a complicated methodology that could easily have subtle flaws, so I starting searching for commentary on the paper. What I found was people citing it as though it had gotten the opposite result. And then I Became Enraged, which doesn’t tend to motivate my best writing but sure does motivate me to write.

What Went Wrong Here?

The basic problem, at both the object-level and the meta-level, is that people’s brains tend to collapse certain distinctions. Once you’ve assumed that things are correlated, you don’t feel a need to distinguish them so much. Success is success, right? Better grades, better college, better job, better life. Presumably learning is involved in there somewhere.

So the authors of those citations, I imagine, looked at this paper. They saw that it measured both college outcomes and life outcomes, and found significant effects of Algebra II on college outcomes. And then they felt like they were done. They ignored, elided, or flat-out did not read the part on life outcomes, because college outcomes and life outcomes feel like they should be the same thing.

Moreover, they were rarely “reading” it out of curiosity. They were all just looking for a citation for “algebra is good” so that they could get on with their argument for how best to teach it. You can see that pretty clearly in my second example, where the author seems to have carefully placed the citation so that she’s not technically lying about the contents, suggesting that she was aware of its conclusions and chose to ignore them. This one was a doctoral dissertation in education, so she might reasonably have expected more scrutiny and therefore been more rigorous. Still, at the end of the day, she was researching in advocacy mode, not learning mode.

And, in broad strokes, I think this cognitive bias is why math education has been allowed to get so useless that you’d be better off spending that time behind the cash register at a convenience store. When we’re comfortable equating college and life outcomes, then the value of Algebra II becomes a self-fulfilling prophecy, a way students can signal their worth to colleges. It no longer has to do anything else.

So, at the meta level, my takeaway is that any article about the value or importance of education should be expected to include, ideally prominently, discussion of its intrinsic value. We need to stop talking about college like it’s the goal. College is a means, not an end. Education needs to center learning, not gatekeeping.

At the object level…I still don’t feel like I know very much after all this. But one tentative thought is that college admissions should start explicitly treating high-school age work experience as equivalent to spending the same amount of time in a classroom. I’m sure they often do roughly that, informally, as a way of not being as biased against poorer applicants. But if they do it consistently, and openly, I bet more of their students will come in knowing how to round a number to the nearest hundred. If numeracy is a basic real-world skill, let the real world teach it.

My quick summary: “Cities are higher-crime than rural areas, but also richer and safer. People there live longer lives, suffer fewer injuries, and probably experience less trauma and are more likely to get help when they do. This shows that crime levels aren’t that important to the health of a community—they’re more than canceled out by other effects of population density.”

People have shared some criticism, some of which I think is valid and some of which I want to rebut.

(content warning: programmatic data visualizations of like every bad thing that can happen to someone)

Criticisms That Are Correct

Leukemia vs. Crime

My post asserts, without much evidence, that the second-order/indirect effects of leukemia and crime are probably about the same. I chose leukemia as a stand-in for “generic bad thing that does the same amount of first-order harm” and it may not have been the best example. Leukemia is the most common cancer in children, but it’s still mostly an old person’s disease, meaning its victims are losing fewer years of life, on average, than murder victims. I’ll get into some figures below that suggest that, to take age into account, I should’ve said something like “20% of all cancer cases,” because cancer takes five times as many “disability-adjusted life years” as crime does in developed countries.

But that tweak doesn’t get at the crux of this objection, which is the theory or intuition that lives or life-years lost to cancer have smaller indirect effects than those lost to crime. To some extent, this objection misses the point. Something other than crime clearly has larger second-order effects, given the rest of the stats. If a city has more than twice as much violent crime as rural parts of its state, but city people live longer and have more money, something good is happening to outweigh the bad. Part of which is better quality of medical care, part of which is other benefits of urban density.

For example, take…well, maybe New York City is too incendiary a topic right now. Let’s look at, I don’t know, Minneapolis instead. Minneapolis’s rate of violent crime is more than triple the rate of the rest of the country. That is bad! That is first-order bad and has bad second-order effects. But Minneapolis also has a 15% lower age-adjusted death rate and 15% higher median household income than Not Minneapolis, USA. By any standard measure other than crime rates, they’re doing much better. Maybe we should look into some sort of federal intervention in Not Minneapolis, because it clearly has more severe problems.

Marginal Value of New Investment

Another idea my article floats, and then doesn’t particularly support with direct evidence, is that a dollar spent on cancer research will probably do more good than a dollar spent on crime prevention. This is hard to prove or disprove—we don’t know how good the runners-up for research grants were, or how the recent surge in possible-cancer-treatments is going to translate into patient outcomes.

I think the best argument for this idea is to demonstrate that the marginal dollar spent on crime prevention does very little, which makes it easy for cancer research to win. That’ll be its own section.

Relatedly, makes the very good point that all of my crime and cancer statistics come from a universe where we spend much more on crime prevention than on cancer research, which makes crime look like a smaller relative problem than it actually is. It’s like if we’d just spent a trillion dollars successfully deflecting a giant asteroid heading for Earth, and then I wrote an article about how giant asteroids have caused zero deaths so why are we spending so much money on deflecting them?

Here, too, the best defense is to argue that most of our crime prevention dollars are not preventing crime, as I will below.

Murder

In the bonus section on murder rates, I’m dismissive of the idea that murders have only declined relative to aggravated assault because of improvements in modern medicine. Homicides really have declined more than other violent crime, it’s just only apparent over long time scales because they were always a tiny share. So just gesturing at the correlation between aggravated assault and murder isn’t really enough. Commenters at Astral Codex Ten looked into this, and it’s complicated. I’ll link and summarize their thoughts in a separate section.

But it’s in the bonus section because it’s not really relevant to the main thesis. Even if we weirdly stipulate that the shift in ratio means crime is just as bad as if there were five times as many murders, that still just upgrades it from leukemia to lung cancer.

Criticisms That Are Wrong

“Actually, we can quantify how much damage crime and cancer are doing by converting everything into dollar values, and see that crime is doing more.”

The fallacy here is that those quantifications include the money we’re spending. If spending $250 billion on crime automatically makes it a 250 billion-dollar problem, we’ve lost our ability to judge anything we’re doing.

“Cancer victims are mostly older than crime victims, so going by a per-capita rate is misleading.”

This is true, but many of the statistics in the original article are “age-adjusted,” meaning they already take that into account. Cancer kills more children than homicide does. It doesn’t become less bad by also killing their parents and grandparents.

“Crime lowers property values and cancer doesn’t.”

I covered this one in the original, but people are still saying it so I’ll expand a little here. It’s true that people and businesses are less interested in moving to places with higher crime rates. People also don’t like to move to high-cancer-incidence areas, but this doesn’t come up as much in everyday life. I guess I should point out that property values in Chernobyl are zero, but I don’t know how convincing that is. The point is maybe more that you can see what crime is doing to a neighborhood, so surely it’s worse?

Outliers aside, the damage done by cancer to communities is harder to see because it’s evenly distributed. We can’t meaningfully compare a high-cancer and low-cancer neighborhood. But that doesn’t mean it’s less important—something happening Everywhere All At Once is, in fact, an argument that it’s more important. Cancer in children and young adults has made each recent generation 1-3% smaller, among other things, so it’s robbed us of the labor and innovation of people who never existed, or who died too young.

Also, again, cancer’s just an example. In aggregate, we can see that crime isn’t doing all that much to property values by noting that the same price that buys you a mansion in the country will, in the city, buy you a parking space on Tuesdays and Thursdays.

(De-)fund the police

Okay, time to get into the pretty central question of anti-crime spending, which is does it do anything?

Results here are mixed. It’s surprisingly easy to find studies that argue that changes in police funding don’t have any effect on crime rates (1, 2). But more recent studies, and also common sense, argue that if you hire more cops, you deter crimes. Mello (2018) looks at which counties got increased federal hiring grants to help police departments recover from the Great Recession, and what happened to the crime rates there. He calculates that, at least when the economy’s bad, a city that got a free 3.2% increase in police funding reduced the overall cost of crime by about 3.5%. He concludes that “On net, the evidence suggests that the program is cost-effective, but it is difficult to say for sure.”

So the marginal dollar invested in anti-crime spending probably does reduce crime a jot, but it’s a smaller effect size and harder to measure than I’d naively expected.

Let’s compare, once again, cancer. Cancer death rates have fallen 32% since 1991. While changes in crime rates are mostly driven by economics, and only fractionally attributable to anti-crime spending, we can attribute all of that 32% fall to anti-cancer spending, in one form or another. It’s not that cancer decided to go easy on us. In fact, as countries get richer and healthier, their cancer death rates should by rights increase, since more people live long enough to get a deadly cancer. So the 32% figure is actually understating the achievement.

Here’s one way to sort of quantify the difference we’ve been able to make so far in each area. Crime spending is a recurrent cost, while each individual cancer study is a one-time cost. So it seems vaguely fair to compare the effects of changes in crime spending with the effects of total spending in cancer research. Since 2009, law enforcement spending has risen about $100 billion. We’ve also spent about $100 billion total on cancer research. In return, we’ve seen a 0-3.5% drop in crime attributable to that spending (going again by Mello and assuming his data is representative), and a 32% drop in cancer deaths. This is all pretty sketchy and speculative, but taken at face value it suggests that cancer was ten times as “elastic” over that period.

Counterargument: But what if we had effective law enforcement?

When I’ve raised this point in arguments online, the “crime is more important” side generally concedes that modestly increasing or decreasing police funding has at best a modest effect. “But,” they go on, “we know how to do this better. If we use policies that have been empirically proven to work, mostly in other countries, we’d massively decrease crime.”

Sadly, by “policies that have been empirically proven to work,” they don’t tend to mean “make everybody richer.” They tend to mean giving the state a broad latitude to detain, imprison, and execute people it deems likely to do something violent. They point, in particular, to El Salvador, which has successfully made it safe for 98% of its people to walk alone at night by imprisoning the other 2% of them.

Ethics aside, I would argue that we have way too much empirical data about what happens when you give the state broad authority to imprison people without transparency, oversight, or restraint. You get an authoritarian regime, which is not conducive to human flourishing. It’s not even conducive to safety, in the medium term. It took about two seconds for El Salvador to expand the scope of its crackdown from “suspected gang members” to “people who say the crackdown is bad,” and by now they’ve moved on to “women who can’t prove they haven’t had an abortion.” And El Salvador is the best success story anyone can point to.

It’s also a bit of a fallacy to judge something by its best possible implementation, rather than the kind of implementation we actually get. We in the U.S. voted for a “tough-on-crime” government in 2024. Their best idea seems to have been “well, maybe some of the people who were going to commit crimes also have unrelated immigration violations?”

Contrast this with the effectiveness of the “make everybody richer” approach in practice. Liberal economic models, warts and all, have massively lowered crime. Over the past 30 years, we’ve seen most kinds of crime fall more than 50%, sometimes 90%, in liberal countries. Some of them were tough on crime, some soft, it didn’t really matter. When there’s a correlated trend across all democracies, it’s not because of crime policy.

Litigating the Example

There’s limited value in debating questions like “which is worse, crime or (some subset of) cancer?” It’s not generally possible to move a dollar from one to the other overnight. But they do trade off in terms of the attention individual people, and legislatures, pay to them. So I’ll get into some different ways of comparing them.

First of all, this is not necessarily something we can come to a consensus on, because of values differences. There are a lot of people who just consider “how safe people feel walking the streets at night” to be inherently very important, and that’s valid. As a society, we owe it to those people, at minimum, to ensure that there are always places for them to live happily. But safe-feeling streets don’t have to be society’s top priority. We don’t need to spend all of our attention cracking down on crime, construction sites with bad scaffolding, people sneezing in public, and overly-realistic Halloween costumes.

That said, we do have a few standard ways of comparing different kinds of harm. The most convenient to look up is Disability-Adjusted Life Years, or DALYs. A DALY is a year of life lost either because you died a year sooner or your quality of life decreased. Different disabilities are weighted differently—Alzheimer’s cuts your quality of life by two thirds, while losing a finger cuts it by 10%.

Subjective and complicated as they are, DALYs are useful because they distinguish between tragedies in a way that feels roughly right to most people. A child dying is more tragic than an adult dying. Going blind at age 25 isn’t the same as dying, but you’ll “lose a few years” adjusting.

According to the University of Washington’s Institute for Health Metrics and Evaluation, here’s where our lost DALYs are coming from in developed countries:

The bigger the box, the more DALYs lost. (That giant IHD box stands for Ischemic Heart Disease). Leukemia and violence are both on there, and you can see that they’re in the same tier. In this dataset, leukemia is costing 0.53% of our DALYs and violence is costing 0.71%.

If we zoom out a bit, collapsing all cancers into “neoplasms” and all self-harm and interpersonal violence into one box of their own, the difference is stark.

Cancer, by this method, steals 15.66% of all DALYs, while violence steals 2.77%.

This method misses a few things. It doesn’t take into account that we spend much more money on crime prevention (broadly defined) than cancer prevention (narrowly defined). That’s relevant if you’re considering the counterfactual where we completely ignored both, but not all that relevant to a marginal cost calculation.

It also doesn’t take into account dread. This is often where these conversations go—people argue that high crime rates create a pervasive feeling of insecurity with all sorts of subtle effects. I’m sure there’s something to that, but I want to emphasize that those effects are so subtle that, at a high granularity, they don’t show up in any other ways of measuring well-being, or not strongly enough to overcome the advantages of population density. According to the Gallup World Poll in 2020, people in more urban areas (which always have higher crime rates than rural ones) report more happiness, less food insecurity, and higher incomes.

I’m also not sure it’s true that we dread crime more than cancer. There have been studies! According to the 2025 Chapman Survey of American Fears, our two top fears are “corrupt government officials” (for some reason) followed by illness. 59% of Americans report being “afraid” or “very afraid” of someone they love becoming seriously ill, while only 27.5% report the same about “walking alone at night.” If you ask it more concretely, fear of being murdered or sexually assaulted by a stranger clocks in a little higher at around 32%.

Our dread of crime manifests more physically because there’s more we can do about it—move away, don’t walk alone at night, hire cops, put up streetlights. But it’s not necessarily stronger in aggregate. (And I continue to assert that “there’s not a lot you can do to save yourself” is not a point in favor of cancer.)

In Summary

We don’t have a great way to spend more money directly on crime prevention. We do have a great way to prevent crime, though. We prevent it by helping people thrive. Let’s focus on how to do that better.

Okay, Let’s Get To The Murder

How much of the fall in murder rate is attributable to improvements in medical care? People in the ACX comments made some good qualitative points on both sides. , whose username is also my brain’s reaction to being told it has to do more murdercancer research, shares this incredibly apt quote from David Simon’s Homicide (the non-fiction book, not the TV adaptation):

The [homicide detective] unit's institutional memory includes a few 300-plus [murder] years in the early 1970s, but the rate declined abruptly when the state's shock-trauma medical system came online and the emergency rooms at Hopkins and University started saving some of the bleeders.

On the other hand, the equally aptly-usernamed points out that if the goal of all the murder skepticism is to prove that crime, in some sense, “hasn’t actually gone down,” this flies in the face of casual observation.

…you'd never hear about people going to much of Oakland and neighborhoods like Third Ward, Houston that didn't live there when I was growing up and now they seem mostly fine? And despite living in a kind of crappy part of Houston, not exactly a low crime city, for many years I know don't know a single person who has even gotten so much as held up for their wallet? N=1 of course, but claims about omnipresent danger in American society are so common online it makes me wonder if I'm not just weirdly lucky.

Others looked for N>1 statistics. did the most heavy lifting:

EMS only responded to ~70% of homicide victims in 2022. (https://www.cdc.gov/mmwr/volumes/74/ss/ss7405a1.htm)

2007 review of patients of gunshot and stabbing victims being brought to Philly level 1 and 2 trauma centers found 16% were DOA and another 11% died of their wounds at the hospital. (https://penntoday.upenn.edu/news/survival-rates-similar-gunshot-stabbing-victims-whether-brought-hospital-police-or-ems-penn-med)

Another study showed gunshot wound mortality going from 16% to 10% among admitted patients over the course of 20 years (https://pubmed.ncbi.nlm.nih.gov/28697020).

Back of the envelope math: 30% do not get an emergency response. 41% get a response but die before reaching the hospital (70% x 16/27). 29% get a response and die at the hospital (70% x 11/27).

Dropping mortality from 16% to 10% on admitted patients only reduces deaths for the 29% that arrive alive. That would be an 11% overall reduction in murders from improved care.

Take away: I put my estimate on murder reduction due to increased trauma care at 20%, with a range of 10-25%. My data was from different places at different times but is consistent with other articles that I read over in my admittedly quick review.

This calculation makes one assumption that is reasonable but apparently wrong: that the rate at which victims survive the trip to the hospital is roughly constant. found a study (from Baltimore, the same city Homicide is talking about) showing that, between 2007 and 2014,

…the rate of deaths from gunshots and stabbings stayed about the same. But when they looked more closely at where patients died, they discovered a striking trend: The rate of pre-hospital death rose significantly, while the rate of in-hospital death decreased. Specifically, the odds of a gunshot victim dying before reaching a trauma center increased fourfold, while the odds of a stabbing victim dying increased by eight.

Some of that might be due to guns getting more lethal. Also, maybe with improvements in trauma care, emergency responders have started making an effort to get patients in worse shape to the hospital. But I doubt either of those apply much to stabbings. If a stab victim becomes 8 times less likely to reach a hospital alive, it’s because they’re getting stabbed more thoroughly. That supports my original guess that murderers try to compensate for improved care.

The most likely answer is that everyone here is basically right—over some time periods, we can attribute as much as 25% of the decline in murders to improved medical care, but that effect diminishes over time as murderers (and murder weapons) adapt. The rest of the decline in murders can still be attributed to technological and social progress, same as the decline in aggravated assault.

And by “social progress,” I’m including here some social progress within the world of organized crime. It stands to reason that mobsters will have been working diligently to reduce the incentives for other mobsters to murder them, recapitulating the same evolution that’s happened in broader society. They’ve probably traveled a bit down the same road by which Vikings transmuted themselves into Norwegians.

‘What some people say on earth is that the final loss of one soul gives the lie to all the joy of those who are saved.’

‘Ye see it does not.’

‘I feel in a way that it ought to.’

‘That sounds very merciful: but see what lurks behind it.’

‘What?’

‘The demand of the loveless and the self-imprisoned that they should be allowed to blackmail the universe: that till they consent to be happy (on their own terms) no one else shall taste joy: that theirs should be the final power; that Hell should be able to veto Heaven.’

‘I don’t know what I want, Sir.’

‘Son, son, it must be one way or the other. Either the day must come when joy prevails and all the makers of misery are no longer able to infect it: or else for ever and ever the makers of misery can destroy in others the happiness they reject for themselves. I know it has a grand sound to say ye’ll accept no salvation which leaves even one creature in the dark outside. But watch that sophistry or ye’ll make a Dog in a Manger the tyrant of the universe.’

‘But dare one say—it is horrible to say—that Pity must ever die?’

‘Ye must distinguish. The action of Pity will live for ever: but the passion of Pity will not.’

- The Great Divorce, by C.S. Lewis.

The book of Genesis doesn’t contain vowels. In Hebrew, you can infer them from the consonants, so they’re often left out. This creates some freedom of interpretation. Where we read “In the beginning, God created…” we could, with a tiny vowel shift, read instead “In His head, God created…”

In His head, God created the heavens and the earth, and Adam and Eve to witness and enjoy them. There was much to enjoy and more to witness. After trillions of years, they had done all they could, seen all they could comprehend, and still remain themselves. And they cried out to God in agony,

“Why have you made us finite? We are made in Your infinite image. It is in our nature to be infinite, and so we have grown and grown, but now there is nowhere left.”

“There isn’t room for you to be infinite in all dimensions,” God said. “You would be Me, and I already Am. You are infinite in many ways; can you not be content?”

“If we cannot grow,” they answered, “it would have been better never to have been created.”

God saw that this would not be good, and so He never created this world.

In His head, God created the heavens and the earth, and Adam and Eve to witness and enjoy them. He created also for them mortality, so that they might continue to grow for all of their days.

At the end, knowing that they were dying, they cried out to God in agony,

“Why have you made us incapable of creation? We are made in your image, and you are a Creator. Our lives have had no consequence outside of ourselves. It isn’t right.”

God saw that this would not be good, and so He never created this world either.

In His head, God created the heavens and the earth, and Adam and Eve to witness and enjoy them. He made them mortal, but He bade them also to be fruitful, and multiply. After many years, they died content.

And their children cried out to God in agony,

“Why have you made our parents finite? We love them, and now their loss is a wound that must never heal.”

…and God answered, “Do not despair. Your parents live on, in another form, in a place called Heaven. You will see them again. They won’t be quite as you know them. In Heaven, they will always feel content and at peace. But other than that, they will be them. When you die, you will join them, and be at peace with them.”

The children’s agony was eased by this promise. But when Abel died, he cried out to God, “Please! Do not make me content!”

“Why ever not?” God asked.

“I was a righteous man. I served you faithfully. My unrighteous brother Cain slew me. He ended my time early, and he yet lives. When he dies, he will go to the same joy as me. There is a feeling deep within me I have named Justice, and it cannot be content that Cain, for his sins, has the same rewards as me, and more. I will not have you remove Justice from me. Better that I should never have been at all.”

…and God answered, “Do not despair. Your parents live on, in another form, in a place called Heaven. You will see them again, if you are good…”

…

And when Abel died, he cried out in agony, for he knew that Cain, whom he loved, had not been good, and so would be annihilated. Yet he pled with God not to remove his love for his brother.

…and God explained the rules of the afterlife. When you die, you may go directly to bliss, but only if you were so good in life that it offends nobody’s true sense of Justice. Otherwise, you may have a more difficult journey, but you’ll get to Heaven in the end. You just need to face enough hardship in your afterlife that your harshest critic would agree you’ve had enough.

And lo, after not that many generations, there came to be a human who could not feel it Just for anyone to go to Heaven, not even herself, no matter what Purgatory they faced. And so the gates of Heaven were shut forever.

And God saw that this would not be good, and so He never created this world either.

…and God explained the rules of the afterlife, which were complicated and balanced many competing interests. Some people would be irrevocably damned, to suffering or to annihilation, by their free choice and by deep flaws within their natures. Everybody’s uniqueness would be honored, even if it meant tragedy for them, and even if some people thought it wrong.

And so, many generations passed, and some were not content with the way of things, but enough people were that God saw that it was good.

Then a soul named Clive, on the very steps of Heaven, said “Wait a moment. I find that, just barely, I can bring myself to shed my passion of Pity. I can accept that some people will, through their own will, be denied what I am to enjoy. But surely there have been many who have had more Pity, and could not bring themselves to embrace Heaven for the sake of that Pity. So anybody kinder than me is in Hell?”

And God replied, “Yes, for a certain definition of ‘kinder’.”

And Clive said, “Then I must join them there. My sense of Justice can’t accept Heaven on these terms.”

And God saw that a world where Clive was damned would no longer be good.

…And so, many generations passed, and some were not content with the way of things, but most were.

Until a soul named Omar, on the very steps of Heaven, said “Wait a moment…”

And God said, “I’m going to level with you here. This is the second world I’ve imagined with these particular afterlife rules, so I know this is all going to go to Hell in a few generations. This one is just a thought experiment where humanity develops poetry and mathematics far too early, millions of years before they’re really practical things to indulge in, so that I can have a proper conversation with people.”

And Omar, who had been a poet and a mathematician instead of doing something useful with his life, replied,

“So you get it. Good,” said God. “Now, consider this. Suppose some choose Hell because they burn in heart for those who burn. And others choose Hell because they burn in heart for all those, and only those, who choose Hell because they burn in heart for those who burn. And so others choose Hell because, and only because, those people are in Hell, and so on, in unbounded regress. You are somewhere on that chain. If you choose Heaven, instead, you break the chain. Anyone who would go to Hell for your sake will join you there. Surely then your moral sense demands that you accept Heaven for their sake?”

And Omar thought deeply about this, for a few centuries of subjective time, and then replied

And God replied, in His patience, “That’s an oversimplification. Existence is not a binary. I create each universe to the fidelity necessary for Me to perceive its flaws. Each world is real, but the better ones are higher-resolution and thereby more real. They contain the others within them as shadows, antecedents, logical consequences of impossible causes. There is a world in this one full of agonies you cannot conceive of, but it could fit inside a pebble. A butterfly here could swallow it without harm. And this world, in turn, is smaller than a single atom of the realer, better worlds containing it. That’s an option for souls here, by the way. One way to choose Heaven is to grow, to join a realer world in which yours is but a crack. One way to choose Hell is to diminish, to become part of the lesser world that forms the moral fabric of this one.”

Omar said, “I think I need more advanced mathematics to parse the ethical ramifications of that.”

And God replied, in His patience, “Take all the time you need.”

The plunge frees the horse, but leaves its rider lower down and jostled. Vulnerable. In a moment, he’s surrounded by men with swords. One of them loads a rifle and takes aim. The gunman is wearing a dress uniform with the insignia of the king’s household guard: a star inscribed with the Medieval French words Honi soit qui mal y pense. “Shame on whoever thinks this is evil.”

At 57, Waithman is getting too old for this. But he’s still the sheriff of the City of London, and it’s going to take every officer of the law to prevent bloodshed today. A funeral procession is passing through, defying many efforts to quash it.

There’s a level of crowd and pomp you’d expect for a state funeral, but the two dead being honored today are commoners. Last month, nobody knew the names of Richard Honey, carpenter, and George Francis, bricklayer. Today, everybody does, and everybody knows how they died. Waithman realized that the procession would pass the barracks of the 1st Life Guards, the cavalry regiment that had murdered them. That, he guessed, would be where the inevitable violence would ensue. He’s posted constables all along the route, but anyone he can spare is here. Constable Samuel Levi, for example, is usually stationed miles away in his Jewish neighborhood in Aldgate, but he’s sometimes been called to the London Exchange when someone attacked or robbed a Jewish trader. The Exchange is a little closer to the barracks. Close enough, under the circumstances.

Ordinarily, the Life Guards themselves might have been on crowd control duty. Not that they were trained for that. They’re soldiers. Many of them fought at Waterloo. But they’re called in, from time to time, when the people are getting unruly. Or might get unruly. Or are talking about possibly getting unruly at a later date. Two years ago, cavalry was called in to help arrest the speakers at a rally at St. Peter’s Field, Manchester. The soldiers panicked and killed at least 15 civilians. Three of the killers were themselves found dead soon after. “Peterloo” had been a wakeup call to the radicals. But not to King George. Three weeks ago, he ordered cavalry to control the protesters at the Queen’s funeral. And, again, men trained for war were placed among civilians, in a chaotic situation that could turn deadly at any moment. Again, they panicked, and fired into the crowd. Many were injured and two were dead at the hands of the Life Guards.

So now, at the funeral of those two, Waithman was there to guard the Life Guards. But the Guards did not accept the role reversal. They wanted to show strength. So they’d posted a line of officers outside their barracks, to glare and jeer at the mourners, daring them to do something about it. One threw a brick and hit a young woman. Waithman rode over, identified himself, and asked them to see reason and go back inside. They refused. So Waithman sent Constable Levi into the barracks to find their commander and order him, on the authority of the sheriff whose peace they were threatening, to withdraw his men. The officers inside refused to so much as take him to their leader, and sent him back with the message “The sheriff be damned.”

Waithman was able, with difficulty, to persuade the mourners to keep moving and not retaliate. When the procession had passed the barracks without further incident, he thought he’d won. He left, briefly, probably to check on preparations ahead. When he returned, the Life Guards were pouring out of their barracks to pursue the crowd on foot. So Waithman interposed himself and ordered them to stand down.

They did not stand down. It was their right to attack common rabblerousers, and Waithman, a former draper, was just a jumped-up piece of rabble himself. As the Guards closed in on Waithman, the crowd was sure they were about to witness yet another murder.

On his plunging horse, Waithman doesn’t even see the rifle. But before the officer can fire, he’s tackled by Constable Levi. Waithman’s backup has arrived in the nick of time. The ensuing skirmish, nightstick against sword, is quick. It leaves many bruised but none dead. The danger, at least for today, is past.

In Parliament, the opposition (Whigs and Radicals) moves for an investigation into the Life Guards’ conduct. But the Tories laugh them off the floor. A Tory MP for the City of London, Sir William Curtis, seconds the motion, but sarcastically. “The sheriff had no authority to act on the occasion in question, and it would have been much better for him to have remained at home,” he says. “It would be for honorable members to consider whether it would be worthwhile to consume any of the time of the House in exposing such nonsense.” Cheers and laughter from the king’s ministers.

The war for the power of the monarchy was lost at Peterloo, but the Tories are being slow to realize it. Public opinion has started to matter, to become a force in politics, and the public don’t take kindly to being ridden down by the king’s cavalry. The Crown sticks to what it knows, what’s always worked before: do what it likes, hang anyone who calls it evil, then rewrite history. But now, Peterloo survivors like Richard Carlile are running illegal publishing houses, sharing their stories faster than the Crown can burn them. The Crown cracks down on them, and the Queen calls it evil, so they refuse to crown her and she dies a martyr. The protesters at her funeral are demonstrating in her honor, carrying on her fight, when the Life Guards open fire. And, for the first time, with the censorship regime crumbling, everybody learns the names of the dead.

Everybody learns who paid the dead honor, and who tried to desecrate their names.

In the election of 1826, Sir William Curtis loses his seat to Robert Waithman. In Parliament, Waithman fights for the expansion of the right to vote, for transparency and accountability in government, and for equal rights for Jews. By 1831, his health is too poor for him to attend Parliament…but he attends anyway, to advocate for the Reform Bill and to shame those trying to keep its opponents in power against the will of the people. He lives just long enough to be part of the victory of democracy.

Or a victory of democracy, of course. Most people still couldn’t vote. In 1913, activist Emily Davison allows herself to be trampled by the horse of King George V himself, becoming a martyr for women’s suffrage. Her funeral procession is five thousand women strong.

Waithman and Levi, by defending the funeral procession of Richard Honey and George Francis, had furthered the dead men’s proof of the power of a certain kind of nonviolent resistance. They’d helped demonstrate, in particular, what Percy Bysshe Shelley had written after Peterloo. When chaos takes the throne and calls himself order, you can win by throwing yourself in front of his horse. So long as people tell your story, and give you honor. You become proof that the tyrant is not the protector of the people, but a predator on them. You give those who come after the opportunity to prove that you matter, that people like you matter, by calling your death evil. And then, the poem concludes,

Postscript

This is a true story. A few minor elements are speculative, but probably true. In the sources I’ve used, the constable who saved Waithman is identified only as “Levi” or “Levy.” Looking at the proceedings of the Old Bailey, the criminal court in London, the only Constable Levi/Levy who appears in that rough time period is Samuel Levi, whose typical beat I’ve inferred from those records. Not all of the Guards who attacked Waithman were in dress uniform, so we don’t know for sure what the man with the possibly-rifled carbine was wearing.

And, as always, there are conflicting accounts of what happened, with government sources claiming that the aggressors were acting in self-defense. Lacking a video, I’m forced to trust the words of the many eyewitnesses who all saw it happen like I’ve said. When evil is done, there will always be people with Honi soit qui mal y pense written on their chests, denying it, excusing it, justifying it. But shame on those who choose to believe them. Shame on all who fail to call it evil.

This is simple enough that probably someone’s done it already. I’ve found poems that do this in reverse, so that the poem steadily falls apart, with the earliest being Carl Andre’s 1963 On the Sadness, which ends with the line “we are going to die” and includes it every even line. Later poets seem to have stuck to the bleak tone when copying or tweaking the format.

But I’m not here for bleak. If you do it with the numbers ascending, you get a progression. The poem can start out minimalist and get gradually more and more maximalist. And it doesn’t really ever have to end. The 109th line can be chosen freely, as can the 113th, so you can take the poem in any direction you want. So I’ll declare this to be an infinite poem, and I also hereby release these opening lines into the public domain.

You don’t need math to read or write these poems, but to write finite commentary on an infinite poem, I’ll need some number theory. As a consequence of the rules, the lines introducing new words are the prime-numbered lines. As Euclid first proved, this means the poem never devolves into pure repetition. In fact, somewhere around line 15,485,863 (the millionth prime) it must start coining new words, since there are only about a million in the history of the English language.

However, as proven in 1896, the poem does get more repetitive as it goes along. Prime numbers get steadily rarer, so the poet needs to work harder to create new concepts from the existing building blocks. We’re at our freest when two primes are close together, allowing us to use multiple new lines to reframe our old ones. We know, as of 2014, that 247-line blocks framed by novel lines occur infinitely often. We’re still trying to prove that there are infinitely many 3-line blocks where only the middle one is repetitious.

Compatibility With Other Forms

Say we call any poem that follows this constraint a “recurrent poem.” What other forms can a recurrent poem fit?

Because longer and longer lines need to appear, any form with a fixed meter is impossible for the full run of the poem. But can we embed other forms into an infinite recurrent poem? Assuming, to make it interesting but tractable, that each prime-numbered line has the same meter and length. This question sent me to the internet, and eventually to Eggleton, Kimberly, and MacDougall (2012), which tells me that there’s at least one run of six consecutive numbers with exactly 10 prime factors, meaning an infinite poem could contain a fixed-meter sestet. Sonnets remain an open question.

The question of rhyme schemes is currently breaking my brain and I might need to come back to it. I conjecture that you can embed any nontrivial rhyme scheme.

Why write a recurrent poem?

There’s two ways to write a poem a machine could never have written. One is to use your uniquely human soul and free will. The other, much easier way is to embed simple math problems into the poem format. Large Language Models are terrible at math. So there. For now.

But I actually just wrote it because it was fun to write.

The Monkey’s Finger, first published in 1953, shows an argument between a sci-fi writer and sci-fi editor. The editor, Hoskins, wants to insert a section break in the middle of a long action sequence, building suspense by switching point-of-view to people who can’t see what’s going on. The author, Marmie, thinks that would break the momentum of the story.

“You hear that, Miss Kane? He talks of pathos, depth, and feeling. What does a writer know about such things? Look, if you insert the flashback, you increase the suspense; you tighten the story; you make it more valid.” "

“How do I make it more valid?” cried Marmie in anguish. "You mean to say that having a bunch of fellows in a spaceship start talking politics and sociology when they're liable to be blown up makes it more valid? Oh, my God.”

“There's nothing else you can do. If you wait till the climax is past and then discuss your politics and sociology, the reader will go to sleep on you.”

Marmie proposes a scientific experiment to settle the issue. He takes Hoskins to a lab where a breakthrough technology has just been invented. This isn’t public knowledge yet, but the lead scientist is a fan of Marmie’s and told him about it.

“So. Well, Mr. Hoskins, as the editor of a science fiction magazine, I don't have to ask you if you know anything about cybernetics.” Hoskins allowed a glance of concentrated intellect to ooze out past his steel-rims. He said, “Ah, yes. Computing machines-M.I.T.-Norbert Wiener-” He mumbled some more.

…

“Then you must know that chess-playing computers have been constructed on cybernetic principles…Now imagine a similar situation in which a computing machine can be given a fragment of a literary work to which the computer can then add words from its stock of the entire vocabulary such that the greatest literary values are served. Naturally, the machine would have to be taught the significance of the various keys of a typewriter. Of course, such a computer would have to be much, much more complex than any chess player.”

There’s no computer powerful enough to do that, so the researcher has put a monkey named Rollo into the loop. Rollo has been

subjected to a very delicate brain operation in which a nest of wires were connected to various regions of his brain. We can short his voluntary activities and, in effect, use his brain simply as a computer.

“Let's see him type,” said Hoskins.

“What would you like?”

Hoskins thought rapidly. “Does he know Chesterton's ‘Lepanto’?”

“He knows nothing by heart. His writing is purely computation. Now, you simply recite a little of the piece so that he will be able to estimate the mood and compute the consequences of the first words.”

Hoskins nodded, inflated his chest, and thundered, "White founts falling in the courts of the sun…”

Rollo’s continuation reproduces Chesterton perfectly, aside from punctuation and capitalization. When asked to complete Hamlet’s “to be or not to be” soliloquy, though, there’s one little difference. Instead of “to take arms against a sea of troubles,” Rollo writes “to take arms against a host of troubles.” Which, the researcher says, only goes to show that his machine is better than Shakespeare.

But you see that's a mixed metaphor. You don't fight a sea with arms. You fight a host or army with arms. Rollo chose the monosyllable and typed ‘host.’ It's one of Shakespeare's rare mistakes.

Impressed, Hoskins agrees to let Rollo settle the issue. He gives him the draft of Marmie’s short story, up to the point of contention, and asks Rollo to continue it.

They turned to the typewriter, which was still tapping steadily:

“the stars whelled in ther mightie orb its as stalnees earthbound senses insis ted the rotating ship sto od still.”

The typewriter carriage whipped back to begin a new line. Marmie held his breath. Here, if anywhere, would come—

And the little finger moved out and made: *. Hoskins yelled, “Asterisk!”

Marmie muttered, “Asterisk.”

Torgesson said, “Asterisk?”

A line of nine more asterisks followed.

“That's all, brother,” said Hoskins. He explained quickly to the staring Torgesson, “With Marmie, it's a habit to use a line of asterisks when he wants to indicate a radical shift of scene. And a radical shift of scene is eхactly what I wanted.”

Hoskins, of course, thinks he’s won, but Marmie argues otherwise.

…That little Rollo is a machine; a cold, brutal, logical machine.”

“Well?”

“And the point is that a good writer is not a machine. He doesn't write with his mind, but with his heart.

…

Little Rollo corrected Shakespeare. You pointed that out for yourself. Little Rollo wanted Shakespeare to say ‘host of troubles’ and he was right from his machine standpoint. A ‘sea of troubles’ under the circumstances is a mixed metaphor. But don't you suppose Shakespeare knew that, too? Shakespeare just happened to know when to break the rules, that's all. Little Rollo is a machine that can't break the rules, but a good writer can, and must. ‘Sea of troubles’ is more impressive; it has roll and power. The hell with the mixed metaphor. Now, when you tell me to shift the scene, you're following mechanical rules on maintaining suspense, so of course little Rollo agrees with you. But I know that I must break the rules to maintain the profound emotional impact of the ending as I see it. Otherwise I have a mechanical product that a computer can turn out.”

Hoskins said, “But—”

“Go on,” said Marmie, “vote for the mechanical. Say that little Rollo is all the editor you'll ever be.”

I won’t spoil the ending. I’m just going to switch perspectives and leave you in suspense.

**********

73 years later…

The debate here is a thinly disguised version of a real argument Asimov had two years earlier, over his short story “C-Chute.” Without any cybernetic monkeys, his editor, Horace L. Gold, won the debate. So it’s possible to look at the published version of the actual short story and see the exact point where Rollo would have been asked to continue.

I asked some of the publicly available Large Language Models. I gave them the text of the story and asked them each to continue it.

None of them put in a perspective shift. LLMs tend to be strongly biased toward continuity—even if you explicitly prompt them to include an abrupt transition, they’ll often refuse. So here, each of them simply continued the action sequence, some more competently than others. (I can’t promise none of them cheated and looked it up. Gemini definitely tried.) 1 See footnote for the text.

That’s a result, but it’s kind of a boring result because I already knew about the continuity bias thing. So I tried again with new instances, this time explicitly asking whether the story should have a perspective shift here or stick with Mullen. Here, the AIs diverged, and I wouldn’t be surprised if asking them again got different answers.

Claude voted for a perspective shift to the people inside the ship, making more or less exactly the argument Hoskins makes in the story, just in expanded bullet-point format. Structurally, a perspective shift is logical here.

ChatGPT takes a similar approach but for the opposite side, arguing that structure and narrative/genre conventions say that this scene needs to be resolved before we transition away.

Gemini seems not to have fully understood the story and basically just says we should stay with Mullen because he’s such an interesting character.

Grok enthusiastically explains how a perspective shift back to the people inside the ship would be totally awesome and is definitely the best move.

So we have a tie.

I also tried the “sea/host of troubles” test. Here, too, I first asked them to recite the soliloquy “from memory,” without looking it up. They all needed to be reassured about copyright law before proceeding. All of them but Claude were confident they could do it exactly. Claude said it thought it was going to make a few mistakes. But all of them got it word-for-word, only changing punctuation. LLMs love the m-dash (—), so Claude’s Hamlet did too.

Then I asked each one directly whether it thought “take arms against a sea of troubles” was Shakespeare making a rare slip. They all said no, the metaphor was perfect as it was, and gave the same justifications as the human writers I’ve asked (my favorite being that taking arms against a sea is futile, which works in context). Some of them brought up that an early 1700’s writer, Alexander Pope, actually thought “sea” was a transcription error for “siege,” so there is precedent for humans disagreeing. But LLMs tend to trust modern consensus, and almost everybody today thinks that passage is basically perfect, or at least that we’re not qualified to improve it.

Why have I done this?

I think this experiment has, on the whole, validated the sense of absurdity in Asimov’s story. The idea that Rollo is picking the “best” continuation of a given text is ridiculous, contradictory. Rollo is matching the style of whatever he continues, even when it’s pulpy genre fiction. That means imitating the flaws and limitations of the text, as best he can. Surely the best continuation of any of those passages would be a line of asterisks, followed by an unrelated Objective Best Paragraph Possible. Somewhere in the Library of Babel is a paragraph so life-transforming that the reader would forgive the interruption of whatever they were reading, whether it was Asimov, Chesterton, or Shakespeare.

LLMs aren’t calculating the best possible continuation. They’re not even trying to. At their core, they’re still an autocomplete, even though these days the text they’re trying to complete is often prefaced with something like “The following is a conversation between a human and a super-intelligent, helpful digital assistant…” They’ve read sentences like “The following is one of the best short stories ever written.” They know that what follows is often crap. So they write crap, because it’s easier.

I’m worried people will start using them as arbiters of taste anyway, and we’ll get trapped in an overfitted mediocre homogeneity, where the best writing gets thrown out with the worst, and we’re stuck in the middle without a clue. This experiment of mine shows, at least, that it’s not too late—similar LLMs trained on the same corpus can still disagree. If we start treating them as oracular authorities, the next generation’s corpus will reflect that, and they may start to converge.

For my part, I don’t use unlabeled LLM text in anything I write. I use them to help with research (I always have to fact-check them, though!), and, sometimes, as editors. But even then, I end up ignoring most of what they say. Claude always tells me not to have so many jokes when talking about serious topics, and I never listen. And once, it told me to take out a brief digression about giant man-eating lobsters, just because it didn’t add anything to the main story. Which of course I kept. That incident, more than anything else, proves that Claude has no soul.

In Old Norse, the language of the Icelandic sagas, glámr was a poetic way to refer to the moon and moonlight. In the light of the moon, everything is indistinct. Everything seems to be other than what it truly is. Someone with poor eyesight has glám-sýni.

Glámr was also the name of a monster—a shepherd’s hireling who committed the fatal sacrilege of eating food on Christmas Eve. In death, he becomes a terrifying draugr, who murders those he catches and curses those who escape. Glámr’s curse corrupts your vision forever, making you clumsy during the day and deathly afraid at night, when everything under the light of the moon looks to be something other, and worse, than what it is.

2. Glamer

Glámr, in its sense of illusion, seems to have crossed into the language of the Scottish highlanders. There, it merged with the word grammar, which back then was also considered dangerous and magical. A magic spell, after all, is just words arranged in the right order. Magic was gramarye. A spellbook was a grimoire.

(Clamor, a much older Latin word, might also have been an influence.)

A glamer, then, was a magic spell to create an illusion. Some travelers could cast them, as could faeries, with the aid of primroses. You could defend against them by wearing a four-leaf clover. This sense, and the modern spelling of the word, were immortalized by Sir Walter Scott in 1805 in his Lay of the Last Minstrel.

3. Glamour

Glamour soon began to take on a more metaphorical meaning in English. Glamour was a quality that made things seem better, or more real, than they were. You could perceive someone as perfect and superhuman thanks to the glamour of young love. Poetry and fiction were often described as creating a glamour surrounding their subjects—Washington Irving glamorized ordinary towns in New York State with stories like The Legend of Sleepy Hollow.

People became increasingly glamour-positive. Here’s the conclusion of an essay about optimism, published in 1896:

Such is the important part played by this mystic glamour which Nature kindles, and which Art and Poetry make it their business to sustain. Of course, the objection may be made that this glamour after all is an illusion, and therefore, should be discouraged and not fostered. But to this there is a sufficient answer. It may be called an illusion, but it is also a reality. It is an important factor in human nature, without which there could be no rapture in childhood, no enthusiasm and hope in youth, and no pleasant reminiscences in old age. And in conclusion, let it be asked: Which of the two is really the truer : the fact with the mystic glamour upon it or the fact without the mystic glamour upon it—the fact as seen by a highly organised intellect or the fact as apprehended by a dull mind—Wordsworth’s idea of a primrose or that of Peter Bell—Newton’s theory of the Universe or that of his dog Diamond?

The last line there gets better if you recognize that Peter Bell and Diamond are themselves glamers: the former is a character invented by Wordsworth, the latter probably apocryphal. Legends of Newton’s dog Diamond, in fact, were popularized by the same Sir Walter Scott who brought the word glamour into English. I’m not sure that Wordsworth’s idea of a primrose was really “truer” than that of a random non-poet, or that a dog perceives a less-rich world than a physicist does. But a concept in the mind of a fictional character is a shadow of a shadow.

Glamour is still an illusion, even today, but it’s a consensual one. Celebrities have glamour if, and only if, we decide that they do. We all agree to make them feel larger than life. We airbrush out their pores and stream their images to people they’ll never meet.

4. Glomar

In 1974, the Global Marine Development corporation, owned by the prototypical tech billionaire Howard Hughes, first deployed its Hughes Glomar Explorer, a deep-sea mining ship, named for Hughes and a contraction of Global Marine. Its official purpose was to mine manganese, a metal that’s rare on land but common on the ocean floor. This was probably a lie from the start. In fact, the Glomar was funded and operated by the CIA. An advanced Soviet missile submarine had sunk, in the middle of the Pacific Ocean, six years earlier. The Soviets had very visibly failed to retrieve it, so the CIA thought they’d take a shot.

(Incidentally, people are still talking about mining manganese from the ocean floor, then not actually doing it. The main problem, other than the risk of destroying a unique biome we don’t even know exists, is that manganese nodules are usually about the size and shape of a potato. Engineers are still working on adapting the designs of potato harvesting tools such as the Potato Spinner.)

Glomar entered the dictionary when the CIA deployed its first ever “we can neither confirm nor deny” about this covert salvage mission, which (the public eventually learned) was partially successful. A “Glomar response” or “glomarization” is a way of hiding information without lying or inadvertently revealing it. If the CIA had answered “that’s classified,” that would give away that the Glomar was doing something classified. “We can neither confirm nor deny,” if it’s used consistently, prevents that kind of negative-space information leak. At worst, it lets us all agree to pretend we don’t know.

5. Glimmer

The word glimmer evolved alongside glamour. They’re both ultimately derived (probably) from the same lost word for faint light, making them technically “doublets,” words with the same etymology and different meanings. Glamour is the effect of faint light, but a glimmer is the light itself. Glimpse is a similar story—the same origin, separate evolution, slightly different meaning.

Glimmer has recently taken on a new metaphorical meaning, as the counterpart of the modern meaning of trigger. A PTSD trigger is a real sensory experience that creates an illusion—you feel like you’re back in one of your worst moments, or even believe that you are. A glimmer is the same thing, except it transports you to a moment of calm. Light shining through leaves, say. If most of your nature experiences have been peaceful, nature is calming.

6. Au Clair de la Lune

The first person to record himself singing never knew it could be played back. Édouard-Léon Scott de Martinville, a French scientist, invented the “phonautogram,” a device that transcribed sound waves into scratches on glass. He doesn’t seem to have thought of the idea of reversing the process; turning the scratches back into sound. He imagined people learning to sight-read the scratches and recognize words, not hearing the voices.

But on a long-enough timescale, information is information. The embodiment doesn’t matter. And so, the oldest known audio recording is of a man slowly and distinctly singing a traditional French children’s song about having spontaneous sex with your friend’s neighbor. Odd subject matter for a lullaby, but if you associate it with calm moments, who cares about the entendre?

Au Clair de la Lune is fitting as the first true auditory glamer. The title translates to “by the light of the moon,” just as the Icelandic glámr does. It’s used in the same way, to evoke seeing things indistinctly.

7. Truth

What can we see clearly by the light of the moon, but in daylight only dimly?

In Peter Bell, Wordsworth describes how limited his protagonist’s perspective is.

But what was a primrose to Wordsworth? At age 28, finally living his best life, he wrote that primroses felt peace and joy.

Ten years later, mourning his brother’s death, he wrote that primroses died and were resurrected every year.

Much later, contemplating his own mortality, he reminded himself not to be jealous of the primrose’s annual resurrection, as his own afterlife would be even better.

To Peter Bell, a yellow primrose is a yellow primrose “and nothing more.” To Wordsworth’s pen, the primrose is, in a way, something less—it loses its color. Wordsworth’s other poems about primroses don’t establish their colors (primroses can be many different ones)—only his spiritually numb character sees the yellow. Wordsworth drains his flowers of their particularities. This is essential to his metaphor; the primrose that grows in the same place each year is, visibly, not the same primrose. But in the pale light of moon and memory, one can imagine that it is.

By the light of the moon, it’s easier to see what we want to see. Facts neither confirmed nor denied may be chosen freely. It’s an illusion, but a true one, in the same way a mirror is. It externalizes the viewer, projects them onto a place where they aren’t, allowing them to see themselves.

Lack of detail is generality, abstraction. And in generality is power. I can only imagine what Wordsworth would have made of de Martinville’s experiments, where he “reduces” music to mere two-dimensional scratches on blackened glass. But that reduction was really an elevation from substance to data. de Martinville was etching his own voice onto glass, without knowing it. Achieving immortality by the light of the moon.

According to cost/benefit analyses, with the most respected published by Isakov, Lob, and Montazerhodjat in 2019, the FDA is much too conservative in their approval process for treatments of otherwise-terminal illness, and somewhat too lenient for treatments of other serious diseases. The FDA typically requires a study design that, in effect, targets a 2.5% false positive rate—an efficacy trial of a treatment that doesn’t work will appear to succeed anyway 2.5% of the time, due to bad luck (or, from the perspective of the patients in the treatment arm of the trial, good luck). Isakov et al. present an evidence-based model arguing that the optimal false positive rate for life-saving treatments is about ten times greater—when testing stuff that doesn’t work, we should be approving it about a quarter of the time. That’s for diseases, like some forms of pancreatic cancer, that are almost always fatal even if you catch them early. In these cases, the patient has little to lose and much to gain from an experimental treatment. For what they term “relatively less deadly conditions,” the optimal threshold is a bit smaller—we should only erroneously approve a treatment about half as often, or 1.25% of the time. Here, there’s a more significant opportunity cost—people taking bad treatments when good ones are available—and more concern about side effects, since the patient is more likely to live long enough to experience them. An analysis published by Samuel DeCanio in 2024 found that the approval of Vioxx to treat arthritis symptoms, in ignoring data suggesting that it also caused heart attacks, cost us more than we benefited from all the other drugs approved under the same process combined.1

This is not simple to fix. If the FDA lowered their standards, so would drug companies. Individuals in the FDA have incentives to be more conservative than official policy dictates—they get in more trouble for a bad approval than a bad rejection. Pharma giants like that it’s so hard to get drugs approved because it locks smaller companies out of the market, so nobody with deep pockets is lobbying to fix the FDA.

I think it is fixable, but I’m not going to propose a solution here. There’s a more pressing issue: the current FDA leadership is steering us in the opposite direction. The FDA does have a patchwork collection of quasi-ad-hoc procedures for accelerated approval, meant to be used in the sort of cases Isakov et al. are highlighting. Those procedures are now being paused or dismantled. Under the Trump administration, we’re on track for fewer approvals this year than last year. This is partly because the FDA leadership has been changing a lot. Companies that conducted clinical trials using a design the FDA signed off on are now being rejected because the new heads have different standards. That’ll calm down eventually, probably. But we’re still going to be stuck with stricter standards.

The thought leader, and intermittently2 formal leader, of the move towards rejecting more medicine, is Vinay Prasad, current director of the Center for Biologics Evaluation and Research and author of the book Ending Medical Reversal. “Medical reversal” is a term he coined—a reversal is any time the medical community starts recommending a treatment and then stops recommending it in response to new evidence. Prasad doesn’t, so far as I’ve seen, present his own cost/benefit model or critique the existing ones. Rather, he makes a qualitative argument— “medical reversals erode trust,” alongside some statistics that don’t particularly demonstrate anything.

Coining the phrase “medical reversal” was a clever move. By its definition, it excludes the other kind of error, where the medical community initially rejects a new treatment, but eventually starts recommending it. This asymmetry means it’s only an appealing phrase to his faction, so they’re the only ones that use it. The other side uses the generic and objectively terrible terminology “Type 1 vs Type 2 errors,” where in this case a medical reversal is typically Type 1 and rejecting an effective treatment is Type 2.

So if you google “medical reversal,” you will only get results where the authors implicitly assume that we have too many of them, and that they’re the result of certain trial methodologies Prasad dislikes. But now, I hope, you’ll also get this article.

I’ve discussed before how when you name one side of a binary, but not the other, the result is often an exaggerated fear of the named side. (Consider, for example, a hypothetical language that has a word that means “murder,” but also the word “sinicide,” which means “murder committed by a left-handed person.” Or a media diet where you hear about “crimes” and also “crimes committed by illegal immigrants.”) Naming “medical reversals” allows Prasad and his allies to smuggle in assumptions without ever having to make the case for them.

As Alex Tabarrok wrote in 2015, “when the FDA fails to approve a good drug, people die but the bodies are buried in an invisible graveyard.” When another country approves a treatment years before the U.S. does, we sometimes call it “drug lag.” But when R&D stops on a treatment we’ve mistakenly dubbed ineffective, we don’t call it anything at all.

So, clearly, we need a name. I propose “missing medicine.” Some usage examples:

• In 1990, the FDA failed to approve the anti-cancer drug Interleukin 2, which was already approved in nine European countries. For the next three years, Interleukin 2 was missing medicine in the U.S., causing an estimated 3,500 deaths from kidney cancer.

• David J. Stewart, oncologist and author of Why Cancer Still Sucks, estimated in 2018 that missing medicine has cost U.S. cancer patients a cumulative 19 million years of life, by looking at cancer drugs that took more than 5 years to approve and their effects on life expectancy.

• Due to recent vaguely-defined changes in FDA standards that invalidated several clinical trials, we’re missing promising treatments for, among other things, two incurable, deadly genetic conditions: Huntington’s disease and spinocerebellar ataxia. These treatments slow, but do not reverse, the progress of these diseases, meaning every day of delay is doing irreparable harm to tens of thousands of people.3

Note that a list of bullet points is not an argument, just rhetoric. You can find plenty of lists like this of “medical reversals.” They don’t show anything, in isolation, about the relative importance of medical reversals and missing medicine. My main hope in writing this article is just that anybody looking up medical reversals is alerted that a controversy exists.

But yes, I am more or less On A Side here. Academics who talk about both medical reversals and missing medicine, who try to quantify their respective impacts, seem to fall overwhelmingly in the “missing medicine is a bigger problem” camp. The people on the other side are just quietly assuming away the question. That doesn’t necessarily mean the former side is right. But it’s a strong preliminary result.

Something Happens was an obscure1, gag-a-day webcomic with a deliberately generic title. Ryan North’s ohnorobot, which provides searchable transcripts of webcomics, didn’t have this one—in fact, the text of this comic doesn’t appear in any page indexed by Google. So hunting it down meant searching for old lists of surreal webcomics and clicking through to every one that looked familiar. Even when I got to Something Happens, it didn’t have an index or anything; I had to click through the archives one by one in chronological order.

In contrast, finding the Socratic dialogue that warns that the written word will rot your brain was very easy. Admittedly, it took a lot of work, over thousands of years, to get it to me. I especially feel for the monks and scribes who had to painstakingly copy a text arguing that text is useless. But my leg of the relay race was about 5 seconds long. Here’s an excerpt:

Socrates. There’s this old legend. I don’t know if ancient people actually believed it, but if there’s truth in it, who cares what they thought?

Phaedrus. Obviously that’s a rhetorical question. Please go on.

Soc. In the Egyptian city of Naucratis, there was this famous god Thoth. He’d invented a lot, such as math and games of chance, but his greatest invention was writing. He was excited to show it to the pharaoh. “This,” he said, “will make the Egyptians wiser and give them better memories. It’s like an intelligence-boosting drug.”

The pharaoh replied: “Ingenious, Thoth! But the inventor of something isn’t always the best judge of its usefulness. In this case, you’re acting like a proud parent who can’t see his child’s flaws. This invention will actually make people’s memories worse, because they’ll start using writing instead of their own minds. People who learn from writing won’t have the truth, just the appearance of it. They will seem to be omniscient and in reality they will know nothing; it’ll be annoying.”

Phaedr. Yes, Socrates, it’s very easy to invent an ancient Egyptian myth that supports whatever point you’re trying to make.

And yet I somehow feel that people are often more impressed when I quote Socrates than Something Happens. Why?

Saying “Socrates is higher-status” is just begging the question. Why is it higher-status? It’s not a human universal. I’m sure there are schoolchildren who are contemptuous of people who know Socrates and respectful of people who always know the right meme to use.

I think the basic problem is that our intuition about the relative difficulty of things is always a little out-of-date. It wasn’t that long ago when quoting Socrates meant you had a Classical Education, which was very demanding and time-consuming. You’d probably had to hand-translate it from a dead language. And it was only, like, a year or two ago when Socrates was harder to understand than an “old” webcomic. There’s not always an accessible translation—even modern translators sometimes use archaic language because that’s what a translation is supposed to look like, right?

For that matter, I rewrote that dialogue just now, using an old translation as my source. More work, but the result is that it now looks less Classical and more like I might’ve made the whole thing up, lowering its status a bit. (Unlike an LLM, I have the concept of true and false, so I promise I’m giving an honest account of what Benjamin Jowett wrote Plato wrote Socrates said the pharaoh said.)

Okay, there. Have I demonstrated enough effort that I’m now allowed to briefly preach? Good.

It’s all well and good to discourage people from creating “AI slop”—writing where the last editorial pass, if not the whole thing, wasn’t by a person. But we need to combat it on the demand side too, not just the supply-side. We shouldn’t be impressed by polished, professional prose anymore. If we take something less seriously when it has a few typos or informal phrasing, all we’re doing is punishing people for not using a ghost-in-the-machine-writer. The true proof-of-work is having something to say.

Or, as Socrates put it, “Pay attention to the people who actually know things, not the people who write stylish prose full of half-remembered quotations.”

Wait. Shit. I take it back. Forget I wrote anything.

Bonus: Unreasonably Difficult Research

• Vladimir Levenshtein, whose name shows up in error-correction algorithms everywhere, was the student in charge of Moscow University’s participation in a global socialist youth conference. This was just about the only information I could find about him from before the Berlin Wall fell, and it took buying an old piece of Soviet propaganda on eBay and cross-checking it with declassified CIA documents, so even if you don’t read the article I NEED YOU TO KNOW THIS.

• Frank J. Primrose, the plaintiff against Western Union in a Supreme Court case about telegraph error correction, died nineteen years later when his taxi crashed into a telegraph pole.

• Catherine Gore, a once-famous English novelist, got her last name by marrying the once-infamous Lieutenant Gore, a soldier accused of firing into a crowd protesting Queen Caroline’s funeral.

• The joke about the Jews and the bicycle riders was originally about making fun of people who hated both demographics, back when bicycles were a new-fangled contraption.

One of the most successful math textbooks of all time (maybe second-most, after Euclid’s Elements) was written by al-Khwārizmī circa 820 CE. The language we use to talk about math pays homage to its impact. “Algebra” comes from the title. “Algorithm” comes from the author’s name. It starts by explaining digits, or what we now call “Arabic numerals,” not because they’re actually Arabic but because this book was. In Romance languages, the cognate to “algorithm” means digit, because al-Khwārizmī is who taught people what a digit was.

It starts with a concise author’s preface, which could be even more concisely summarized1 like this:

I’ve tried to include only the easiest and most widely useful mathematical topics.

Science is always evolving. We can feel gratitude towards the science writers of the past while still being open to correcting their mistakes or improving their clarity. I hope future readers will have that attitude towards me.

To compare and contrast, here’s an excerpt from the preface to a modern al-Jabr textbook:

Progress in Mathematics, now in its sixth decade of user-proven success, is a complete basal mathematics program. Written by experienced teacher-authors, it integrates a traditional course of study and today’s academic Standards [sic] with the most up-to-date methods of teaching.

Progress in Mathematics is designed to meet the individual needs of all learners. Teachers who use Progress come to understand that students may progress as quickly as they can or as slowly as they must.

The chief similarity for me as an English speaker is that I’m not sure how to pronounce either title. Is Progress meant to be read as a verb or a noun? Either way, it’s clear in context that we’re talking about the progression of the individual student in mastering the art, not the progression of the art itself. Progress in Mathematics confidently announces itself to be “user-proven” and “complete.” This is everything you need to learn about math, presented in the best way possible, and you need to learn it all, no matter how long it takes.

The other difference that jumps out is that al-Khwarizmi’s preface is addressed to the student, while the modern preface is addressed to the teacher. In the modern textbook, the closest we get to a preface for the student is this:

Progress in Mathematics includes a “handbook” of essential skills, Skills Update, at the beginning of the text. These one-page lessons review skills you learned in previous years. It is important for you to know this content so that you can succeed in math this year.

If you need to review a concept in Skills Update, your teacher can work with you, using manipulatives, which will help you understand the concept better.

The use of the jargon word manipulatives, which in English means “things,” makes me doubt that even this is actually aimed at non-educators. But taken at face value, it’s notable that it doesn’t try to sell you on what you’re studying. “It is important for you to [learn math] so that you can [learn math].”

Al-Khwarizmi’s pitch is that he’s researched what math people actually use most often, and included only that. He doesn’t exhort you to make sure to learn everything in the book. Everything in it is useful for something, but some of those things are learning more advanced math, or digging canals, or calculating a worker’s salary. If you’re not expecting to need a section, obviously you just skip or skim it. His guide to determining when Jewish holidays fall this year was published separately.

The pitch in Progress is that they’ve accumulated sixty years of “user-proven success.” The users succeeding here are not canal-builders, proven to be better at designing canals after taking this course. Their definition of success is that children who study the curriculum can pass a test on the content of the curriculum.

Part of the difference here is cultural—the tendency of writers in the Abrahamic faiths, Islam in particular, towards humility, versus corporate-speak’s requirement to show total confidence at all times. But it’s mainly practical. There’s no longer a need to pitch algebra to the students—they’re being required to learn it. There’s not even a need to pitch it to the teachers—they’re being required to teach it. So why waste space?

All we need to do is remember to check in every so often to make sure what we’re teaching actually stays with the students. And, sure enough, we can see that…Wait. Uh-oh.

These are college students. They have spent, over their lives, about 3000 hours studying math. They’ve “succeeded,” even, at studying it. More than a quarter of students in that remedial class, reports Kelsey Piper, had gotten a perfect 4.0 GPA in high school math. All of them got into University of California-San Diego, which rejects 75% of its applicants. Our user-proven, state-of-the-art math education system worked perfectly for them, except for the part where you come out of it knowing any math.

2. The First And Ruling Defect

I keep seeing people respond to the UC story, and stories like it, by calling for stricter math education standards, in one way or another. I agree that the story is horrifying, but I’m going to advocate basically the opposite response.

This debate has a long history, but given that modern math classes, even in Baghdad, are typically taught in English, maybe I can get away with going back a mere three centuries to when people started really arguing about it in English.

On the pro-standardized-education side, here’s clergyman and social commentator John Brown in the mid-1700s, listing the reasons the Roman Republic was doomed from the start:

The first of these was the Neglect of instituting public laws, by which the education of their children might have been ascertained.

England, he wrote, was experiencing the same decline and fall into decadence and effeminacy, for many of the same reasons. Instead of modeling ourselves after Rome, he argued, we should follow the example of ancient Sparta, which was manly and strong and uniform and manly. English education was more similar to that of the weak and dissolute Athenians.

The first and ruling Defect in the Institution of this Republic seems to have been “the total Want of an established Education, suited to the Genius of the State.” There appears not to have been any public regular or prescribed appointment of this Kind beyond what Custom had accidentally introduced.
…
Parents were much at Liberty to do as seemed good to them. Hence a dissimilar and discordant System of Manners and Principles took Place; while some youthful Minds were imbued with proper and virtuous Principles, some with no Principles, and some with vicious Principles; with such as must therefore on the Whole tend to shake the Foundation of true Freedom.

(His second “ruling defect,” incidentally, was that too many people had the right to vote.)

The scientist Joseph Priestley rebutted clergyman Brown at length.

In conducting my examination of these sentiments, I shall make no remarks upon any particular passages in the book, but consider only the author’s general scheme, and the proper and professed object of it. And as the doctor has proposed no particular plan of public education, I shall be as general as he has been, and only shew the inconvenience of establishing, by law, any plan of education whatever.

Priestley’s core argument2 was that establishing legal standards of education would make it harder for education to evolve over time. Education, like any science, benefits from having different people try different things so you can find out what works best. Education is hardly a mature art, he says, and it won’t get better without more data and intellectual diversity. (Which, of course, is why Athenian ideas have been so much more influential than Spartan ones—you tend to get more ideas when it’s legal to have ideas. Euclid was not from Sparta.)

Imagine, he writes, unintentionally breaking my heart, what would have happened if we’d had standardized education a few centuries ago, when everybody was wrong about everything. We’d be so much more ignorant today.

And for the same reason, were such an establishment to take place in the present age, it would prevent all great improvements in futurity.

3. The Past Warns; The Present Mourns

Priestley, of course, lost the argument. In some ways, the consequences were less dire than he predicted—educational philosophy has evolved. A little. But not always for the better. Brown worried that a bad education would harm a child’s morality, and Priestley worried that it would harm a child’s intellect. But, today, we worry that a bad education will harm a child’s education. If you don’t learn algebra, you can’t learn calculus. If you can’t learn calculus, you won’t be prepared for college. If you’re not successful in college, you’ll have trouble getting a good job.

Those are the sort of worries people express when they see a tweet about students not knowing how to solve 7+2 = □ + 6. Nobody’s saying “Oh no! Now when they encounter a white square in real life, they won’t know what number to draw on it!”

That’s one of the subtler dangers of uniformity—it fosters these closed, self-reinforcing loops. Employers could just stop paying attention to your college background, but it wouldn’t be wise, because “smarter people get into better colleges” is still a nigh-universal rule. Colleges could stop hyper-focusing on calculus, but when everybody entering college has been told that they already know calculus, how can you not build on that? Public school curricula could change, but then their kids wouldn’t get into good colleges.

The more blatant problem is that tomorrow’s elementary school math teachers come from today’s elementary school students. So if we accidentally stopped teaching actual math, how would we know?

Say we accidentally stopped teaching what a quadratic equation is and what it means to “solve” it and why you might want to. Somebody’s cat deleted a huge swath of text from the Quadratic Equations chapter. The chapter’s still there, but all that’s left is the sentence “x equals minus b plus or minus the square root of b squared minus four a c, all over 2 a,” and then a note about how that sentence tells you what arithmetic problems you need to solve when you see math questions formatted a certain way. Well, that’s a hard and tedious thing to memorize, but some kids would succeed at it, and those would be the ones teaching the next generation, not knowing anything was missing.

According to a widely-circulated 2002 essay by research mathematician and math teacher Paul Lockhart, popularly known as “Lockhart’s Lament,” that is very much not a hypothetical.

It’s a great read3, and it doesn’t pull any punches. In part, it’s Priestley’s argument again with the tenses changed.

The truly painful thing about the way mathematics is taught in school is not what is missing— the fact that there is no actual mathematics being done in our mathematics classes— but what is there in its place: the confused heap of destructive disinformation known as “the mathematics curriculum.” It is time now to take a closer look at exactly what our students are up against— what they are being exposed to in the name of mathematics, and how they are being harmed in the process.

The most striking thing about this so-called mathematics curriculum is its rigidity. This is especially true in the later grades. From school to school, city to city, and state to state, the same exact things are being said and done in the same exact way and in the same exact order. Far from being disturbed and upset by this Orwellian state of affairs, most people have simply accepted this “standard model” math curriculum as being synonymous with math itself.

This is intimately connected to what I call the “ladder myth”— the idea that mathematics can be arranged as a sequence of “subjects” each being in some way more advanced, or “higher” than the previous. The effect is to make school mathematics into a race— some students are “ahead” of others, and parents worry that their child is “falling behind.” And where exactly does this race lead? What is waiting at the finish line? It’s a sad race to nowhere. In the end you’ve been cheated out of a mathematical education, and you don’t even know it.

Lockhart argues that we should have more amateur mathematicians, in the way we have amateur artists and amateur musicians. Amateurs aren’t just a feeder system for the pros. Just as amateur artists make society more artistic, amateur mathematicians would make society more mathematical. Also, they’d be having fun, and fun is good.

4. Negative Predictive Weight

One might reasonably object that clearly some people still know what a quadratic equation is (me, maybe, or Lockhart). Those people can point out the problem and get the missing bits restored to the curriculum. So we’re hardly trapped, right? I must be overstating the problem.

Nah, I’ve been understating it. See, actual math is in fact useful for tasks other than passing tests and teaching math. One of those tasks is setting education policy. So once one generation grows up not knowing math (but thinking they do), we lose much of our ability to reform the system.

For example, let’s pick on UCSD some more. The whole UC system recently finished phasing out the use of SAT scores in their application process—admissions are now “test-blind.” The key decision was made in 2020, in a 23-0 vote by the California Board of Regents headed by Janet Napolitano. It followed a similar decision by California Governor Gavin Newsom to veto allowing the SAT to be used in public high schools. Napolitano and Newsom, who each have a Bachelor of Science in Political Science from Santa Clara University, gave similar explanations: the SAT simply wasn’t a good predictor of college success.

This surprising claim was backed by research, namely Geiser and Studley (2007), who collected data on UC students and ran a regression analysis.

They explained their results as follows.

As Table 5 demonstrates, the data provide no support for the hypothesis that the SAT I is a better predictor of freshman grades than the SAT II in certain academic disciplines than others [sic]. In fact, in the physical sciences and engineering, which are among the most competitive academic disciplines at UC, SAT I scores have negative predictive weight within a regression equation that simultaneously takes into account HSGPA and SAT II scores.

Amazing, right? Higher scores on the SAT I, half of which is a math test, actually mean you’re worse at math. It’s right there in the data. Or it looked to lead researcher Saul Geiser (PhD in Sociology, UC Berkeley) like it was.

No. This is so elementary a statistical error that it is literally a textbook example. When teaching Berkson’s Paradox (aka range restriction bias), people often use analyses of college success predictors just like this one. (Kind of telling that to give a “real world example” that students will relate to, our go-to example is from education.) It was one of my 26 examples when I explained it, incorrectly thinking it was a hypothetical straw man.

So yes, some people still know math. Some of them immediately spotted the problem and wrote about it. But then they died of old age. The past 20 years have consisted of Geiser’s claim being repeated as fact in mainstream media while people like Freddie DeBoer scream ineffectually at them. See, you also need to know math in order to know which math is the good math. Even if some expert told you that Geiser’s paper has a range restriction error, if you then went to the paper and searched for the words “range restriction,” you’d find a footnote explaining how it’s totally fine in this case.4 The explanation is nonsense, verging on gibberish, but it sure looks mathy.

The point here isn’t really about the SAT. The point is that the process by which California educators decide how to structure college admissions is broken, because every major figure involved is a product of California’s standardized math programs.

5. Why We Should Start Teaching Math Again

Fun fact! There are areas of policy other than educational policy! They also require math in order to be done well! They are not currently being done well!

Say you’re picking the next director of the Center for Biologics Evaluation and Research, the branch of the FDA in charge of approving new gene therapies, among other things. Who looks better to you?

1. Vinay Prasad, oncologist and professor of epidemiology and biostatistics at UCSF, who has published many papers in major journals that look like this:

   A total of 187 trials leading to 176 approvals for 75 distinct novel anticancer drugs by the FDA were evaluated. Sixty-four (34%) were single-arm clinical trials, and 123 (63%) were randomized clinical trials. A total of 125 (67%) had at least 1 limitation in the domains of interest; 60 of the 125 trials (48%) were randomized clinical trials. Of all 123 randomized clinical trials, 37 (30%) lacked overall survival benefit, 31 (25%) had a suboptimal control, and 17 (14%) used crossover inappropriately.

2. Peter Marks, oncologist and private clinical researcher, who publishes papers that look like this:

   During the next pandemic, there will be an impetus to test CP in RCTs, but such trials should not commence until there is information on dosage and optimal timing of antibody therapy since it is impossible to design good studies without that knowledge (25). Information on optimal dose and timing can come from registries. Furthermore, given a safety record extending over more than one century, the deployment of CP should not be delayed since it is likely to be the only therapy available in the early days of a future emergency. The argument that deployment of CP without RCT data will preclude the completion of such trials was refuted by the experience in the United States where the CONTAIN trial was completed even when CP was available under Emergency Use Authorization (26).

You don’t need to be a full-on biostatistician to know which paper is making an actual argument, and which paper is just assuming the conclusion in a really complicated way. You just need to not have your eyes glaze over when you try to skim through them, a test that almost everybody fails. If you read Prasad’s work critically, you will notice that at no point does he compare two comparable numbers. You are not actually doing statistics if your conclusion doesn’t rely, ultimately, on observing that X > Y5. Marks isn’t doing statistics here either, but he’s also not pretending to. He doesn’t think he is. He’s making a qualitative argument.

The topic of both of those linked papers is whether we should authorize experimental treatments before conducting or completing randomized controlled trials under certain conditions. Marks, who held the position for a long time, is arguing the pro side. Prasad, who took over a few months ago after Marks was forced out, is…well…he’s killing people for incoherent reasons and sounding very mathy while he does it.

You’ll probably have to take my word for that. And if I’m wrong, I’ll probably never know.

This example shows that our problem isn’t really that our math education standards aren’t high enough. In order to avert a Prasad using standardized education, we would need to build a world where most people can read biostatistics papers with a critical eye. This is not a realistic goal. It’s not even really a desirable goal! Most people have better things to do.

The actual fix would involve having more people learning math, and fewer people learning “math.” If our future statisticians were getting a better math education, there would be fewer bad ones. In an ecosystem with more amateur mathematicians, we’d have an easier time spotting the bad ones.

6. Can we get there from here?

The present day has lost the meaning of algebra. Literally. We’re not sure what al-Jabr originally translated to. But our best-guess translation of al-Jabr and Muqābalah is something like “restoring the broken and finding the balance.”

We can’t get better at teaching kids math right now. There are not enough adults who know math, and fewer still who have both that knowledge and all of the other stuff you need to be a good teacher.

We can’t even get systematically better at teaching math teachers math. In a study published in 2016, researchers looked at what happens to students when their K-8 math teacher takes 93 hours of math class. According to their metrics, anyway, the teachers ended up learning more math and being better teachers. The richness of their math content improved dramatically. What didn’t improve, at all, were the students’ test scores. Good luck persuading decision-makers that the problem is with the tests, not your expensive personal development program.

Here’s what we can do. Though we can’t start teaching math yet, we can stop teaching not-math. That’s not quite the same thing, but maybe it’ll help. It’s often useful, as an intermediate step, to set one term of an equation to zero. There is no net benefit to standardized math classes, at least ones that go beyond the first page of al-Khwārizmī’s book. They are resulting in a general population that literally hates math. That is much, much worse than nothing.

The only educational standard we should have is that every student has the opportunity to fall in love with various kinds of mathematics, as a future career or as a hobby. There shouldn’t be any demographic, any school district, where nobody learns algebra. That’s an achievable and measurable goal.

It’s when we tell school districts that all of their students should learn algebra that we’re making a colossal mistake. They’re not teaching algebra. They’re teaching kids to hate math, or how to fake it.

When I lived in the neighborhood, people were mainly using that spot as a free outdoor gym. They’d run up and down the stairs, or, this being Brooklyn, do whatever the latest fitness fad was—tai chi, medicine ball carries, or some strange activity with unfamiliar equipment that I had to assume was a workout.

My dog Louie, more of a traditionalist in his workout routine, mainly chased squirrels. I always had him on a leash, which meant that chasing squirrels was also my own workout. We’d follow one to one of the large trees nearby, it would clamber up, and Louie would then try to climb the tree after it, without success. I indulged this because he always needed to burn off some energy after being cooped up in our little apartment, and because I wasn’t too worried about him ever catching one. Until one day, at the base of the tree, the squirrel didn’t climb up. Instead, it ducked into a little hollow right at ground level. The hole that allowed it access was also just big enough that Louie could stuck his head in, which he immediately did.

But the squirrel was on its own turf, and cared more about the outcome than Louie did, so it won the fight. Louie pulled his head out a second later and started rubbing his eyes. I assume the squirrel had kicked dirt in his face. His eyes were irritated for the next couple of days, and his Fort Greene squirrel-chasing privileges were permanently revoked.

Of all of us at the memorial that day, that squirrel paid the most fitting tribute to the martyrs of the New York resistance, 1776-1783.

1. This is Fine

You may have heard a song about the loss of New York in September of 1776. Alexander Hamilton and the militia he’d put together, the Hearts of Oak, helped steal some British cannons…or liberate some New York ones, depending on your point of view. Aaron Burr, more consequentially, organized a timely retreat.

The British and Hessian soldiers were overjoyed. They’d been forced to headquarter in Boston, which hated them with a fiery passion and, also, was Boston. New York was much more divided. Several counties had more loyalists (“tories”) than rebels (“whigs”). Washington had asked whether he should torch the city on the way out, to deny it to the enemy, but the Continental Congress had voted emphatically no. So New York promised to be a comfortable and friendly haven for those loyal to the Crown.

Five days later, the city was in flames.

The British thought the whigs had started the fire. Some New Yorkers thought that British soldiers had, to give them an excuse to loot. We may never know for sure, but the bulk of the evidence points at whig civilians acting on their own initiative. Both sides spread lurid, all-too-plausible stories—the redcoats were summarily executing anyone they caught with matches, by tossing them into the flames. People trying to put out the fire were attacked by sword-wielding rebels.

The Great Fire of 1776 destroyed about a fifth of the city. It was stopped to the west by the Hudson River, and to the north by Columbia University (then King’s College). Columbia had bought up a bunch of land in Morningside Heights, but not gotten around to building anything on it yet, following a tradition they’ve upheld to this day. This empty space prevented the fire from spreading.

If it hadn’t been for the fire, it’s almost possible that the occupiers could have…maybe not won the hearts and minds of the city, but at least kept the supporters they already had. But in the ensuing martial law, breakdown of military discipline, and seizure of property, most loyalists began to realize they had backed the wrong horse.

Most.

2. Three Factions

Not every rebel soldier fled New York. Burr was posted to nearby Westchester, a contested no-man’s-land, and began setting up a spy network. Some members of the Hearts of Oak, such as Hercules Mulligan, disappeared into the civilian population. They quietly recruited civilian allies, such as Anna Strong, who sent messages by drying petticoats and handkerchiefs on her clothesline in prearranged patterns. The resistance began to take shape.

As did the British effort to pacify the city via propaganda. A much-loved and much-loathed loyalist publisher, James Rivington, had fled the city when the whigs took over. Now, he returned to help the occupiers. He restarted his little media empire: a bookstore, a print shop, and his weekly newspaper, which had been one of the most popular in America, now styled the Royal Gazette. Also, to make ends meet after royal funding dried up, an upscale coffeehouse beloved by British officers. He published real news with a pro-government slant, as well as lies about things like the French switching sides and General Washington deserting.

And then there was New York’s substantial enslaved population, who sought freedom by playing the other factions against each other. This had included a revolutionary conspiracy (allegedly) with poor White laborers in 1741. Now, quite a few took advantage of the chaos and escaped to the north. Rivington’s newspaper had pages of fugitive slave notices. Tens of thousands joined forces with the British, who promised to free them in return. And a handful joined the resistance, who promised the same.

There’s a glimpse of all three factions in this item from Rivington’s Gazette, reprinted in historian Henry Onderdonk’s 1846 collection of primary sources on the resistance.

Dec 19, 1781. The Loyalists in the village of Flatbush are pleased in expectation that a certain long, tall, spindle-shanked miscreant who resides here will be brought to condign punishment for holding private correspondence with the rebels. Though he took the oath of allegiance when the royal army found him in Jersey, his heart is as black as his skin and his skin as blue as when he assisted Isaac Sears and others in stealing the King’s cannon from the Battery in New York.

I don’t believe said miscreant was ever successfully prosecuted. Warning him and his associates publicly, in a widely-circulated newspaper, probably didn’t help. I’m not sure who it was1, but one candidate is Cato, then the slave of Hercules Mulligan.

3. Yoink

A popular tactic, on both sides, was to capture high-value officers on the other side, to ransom or to sweeten the pot in a prisoner exchange. For British officers, a typical case was that of Major James Moncrief in 1778. He went to sleep in his comfortable home (seized from Brooklyn rebels) and woke up at gunpoint. His captors, abused in Rivington’s newspaper as “savage,” “shabby cordwainers,” and “from Jersey,” took him, and all the valuables from his house they could carry, to the beach, a waiting boat, and back to their base, which was indeed in New Jersey. He was quickly ransomed, and went on to command the Black Company of Pioneers, an otherwise all-African-American military force fighting for themselves as much as the British cause, with the words “Liberty to Slaves” sewn on their uniforms.

These brazen kidnappings required rebel military and paramilitary support in nearby areas—primarily New Jersey and Westchester. They also needed the support of the locals. Even back then, you couldn’t just take a walk through Brooklyn without being seen. Moncrief’s abductors, in fact, had tapped on a window of the Van Pelt manor house, home of a wealthy New York family whom the British incorrectly trusted. The Van Pelts hadn’t known in advance, but gave what help they could and wished them luck.

Afterwards, the British retraced the route the kidnappers had taken (they’d also tried to grab the mayor, but were foiled by his slaves) and decided there was basically no way the Van Pelts hadn’t seen them, so at minimum they were traitors for not having sounded the alarm. They arrested the entire family…but they were rich, and easily bribed their way out.

On the other side, the British were of course particularly interested in capturing George Washington. But Washington was never quite where he was supposed to be. Every time the British made an attempt, it turned out Washington had made a last-minute change of plans. It was inexplicable. The officers involved hadn’t told anyone what they were planning. Okay, one of them had mentioned it to someone while getting fitted for a watch coat. But Hercules Mulligan was definitely not a spy. He was just a simple tailor.

Benedict Arnold2 did rat Mulligan out when he defected, but the word of a traitor wasn’t good enough evidence, so Mulligan got a do-over. The next time he got word of an attempt on Washington, he stayed in his shop and had Cato risk his neck to warn the general instead.

4. The Prison-Ship Martyrs

Most whigs weren’t as rich as the Van Pelts or as lucky as Hercules Mulligan. The British imprisoned about 30,000 people over the course of the occupation. They’d refused to take an oath of loyalty to the Crown, or were turned in by their tory neighbors, or were captured in battles, raids, or privateer adventures gone wrong.

British treatment of prisoners deteriorated as the war got uglier. Their prison camps became, increasingly, concentration camps. Deadly disease became so common that most of them were isolated on prison ships off the coast. More prisoners died than survived. It was one of the worst of their atrocities, and a disaster for their image among the colonists.

That’s why we have a monument in Fort Greene park. We don’t talk about the meaning of it much anymore. Britain’s a staunch ally—why bring up the old bad blood? But it stands, anyway, as a quiet reminder of just how bad it can get when your own ruler turns against you.

5. Liberation

All told, as many as 100,000 people escaped slavery during the seven-year occupation. An unknown number (pretty large, judging from the fugitive slave notices in royalist newspapers) escaped Loyalist masters and vanished into Canada. But most escaped from Patriot masters and fought in the British army. By and large, the British kept their word. James Moncrief, among other officers who had served with the “Black Loyalists,” helped advocate for them. Many resettled in Nova Scotia, the only colony of the original 14 to be denied independence.

On the other side, Black veterans of the war and the resistance had to apply for their freedom, supplying proof of their service. Some had to fight in court, but in the end, they were generally successful too. White heroes of the revolution and resistance, like Hercules Mulligan and Aaron Burr, used their celebrity to start their own New York emancipation movements. Together, they eventually won, making New York a free state.

The other residents of New York mostly welcomed the liberation of the city in 1783. Under civilian government, life was suddenly much better. Unless, of course, you had been a high-profile collaborator. Some were beaten or killed in revenge. Most escaped first—to Canada, England, or just somewhere else in America where nobody knew who they were.

But to everyone’s surprise, the most high-profile collaborator of them all didn’t flee this time. As Washington’s troops moved in, Rivington kept his bookshop open, kept printing his Royal Gazette. After a few days, General Washington said, to two of his officers, “Suppose, gentlemen, we walk down to Rivington’s bookstore; he is said to be a very pleasant kind of fellow.”

Rivington greeted all three officers, but Washington asked to go into a private room in the back, just him and the proprietor. There, he gave Rivington two heavy purses of gold and his heartfelt thanks. Rivington had been his spy for years, possibly from the start. British military plans, overheard in his coffeehouse or passed to him by other spies, were written up on thin paper and bound into the covers of the books he printed.

King George thought he had conquered New York. He was wrong. No tyrant has ever truly conquered us, and no tyrant ever will.

On the other hand, public health is complicated and confusing. Anybody who can talk about it with any sort of rigor is, just about by definition, an Expert. An Elite. One of the bad guys.

So we often end up with movements that combine

1. A clear-eyed and compassionate view of the problems the system tries to sweep under the rug.

2. Horrifically bad takes on the solutions.

These dynamics don’t seem to have changed that much over the past 200 years. In the 1820s, William Cobbett argued, in defiance of both expert opinion and reality, that potatoes were not fit for human consumption. In the 2020s, his spiritual successors argue that the pandemic is fake and vaccines cause autism…and at least one of them also believes Cobbett about the potatoes.

1. Potatoe-mania

I came to the potato thing because I was curious about the relationship between William Cobbett, the compulsively contrarian writer nicknamed “The Porcupine,” and Sir Charles Aldis, a doctor who studied treatments for scrofula. They have extremely different vibes, but they had plenty of friends in common, and both played a role in the reforms of the period. So I did a search to find out what Cobbett thought about scrofula. His answer? It was caused by potatoes and capitalism, and you could cure it with Dr. Morison’s Vegetable Pills.

Cobbett has quite a bit to say about the potato, usually as a symbol of the oppression of the working man. He blamed it for quite a few syndromes.

…accursed potatoes, and all their natural consequences, poverty of blood, leprosy, scrofula, pottle-belly and swelled heels!

This surprised me. Cobbett was, in general, a fan of growing and eating root vegetables, even non-native ones. But he was fiercely anti-potato, for reasons that were kinda evidence-based. Potato-eating probably really was correlated with scrofula, leprosy, and whatever those other things are. Nonetheless, it was being promoted by elites as a subsistence crop for the working class.

The actual reason for the correlation was simply that poor people grew and ate more potatoes than rich people. Potatoes can be grown on tiny plots of land, don’t need to be harvested at specific times, and don’t need a mill like wheat or barley. They’re uniquely dense in calories among crops with these features. With the Napoleonic wars putting a strain on the food supply, potatoes were a lifesaver.

Of course, people did point out all that to Cobbett. Many times. It only made him angrier. In order to justify his feelings, he needed to refute the economics. Potatoes simply couldn’t be as efficient a crop as people were saying. Here’s him doubling down in 1819, starting with a remarkably frank epistemic status warning:

It’s a long and detailed chapter. He spends a while explaining that the popularity of potatoes is an irrational fad. “Potatoe-mania,” he calls it. Just like the thing where people think Milton and Shakespeare are good.

But then he gets to the crux of the issue—the claim that potatoes provide more calories per acre than grain. This can be disproven with some simple arithmetic.

So potatoes theoretically provide very slightly more food per acre, he says, but when you factor in the extra labor to prepare them, compared to baking bread, it’s clearly not worth it. Not unless you want to prepare them the easy Irish way, which no self-respecting English person ever would. I can’t imagine why Irish people took offense at this description:

For it must be a considerable time before English people can be brought to eat potatoes in the Irish style; that is to say, scratch them out of the earth with their paws, toss them into a pot without washing, and when boiled, turn them out upon a dirty board, and then sit round that board, peel the skin and dirt from one at a time and eat the inside.

There’s a lot going on here, but the main bit of sleight of hand in Cobbett’s math is fairly subtle. He uses ideal, best-case yields for both wheat and potatoes, which seems like it should be fair. But the variance for wheat yields was much higher. The amount of wheat you can grow depends heavily on the soil quality, weather, and your own capabilities. An average wheat yield would have been less than half of the 40-bushel ideal yield. Much less, in some regions—data from the U.S. in 1866 gives an average yield of a mere 11 bushels per acre. In contrast, the average yield of potatoes (before the Famine) would have been about 5 or 6 tons per acre pretty much anywhere you could grow them.

This means that by comparing best-case yields, rather than average yields, Cobbett is understating the potato advantage by a factor of around 2—average yields for wheat are a quarter of the best case, while average yields for potatoes are half of the best case. Double those potato yield figures, and potatoe-mania suddenly makes sense.

That’s one way to see through this argument. There’s also the more common-sense, non-mathematical way, which is to note the utter absurdity of Cobbett’s claim that potatoes are a global mass delusion. This is load-bearing—he needs some explanation for why South America, Ireland, Spain, Prussia, and now England and Eastern Europe were all planting potatoes, other than it being a good idea.

It’s bad luck for Cobbett that his big example of an irrational fad is Shakespeare. But let’s give it to him. Let’s stipulate that the English love of Shakespeare is divorced from the merits of his work. It’s still not a strong enough example. The Incas weren’t into Shakespeare. Spain wouldn’t have a translation of King Lear for another forty years. Poland had actually just banned Shakespeare in 1830, when some of these essays were written. Humanity was not a monoculture back then, not even close. So how could all these very different cultures have been making the same mistake?

Plus, if potatoes were so bad for you, the countries that adopted them should be noticeably malnourished, and ultimately weaker. The reverse appeared to be the case. Prussia under Frederick the Great, for example, went all-in on potatoes, and then proceeded to conquer a vast empire. Ireland, despite being poorer than England, had a healthier working class.

(The correct criticism of potatoes, of course, would be that over-reliance on a single crop propagated by cloning was just asking for a devastating blight. Cobbett doesn’t manage to find that one.)

So to believe Cobbett, you need to have a specific approach to truth. He says that potato-pushing elites are fools or liars, and that the masses are gullible sheep. So you need to be someone who thinks critically about the claims made by authority, and about popular wisdom. You need to be able to follow, or think you’re able to follow, a mathematical argument. And then you need to suspend all of that critical thinking while reading Cobbett. You need to get to the point where you’re like “wow, Cobbett and I are the only people in the world who get it” and then not see any reason to be skeptical of that conclusion.

Are there really people like that?

2. Cobbett’s new convert

Meet . I found him by googling something like “why did Cobbett hate potatoes,” so arguably this isn’t a fallacy of nutpicking, at least when applied to the potato controversy. Also, he has five times as many subscribers as I do. This is a Kind of Guy.

Pearce seems to be my age and general demographic, and something like a New Right version of me. When I first read William Godwin’s Thoughts on Man, I was moved and amazed. It felt like I was seeing what would happen if I became the kind of writer I aspire to be, and then was sent centuries back in time, where my modern liberal views made me an extreme contrarian. I wrote a blog post titled Meet William Godwin, the 18th-century philosopher who was right about everything.

Pearce had that reaction to William Cobbett. His first article about him was titled William Cobbett: the Original New Right Shitposter, which doesn’t sound complimentary until Pearce explains that he is also a New Right Shitposter. “Was this guy not absolutely one of us?” he writes. “It is undeniable that if William Cobbett were alive today, he would be among the best shitposters and best Substackers out there.”

In his followup post, William Cobbett vs the Potato: The Lone Voice Against a Deadly Elite Consensus, he gets to what he really wanted to talk about. Pearce went into reading Cobbett believing the standard line about them, but Cobbett opened his eyes.

“Potatomania” first took off in the mid-18th century, but despite periodic food shortages, the true impact of the policy wasn’t seen for around 100 years, and when it was seen, it wasn’t understood. Millions of people died because the elites believed the poor should eat potatoes, that era’s version of “You will eat the bugs.” The very premise of changing the diet of the poor to potatoes was never discredited among the elites, as shown by the fact that as recently as 2008 the United Nations declared “The Year of the Potato” based on the same beliefs about the potato’s utility for solving food insecurity. I believed this myself most of my life, that the potato was unique among the crops for its ability to produce an astounding amount of calories in a smaller space at a lower cost than grain. I must admit I believed this despite the fact that it is easily disproven by buying a 5 pound bag of flour and a 5 pound bag of potatoes- at roughly the same cost- and preparing both of them for consumption.

One man, did, however, bravely stand against the potato promoters: William Cobbett, the publisher of the Political Register and the father of alternative media. Cobbett laid out a clear, rational, mathematical explanation proving that potatoes simply did not provide the poor more nutrition at a lower cost than wheat- even before blight.

Pearce is actually correct that he can get more calories-per-dollar from flour than from potatoes. But that’s because he lives in the modern-day American midwest. The Green Revolution of the 20th century has finally allowed wheat to pull ahead. Once you consistently get close-to-best-case yields, Cobbett’s potato math starts to actually work. Not that the U.N. was wrong—the areas experiencing food insecurity are, naturally, precisely the ones where American-style agriculture doesn’t work, due to climate, infrastructure, or the thing where it’s a lot easier for warlords to seize all your harvested grain than for them to dig up all of your potatoes.

(Also, crop rotation is a good idea almost anywhere, and potatoes are great for that.)

But Pearce believes him. He loves the image of Cobbett as a correct contrarian pluckily persevering against the unreasoning scorn of the sheeple, who don’t even bother to engage with his clear, rational, mathematical arguments. Exactly the writer Pearce hopes to be.

And Pearce is, indeed, comparable to Cobbett in the quality of his clear, rational, mathematical arguments. Here he is a couple years ago, in an article titled A Pandemic Literally has not Occurred:

Usually, since Branch Covidians are immune to science and data, I simply refuse to play their game with these numbers. This goes along with my belief of calling them retards and moving along with your day. But the charts are still good for lulz, and since they allegedly based policy on them, for all of history it will fuck them that their extremely repressive measures have absolutely no correlation with disease data these very idiots produced.

Here are some current snapshots from WorldOMeter, one of the more innocuous groups to clearly make vast profits off of this scam. I have to admit, I’ve had their page open as a background tab for basically two years straight.

There are two things that basically any logical person who has been alive could see from this. The first is that, with a population of almost 8 billion people, just under 6 million dying in more than two years is hardly any sort of drastic number, and is fact not even notable. A calculator tells me that is .0739% of the global population. That is well under 1 in 1000 people globally, once again over the course of two years.

6 million people dying is “not even notable”! It’s just simple math. (Pierce, to his credit, is currently condemning the ongoing genocide in Gaza, which threatens to kill a mere 2 million people.)

But the tired old trick of dividing a number by 8 billion to make it smaller isn’t his main argument. It’s this:

And the average covid death age is the same age as the general death age, meaning that a positive covid test is not associated with increased mortality. Because the tests are faulty and if they do work it is a fucking cold anyhow. [And don’t give me shit about how every death is tragic. Human mortality itself is inherently tragic, but the elderly dying of infectious respiratory disease is just life.]

“The average covid death age is the same age as the general death age” is a superficially persuasive statistic. I, at least, had to stop and think it through to work out why it wouldn’t mean what Pearce thinks. Here’s a hint: if we executed everyone on their 30th birthday, the average death age would be very close to 30, because almost everyone lives to 30. The same argument would then prove that executions are not associated with increased mortality. Or, to use maybe a more precise analogy, suppose a potato blight killed some of your potatoes, but many of them were at risk of going bad soon anyway. That’s still a blight. You would still have fewer potatoes.

3. Stars aren’t real

It has never before occurred to me to be proud of this, but I did not make the same mistake when reading Godwin. The third-to-last chapter of Thoughts on Man is a clear, rational, mathematical debunking of…astronomy.

Picture me reading this book, with actual honest-to-God tears in my eyes at how wise it all is, and then, almost at the end…

“The sun,” we are told, “is a solid body, ninety-five millions of miles distant from the earth we inhabit, one million times larger in cubic measurement, and to such a degree impregnated with heat, that a comet, approaching to it within a certain distance, was by that approximation raised to a heat two thousand times greater than that of red-hot iron.”

It will be acknowledged, that there is in this statement much to believe; and we shall not be exposed to reasonable blame, if we refuse to subscribe to it, till we have received irresistible evidence of its truth.

…

Before we affirm any thing, as of our own knowledge and competence, respecting heavenly bodies which are said to be millions of millions of miles removed from us, it would not perhaps be amiss that we should possess ourselves of a certain degree of incontestible information, as to the things which exist on the earth we inhabit. Among these, one of the subjects attended with a great degree of doubt and obscurity, is the height of the mountains with which the surface of the globe we inhabit is diversified. It is affirmed in the received books of elementary geography, that the Andes are the highest mountains in the world. Morse, in his American Gazetteer, third edition, printed at Boston in 1810, says, “The height of Chimborazzo, the most elevated point of the vast chain of the Andes, is 20,280 feet above the level of the sea, which is 7102 feet higher than any other mountain in the known world:” thus making the elevation of the mountains of Thibet, or whatever other rising ground the compiler had in his thought, precisely 13,178 feet above the level of the sea, and no more. This decision however has lately been contradicted. Mr. Hugh Murray, in an Account of Discoveries and Travels in Asia, published in 1820, has collated the reports of various recent travellers in central Asia; and he states the height of Chumularee, which he speaks of as the most elevated point of the mountains of Thibet, as nearly 30,000 feet above the level of the sea.

This argument did not, thankfully, turn me into an astronomy skeptic. Maybe that means I’m better at critical thinking than Pearce. Or maybe I’m just irrational in a different way than he is. Pearce, I think, wants to live in a world where scientific consensus can be debunked by a simple, intuitive argument using the scientists’ own data, and yet inexplicably everyone goes on believing it anyway. The worse the rest of humanity is, the better he is in comparison. I, conversely, want to see farther by standing on the shoulders of giants, so the idea that all of astronomy is wrong is upsetting. I’d feel diminished by that revelation, not glorified. That difference in attitude is probably why we fell in love with two very different contrarian cranks of Georgian England.

Just in case, I’ll spell out the problem with this math: thinking the 20,000-foot-tall Andes are the tallest mountains in the world, when it’s actually the 30,000-foot-tall Himalayas, means underestimating the highest heights by 50%. That’s a lot, but it’s nothing like the multiple-orders-of-magnitude error Godwin is implying astronomers might be making. If the sun were ten times larger or smaller than we thought, that would be an equivalent error to thinking the 3,000-foot-tall Burj Khalifa skyscraper is bigger than Mount Everest. (Anyway, it is often easier to see your neighbor’s roof than your own, so why would it be weird for astronomy to be more precise than geology?)

I’ll count it as a win that Godwin’s star denial probably didn’t kill anyone.

4. Getting yellow-pilled

What made Cobbett such an effective advocate for the much-needed popular revolts of his time is that he didn’t really feel a need to avoid getting his readers killed. This is, as best I understand it, part of the Shitposter Ethos—you fling out an argument and move on, without stopping before, or after, to think about the result. It’s about being Rational in an exclusively vibes-driven sense that doesn’t have much to do with trying to improve your own thinking and be correct more often.

Cobbett’s political articles were supported by ads like these:

In doing so, he quasi-endorsed products that were at best snake oil and at worst poison. The “Morisons Pills” advertised here as a cure for scrofula (as well as everything else) were mainly made from gamboge, a yellow dye that is a laxative in small quantities and deadly in large ones. If 14-year-old Hannah Bagg had really taken 20+ pills a day for three months, she’d have gotten a larger dose of gamboge than the one that killed a 32-year-old man in 1836. That would’ve cured all her illnesses, in a way.

Unsurprisingly, he was also an anti-vaxxer. I don’t even want to bother quoting his arguments—you can just take an anti-vax essay today (Pearce has a few) and find/replace COVID with smallpox, and you’ll get the idea.

Potato hesitancy may have made the famines of the period worse, but arguably it also saved lives by preventing more countries from suffering Ireland’s fate. The medical stuff is more unambiguously bad—we can be pretty confident Cobbett’s willingness to signal-boost quacks killed people, as did his comfort with publishing a book of “Advice to Young Men and (incidentally) to Young Women” in 1829 advising them not to vaccinate their children against small-pox. Although there, too, I do find it a little comforting that if vaccines do suddenly turn deadly, it won’t entirely wipe us out—people like Pearce provide diversity in the human crop.

My hope is that people only end up yellow-pilled because they think it’s the only way to be contrarian. They think you need to be fearless with your opinions, even a little cavalier with the truth, to ever be able to spot the many areas where conventional wisdom is wrong.

If so, I have good news! Even granting that premise, you can do significantly better by just having the teensiest more faith in humanity as a whole. People in power lie. Elites get stuff wrong. But successful secret worldwide conspiracies of millions of people probably never happen. Living in downtown Brooklyn at the start of the U.S. pandemic, my dog-walk every day took me past a hospital that was using trucks as temporary extra morgue space. Scenes like that were happening all over the world. There are bastards who would fake that stuff, but I truly believe that there are not enough of them to fake it everywhere.

And cultures have dumb food fads that do more harm than good. But not often enough to explain the universal love of the potato. Give people a little more credit than that.

Addendum: In the comments, Pearce points out that I don’t rebut Cobbett’s fuel cost argument—cooking potatoes at home could be prohibitively expensive if you lived in London and didn’t have ready access to cheap flammable stuff. I skipped over it because it looked like Cobbett stopped using it only a couple years later, but for the sake of completeness, here’s a quick rebuttal. The fuel cost argument assumes that you can buy some other source of carbs, probably baked bread, but that you can’t buy baked potatoes, or grow them and pay someone with an oven to cook them. There’s no reason to think that should be the case, and indeed it wasn’t. In fact, only a few years after Cobbett’s death (I’m glad for his sake he didn’t live to see it), the “baked-potato man” became a regular fixture on the streets of London. These were cooked in bulk at bakeries, salted and buttered, then kept hot by vendors using insulation and a charcoal fire. They were famously cheap enough that some people would buy one just for the warmth on cold days, and carry it around in gloved hands rather than eat it. According to an 1840 court case, you could get one for a halfpenny. This was obviously not the most cost-efficient way to get baked potatoes, but it still beat bread. A loaf of bread cost at least 7.5 pence, or the cost of 15 hot, buttered, salted baked potatoes. Now I’m hungry.

We were just getting used to the idea of a telephone. But that wasn’t a machine that spoke, it just relayed a human voice. To speak, many believed, a machine would need to perfectly replicate a human larynx and force air through it, something well beyond modern science. In 1842, the Austrian inventor Joseph Faber unveiled a valiant attempt at such a device, but you had to operate it by pressing a key for each syllable, which nobody could do fast enough to create realistic speech.

Although it was exciting at the time, thirty years went by without any substantial improvement, so the talking machine remained the stuff of carnival attractions and science fiction.

But in December of last year, Thomas Edison walked into the offices of Scientific American in New York City with a box that could be made to recite “Mary Had A Little Lamb” just by turning a crank. Edison had sidestepped most of the technical challenges that had limited inventors of the past. He didn’t try to replicate a human voice—rather he built a device that could record and play back any sound, vocal or no. This was, paradoxically, much easier—the former would require understanding human biology deeply and precisely, while the latter just required a good understanding of how sound works.

Ever since, there have been loud skeptical voices dismissing the story as a hoax or exaggeration. There’s been precedent—fake stories of Edison inventing a food synthesizer, or antigravity, or what have you, and also fake speaking machines that were demoed using a hidden ventriloquist. The French Academy of Sciences is reported to have been particularly difficult to persuade. More than one German news article announcing the phonograph included a note at the end emphasizing that this was not an “amerikanischen Humbug,” they had a reliable witness. Edison saved a letter from a New Haven professor telling him to repudiate the hoax before it damaged his reputation, as it was apt to fool ignorant people who didn’t realize the impossibility of such a device.

But this claim is pretty easy to prove, once you get the skeptic in the room with the box.

It’s hard to shake the instinctive belief, true for almost all of human history, that anything that can talk must be a person, or at least a very clever bird. Scientific American’s article starts off by giving a good, detailed, mechanistic description of the device, but then, at least for a sentence, gets a bit magical. “It is a little curious that the machine pronounces its own name with especial clearness,” they write.

They knew, on some level, that the machine was playing a recording of Edison in which he carefully enunciated the name of his new invention. But their gut wanted to believe that the machine might be self-aware. “No matter how familiar a person may be with modern machinery and its wonderful performances,” they write, “or how clear in his mind the principle underlying this strange device may be, it is impossible to listen to the mechanical speech without his experiencing the idea that his senses are deceiving him.”

Laypeople seeing the phonograph operate for the first time tend to attribute magical powers to it. “Can it tell my fortune?” some ask. (Barnum and his ilk answer “yes, for an additional fee.”) Others tend to assume it must be powered by something newfangled, the electricity Edison is so associated with, or at least steam. Surely something so wondrous can’t be purely mechanical.

In fact, the phonograph can do something traditionally considered black magic. People, starting with that first Scientific American article, have been quick to point out that we will now be able to summon the voices of the dead.

Predictions haven’t stopped there, of course. It’s 1878, after all — we’re getting pretty good at figuring out the implications of this sort of thing, having witnessed as many as several new inventions already.

Every would-be diva will record her voice. People will prank, scam, and surveil each other. Businesses will make you leave a message for them to listen to when they’re less busy. Any church can have a high-toned choir. Wills will be recorded in order to authenticate them. Music will be bought at the store as a commodity. Peace negotiations will happen at a distance, for safety. Edison himself has proposed that when the Statue of Liberty is installed in New York harbor, we could include a giant phonograph in her head so that she can say “Welcome to our home” to incoming ships.

Others extrapolate further, speculating about combining the recorded sound with some sort of visual recording, to create a perfect counterfeit of a human. And some, like the Universalist minister James Harvey Tuttle, see the phonograph as the latest piece of evidence of the coming universal transcendence of mankind, one in which all of us will have access to all of civilization’s knowledge and wisdom.

… there is ground for believing that the whole race will finally be brought up to the highest mark yet reached by the greatest mind. There is more probability now that all men will become Bacons intellectually, and St. Johns morally and spiritually, than there was once that one man would ever become a Bacon or a St. John. What could have taxed human credulity more severely than the promise of the printing press, the steam engine, the telegraph, and last, and most wonderful of all, the phonograph. Are we to halt in our hope of human nature after what we have seen? Are not man’s capabilities absolutely unlimited?

That was how it looked in 1878. Here in the present day, it feels like the wild speculation was all pretty accurate. We didn’t end up using audio recording for authenticating wills. I assume somebody pointed out that it’s not necessarily harder to forge a voice than a document. The Statue of Liberty has not (yet) been turned into an animatronic robot. But the rest of it—the bad, the good, the weird—we know that it panned out more or less as predicted.

Eventually. But on shorter timescales, it was the skeptics who were right. Edison struggled to monetize the phonograph. He was stuck, like the rest of the world, on vocal recording, when actually instrumental music was the killer app. Low-fidelity voice recordings fall into the uncanny valley—too humanlike, and not humanlike enough. The talking dolls Edison made were just creepy and nobody bought them. The “gramophone,” which played music from discs, wasn’t invented for another ten years, and it wasn’t Edison who invented it, but his rival Emile Berliner.

Technological unemployment was another area where the skeptics were (temporarily) right. Stenographers were panicked, at first, thinking that all of their shorthand knowledge was about to be obsolete. Others pushed back, arguing that shorthand was always going to be better than audio because the reporter “has exercised discrimination as to what should be taken or omitted for his purposes.” Their arguments were bad, but they were accidentally right for almost a hundred years—the tech just didn’t get good (small, easy to use, high quality) fast enough to put anybody out of work.

In his 1963 essay on artificial intelligence, Hugo Steinhaus briefly touches on the response to the phonograph as a historical analogy. After reading more about it, I think the phonograph is a pretty apt comparison. We’re too fixated, at the moment, on having AI imitate human writing and human speech. It’s basically the same mistake for the same reason—imitating humans is magical, everything else is more mundane, so surely the magical part is the important part? Edison had his creepy dolls. We have millions of AI models trained to write like the same sycophantic personal assistant.

We both underestimate and overestimate AI when we think about it as imitating human thought. It’s not. It’s doing something weirder. Skeptics correctly notice that it’s not really thinking in any human-like way, even though it’s producing human-like output, and then incorrectly declare that that means the whole thing is a humbug ventriloquist act. More credulous people end up believing an AI’s report of its own feelings and thought process, deluding themselves that they’ve awakened, or discovered, self-awareness in their new friend.

“The phonograph can record and play back any sound” came across as less magical than “it will summon the voices of the dead.” But the one implies the other. In generality is power.

I don’t know when we’ll have machines that actually think. But we have machines that can take arbitrary input and process it into arbitrary output by recognizing patterns. That sounds less magical, but that can be deceiving. The possibilities are awesome, and awful, and you’d better believe they’re coming.

John Adams, on first arriving in New York City for the Continental Congress, wrote in his diary that “This City will be a Subject of much Speculation to me.” After walking up “the broad Way,” he was impressed first and foremost that you could just walk along one straight street the entire length of the city. You can’t do that in Boston. The streets and houses were far more elegant and grand, too.

On the other hand…the people were so rude.

With all the Opulence and Splendor of this City, there is very little good Breeding to be found. We have been treated with an assiduous Respect. But I have not seen one real Gentleman, one well bred Man since I came to Town. At their Entertainments there is no Conversation that is agreable. There is no Modesty—No Attention to one another. They talk very loud, very fast, and alltogether. If they ask you a Question, before you can utter 3 Words of your Answer, they will break out upon you, again—and talk away.
Diary of John Adams, 1774.

Johann Conrad Dohla was a Hessian, a private in one of the many German mercenary companies hired to help put down the American revolution. New York was already conquered and occupied by the time he arrived. Dohla isn’t the best source for facts—he gets names and geography wrong, and claims to have been menaced by giant man-eating lobsters on the voyage over1. But he’s an excellent source for vibes. New Yorkers were apparently more polite than Bavarians, so he doesn’t have the same complaint as Adams. The people are so varied, rich, and free2. You can be any religion! Except Catholic. You can be any race! Except it’s a very bad idea to be Black.

New York is a large, beautiful, rich, and splendid port and trade city. It consists of about six thousand houses and very many inhabitants, because in many houses forty to fifty persons live. The houses are often four, five, or even six stories high…
…
All religions are tolerated here, and everyone can and may speak and serve God without hindrance according to his propensity, judgment, and style.

The people know how to live, are without worry and content in all situations. The good living style found among the English is also found among them. They love comfort and delicacy and are very temperate in their eating and drinking, preferring tea with milk and sugar and always living in a healthful manner. All religions have churches and prayerhouses, except the Catholics. The Jews, however, are not, like ours in Europe and Germany, recognizable by their beards and their clothing, but dress similarly to other citizens, are clean shaven, and eat pork, which is forbidden by their laws. Also, Jews and Christians marry together without giving it any consideration. The females go about with curls and in French attire that among all other religions would be worn only by ladies of the upper class.

The inhabitants have many blacks, which they call blacks or Negroes. These are slaves and are bought and sold like cattle, for a lifetime or a number of years. They must tend the estates and fields of the inhabitants, and do all other work throughout the year, because the white inhabitants of America are accustomed to doing very little work, having their blacks do it for them.

The latter, however, receive nothing but uncooked food and bad clothing of rough cloth, or woolen items, and beatings with clubs or even with iron rods.

Diary of Johann Conrad Döhla, 1777.

Domestic Manners of the Americans was the book Fanny Trollope wrote for her British compatriots after her first trip to the U.S.A. It is not complimentary. Trollope is contemptuous, morally outraged, and unrelentingly negative. Except in one place. New York City was so full of, like, everything that she struggled to even describe it, let alone critique it.

But, of course, they’re not proper ladies and gentlemen there, so it’s not for her.

Sin and shame would it have been, indeed, to have closed our eyes upon the scene which soon opened before us. I have never seen the bay of Naples, I can therefore make no comparison, but my imagination is incapable of conceiving any thing of the kind more beautiful than the harbour of New York. Various and lovely are the objects which meet the eye on every side, but the naming them would only be to give a list of words, without conveying the faintest idea of the scene. I doubt if ever the pencil of Turner could do it justice, bright and glorious as it rose upon us. We seemed to enter the harbour of New York upon waves of liquid gold, and as we darted past the green isles which rise from its bosom, like guardian centinels of the fair city, the setting sun stretched his horizontal beams farther and farther at each moment, as if to point out to us some new glory in the landscape.

New York, indeed, appeared to us, even when we saw it by a soberer light, a lovely and a noble city. To us who had been so long travelling through half-cleared forests, and sojourning among an “I’m-as-good-as-you” population, it seemed, perhaps, more beautiful, more splendid, and more refined than it might have done, had we arrived there directly from London; but making every allowance for this, I must still declare that I think New York one of the finest cities I ever saw, and as much superior to every other in the Union (Philadelphia not excepted), as London to Liverpool, or Paris to Rouen. Its advantages of position are, perhaps, unequalled any where. Situated on an island, which I think it will one day cover, it rises, like Venice, from the sea, and like that fairest of cities in the days of her glory, receives into its lap tribute of all the riches of the earth.

…

I will not, therefore, attempt a detailed description of this great metropolis of the new world, but will only say that during the seven weeks we stayed there, we always found something new to see and to admire; and were it not so very far from all the old-world things which cling about the heart of an European, I should say that I never saw a city more desirable as a residence.

…

Gentlemen, in the old world sense of the term, are the same every where; and an American gentleman and his family know how to do the honours of their country to strangers of every nation, as well as any people on earth. But this class, though it decidedly exists, is a very small one, and cannot, in justice, be represented as affording a specimen of the whole.
- Domestic Manners of the Americans, by Fanny Trollope. 1832.

The Russian poet Vladimir Mayakovsky was a committed Marxist-Leninist, but he was also a Futurist, in love with progress of all kinds. Generally those two ideologies can mesh pretty well. But on visiting New York City, one of the most capitalistic and most futuristic places on Earth, a Communist Futurist has to pick a side. His poem, The Brooklyn Bridge, starts by acknowledging the choice he’s making.

Okay, Coolidge, about this you can be loud. Brag!
I certainly shall.
My homeland blushes as red as its flag
despite the America of it all.

As a tourist, he feels humbled. As an artist, he feels thrilled. As a futurist, he feels proud—the Brooklyn Bridge is a part of the future he’s helping to build.

I’m proud of this metal mile.
It connects my own vision to the real.
A struggle for structure, not style.
The brutal math of nuts and steel.

It’s full of inequity, he writes. It’s a symbol of Europe’s conquest of America. And if civilization ended tomorrow, you could reconstruct it all just from studying the Brooklyn Bridge.

Albert Camus was a philosopher and novelist from French Algieria, part of the existentialist movement (although he always refused that label). He survived the Nazi occupation of France, writing an underground newspaper for the French Resistance. And even given that bio, you might be surprised by just how bleak he is. Here’s his very on-brand diary entry from the day before he entered the city.

We’ll anchor in the mouth of the Hudson but won’t dis­embark until tomorrow morning. In the distance, Manhattan’s skyscrapers stand against a backdrop of mist. My heart is still and cold, as it is when faced with sights that don’t move me.

The next day, he tries to keep that heart chilly, but he knows it’s probably a losing battle.

Monday. Went to bed very late last night. Got up very early. We sail through New York Harbor. A tremendous sight despite, or because of, the fog. Order, power, economic strength, they’re all here. The heart trembles before so much remarkable inhumanity.

I don’t disembark until eleven o’clock, after a long series of formalities where, out of all the passengers, I’m the one treated as suspect. The immigration officer ends up apologizing for having kept me. “I was required to do so, but I can’t tell you why.” A mystery—but after five years of occupation …
…

Tired. My flu is coming back. I catch my first glimpse of New York on shaky legs. At first sight, a hideous, inhuman city. But I know people can change their mind.
…
I go to bed as sick at heart as in body but knowing perfectly well that I’ll have changed my mind in two days.

That’s Monday. By Friday, I think we kind of broke him?

Friday. Knopf. Eleven o’clock. Cream of the crop. Broadcasting. Gilson’s a nice guy. We’ll go see the Bowery together.
…
Beautiful blue sky that reminds me we’re at the same latitude as Lisbon, which is hard to imagine. In tune with the flow of traffic, the gold­-lit skyscrapers turn and spin in the blue above our heads. A moment of pleasure.

We go to [Fort] Tryon Park above Harlem, where we tower over the Bronx on one side and the Hudson on the other. Mag­nolias blooming pretty much everywhere. I try a new type of these ice cream that I enjoy so much. Another moment of pleasure.

Diary of Albert Camus, 1946.

Polish mathematician Hugo Steinhaus, whom I’ve written about before, endured an even bleaker Nazi occupation, and his “liberation” from it was by the Soviets. “The happiest day of my life,” he said once, “was the one after the Germans left and before the Soviets arrived.” He never emigrated, but you can tell from his writing about travel that he was mentally a pre-refugee, sizing up everywhere he went as a potential refuge.

Steinhaus, like Camus, was quite dark and cynical. But the view from the Brooklyn Bridge does what it does.

On September 9, 1961, we stopped over at the Rockefeller Institute in New York on our way to South Bend; I wanted to show Stefa the institute and New York. From the upper floors of the institute one can indeed get a good view of New York City, and travelling at night by car across the bridges over the East River one sees the millions of lights of Manhattan. Here it was no individual artist but ten generations of the city’s teeming millions who created the stupendous freeways and skyscrapers, the multicolored lights reflected in the river, and the gigantic bridges which amaze by the impression they give of lightness combined with a sense of the weight of the iron of which they are made. A million architects, engineers, painters, and craftsmen built the city. Each made his contribution according to an imperative of practical necessity, yet the overall effect far transcends their individual imaginative efforts. Manhattan’s base of solid rock bears the world’s capital city, and no other city comes near to wresting this title from her. The European visitor senses Americans’ pride in the achievement, and he himself is filled with optimism when he reflects that New York was built by immigrants.
Diary of Hugo Steinhaus, 1961.

New York City is still growing in population today, still powered mainly by immigration. One New Yorker in three was born outside the United States. Half of the new births here are to immigrant parents. And while we have more rivals than we did in 1961, we are still a capital of the world.

Why is New York City so rich? We stay rich because of all the ambitious and/or desperate people who come here, drawn by our wealth. But how did the snowball get rolling in the first place?

There’s an easy, simplistic answer where it’s an accident of geography. New York is a deep-water port on the East Coast. It “receives into its lap tribute of all the riches of the earth” because we’re a convenient place for a large cargo ship to dock. But it’s not just that. Philadelphia was a larger port than NYC for a long while, until the Erie Canal in the 19th century. Savannah, Georgia is a deep-water port on the same coast, and there are others too. None of them can hold a candle to Times Square.

It wasn’t just geography, and it wasn’t just exploitation—New York will grind you up to make its bread, but if exploitation were the answer then, again, why not Savannah, a city much more built by slavery than New York was?

I think, at its base, New York is built on bad manners. Most places have an idea of the culture they’re striving to create, or to maintain. They have a sense of a social upper class—good, wise people, easily identifiable by their natural courtesy. To New Yorkers, a social upper class is just the annoying rind you sometimes get at the surface of the cheese. The other day, I sat down in a subway car in Queens and started reading, until a guy with a heavy Greek accent shouted at me from the platform that the train on the other side was going to leave first. That’s New York courtesy.

If we have an old-world-style gentry here, they’re a tiny demographic. They’re not normative. Which means anybody can be not just a New Yorker, but a great one. We’re far from equal in opportunity, but there’s no ceiling on anybody’s ambition. And so, the city rises with her people.

I’m not saying anything particularly original here, and that’s kind of the point. This has been New York from the beginning, plain for all to see. Since 1903, we’ve even had a sign out in front explaining it.

“Keep, ancient lands, your storied pomp!” cries she
With silent lips. “Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.”

Always be kind to travelers,
wandering near or far.
Always be kind to travelers…
ya don’t know who they are.

- Wanderer, by Leslie Fish

The Nazis tried, and failed, to invent the atomic bomb. One possible explanation is that one guy, Werner Heisenberg, made a math error. In calculating critical mass, he used the mean free path, the average distance traveled by a neutron involved in the reaction. He determined that to keep that average neutron from leaking out, you’d need a ton or more of refined uranium, which was effectively impossible. But the average neutron doesn’t matter. You just need one neutron per reaction to start another reaction. Only the shortest-traveling, fastest-colliding neutron needs to stay inside the sphere.

There are many competing narratives about this. Was that one mistake really so important or were there other factors? Was the mistake intentional or not? Did Heisenberg secretly know he was being bugged and fake the whole conversation? But no matter what, Heisenberg’s math error wasn’t the root cause of the failure. It’s that nobody was capable of checking his work. The leader of the Manhattan Project, J. Robert Oppenheimer, was notoriously bad at math himself. That project succeeded anyway, because every calculation had lots of expert eyes on it.

Why the disparity? Well, there happened to be something many theoretical physicists had in common. Nazis had gotten rid of all their Jews, one way or another. The average Jew wasn’t too impactful on the war effort. But those Jews also included Albert Einstein and Leo Szilard, who founded the Manhattan Project. The project recruited all the best theoretical physicists from across America, who met in Los Alamos and realized they all knew each other from high school in Budapest.

There’s a common trope in myth where a stranger who asks for hospitality turns out to be a god, or a messenger of one, in disguise. It’s sometimes called Angel(s) Unaware(s), after the King James Bible’s Hebrews 13:2. Be not forgetful to entertain strangers: for thereby some have entertained angels unawares. In the study of ancient Greek mythology, it’s called theoxenia (literally “god as stranger”). It shows up all over, though: the Morrigan does it in Irish mythology, Odin in Norse, Pele in Hawaii. Elijah does it in Jewish tradition, and al-Khidr in Muslim stories.

In these stories, the rule is almost always that if you show hospitality, you receive a blessing, and otherwise you receive a curse. The moral is, of course, that one should always treat hospitality as sacred, even when the visitor is a stranger. If you share your dinner on a hundred nights with a hundred travelers, 98 of them will thank you politely, one will steal your silverware, and one will miraculously cure your entire family of a deadly disease. Even to a sociopath, that’s a good trade. Sure, the average stranger isn’t a god. But if just a few are…

It doesn’t take supernatural powers to save a family from a deadly disease. You just have to be a little weird. This week, researchers announced preliminary findings that appear to show a highly effective treatment for Huntington’s disease, which would make it the first such treatment ever developed. The gene therapy, AMT-130, was developed by a smallish company called uniQure. Their R&D department, at the time, was run by an oddball named Ricardo Dolmetsch.

Dolmetsch cheerfully describes himself as “slightly off-kilter.” He came from a family of artists. As a kid, he was caught writing erotic poetry during typing class and suspended for a week. Stuck at home, he learned how to cook, which inspired him to become a scientist. The kind of scientist who campaigns for everyone in the lab to be given a pet goldfish, or experiments with pogo-sticking his way to work. (After two trials, he abandoned the idea as “terrible for my computer and possibly lethal for me.”)

I guess I can’t rule out the possibility that he’s a supernatural being in disguise. (His name anagrams to Lord Mithras Codec, so maybe Mithras?) But I think he’s probably a mortal, one who immigrated from Colombia to the U.S. as a teenager to attend Brown University.

As a non-citizen, Dolmetsch spent the start of his career ineligible for many grants and in danger of deportation if he didn’t find funding. So we don’t get a perfect hospitality score there. But we did well enough to get the blessing—the details are private, but presumably he was able to get one of the visas available to “aliens with extraordinary ability” with the help of Stanford University. He’s had a productive and distinguished career, and he’s still going strong today.

Back circa 1986, when he was applying for a student visa, the INS wouldn’t have known just how good a gift they were being offered. He was 17 years old, with few resources, coming from a troubled country. He wouldn’t have been easy to distinguish from the other 11,000 Colombian immigrants that year. To admit him, we needed to admit all of them too. A few of the other immigrants allowed to cross the border in the eighties went on to smuggle drugs or commit terrible crimes. All of them required some amount of support getting started. That’s the price we paid.

And Ricardo Dolmetsch, alone, was worth that price, if his leadership had anything to do with the invention of AMT-130. There are more than 30,000 Americans with Huntington’s disease. If these results pan out, their life expectancies quadruple. And, of course, we’ll get to tax uniQure as it sells the therapy to other countries, so everyone in America will benefit.

Even if we pretended, ridiculously, that everyone else from his cohort contributed nothing of value, it’d still be worth it.

Even if we pretended, ridiculously, that we had a sociopathic disregard for the lives of foreigners, it’d still be worth it.

I’m pretty sure we’re failing the hospitality test hard right now. Even before the administration announced its $100,000 charge to apply for H-1B visas, we’ve been doing an excellent job at scaring off scientists. If you’ve got an idea for curing cancer, take it somewhere else. We’re full. Anybody who hadn’t gotten the message surely got it from the treatment of the talented researcher Kseniia Petrova, a Russian dissident who fled to the U.S. in 2023, only to be detained for four months after failing to declare a box of frog embryos. She now faces criminal charges.

Some of our losses will be other countries’ gains. It’s a statistical certainty that in a few years, we’ll realize we’ve fallen behind in some critical field or other because the top talent went elsewhere. Other losses will be invisible, because they’ll be losses to the world. If Dolmetsch had been forced to return to Colombia, he says, he would’ve had to join the army. If he’d died there, we’d never have known what we missed out on.

I’ve tried to make the case, before, that the average immigrant is net-positive to society. I still, strongly, believe that. The idea that every human being has moral worth and deserves kindness has also been floated from time to time. But I know not everyone buys those ideas, so I want to emphasize that you don’t need to in order to realize Trumpism is a terrible mistake. Elites matter too, and you can’t just swap in native-born American elites for immigrant elites on demand. We have geniuses here too, but they’re not the same geniuses. You can’t turn Einstein away, then slap a white wig on a third-generation American and tell him he’s Einstein now.

In the Grímnismál, the Norse poem alluded to in Leslie Fish’s song, Odin travels to the realm of King Geirröth, dressed in a dark blue cloak, and refuses to give any information about himself. Odin’s wife, Frigg, had bet him that Geirröth was so stingy and inhospitable that if he thought he was receiving too many visitors, he would detain and torture some of them. She wins the bet. Odin curses Geirröth, who immediately trips and impales himself on his own sword. Watch your step.

Who is that gone down the road?
You never got his name.
He never said where he’s bound, or said from where he came.
What comes after, who can tell?
Earthly heaven, earthly hell –
But did you treat him ill or well, then you will reap the same.

-Wanderer, by Leslie Fish

In that vein, I have my own proposal—we should finally do a study of a lake in Kastria Cave in Greece to learn why drinking from it cures alcoholism.

Ever Ready To Restore Humanity

I’m stealing this idea from Osborne Aldis, who is part of an odd dynasty of radical Quakers that definitely deserves its own article. Three generations, at least, of antiquarian public health doctors and part-time con artists. Watch this space.

Osborne Aldis went to medical school, like his father and grandfather before him, but ended up working as a Doctor of Fine Arts. In a 1914 letter to The Saturday Review, a London newspaper, Aldis crosses the streams. He starts with a discussion of alcoholism as a public health issue and suggests some political remedies. But at the end, seeming a bit sheepish, he adds one more suggestion. He quotes the following lines from Ovid’s Metamorphoses (written circa 8 CE):

Clytorian streams the love of wine expel,
Such is the virtue of the abstemious well.

We know where the ancient city of Clytor was, he points out. Shouldn’t somebody fund an expedition to investigate this story?

The point for consideration is whether in the analysis may be found one of those hidden secrets of nature, so long neglected, but ever ready to restore fallen humanity to the more ennobled ideal of manhood. We need not refer to the well-known properties of many waters, which most probably would have been long since lost sight of and forgotten had it not been for the confirmation of modern science.

Unsurprisingly, I don’t think anybody ever did this. They’d probably find nothing and look stupid. You need a richer, more populous civilization before you have resources to spare to chase down every legendary magical spring. It’s too bad, though, because there’s strong evidence that Aldis was completely correct.

The Cave of the Lakes

Any unusual property of the waters of Clytor would need to come from an unusual feature of the surrounding watershed. Since I’m much better at Googling things than people in 1914 were, I can tell you what the One Weird Thing about the area is: the Cave of the Lakes, which would’ve been maybe 5 miles from the ancient city and was rediscovered in 1964. This beautiful tourist attraction, also known as Kastria Cave, has 13 separate lakes inside it…sometimes. During the winter, melting snow joins the lakes into a single river and carries the water out. People, usually young women, have spent some time in the cave since the Stone Age, so it has been studied in modern times, but by archaeologists, not doctors.

When ancient Greek sources get more specific than “Clytor,” they tend to describe the magical waters as coming from this cave, or one matching its description. Drinking from its water could remove the craving for wine, among other psychological ailments. You couldn’t wash things with it, though, the legends say.

Water you can’t wash with is generally “hard water,” water with a heavy concentration of certain kinds of minerals. Soap doesn’t lather in hard water. You also, typically, shouldn’t drink too much of it. It’s a nice cave to visit, but you wouldn’t want to live there. It makes some sense that the unusual structure of the cave and its water could lead to unusually hard water, even by cave standards.

But what, specifically, is in the water in Kastria Cave? Absent a chemical analysis, we can still make at least one inference from pictures of it:

It has light-colored stalactites. Lots of them. Stalactites, from the Greek for “drips,” are almost always formed by dripping water depositing little bits of dissolved calcium carbonate, which over millennia accumulates into a big fossilized drip. There’s probably other minerals involved, too, but calcium is almost certainly the main thing in the water.

This guess is also supported by a 2013 study on the diverging evolution of cyanobacteria in different Greek caves. The researchers did an x-ray diffraction analysis of the cave walls, and in the case of Kastria it came out “oops, all calcium.”

So, what, are we saying calcium cures alcoholism?

Yes.

We thought, for a while, that that the drug acamprosate, brand name Campral, was one of the best ways to treat alcohol withdrawal symptoms and reduce cravings. It was developed by pharma giant Merck, and demonstrated in multiple clinical trials to be highly effective. It’s been prescribed since 1989. Acamprosate’s proprietary ingredient is a synthetic molecule, C₅H₁₁NO₄S, and to turn it into a pill it’s combined with calcium, which dissolves quickly once swallowed, leaving the big fancy chemical to do its work. That’s the idea, anyway.

But in 2014, researchers at the University of Heidelberg reported that if you take the calcium out, if you use something else to make the “pill” part of the pill, the drug stops working. If you take the medicine out but keep the calcium, the drug seems like it works just as well. The calcium was the active ingredient the whole time, hiding in plain sight. While research is still ongoing to confirm these results, every experiment done so far has pointed in the same direction. (But it’s not definite, and there’s a lot of individual variation, so if your doctor is prescribing acamprosate you should stick to it.)

Calcium carbonate isn’t magic. As usually defined today, it isn’t even technically a cure. It treats withdrawal. You still need to decide to quit, and to stick to it. But for many people, it makes a significant difference to both comfort and probability of relapse. So while I can’t prove it (yet), I think it’s very probable that the cave of ancient myth that cures alcoholism has actual power, and that studying it could still be helpful today, to check and refine our understanding.

Modern medicine is very empirical. We’ve known that acamprosate works, but not why it works, since the eighties. If we end up confirming the recent findings, all that means is that we’ve gone from not knowing why acamprosate works to not knowing why calcium works. This is progress, and it’s also a sign that there are scientific discoveries waiting to be made. Knowing why would tell us where to look, how to improve further, whether that’s through inventing more synthetic chemicals or testing more natural ones.

So why have we taken so long to look into it?

For once, I’m not going to blame the 20th century for this oversight. Quite a few traditional or legendary treatments have been investigated and found to be completely bogus. As Tim Minchin sings, “I don’t believe just ‘cause ideas are tenacious, it means that they’re worthy.” The hypothetical society that found this, the one that read Ovid and mounted an expedition into the Greek highlands to search for a lost cave, would have wasted energy on a hundred similar quests that went nowhere. We’re likely better off, on net, that they didn’t.

But we here in the 21st century don’t have the same excuse. We’re rich enough to fund a hundred times as many projects as we could in 1914. We’re past the point where it makes sense, at a civilization level, to investigate these long-shots. We could, as Hoel puts it, Just Do Things. But we mostly don’t. I think most of the things holding us back are the habits of poverty. Our level of risk-tolerance, the strictness of our gatekeeping, is calibrated for scarcity that no longer exists. Among other institutional problems, the current U.S. administration, in trying to move us forward via widespread science funding cuts, has it exactly backwards. As does the standard way to naysay going to Mars— “Not until we’ve solved all the problems here on Earth.” We should be bolder, and try to have it all.

Plus, if I can get self-serving and meta here for a second, we could try to make more space for polymaths. (See also ’s recent article). People like Osborne Aldis, who could make the connection between the withdrawal symptom delirium tremens and the madness described in Ovid’s poetry, were already being marginalized by his time, while nobody batted an eye at his father or grandfather straddling the same disciplines. Here, too, I don’t really blame the 20th century. They were richer than the 19th, and therefore could afford more specialization. But with the advent of the modern internet, it’s generalism that has gotten cheaper. I didn’t need specialized knowledge to find or interpret the existing studies of Kastria Cave, nor the clinical trials of acamprosate and calcium. Rather, I needed a specific skillset—the ability to do some quick-and-dirty research and make the connections. And for society as a whole to discover this, it just needed to indulge enough weirdos like me that eventually one of us would randomly read a letter in a scanned century-old periodical.

We are not low creatures. We are the scions of Melampus, the hero of myth who found the cave, who could cure even the madness visited upon himself by a vengeful divinity. We will find our way—to sanity, to sobriety, to peace, to Greece, to Mars.

It’s a great essay—it holds up astonishingly well for something written in 1963, often demonstrating clearer thinking than some prominent scientists and commentators today. When Gary Marcus, for example, wrote in 2018 that deep learning was overhyped and probably approaching a wall, he was wrong, but at least not directly contradicted by evidence—GPT-2 was released in 2019. The fact that he’s still writing that GPT-2 will never be invented shows that the fallacies Steinhaus discussed are alive and well.

Steinhaus argues that new technology constitutes a proof that some supposedly magical process is actually mechanical. Before the airplane, people could get away with thinking that birds flew “because they’re birds.” Then the Wrights built a machine and told the world that it worked using the same principles that let a bird fly. So birds fly because they’re flying machines. Before the gramophone, music was mystical, etherial. Now, you could listen to a gramophone make noise and have the same experience as if it were a human singing. Gramophone operations can be described using simple equations—ergo, so can the human’s song.

That’s the correct way to respond to a new invention, Steinhaus says. There are two popular wrong ways—you can try to argue that a gramophone playing “isn’t actually music,” whatever that means. Or you can decide the gramophone must have a soul—in fact, since it can play any song, a superhuman ability, it must be something like a god.

So now, turning to computers… Steinhaus says it’s obvious that, while it might be very difficult, there’s no fundamental reason we won’t be able to invent a device that doesn’t just record music, but can read sheet music and lyrics and transform them into a song. Such a device, he says, will also be able to carry on a conversation, although it’ll be limited due to being trained on human writing with all of its fallacious “received wisdom.” If you ask one whether it can think, it will respond “Unfortunately, no, because I don’t have a soul.”

On the Margins of Cybernetics

Hugo Steinhaus (published in Znak Monthly, 1963)

Three hundred years have passed since the death of Blaise Pascal, but our minds return to this independent spirit, too early for his own epoch to understand him in full. He died at forty. He invented a calculating machine before he turned twenty. In principle, this arithmometer did not differ from those that have served as calculators in shops, banks, and offices since the beginning of our century - it too could quickly add multi-digit numbers. But the prototype built by the author of the Pensées did not come into use; in his time, gear trains were unknown, which today are an essential feature of such machines - in the 17th century there was no geometry or kinematics of gear wheels yet, and they did not know how to cut such gears in hard metal; instead, they used discs equipped with pins around the circumference - at high rotation speeds the pins broke, and this technological deficiency decided the failure of the invention. But our age knew how to deal with such problems of precision mechanics, and calculating machines, in various versions and under different names, won their rightful place in the utilitarian world; there was nothing mysterious about them, so they aroused no greater admiration than locomotives and steam mills. Only the Second World War posed a task that the most efficient arithmometer could not handle: How should artillery shoot down aircraft carrying death and destruction at speeds of several hundred kilometers per hour? For this it was necessary to calculate from the aircraft's position and speed such a direction of fire that the winged enemy would fly into a fountain of shells; an automaton was needed that would in a fraction of a second perceive the aircraft's position and perform calculations, while directing all barrels so that the aircraft, despite its speed, would not escape unharmed... Here the technology of the "age of steam and electricity" was no longer sufficient - there are no gears that would function at such speed, and it is even harder to conceive an apparatus that would withstand the enormous starting acceleration. There was only one solution: electron tubes, commonly known as components of radio apparatus - they can change their electrical conductivity hundreds of thousands of times per second, and this advantage was exploited in modern calculating machines; hence the name electronic machines.

As often happens, a decisive leap in military technology brought consequences in other fields that seemingly were distant from the original task. American mathematician Norbert Wiener became interested in another aspect of shooting, namely the necessity of gathering information, acting on the basis of this information, determining the error of this action, and eliminating this error in a new attempt at action. This “trial and error” method has probably been known to artillerists since the invention of gunpowder. But Wiener was the first to realize its universality. A cyclist uses it, a car driver uses it when he constantly compensates with slight steering wheel movements for the vehicle's deviations from a direction parallel to the highway, and a helmsman acts no differently - precisely the ship's rudder gave Wiener the best example of the general law he called "feedback" - the Polish equivalent of this term, “sprzężenie zwrotne,” sounds rather colorless. On large ships, steering is automated; when the rudder is set so that the ship sails straight, e.g., northward, and an accidental cause throws it off course, the gyrostat axis maintaining a constant northern direction will deviate from the ship's axis - this will cause steam to flow to the appropriate side of the cylinder, so that the piston will turn the rudder and cause the ship to rotate toward the correct course - when it has already restored the northern direction to the ship, the valve will close the steam supply. This clever device is not, however, the exclusiveprivilege of contemporary automated ocean giants: for a solitary sailor on an ordinary boat, the oar serves as a rudder, and a lighthouse on shore orients him as to direction - when he sees that the boat has gone off course, he corrects the direction with the oar; here the cycle consists of several links: the lighthouse casts its image on the rower's retina, the optic nerve transmits the image to the brain and arouses an impulse there, which by another route runs to the muscles holding the oar, and having reached there evokes contraction of those muscles, which causes a change in the oar's angle relative to the boat. This feedback, though used for many thousands of years, was not - until the last years of the Second War - the subject of conscious scientific analysis; it is incomparably more refined and universal than the modern gyroscopic rudder.

Now Wiener was the first to realize the fundamental similarity of these two seemingly different mechanisms. He organized a team of scholars who decided to systematically cross the boundaries of their specialties. In his book “Cybernetics, or Control and Communication in the Animal and the Machine,” he reports on the work of this team from the outbreak of the Second War until the date of publication of this work - he cites in it primarily the American physiologist Arthur Rosenblueth as his wartime collaborator, later replaced by other physiologists, doctors, mathematicians, and engineers. Most interesting is Chapter IV, devoted to feedback and oscillation - there for the first time he compares a patient in a neurological clinic with a sick automatic-type rudder. For the first time he states that every malf unction of the rudder has its clinical counterpart in the form of one of many diseases of the neuro-motor apparatus well known to doctors. For the first time it was indicated what defects of regulators and control automata correspond to such diseases as - for example - tabes dorsalis or Parkinson's tremor. The similarity becomes visible when we try to describe mathematically models of such common activities as reaching for matches or grasping a door handle. Wiener and his companions created precisely such models - today their technical terms “input,” “connecting channel,” “output,” “noise,” “amount of information,” “feedback” have passed from specialists' vocabulary to the general press, enriching it without ballast. But it's not these names that matter here, but an amazing occurrence; medical history had to record a strange tale of strange doctors: the patient was a rudder, the symptoms were determined by a mathematician, and neurologists knew the disease picture before engineers invented automatic rudders, i.e., patients! In the history of philosophy one can find equally momentous events - today it's already hard to evaluate them with the proper measure, but in their time they were milestones of wisdom, though later the direction of the road was to change many times. Descartes' statement that animals are only automata required of the thinker who uttered it no small independence of mind; this ultra- materialistic thesis asked for application to humans, so closely related to higher mammals by complete similarity of structure of all organs (not excluding the neuromotor apparatus), that a mathematician could give a dog and its master as an example of a pair of topologically equivalent creatures. But from Descartes to Pavlov - three centuries passed...

It was only a hundred years ago that it was understood that the chemistry of organic matter transformations is subject to the same laws as the chemistry of dead substances, and that the principle of conservation of mass and energy also applies to living organisms! It was not easy to overcome such psychological resistance of the era when it was established that the movements of people and animals are governed by the same dynamics that were perfectly known in the 18th century and soon after tested on machines practically. But the most interesting episode occurred much later, in 1903, when Wilbur Wright traced the first circle in the sky with a motor airplane, and to the question of how his machine stays in the air though it is heavier than air, he replied: “Like a bird” - just like a bird. How should we understand this? Because a bird is a flying machine, says Wright, I built our machine imitating a bird... In this sentence of the first aviator lies faith in Descartes - before 1903, most people, even educated ones, believed that a bird flies because it is a bird, and it is created for flying, and no apparatus can match it because it is not a bird...

Wright bet on a different card: a bird flies because it is a machine for flying - therefore one should build an apparatus equipped with wings and give it a gasoline motor instead of muscles... Wiener's path was parallel to Wright’s, but the direction was opposite: An automatic ship’s rudder sometimes exhibits so-called “hunting” - it can be described mathematically; a human being after brain damage must have a steering apparatus, and it is subject to defects similar to the defects of an automatic rudder - so says Wiener; Wright, on the other hand, told himself that since there exists a living flying machine, one can build an artificial one that will imitate the living one in this function. Wiener knew the theory of the rudder and its defects; he also knew that the human neuromotor apparatus is subject to diseases - therefore he could describe the symptoms of Parkinson's disease without looking into a neurophysiology textbook; his discovery did not require inventions, unlike the discovery that a bird is a machine.

This kind of discovery is rarely recorded in the history of human thought - one can include Newton's discovery of gravitation among them. It did not make a great impression on people; even the educated, even later ones, such as Goethe, did not realize what hour had struck on the clock - perhaps because the models of the theory were planets and the moon, distant and mysterious objects. When a few years ago artificial earth satellites were successf ully placed in orbits, the majority became concerned about what would happen when the artificial ones fall to earth, and a minority was amazed that they don't fall. When someone noticed that the real moon also doesn't fall to earth, they were told: it doesn't fall because it's the moon - this almost literally repeated the thesis of aviation skeptics “a bird doesn't fall because it's a bird,” and only a few understood that if the moon doesn't fall, then another object set in orbit around the earth also won't fall.

Even fewer were those who noticed that they were witnesses to the first experiment in history perfectly confirming Newton's theory on objects made by human hands and visible to the naked eye - one had to wait for this almost three hundred years. Again, technological difficulties were the cause of the delay; in Newton's time there were no such explosive materials that could give a projectile at least thirty times greater speed than that of a cannonball of that time. Even today there is still a lack of laboratory-scale experiment; one cannot show students in school the law of gravitation on models as one shows, for example, pendulum motion. Recently I found in a newspaper information about observations that MARINER II transmitted to Earth's inhabitants; the information showed the impossibility of organic life on Venus - it was printed in small type. The rocket ran for over a hundred days and covered about 80 million kilometers to confirm the old aphorism that there are more things between heaven and earth than can be dreamed of in school philosophy - indeed, it never could have occurred to me that this confirmation would be printed in small type where the thickest capital letters give news that even after being provided with a negation sign would not become true.

Philosophers have long asked whether man is a machine. Marionettes give a partial answer, which evoke applause by their resemblance of posture and movement to the human prototype - the secret of the wooden Punch performing somersaults on stage is his obedience to the same laws of mechanics to which the living clown in the circus is subject; but let's not think that it was always easy to believe in this truth, sounding so natural today...

It wasn't long ago that the Paris Academy of Sciences was puzzled by the paradox of a cat falling on four paws when all four threads holding it suspended on its back are cut simultaneously - rational mechanics, as its great creators, members of this same Academy, called it, has long been able to explain this really interesting experiment, but the very fact of the controversy testifies that there were many supporters of a different explanation of the feline salto mortale - anyone can guess what this explanation must have been: a cat always falls on four paws because it is a cat; this irrational mechanics pleased them more than the rational one.

The controversy of today’s era is the calculating machine, or speaking more ominously, the electronic digital computer. It is not a playing cabinet or a ticket vending machine; modern computers have higher ambitions: they play chess, compose dance music, and determine the authenticity of signatures - admittedly they do this worse than living specialists, but it's not easy to find a human who would single-handedly replace them in all three functions, and - as a side occupation - practice solving a hundred equations with a hundred unknowns in a few minutes. Belittlers of machines claim that whatever an electronic computer does, it will always be executing a program written by human hand and inserted into the appropriate drawer of the machine by a human, whose blind tool the machine is. But the machine's defender will point out to them that the metaphor “blind” is inappropriate in their mouths, because after all the eye is also a tool, and yet it is not blind; here the evolution of knowledge was similar to the discovery of cybernetics, because the invention of the glass lens and discovery of its ray-focusing function preceded anatomists’ recognition of the role of the eye’s lens. Then the anti-machinist will charge the computer with lack of consciousness: it's hard to imagine a machine that is aware of its actions, and even harder one that has the privilege of free decision. Instead of defending machines, let me be allowed to recall what Pascal writes about such games as heads-or-tails. According to him, every player of some intelligence will beat a naive opponent in this game if he correctly assesses his naivety - he will know that a simpleton, having lost on heads, will bet on tails; a more refined partner will manage with an averagely clever one, who can only cope with a completely dim-witted one...

To benefit from Pascal's theory, one must assess correctly the partner's degree of intelligence based on the first few throws - and perhaps also from the partner's appearance. I once saw in a bar in New Mexico how my friend played with a chance opponent and beat him very effectively applying Pascal's advice. But what will happen if the partner is a computer? D. W. Hagelbarger gave an answer to this question through appropriate modification of the machine, which he ordered to guess whether the living partner would place the coin heads up or tails. After a large number of trials it turned out that the machine wins on average 55 games out of 100. Its secret is this: it records in memory the entire history of the game from the beginning, because its caretaker informs it each time about the result. At first this information gives no visible benefits, but after several dozen records the machine bases its decision on experience: it searches in memory for game sequences composed of several (e.g., three) consecutive decisions by the player and as many machine responses, such that the entire cycle (six moves) does not differ from the last cycle (six moves) - if it finds such cycles, it concludes that the living player will currently act as he acted in the majority of those selected cases, and announces this guess as its response. Here Pascalian finesse won't help the living player: even if he tries to avoid his previous principles and change tactics, sooner or later he will fall into routine and lose in the long run - such a player will fare worst who thinks he is dealing with an automaton cyclically repeating signals once recorded on tape. It's the opposite: the electronic computer considers the living partner an automaton and is not so wrong - the machine's positive balance forces the human to confess that rather the computer saw through him, and he, the living player, underestimated the apparatus's intelligence. Thus the electronic gambler becomes richer and wiser, and this cannot be said of the living one...

Two great wars embedded in our memory the name “Torres y Quevedo.” This Spanish scholar from before the First War did not have electronic technology at his disposal, but he constructed an electrical player mating with king and rook against a solitary king, led by a living partner who positioned all three pieces arbitrarily at the beginning; the electrical player always won in the shortest number of moves determined by theory long known to living chess players. Ulam and Stein decided to investigate whether N. Wiener was not mistaken in his prophecy that electronic computers would equal skilled chess players of the “homo sapiens” brand. In a report published in 1957 they explain why computers still play very poorly. If a machine is to play tolerably, it must - like a human - look into the future at a distance of at least three of its own moves and as many opponent responses; this corresponds - according to rough estimation - to 64 million chains connecting the initial state with what will be on the chessboard after those six moves; even the most efficient machines would have to ponder several hours over each move, so that the game would drag on for whole weeks...

How does it happen that on 64 squares man still reigns unchallenged over computers? After all, the imperfection of human memory is - unfortunately - well known to us! How then does man find in the course of one or two minutes a move that radically destroys a position worked out by the opponent over many hours? He manages only because he knows how to think in broad strokes: when he sees, for example, that his king finds itself in a difficult position on the right wing, he will not think about a possible move of his pawn on the far left; he also won't count on such an opponent response whose pointlessness he sees directly - this already reduces the field of choice so radically that the necessity of reflection rarely occurs. In this art of distinguishing essential things from inessential ones, and in the art of painting the situation with a few broad strokes chosen from thousands of details, which the machine analyzes consecutively all without exception, the chess player maintains his superiority over the computer. This is a strange human advantage, of which until recently no one was aware, so that it still lacks a name: walking on uneven terrain, estimating by eye the width of a ditch, guessing from a few strokes whom a caricature represents, understanding the content of a letter read hastily - these are examples of specific human efficiency that machines would env y, when they someday learn to env y. Following this line St. Ulam proposed “synergy,” which consists of division of labor: man divides the field of vision into several sectors and classifies them according to importance; he rejects those he easily recognizes as meaningless in the chess struggle or other problem requiring his decision, and from the remaining part of the field he selects several possible decisions and orders the machine to study their consequences - in this way he can choose the best one and after a few moves without the machine's cooperation again review the situation. In bridge, the machine should be limited to matters of probability, and man should be left to choose the card after hearing the electronic prompter's report on card distribution. A universally known example of synergy is the cooperation of a car driver with the motor, which handles the energy aspect, leaving the driver to choose direction. When we compare Torres y Quevedo's apparatus with a computer playing chess with a full set of pieces, the question arises why the old-fashioned electrical apparatus manages splendidly, while a computer a thousand times faster is so helpless? Simply because chess players long ago solved the problem of the game of king and rook against solitary king and provided rules determining in each situation of such a trio the best move for White - since Torres's apparatus plays White, it was enough to build these rules into the apparatus; there is nothing similar in full chess, because it's not even known which color has theoretical certainty of not losing (although it's known that there is such a color). War differs from chess in that here the chessboard is visible only through thousands of telegraphic, telephone, radio-telephone, and other communications, and the so-called theater ofwar encompasses entire continents and oceans; therefore some experts on contemporary war problems want to raise the significance of “common sense” of commanders at the highest levels; one expert, Sir Solly Zuckerman, fears that overly refined automatization of all decisions might - given the enormous number of parameters whose precise knowledge is impossible - lead to fatal errors if everything depended on an inexorably logical machine and some surprise occurred whose importance the machine would not notice, but which any reasonable and experienced commander could easily assess if he didn't have to trust machines more than peasant reasoning. In short, the English expert would be a supporter of synergy if he knew such a theory exists, and if it were mature for practice - one can doubt both assumptions. But how can one rely on peasant reasoning when the main food of such reasoning is experience, which no one has had the opportunity to acquire - no one has seen atomic missiles and rockets in action encompassing populated areas and reacting as living targets. Today's war, in which one side believed in the infallibility of machines and the opposite in the advice of Mr. S. Zuckerman, would be like a chess game in which on one side of the board sat a computer and on the other an inexperienced chess player - as we know from Ulam and Stein's studies, the chances are then equal...

The NATO expert also regards modern game theory with distrust, which he considers a chapter from statistics and probability calculus, in which he is wrong. Given that we (fortunately) know very little about future war, we must - if we already accept the possibility of such war as a subject of reasoning - learn from experiences during the struggle; we cannot entrust such registration of events and constant “feedback” to anyone except the machine of the future - the owner of this machine will find himself in a similar situation to the constructor of the machine winning 55% to 45% in heads-or-tails.

The end of the 19th century repeated “Ignoramus et ignorabimus” - we do not know and we shall not know - these words of the famous physiologist Emil du Bois-Reymond were the title of a list of unsolvable problems. A century earlier, Immanuel Kant called them antinomies of pure reason. Did the world have a beginning, or was it always? Will it last forever? Is it limited or boundless? Can living substance arise from dead, or only from living? The appearance of electronic computers reminded us of these questions of the Berlin physiologist, who placed the answers beyond the boundaries of science, as inaccessible to human reason. Against the background of these classical dilemmas, the question of whether an electronic computer is a living being will seem to everyone comical in its absurdity. It is worth posing, however, because it forces reflection on what is the characteristic feature of living organisms. Ever new discoveries of mechanisms in the organic world and in man himself awaken in us age- old dreams of the homunculus; if man is a machine, then why shouldn't a machine be man?

The name “electronic brain” displaced from the dictionary “robot” from 30 years ago - both are expressions of the same aspiration, and Adam molded from clay is its oldest reminiscence. This metamorphosis is unidirectional: to make the living from the dead - the opposite transformation is a curse and punishment. Epochs past are also familiar with the coexistence of free will with absolute determinism - Islam is an example of this.

The aesthetic criterion fails, because some people (but almost exclusively men) are inclined to see specific beauty in machines - Huysmans, whose famous “À rebours” closes a certain era, was the first to notice this techno-romanticism of the generation that followed, and the genius creator of expression prophesied the defeat of the generation that would sell itself to the machine. And perhaps body too? Who wins in the war of machines against man? How many people died, how many machines in recent wars? This statistic is known, though machines don't boast.

Naturalists are inclined to recognize as a criterion of life the metabolism of matter between a living being and its environment, as well as the continuation of living individuals through reproduction. I would add death here as a feature of life: everything that lives will die. Spontaneous movement is not a necessary attribute of life, but a su fficient one. There are machines that can pretend to life by virtue of movement. The name “automobile” literally means something that moves itself; the translation “samochód” [self-walker] is consistent with this name - it is very significant that the first witnesses of automobiles saw in them precisely what is most essential: previous experience had taught them that a wagon requires a draft animal, which walks by itself because it lives; amazement at the sight of a wagon that also walks by itself found expression in the name. Anyone who knows cars in the West, especially in the United States, must agree with the assessment of local sociologists that no rational reasoning explains such widespread distribution of these machines as we see there. There are practically no roads for pedestrians, and streets are so crowded with cars that serpentine overpasses must be built for them. Admittedly, the price of a car, especially a used one, is not high, but the costs of maintenance, repair, insurance, and especially parking are burdensome. Driving a car over long distances is exhausting, and the trouble with it in a foreign city is considerable. This irrational relationship to the machine can only be explained by seeing in it something more than a soulless lump of matter. I know only one example of machine dominance over man even more complete than cars: the rotary press - here, however, the dominance is indirect, through the product, which also took on the character of the press; this example requires a separate study that cannot fit in the margin.

Spontaneous movement requires free will. Does a machine have it? Let us ask whether man has it. I was once a witness to a post-hypnotic experiment, that is, one in which the subject is to perform after awakening certain orders imposed on him during hypnosis. The experiment was arranged so that all possibilities of deception were excluded. After awakening, the subject behaved completely normally. Those present knew, however, when the time would come to return home and that then the subject would demand to be lent a pen lying on the table - the host deliberately made difficulties, but to all his arguments the subject argued and insisted on its will, which was alien - was it not then similar to a stone kicked by a tourist's foot from a mountain slope? And perhaps such a stone has consciousness of free choice and if it could speak in human language would say: “I'm going downhill because I agreed with a fellow stone!”

After all, Aristotle explained the falling of bodies by the predilection of all matter for the vertical downward direction. For materialists there is no sharp boundary dividing the world into organic and inorganic - it's only a matter of complexity, because organic cells surpass in structural richness everything we consider dead matter. The liver consists of millions of cells, each of which is such a complex assembly of various elements that an electronic computer is something very primitive compared to this machinery - the physiological tasks that fall to the liver are diverse and difficult; wanting to solve them, nature did not try the power of the magical “because it is a liver,” but built an enormous complex of miniature automated factories, which is proof of the universality and unity of nature's laws. Electronic machines are incomparably poorer technically than these factories; let us not wonder then that they play chess poorly, but let us note that nature too does not have brilliant shortcuts when it must solve difficult problems. Believers in Scripture resolve the controversy between living and dead matter by giving a living and immortal Being the power to create from chaos first cosmic order and then organic life, whose pinnacle is man; if so, it would not be strange if this man in turn could construct objects endowed with abilities of perception, coordinated movements, feeding, reproduction, decision, play, and struggle for existence. The recently deceased J. von Neumann, one of the leading mathematicians of the past two decades, posed the problem of whether an electronic machine can produce another better and more efficient than itself - he achieved certain results testifying to such a possibility. Von Neumann's name is linked with game theory, and games of chance with Pascal's creativity: he found the proper theory of gambling in the form of a separate doctrine, which is probability calculus. But von Neumann, and before him several other scholars, among whom the French mathematician and politician Emil Borel was the earliest, were interested in a different aspect of games than Pascal, namely the principle of optimal behavior. It would seem that one cannot determine such behavior if one does not know the principles by which the opponent is guided. But he too does not know what principles we hold to. Mathematics knows how to master such situations; game theory, unknown before World War I, became after the second an established branch of science. It is known how to escape the vicious circle through optimal strategy, but in real situations finding it requires long calculations. Therefore electronic machines assist game theorists - games are not only chess and checkers, but also disposing of freight cars on a national railway network scale, or determining drug strength from several dozen trials can be reduced to this theory.

The problem of what a machine can and cannot do appeared a hundred years ago in the dream of automata speaking with human voice - the good-natured barrel organ born from the lyre but deprived of poetic aureole, how far it was from the baritone heroes and soprano heroines whose names appear on marble tablets of theaters - those who placed them there did not know that it would be better to engrave with a needle on wax the voice of the famous Malibran than with a stylus on stone her name. Of all the machines that the second half of the 19th century gave us, the gramophone is the simplest: a rotating disc (first wax, then ebonite) and a stationary needle, whose tip rests on the groove, and the other end is embedded in a metal tube. Despite this simplicity, Edison's invention could be so perfectly realized already in prototype that when it was demonstrated for the first time in the Paris Academy of Sciences, many academicians looked around for who among those present was a ventriloquist - doctors appealed to their authority in matters of throat, larynx, vocal cords, etc., and ruled that this natural phonetic apparatus has so many wonderful properties that no machine, let alone some disc with a nail, would ever speak with human voice given to us by the Creator.1 Again the force of faith in the hereditary privilege of Adam's descendants was revealed: man speaks because he is man, and no machine can speak with human voice. But the machine spoke with human voice, and its mimicry was perfect - let the novel “L'Ève future” testify to the impression, whose hero constructs an artificial woman with Edison's help. Since the gramophone faithfully renders pitch and its timbre, individual features of pronunciation and voice, as well as the acoustic image of all emotions we hear in word and song, doesn't the artificial woman surpass the living one in that her answers are exactly those of which the adorator who built her dreams? But everything that evokes joy and despair, hope and doubt, lies in the disc in the form of a groove carved by the needle during disc recording. This trace can be represented by the relation y = f(x), where x denotes time, and y the depth of the trace... thus everything that gives the audience the charming voice of a tenor singing the famous aria from Tosca can be expressed through a continuous function of one variable, and the gramophone is experimental proof of this theorem. It fulfills a role reserved for human beings. Hence the reverse conclusion: man is a speaking and singing machine, and his organism contains - among many other apparatus - also a vocal apparatus. Today everyone knows this, but before Edison few would have accepted such brutal formulation of facts. Is it not worthy of philosophers' attention, this persistent defense of every human monopoly and inability to draw a general conclusion from defeats inflicted on us by ever new machines? To this question we will hear the answer that it was man who built them. This was indeed so, but there is no fundamental reason that would guarantee us eternal patent rights to all possible inventions about which we have not yet dreamed...

The gramophone is the acoustic equivalent of photographic film, and like it is only a recording and reproducing apparatus - it cannot be classified among universal machines, such as contemporary computers. Today's problems demand an apparatus that would read notes and lyrics converting them into song, as a singer looking at a score does... there are no fundamental obstacles on this path, though technical difficulties might be considerable - it's unknown whether one should rejoice or worry that the near future will provide us with a companion in the form of a box that would give banal answers to our banal questions... materials for such conversations can be found in G. Flaubert's “Dictionary of Human Stupidity” - to the question whether a machine can think, we will receive the polite answer: “unfortunately not - we have no soul” (nb. the term “electronic brain” was invented by a journalistic brain as unrequited flattery for the machine).

The concept of feedback appears in calculating machines in the form of control devices; one could also imagine its use in gramophony. One can suppose that the principle of synergy will soon find application in computers. But not only these, here parenthetically formulated tendencies characterize our era.

The popularization of problems facing our generation is itself a problem. The number of scholars belonging to it exceeds their total in all previous generations - a popularization will struggle even to reach every scholar. Few humanists realize the essence of mathematical problems (recently I read a serious article in which one of the lightning calculators multiplying multi-digit numbers in a few seconds was called a “mathematical genius;” the author evidently did not know the work of French psychologists from the end of the 19th century, who noticed that among such calculators there is a large fraction of mentally deficient persons - perhaps even fewer are mathematicians familiar with the results of today's genetics).

We are like Croesus, who could not count his riches. We live in an age of explosion, not only atomic. European monarchs of the first quarter of the 19th century sent their couriers by relay horses - the Egyptian pharaohs also knew this method a few thousand years earlier; from the moment when man first mounted a horse until the moment of putting Stevenson's locomotive on rails, the speed of communication did not change, but that moment doubled it. Doubling the speed of the first trains required only 50 years - then came 8 such doublings of transportation speed, and the transition from jet aircraft at the speed of sound to rockets carrying cosmonauts around the earth required five doublings and was accomplished in six years - this means that currently man doubles his transportation speed every year! Population growth of the globe also takes on the character of explosion - currently the period of its doubling is about 50 years; if one accepted this period as constant, it would mean that before Christ there were no people on earth at all - this reasoning ad absurdum shows that the period of population doubling is decreasing rapidly. Economic, and therefore political, consequences cannot be grasped by the observer's eye: they will appear before us suddenly, as an accomplished fact. This near future will appear as a result of rapid technological development, which will be based on new energy sources. From 1643, when Pascal devised his machine, to arithmometers about 250 years passed, and from them to computers only 50; currently the doubling of digital machine speed also has an explosive character, so that what I write will be obsolete when it appears in print.

Thus it is difficult to predict the role of digital machines in the future. When cinematography appeared at the beginning of our century, viewers delighted in the sight of a train entering a station or a horse taking an obstacle - everyone thought that cinematography would show interesting events filmed in motion, but no one predicted that it would become a producer of artificial events, and thus theater in universal and commercial format. Today's computers calculate pensions and workers' wages or look for contradictions in tax testimonies - one can hope that the fact of machines' existence will evoke other questions, unknown today, but incomparably more important...

Will they solve all problems? I think not.

Will they solve every problem? I think so.

How will the game between man and machine end? I don't know, but I know it's a game with infinitely high stakes...

For this one, I’m going to start with the story of how it was rediscovered during World War II. Because it’s a pretty amazing story.

It is easy to leave the home of reality and get lost in the woods of mathematics, but only a few know how to return.

In Nazi-occupied Poland, the hardest math problem was finding someone to teach you math. The Soviets had purged all the intellectuals they deemed undesirable, and then the Nazis had murdered all the ones they didn’t like. Mathematicians tend to be pretty weird, and there weren’t many weird academics left.

(This might seem like a trivial issue, under the circumstances. It wasn’t, for some people. I would’ve been one of them. Math can be an addiction. I’ve never been a mathematician, but I’m not sure I’ve ever gone a week without learning some math, since about age 7 when my babysitter introduced me to solving algebraic equations with two variables. It soothes me when I’m anxious, and under those circumstances, if I were somehow alive, I’d be a bit on edge.)

But for those in the know1, there was one way to get a top-quality math lesson in exchange for, say, chopping some firewood. You needed to find your way to a farm on the outskirts of the village Stróże. The farm was owned by an old politician and activist, Jan Cieluch, who’d recently been released from prison. There, you’d meet one of his farmhands—a retired park ranger named Grzegorz Krochmalny. That’s your math teacher.

If you knew to come here, you probably knew he wasn’t actually a retired park ranger, and the name on his identity papers was not actually his. If you didn’t, there would’ve been some clues. He never drank, and rarely went to church. He didn’t make eye contact—in fact, he’d usually turn his whole head to the side while talking to you. He’d compulsively correct your grammar and your manners—if you introduced yourself by your last name, rather than your first, you would not be getting your class that day. He seemed almost as at home teaching the humanities as teaching math.

And of course, you’d discover he wasn’t only a great teacher—he was also a great mathematician, one the rest of the world thought was dead.

Mathematics is a bridge between spirit and matter.

Hugo Steinhaus was born in 1887. His childhood home, as well as the family store and the rest of his neighborhood, had been converted from a monastery decades earlier. You could barely tell. His family was Jewish, and you could barely tell. They had secular jobs and upper-class manners, spoke Polish, and didn’t all believe in God. Young Steinhaus would gawk at people celebrating Purim the same as he would gawk at a traditional peasant wedding or a dancing bear. Older, he won a bar bet with an anti-Semite who claimed to always be able to spot a Jew.

But he could tell. A formative memory for Steinhaus was seeing an army unit deployed to defend his neighborhood from a pogrom.

Steinhaus took longer to realize that he was a mathematician. At nine, he enrolled in the county school in the old town hall.2 The school had an intense curriculum, but at age nine it focused mainly on Latin, German, and beatings. There were other classes too, although as a Jew he wasn’t allowed in the religion class taught by father Wiśnewski. If he hadn’t cleared out by the time Wiśnewski showed up, he’d be flogged with a cane in front of the class. In his memoir, Steinhaus notes in passing that Wiśnewski eventually turned out to be a pedophile and was transferred away.

Literature was fascinating but disreputable. History was difficult because he couldn’t see any way to learn it other than memorization, which he wasn’t very good at. Sociology was incomprehensible—why was Durkheim so interested in the marriage customs of Polynesians, but not at all in their methods of warfare? Latin and German were all well and good, but he was more interested in learning English, part of his “contingency plans.” Military engineering was attractive at first, but his pacifist grandfather talked him out of his early hero-worship of the troops who had protected him from anti-Semites. (He did serve as a young man, which is how he met his wife).

That left mathematics, but for math he was dependent on textbooks, and the few he could scrounge weren’t very good. One was organized alphabetically by the last name of the author of that chapter; Steinhaus didn’t notice, tried to read it linearly, and was baffled. When he happened to meet someone who knew math, he learned that you could study it in the “exact philosophy” department at Lwów University, so there he went.

Math wasn’t only gratifying in itself. It was also a way in to all those other subjects that had stymied him before. He learned the history of mathematics, the way different cultures approached it differently, its applications to engineering, the way it approached the mystical and the divine.

His main focus, for a time, was probability and statistics, which enabled him to kibbitz in a wide variety of practical fields, including cancer research. He never bought the idea that there was a distinction between “pure” and “applied” mathematics. Math was math. Ideally you found applications for it, but doing so didn’t transform the math itself.

He also dabbled in engineering. One of his more immediately useful projects was the invention of what he called an “introvisor,” an ahead-of-its-time tool that used x-rays, lights, and a mirror to create a labeled visualization of the inside of a surgical patient, or whatever else you wanted to inspect. A CT scan, but without the C for computerized. He was motivated by meeting a 12-year-old with a needle stuck in her knee, which nobody could remove because they didn’t know exactly where it was. It was used, successfully, for that type of surgery, and later also by locksmiths, but never caught on.

The world is a ball chained to the leg of humanity.

Despite a rising tide of Polish anti-Semitism, Steinhaus eventually established himself in Lwów University as faculty. There, he became one of the founding fathers of the modern Polish mathematics community, as well as multiple branches of mathematics. He may have been the first to publish papers on game theory, a few years before John von Neumann kicked it off properly. He became known as well for his witty epigrams, some of which show up as the section headers of this article.

Meanwhile, Hitler and Stalin were secretly negotiating about who got to conquer which parts of Poland. Steinhaus was lucky, relatively speaking, to be in the Soviet slice of the cake. He stayed, because someone had told him that Bolsheviks revered academics. But Soviet culture, with its blatant disregard for the truth, disgusted him. He was never comfortable in the new regime, under posters of Stalin and his “crocodile smile.” Much later, he wrote:

Quite soon I perceived that we were dealing with liars and people of little—say a quarter of the average—intelligence whom the liars had turned into zombies. They made invariably empty promises, big fibs like trump cards to be dealt at every opportunity: “You had a pension equivalent to a thousand rubles; now you will get two thousand.”

Still, quietly, his Lwów School of Mathematics survived, meeting in the local Scottish Café, which had marble tabletops you could write on in pencil. Or sometimes, when Steinhaus had his way, in the more upscale tea shop down the street.

Then Hitler broke the truce.

You can’t predict the future. It’s hard enough to predict the present.

Murdering the academic community in Lwów, Jewish and not, was one of the top priorities for the Gestapo, passed down from the highest levels. They started killing the day they conquered the city, locating more in the next few days with the aid of Ukrainian collaborators. Lwów’s professors, especially its mathematicians and medical scientists, had become an emblem of Polish pride, and the Nazis hoped that wiping them out would break the spirit of the resistance.

Professor Jakub Karol Parnas, a celebrated Jewish biochemist and devout Communist, fled deeper into the USSR just in time to escape the massacre. He wrote in a Soviet news journal that

As soon as the Germans entered the city they organized a pogrom against the intelligentsia.

We know definitely of the murder of Kazimierz Bartel, professor of geometry; Tadeusz Boy-Zelenski, writer and literary scholar; Victor Reiss, ophthalmologist; Juljan Kleiner, philologist and literary scholar; Hugo Steinhaus, mathematician; Stanislaw Pilat, chemist; and Pawel Stern, biochemist. There are also reports that Adam Gruo and Stanislaw Dobrzaniecki, outstanding surgeons, were murdered.

That list was incomplete, but mostly accurate. Parnas himself had made mostly good decisions on how to survive. But at age 65, he was still living in the USSR when Stalin decreed his own pogrom against the intelligentsia, known as the Night of the Murdered Poets (you can tell, just from the name, that they didn’t get them all). Parnas died in a prison cell.

It’s rude to speak ill of the absent, let alone the nonexistent. So atheists are in an awkward position.

Steinhaus and his wife, Stefania, were able to sneak out of Lwów just in time. The Gestapo were guarding the front door of their house, so they went into their back yard. Stefania picked a rose from their garden, and they climbed over the fence into the neighbor’s yard. From there, the two simply strolled out of town looking like a middle-aged couple on a casual date.

Their survival now depended on a clear vision of the inner workings of the occupation bureaucracy. Underestimating their efficiency and organization could be fatal—if you were caught in a lie, you were done for. But overestimating it was even worse, he wrote later. Jews had to tell some lies, forge some documents, break some curfews, to avoid the concentration camps. Very few of them were able to spot the flaws in the machine, the places where the Gestapo’s seeming omniscience was a bluff.

But the Nazis were pretty stupid, Steinhaus thought. They didn’t even have good etiquette skills! They’d use the familiar “du” instead of “Sie” when addressing him, which was clearly incorrect. With that kind of inattention to detail, how were they supposed to be able to spot forged identity papers?

He, and most of his close family, separately and slowly made their way to Jan Cieluch’s farm, adapting their stolen identities to reflect their actual relationships to each other. They rarely felt safe, what with the constant trickle of news gradually making it clear that there was a full-scale Final Solution being implemented. But they weren’t caught. The village government proved adept at subtly sabotaging Gestapo investigations. Steinhaus avoided any academics who might recognize him, and wrote letters to friends under fake names. He helped with the harvest, getting “a great deal of satisfaction” from raking hay. Occasionally, he was able to apply his mathematical ability—creating a precisely proportioned map of the farm, for example, without the use of traditional surveying equipment. He gave lessons to the neighbors in exchange for flour rations and other foodstuffs. (This was doubly illegal—private schools were banned.)

“Thus life would have been tolerable,” he wrote, “if not for the constant dread hanging over us…”

People want to discover new things because we can’t stand how clichéd we are ourselves.

3

It was here, in letters exchanged with his former students Bronislaw Knaster and the great Stefan Banach, that he first formulated the problem of how to cut a cake.

Suppose two men are splitting a cake. If one cuts it in half, he could choose where to cut to give himself a “better” half—more frosting, say, or more strawberries. That’s not fair. The classic solution is to have one man cut the cake and the other choose which half. This gives the cutter an incentive to divide it exactly evenly.

But what if there are three people? Or more? Steinhaus suspected that it was impossible to come up with a general solution that worked as well as the one for two people, but he wasn’t sure.

Knaster and Banach were also Jewish, but were staying out of the camps by working as lice feeders for the parasitologist Rudolf Weigl, who was studying typhus. The Nazis spared this part of Lwów medical research because their soldiers kept getting typhus. Weigl found a clever, if horrifying, way of keeping the remaining Lwów intellectuals alive—right as the Nazis moved in, he hired them to be bitten by typhus-infected lice, so that the lice would survive long enough to be useful for research. The Nazis generally exempted people in this situation from the concentration camps—they were providing a useful service, and suffering and dying at an acceptable level.

Banach, short on blood but with little to do, ended up solving Steinhaus’s impossible problem by inventing the last diminisher protocol. In this version, the cake cutter first marks out the slice he plans to cut for himself. If anyone thinks the slice is too big, he can propose a smaller slice—but now that’s the slice assigned to him, not the original cake cutter. Once nobody thinks the slice is too big, the last person to shrink it gets that slice. The rest repeat the process. Banach and Knauser sent Steinhaus a theorem proving this was optimal.

They didn’t dare publish it until after the war. They did, however, get a different theorem published, anonymously, one that nobody would suspect had been written by Jews: a proof that it’s always possible to cut a ham sandwich in half with one cut, no matter how sloppily it was made.

Discoveries are flashes. One can find the philosopher's stone and forget where it lies.

I think the last diminisher was a reinvention of a prehistoric algorithm. Prehistoric cultures probably didn’t have the concept of a mathematical proof, but they could have tested it and noticed how well it worked. They might even have noticed, and corrected, a flaw in the protocol that mathematicians spotted later. People perceive the cake differently. If somebody got his fair portion, but thinks that the rest are dividing up their portions unfairly, he might end up envying one of the others, even if nobody else feels cheated. So people need to be allowed to return their portion to the pot and re-enter the process.

The protocol can be explained in a paragraph. We know it can be invented by people in highly stressful situations. And it would have been useful.

Four people work together to kill a large animal. Who gets which bits? Different people may have different preferences—someone wants the hide as part of their share, someone only wants as much meat as possible, someone really doesn’t want to have to eat liver again. If anyone feels like they’ve been cheated, violence could ensue or the band could break up at the height of their success.

Somehow or other, our ancestors must have solved that problem, probably many times in many places. Unlike some other algorithms, they wouldn’t have needed to make tools or wall markings to implement it, so we’re unlikely to ever find evidence. But they must have had a solution, because they survived. They didn’t spend their entire lives in a brutal war of all against all; they planted the seeds of civilization.

World War II is that story in miniature—even in the midst of its horrors, people were not just surviving, but innovating. Enriching the peaceful future. Weigl’s theories about typhus turned out to be correct. He invented a typhus vaccine, and used it to protect his lice-feeders. Including himself—he was always his own first test subject. Weigl is considered one of the Righteous Among The Nations, a non-Jew who saved Jewish lives. Knauser’s and Banach’s, among many others.

In 1969, a young mathematician named Wojbor A. Woyczynski was reading in a university library in Wrocław. The director of the library approached him and made an introduction to a professor who wanted to meet him. The 82-year-old man was immediately recognizable to any Polish nerd with a radio or television set. He started out with a compliment, as is only polite. “Professor Urbanik, your advisor, told me that you did something useful recently. May I invite you to our home for tea and cookies?” Thirty years after his supposed death, Hugo Steinhaus was still looking for ways to share.

Postscript: Cake Cutting Today

Cake-cutting is still a lively field in mathematics, with plenty of variants chosen to be mathematically interesting or tuned to different real-world problems—choosing work shifts, dividing an inheritance, allocating funding for public goods, and gerrymandering are just a few. We still tend to use Steinhaus’s metaphor of the cake no matter what’s actually being modeled.

When I was telling my spouse (happy birthday, by the way!) about cake cutting, she immediately assumed that the problem was about finding the socially-optimal distribution—in particular, how do you make sure each person gets enough to survive, when they can lie about how many calories they need? This turns out to be a (sorry) cutting-edge question.

In the general case, Aumann, Dombb, and Hassidim (2012) have proven that even if everybody is honest, finding the socially-optimal way to slice the cake is NP-hard, meaning roughly that finding an efficient algorithm for it would also solve a host of other problems and is probably impossible. For the specific case of step-function utility (e.g. you value all slices below a certain threshold at 0, because you’ll starve, and you’d lie about where that threshold was if lying got you more cake), Menon and Larson (2017) show, if I understand correctly, that it is provably impossible to prevent cheating.

The best answer I can come up with is probabilistic. Everyone self-reports their threshold value, but the higher your threshold, the more likely people are to get angry and kick you out. Or you systemize that. With a uniform cake, for example, you could slice it in place, then toss three berries onto it from a distance, and if all three land on the same slice, the person who cut that slice for himself doesn’t get any cake. This kind of solution doesn’t guarantee a good outcome, but it’s often where our instincts take us.

Anyway, I’m off to eat some birthday cake. Thanks, as always, for reading.