Astral Codex Ten

Pythagoras

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Pythagoras

Article

Pythagoras is a recurring person in the Astral Codex Ten archive, appearing 3 times across 3 issues between August 30, 2021 and February 21, 2025. The archive places it in contexts such as “Shouldn’t Pythagoras have published his theorem in a peer-reviewed journal”; “When we teach the Pythagorean theorem, we should give a sense of who Pythagoras was — a cult-founder”; “mathematicians like Pythagoras and Euclid revolutionized math”. It most often appears alongside Aristotle, Plato, Reddit.

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  • Category: People
  • Mention count: 3
  • Issue count: 3
  • First seen: August 30, 2021
  • Last seen: February 21, 2025

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Source Context

Recovered passages from the original issue text. When the raw archive preserved outbound links inside the source passage, they are listed directly under the quote.

On Hreha On Behavioral Economics
August 30, 2021 · Original source
Green is one of these five studies, and it does superficially find loss aversion. But Fishburn and Kochenberger have done something weird. They argue that “loss” and “gain” aren’t necessarily objective, and usually correspond to “loss relative to some reference frame” (so far, so good). In order to figure out where the reference frame is, they assume that the neutral point is wherever “something unusual happens to the individual’s utility function” (F&K’s words). So they shift the zero point separating losses and gains to wherever the utility function looks most interesting! After doing this, they find “loss aversion”, ie the utility curve changes its slope at the transition between the loss side and the gain side. But since the transition was deliberately shifted to wherever the utility curve changed slope, this is almost tautological. It isn’t quite tautological: it’s interesting that most of the utility curves had a sharp transition zone, and it’s interesting that the transition was in the direction of loss-aversion rather than gain-seeking. But it’s tautological enough to be embarrassing. Still, this is Fishburn and Kochenberger’s embarrassment, not Kahneman and Tversky’s. And Fishburn and Kochenberger included this study in their review alongside several other studies that didn’t do this to the same degree. Kahneman and Tversky just cited the review article. I don’t think citing a review article that does weird things to a study really qualifies as “systematic misrepresentation.” I guess I’m having a hard time figuring out how angry to be, because everything about Fishburn and Kochenberger is terrible. The average study in F&K includes results from 5-10 executives. But the studies are pretty open about the fact that they interviewed more executives than this, threw away the ones who gave boring answers, and just published results from the interesting ones. Then they moved the axes to wherever looked most interesting. Then they used all this to draw sweeping generalizations about human behavior. Then F&K combined five studies that did this into a review article, without protesting any of it. And then K&T cited the review article, again without protesting. I have to imagine that all of this was normal by the standards of the time. I have looked up all these people and they were all esteemed scientists in their own day. And I believe the evidence shows K&T summarized F&K faithfully. Shouldn’t they have avoided citing F&K at all? Seems like the same kind of question as “Shouldn’t Pythagoras have published his theorem in a peer-reviewed journal, instead of moving to Italy, starting a cult, and exposing his thigh at the Olympic Games as part of a scheme to convince people he was the god Apollo?” Yes, but the past was a weird place. As best I can tell, K&T’s citation of G&P agrees with the authors’ own assessment of their results. Their citation of F&K agrees with the reviewers’ assessment and with a charitable reading of most of the studies involved, although those studies are terrible in many ways which are obvious to modern readers. I would urge people interested in the whodunit question to read Kahneman and Tversky’s original paper. I think it paints the picture of a team very interested in their own results and in theory, and citing other people only incidentally, and in accordance with the scientific standards of their time. I don’t feel a need to tar them as “misrepresenters”. III. Okay, But Is Loss Aversion Real? Remember, all that is about the personal deficiencies of Kahneman and Tversky. Realistically there have been hundreds of much better studies on loss aversion in the forty years since they wrote their article, so we should be looking at those. Here Hreha cites Gal & Rucker: The Loss Of Loss Aversion: Will It Loom Larger Than Its Gain? It’s a great 2018 paper that looks at recent evidence and concludes that loss aversion doesn’t exist. But it’s a very specific, interesting type of nonexistence, which I think the Hreha article fails to capture. G&R are happy to admit that in many, many cases, people behave in loss-averse ways, including most of the classic examples given by Kahneman and Tversky. They just think that this is because of other cognitive biases, not a specific cognitive bias called “loss aversion”. They especially emphasize Status Quo Bias and the Endowment Effect. Status Quo Bias is where you prefer inaction to action. Suppose you ask someone “Would you bet on a coin flip, where you get $60 if heads and lose $40 if tails?”. They say no. This deviates from rational expectations, and one way to think of this is loss aversion; the prospect of losing $40 feels “bigger” than the prospect of gaining $60. But another way to think of it is as a bias towards inaction - all else being equal, people prefer not to make bets, and you’d need a higher payoff to overcome their inertia. Endowment Effect is where you value something you already have more than something you don’t. Suppose someone would pay $5 to prevent their coffee mug from being taken away from them, but (in an alternative universe where they lack a coffee mug) would only pay $3 to buy one. You can think of this as loss aversion (the grief of losing a coffee mug feels “bigger” than the joy of gaining one). Or you can think of it as endowment (once you have the coffee mug, it’s yours and you feel like defending it). These are really fine distinctions; I had to read the section a few times before the difference between loss aversion and endowment effect really made sense to me. Kahneman and Tversky just sort of threw all all this stuff out and saw what stuck and didn’t necessarily try super hard to make sure none of the biases they discovered were entirely explainable as combinations of some of the others. G&R think maybe loss aversion is. They do some clever work setting up situations that test loss aversion but not status quo or endowment - for example, offering a risky bet vs. a safer bet. Here they find no evidence for loss aversion as a separate force from the other two biases. Somewhere in this process, they did an experiment where they gave participants a quarter minted in Denver and asked them if they wanted to exchange it for a quarter minted in Philadelphia. 60% of people very reasonably didn’t care, but another 35% had grown attached to their Denver quarter, with only 5% actively seeking the novelty of Philadelphia. Psychology is weird. I understand why some people would summarize this paper as “loss aversion doesn’t exist”. But it’s very different from “power posing doesn’t exist” or “stereotype threat doesn’t exist”, where it was found that the effect people were trying to study just didn’t happen, and all the studies saying it did were because of p-hacking or publication bias or something. People are very often averse to losses. This paper just argues that this isn’t caused by a specific “loss aversion” force. It’s caused by other forces which are not exactly loss aversion. We could compare it to centrifugal force in physics: real, but not fundamental. Also, you can’t use this paper to argue that “behavioral economics is dead”. At best, the paper proves that loss aversion is better explained by other behavioral economic concepts. But you can’t get rid of behavioral econ entirely! The stuff you have to explain is still there! It’s just a question of which parts of behavioral econ you use to explain it. Complicating this even further is Mrkva et al, Loss Aversion Has Moderators, But Reports Of Its Death Are Greatly Exaggerated (h/t Alex Imas, who has a great Twitter thread about this). This is an even newer paper, 2019, which argues that Gal and Rucker are wrong, and loss aversion does have an independent existence as a real force. There are many things to like about this paper. Previous criticisms of loss aversion argue that most experiments are performed on undergrads, who are so poor that even small amounts of money might have unusual emotional meaning. Mrkva collects a sample of thousands of millionaires (!) and demonstrates that they show loss aversion for sums of money as small as $20. On the other hand, I’m not sure they’re quite as careful as G&R at ruling out every other possible bias (although I don’t have a great understanding of where the borders between biases are and I can’t say this for sure). The main point I want to make is that all the scientists in this debate seem smart, thoughtful, and impressive. This isn’t like social priming experiments where one person says a crazy thing, nobody ever replicates it at scale, and as soon as someone tries the whole thing collapses. These have been replicated hundreds of times, with the remaining arguments being complicated semantic and philosophical ones about how to distinguish one theory from a very slightly different theory. If that takes replicating your result on a sample of thousands of millionaires, people will gather a sample of thousands of millionaires and get busy on the replication. Just overall really impressive work. I don’t feel qualified to take a side in the G&R vs. Mkrva debate, but both teams make me really happy that there are smart and careful people considering these questions. And this is just a drop in the bucket. Alex Imas also links Replicating patterns of prospect theory for decision under risk, which says: Though substantial evidence supports prospect theory, many presumed canonical theories have drawn scrutiny for recent replication failures. In response, we directly test the original methods in a multinational study (n = 4,098 participants, 19 countries, 13 languages), adjusting only for current and local currencies while requiring all participants to respond to all items. The results replicated for 94% of items, with some attenuation. Twelve of 13 theoretical contrasts replicated, with 100% replication in some countries. Heterogeneity between countries and intra-individual variation highlight meaningful avenues for future theorizing and applications. We conclude that the empirical foundations for prospect theory replicate beyond any reasonable thresholds. Beyond any reasonable thresholds! IV. Do Nudges Work? or, How Small Is Small? Continuing through the Hreha article: For a number of years, I've been beating the anti-nudge drum. Since 2011, I've been running behavioral experiments in the wild, and have always been struck by how weak nudges tend to be. In my experience, nudges usually fail to have *any* recognizable impact at all. This is supported by a paper that was recently published by a couple of researchers from UC Berkeley. They looked at the results of 126 randomized controlled trials run by two "nudge units" here in the United States. I want you to guess how large of an impact these nudges had on average... 30%? 20%? 10%? 5%? 3%? 1.5%? 1%? 0%? If you said 1.5%, you'd be right (the actual number is 1.4%, but if I had written that out you would have chosen it because of its specificity). According to the academic papers these nudges were based upon, these nudges should have had an average impact of 8.7%. But, as you probably understand by now, behavioral economics is not a particularly trustworthy field. I actually emailed the authors of this paper, and they thought the ~1% effect size of these interventions was something to be applauded—especially if the intervention was cheap & easy. Unfortunately, no intervention is truly cheap or easy. Every single intervention requires, at the very minimum, administrative overhead. If you're going to do something, you need someone (or some system) to implement and keep track of it. If an intervention is only going to get you a 1% improvement, it's probably not even worth it. Uber infamously had a team of behavioral economists working on its product, trying to “nudge” people in the right direction. Relatedly, Uber makes $10 billion in yearly revenue. If they can “nudge” people to spend 1% more, that’s $100 million. That’s not much relative to revenue, but it’s a lot in absolute terms. In particular, it pays the salary of a lot of behavioral economists. If you can hire 10 behavioral economists for $100,000 a year and make $100 million, that’s $99 million in profit. Or what if you’re a government agency, trying to nudge people to do prosocial things? There are about 90 million eligible Americans who haven’t gotten their COVID vaccine, and although some of them are hard-core conspiracy theorists, others are just lazy or nervous or feel safe already. (source) Whoever decided on that grocery gift card scheme was nudging, whether or not they have an economics degree - and apparently they were pretty good at it. If some sort of behavioral econ campaign can convince 1.5% of those 90 million Americans to get their vaccines, that’s 1.4 million more vaccinations and, under reasonable assumptions, maybe a few thousand lives saved. Hreha says that: Every single intervention requires, at the very minimum, administrative overhead. If you're going to do something, you need someone (or some system) to implement and keep track of it. If an intervention is only going to get you a 1% improvement, it's probably not even worth it. This depends on scale! 1% of a small number isn’t worth it! 1% of a big number is very worth it, especially if that big number is a number of lives! A few caveats. First, a small number only matters if it’s real. It’s very easy to get spurious small effects, so much so that any time you see a small effect you should wonder if it’s real. I’m ready to be forgiving here because behavioral economics is so well-replicated and common-sensically true, but I wouldn’t blame anyone who steers clear. Second, Hreha says: To be honest, you can probably use your creativity to brainstorm an idea that will get you a 3-4% minimum gain, no behavioral economics "science" required. Which leads me to the final point I'd like to make: rules and generalizations are overrated. The reason that fields like behavioral economics are so seductive is because they promise people easy, cookie-cutter solutions to complicated problems. Figuring out how to increase sales of your product is hard. You need to figure out which variables are responsible for the lackluster interest. Is the price the issue? Is the product too hard to use? Is the design tacky? Is the sales organization incompetent? Is the refund/return policy lacking? etc. Exploring these questions can take months (or years) of hard work, and there's no guarantee that you'll succeed. If, however, a behavioral economist tells you that there are nudges that will increase your sales by 10%, 20%, or 30% without much effort on your part... Whoa. That's pretty cool. It's salvation. Thus, it's no surprise that governments and companies have spent hundreds of millions of dollars on behavioral "nudge" units. Unfortunately, as we've seen, these nudges are woefully ineffective. Specific problems require specific solutions. They don't require boilerplate solutions based on general principles that someone discovered by studying a bunch of 19 year old college students. However, the social sciences have done a good job of convincing people that general principles are better solutions for problems than creative, situation-specific solutions. In my experience, creative solutions that are tailor-made for the situation at hand *always* perform better than generic solutions based on one study or another. Hreha is a professional in this field, so presumably he’s right. Still, compare to medicine. A thoughtful doctor who tailors treatment to a particular patient sounds better (and is better) than one who says “Depression? Take this one all-purpose depression treatment which is the first thing I saw when I typed ‘depression’ into UpToDate”. But you still need medical journals. Having some idea of general-purpose laws is what gives the people making creative solutions something to build upon. (also, at some point your customers might want to check your creative solution to see whether it actually gives a “3-4% minimum gain, no behavioral economics required”, and that would be at least vaguely study-shaped.) Third, everyone who said nudging had vast effects is still bad and wrong. Many of them were bad and wrong and making fortunes consulting for companies about how to implement the policies they were claiming were super-powerful. This is suspicious and we should lower our opinion of them accordingly. In a previous discussion of growth mindset, I wrote: Imagine I claimed our next-door neighbor was a billionaire oil sheik who kept thousands of boxes of gold and diamonds hidden in his basement. Later we meet the neighbor, and he is the manager of a small bookstore and has a salary 10% above the US average... Should we describe this as “we have confirmed the Wealthy Neighbor Hypothesis, though the effect size was smaller than expected”? Or as “I made up a completely crazy story, and in unrelated news there was an irrelevant deviation from literally-zero in the same space”? All the people talking about oil sheiks deserve to get asked some really uncomfortable questions. And a lot of these will be the most famous researchers - the Dan Arielys of the world - because of course the people who successfully hyped their results a lot are the ones the public knows about. Still, the neighbor seems like a neat guy, and maybe he’ll give you a job at his bookstore. V. Conclusion: Musings On The Identifiable Victim Effect I actually skipped the very beginning of Hreha’s article. I want to come back to it now. It begins: The last few years have been particularly bad for behavioral economics. A number of frequently cited findings have failed to replicate. Here are a couple of high profile examples: The Identifiable Victim Effect (featured in the workbooks I wrote with Dan Ariely and Kristen Berman in 2014)
Inline links: Kahneman and Tversky’s original paper, The Loss Of Loss Aversion: Will It Loom Larger Than Its Gain, https://substackcdn.com/image/fetch/$s_!2VLm!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F8c49b44a-8850-4ac8-9a88-3dd07718a648_397x305.png, Loss Aversion Has Moderators, But Reports Of Its Death Are Greatly Exaggerated, Alex Imas, Replicating patterns of prospect theory for decision under risk, They looked at the results of 126 randomized controlled trials, others, https://substackcdn.com/image/fetch/$s_!1gY_!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fbucketeer-e05bbc84-baa3-437e-9518-adb32be77984.s3.amazonaws.com%2Fpublic%2Fimages%2F5b127d7c-045a-4266-b515-a0e9201ce651_571x382.png, a previous discussion of growth mindset, the workbooks I wrote with Dan Ariely and Kristen Berman in 2014
Your Book Review: The Educated Mind
July 14, 2023 · Original source
Egan’s insight is that these obsessions give teenagers a sense of meaning, and that we can use them as tools to make middle schools that overflow with meaning. From meaningless to meaning-soaked Again, Egan sketches out a new kind of curriculum subject-by-subject. Before, his trick was to ask where the subject first evolved out of; now, it’s to ask who first discovered or created the specific content we’re teaching. “All knowledge”, he writes, “is human knowledge. Everything we know is knowable through the lives of its inventors, discoverers, or users, and we can have access to that knowledge through the hopes, fears, or intentions that drove them”. Middle school math Who first discovered the concepts students learn in math? The answer, of course, is a wide diversity of curious men and women living across the world over the last few thousand years. Egan says: bring those people into how we teach math. If we used gossip and heroes to help students find it meaningful, what kind of math would result? When we teach the Pythagorean theorem, we should give a sense of who Pythagoras was — a cult-founder who worshiped numbers to find God, whose followers (according to a piece of ancient gossip) murdered one of their members who discovered irrational numbers! Q: Well, sure, that works for Pythagoras, but he’s a known nut job; surely most math doesn’t come from such interesting roots? When we teach the Cartesian coordinate system, students should meet Rene Descartes, the Calvinist French polymath who saw the possibility that math could decipher the world, if only we could unite algebra and geometry… and invented the xy-plane to do exactly that. When we teach scientific notation, we should call our students’ attention to the importance of the number zero, and tell them the story of the Pope who tried to introduce Arabic numerals to Christian Europe and may have been assassinated because of it. When we teach algebra, we should ask students why “algebra” is Arabic for “the fixing of bones”, and tell the story of what Muhammad ibn Musa al-Khwarizmi was up to. We could do this all day. Literally everything students learn in school was first invented or discovered by some interesting person who was struggling to accomplish something hard. To learn is to connect with those people, whether we know it or not. Egan says: help kids know it. Math has been dehumanized: re-humanize it. Q: So the math curriculum needs to become a history of math curriculum, and math teachers need to become history teachers? No, the content needn’t change. But with surprisingly little work, we can bring in the gossipy stories of heroes, and their obsessions can spread to students. Middle school science Who first discovered the things students learn about in science? If you’re thinking “scientists”, you’re only partially right. Most of the big-picture ideas that we now think of as “science” were discovered before the word “scientist” was invented, or the discipline was professionalized. Frequently, they were hatched by true amateurs, working in their free time, hungry to unlock the secrets of nature. We can use gossip and heroes to spread their obsessions to students just as we taught math, but Egan points out two twists. The first is that the content itself can take on heroic qualities: everything is impressive, when you look at it in a certain light. In an interview, Egan once said: “My book is an attempt to show that, indeed, everything in the world is wonderful, but that schools are designed almost to disguise this slightly shameful fact. We represent the world to children as mostly known and rather dull. The opposite is the case: we are surrounded by mystery, and what we know is fascinating”. What would even the most boring subjects look like, if we emphasized their heroic qualities? Well: What’s a tooth? Bone, wrapped in rock, surrounding tiny cells that your body feeds with blood. What’s a bar of chocolate? A crystal of jellyfish-shaped fat molecules stacked together; when you put it in your mouth you shake them apart into a writhing confusion. What’s the air around you? The bottom of a 10-mile-deep ocean; when you put your tongue over a soda straw and your Pepsi stops leaking out, it’s not because a “vacuum” is “sucking” it up, but because that ocean is squeezing it into your face. Again, we could do this all day! And in middle school science, we can. Everything in the world is wonderful; we can help students see this again and again. The second twist is that science is a subject rich in extremes. Here Egan introduces a concept that we’ll see crop up again: “15-minute segments”. To help us fit as much wonder as possible into a school day, he suggests we supplement the usual school subjects with a few quick lessons. To infuse science with extremes, he suggests we add on three: “human & natural records”, “extremes of animals & plants”, and “cosmology”. Middle school history Who first made the things students learn about in history? Why, the historical characters themselves! Since we’ve given kids a grounding in history in elementary school, now we can build on that, going through many of the same events as before, but in more depth, and more vividly. We’ll leverage the interest with other people’s inner lives to tell stories focusing on the perspectives of the people who made history — zooming in, when possible, on scandalous details. We’ll leverage the tool of idealism to choose historical characters who chafed against their surroundings, and understand what they were trying to accomplish. What was their vision of the world? What did they hope for, and what did they fear? Q: Isn’t the “great man” approach to history out of fashion? Egan’s approach doesn’t say that “great men” made history — it’s just leveraging gossip to help kids see history as something meaningful that can expand their own possibilities. “Early adolescence is commonly a time of intense and vivid emotional life, and also a time of deepest boredom and depression… [We] can give shape to the intermediate curriculum and offer the students a world that is rich, complex, varied, and as intense and vivid as their own emotional lives”. We also should add on another “15-minute segment” just to pump in as many biographies as possible, and from people who don’t always fit into the normal history curriculum. Call it “Brief Lives”, and throw in anyone who’s struggled to push some limit — Mary Wollstonecraft, Jesse Owen, Dietrich Bonhoeffer, one of the students’ great-aunts, whoever. As students get older, this can transition to “People and Their Ideas”. Here, we’d focus less on the details of the person’s life, and use it as a backdrop to showing how meaningful some of history’s most important ideas could be. Think Aristotle and syllogisms, Edward Said and orientalism, Confucius and propriety, Cornel West and race, Buddha on the four noble truths, Muhammad and the five pillars, Karl Marx and communism, Adam Smith and the invisible hand, Thomas Hobbes and the state of nature, John Locke and natural rights, Jeremy Bentham and utilitarianism, Thomas Aquinas on the sacraments, Martin Luther on faith, Voltaire on the freedom of speech… you get the idea. Q: Can you really get a profound understanding of utilitarianism in 15 minutes? Yes! The point of this segment isn’t to develop a systematic understanding of any one idea, it’s to introduce students to the exciting possibilities of human thought. (As a bonus, this might make them less likely to fall for the first ideology that they encounter later in life.) Diversity is important for this — as it is with culture. Throughout this, we should also be trying to expose students to as much cultural diversity as possible, because in high school, we’ll be trying to make sense of our society, and it’s impossible to do that unless we have something to compare it against. Middle school literature & language You might think that this subject would be easy — that middle school literature is already filled with “strong and clear narratives”, that it deals with “transcendent human qualities such as courage, love, and persistence”, that it focuses on “extremes of human experience”, that it examines “something strange and exotic”. You’d be right! Egan’s pretty happy with a bog-standard middle school literature curriculum, done well. In this part of the book, his spends most of his limited space suggesting three rather odd activities which could also be useful — especially for increasing students’ awareness of language, so they can use it better. The first is etymology — not, however, memorizing lists of roots, but in being told the entertaining backstories of specific words. Take the word “berserk”, for example — we now use it to mean something relatively mild (“if my mom catches me coming home late, she’ll go berserk”), but it comes from an old Norse word meaning “a raging warrior of superhuman strength”. And that’s because ber meant “bear” and serk meant “shirt”: soldiers of the bear cult would don the skin of a bear to, in their minds, transform into one — howling, foaming at the mouth, and gnawing the rims of their shields. (Most adults walk through life with little understanding that the words falling out of their mouths are entities, with their own back-stories. Communication is, at the very least, more interesting when we become aware of this.) The second is to add on another language to learn — not, this time, to become fluent in it, but just to become aware of how very different human languages can be. (For native English speakers, Sanskrit might work well, or Cantonese, or perhaps even ancient Egyptian. Again, the point isn’t for this language to be useful — it’s to explore diversity.) The final one is to study humor — not just jokes anymore, but comedy at its finest. Egan cites (at length!) Monty Python as a group of people who were particularly brilliant in their use of the English language. Examining their skits can lead us into not just an appreciation of semantics (the study of how meaning is made from smaller pieces, like etymology) but also pragmatics (the study of how meaning is made in social situations). Pretty heady stuff, for a conversation about a dead parrot. Part 4: A new kind of high school I’ll confess — I loved parts of high school… and among nerdy folks, I suspect I’m not alone. For some of us, this was a golden time. Even at my local public high school, I had access to academically thrilling classes — especially, in my last two years, advanced literature and history. I felt like I was finally understanding the ideas that mattered. In any case, Egan is quick to acknowledge that, at this level, the sort of education he advocates really is being practiced in some places. What he can add is an understanding of what makes it wonderful, how to make it even more wonderful, and how to make it wonderful for many, many more people. What’s the matter with high school? Far too often, even when high school classes are intellectual, they’re dry. For the majority of students, all this academic stuff is experienced as utterly lifeless, a mass of dead information to be squeezed inside one’s head for a test and then left to evaporate. Egan mocks the curriculum wars that seem to be a permanent feature of the teaching life; quoting the sociologist Pierre Bourdieu, he says “while the academic left and right bicker over whether the curriculum is too traditional or too radical, they fail to recognize that most students absorb so little of academic culture that the bickering is largely irrelevant”. Why so dry? Egan suggests three reasons to explain this. First, because high school academic classes are too often masses of small details with no sign of the big picture. Second, because they’re typically slavishly disciplinary, and aren’t able to address the questions that span the disciplines. Third, because they’re often designed to bring students through what everyone is sure of, and hide away any controversies. In all of these, Egan suggests that what’s called “academics” in high school is too often a dim imitation of what real academics are actually practicing. There’s a fourth reason, though, and it’s probably the biggest of all — by the time they get to high school, most students haven’t actually learned that much! An academic approach is designed to connect small details into the big picture; for people who arrive in high school (and college) classes without having already collected much in their heads, academics are going to taste dry. (An implication of this for anyone trying to improve schools is that we might not want to start with high schools. If your goal is to create a new kind of academic learning, first start at elementary school — or barring that, middle school.) What motivates mad scientists? When we wanted to re-conceive the elementary and middle school curriculums, we looked at what students were already good at — kids’ cognitive strengths and adolescents’ obsessions. For this level it might be easier to look — for reasons that will become clear when we finally unveil Egan’s crazy-sounding definition of education — at the sorts of things that bring intellectuals joy. Q: Which intellectuals? Take your pick. Galileo, Einstein, Smith, Marx, Goodall, Chomsky, Curie… all the people who took to the life of the mind like fish to water. But that’s a lot to hold in my mind at once, so I’m just going to think about Doc Brown from Back to the Future: He was high on intellectualism I’ve never been there, but the brochure looks nice Let’s call these people “mad scientists”. And let’s pretend we once again took up our job of being primatologists, and snooped on these folks “in the wild” (“in the lab”? this is beginning to get recursive…)… what would we find motivating them? Asking simple questions, for one. (What is space? What is society? What is a human? What is language?) Building general schemes (big theories) that hold lots of evidence together. Finding their place in the cosmos. And (perhaps above all) seeking certainty. Once again, Egan suggests we use these as tools to remake the curriculum. From dry to daring What could a high school curriculum look like, if it were rebuilt on these tools? Once again, Egan has a trick. This time, it’s to ask what fights have driven the development of each of these fields forward — and how we can help students enter them. First, a mini-segment! Intellectuals invented the academic disciplines to better pursue the life of the mind, but the disciplines can get in the way. Some of the most important intellectual discoveries that could help students are too big to fit into any of the disciplines. We need a place to introduce them plainly. Egan proposes another mini-segment — again, just 15 minutes a day, a few times a week — called “Metaknowledge”. Q: Isn’t that already in the International Baccalaureate program? Yes, he acknowledges that he’s borrowing from that! This segment would introduce ideas that would enrich student thinking across the disciplines: game theory, cognitive biases, systems thinking, Bayesian reasoning, epistemology, ethics, logic, cultural evolution, and so on. High school literature How can we help students enter the big fights of literature? Intellectuals of a literary bent — professors, critics, poets, novelists — delight in arguing over literature like rabbis arguing over the Talmud. Take, just for one example, the debates over Shakespeare’s character of Ophelia. Does she love Hamlet, or is she a victim of his emotional abuse? Is she truly insane, or is she acting? Is she passive, or is she pulling the strings? Oceans of ink have been spilled arguing over questions like these; our students can, perhaps, spill a few ounces more. The usefulness of arguing literature, for Egan, isn’t that it’s oh-so important for educated adults to know a lot about Ophelia. (This, again, was where the academicists went wrong — in thinking that being educated was about getting the best knowledge in your head.) Rather, arguing over literature is a training arena for the all-important intellectual move of this kind of understanding: building general schemes out of evidence, and struggling with anomalies. One person, for example, might hold that Ophelia is insane, and cite all sorts of obvious evidence — her father just was murdered by her lover, she rants nonsense while (bizarrely) handing out flowers to friends… But then he’s challenged when he reads a scholar pointing out that, to people in Elizabethan England, types of flowers have symbolic meanings. How does he deal with that? He could ignore it, claiming it an over-reading of Shakespeare. (Sometimes a flower is just a flower!) Or he could address it, complicating his own scheme. This intellectual work is best done with other people, who are incentivized to challenge your understanding of something, and go back and forth, building competing models and calling attention to anomalies. This process — the “dialectic” — pops up again and again in the academic disciplines. It’s the center of how understanding works, at this stage. And the nice thing about practicing it on literature is that, more so than in history or science, the evidence is shared knowledge — it’s right in front of everyone, written out. But there are other ways literature class can be helpful to the general life of the mind. Egan also suggests that we’ll want to specially include literature that helps students understand complex ideas. Camus, Orwell, Borges, Calvino might be particularly helpful here… and I imagine that genres like science fiction and magical realism might be particularly useful, too. (Note, though, that once again none of this requires a radical remaking of the curriculum, or of the canon of texts that we traditionally assign to high schoolers.) Q: Oh yes, the canon — what does Egan have to say about the canon wars? When he wrote Educated Mind in the nineties, the long-brewing canon war was approaching its inevitable apocalyptic climax. On one side of this Plain of Megiddo were the pro-canon traditionalists, arguing that we should keep assigning the texts that had been argued over for centuries. Facing them were the anti-canon reformers, arguing the standard texts over-represented the perspective of dead white men. Onto the middle of the plain rides Egan on a white horse, who bellows above the din: “I’VE GOT A BUSLOAD OF HIGH SCHOOLERS WHO WANTS TO JOIN IN, EVERYONE OKAY WITH THAT?” To do so, he says, we need to give students the arguments from both sides. So, for example, bell hooks, Edward Said, and China Achebe should be on the syllabus, as should Allan Bloom, Mortimer Adler, and Diane Ravitch. And of course they should actually read the texts cherished by both sides, too, so they can argue better. High school history How could entering the big fights help us reinvent high school history? First, we might look for dueling histories. It’s time for students to get into historiography and understand that history isn’t just what happened, it’s something we make. We might help kids read chapters from Howard Zinn’s socialist history of America alongside the corresponding chapters from Paul Johnson’s conservative history of America. How could big questions help? We want to help students see how various people have disagreed over some of the big questions of what human history is, at its most basic. We can have them compare Steven Pinker’s theory of civilization’s progress (Better Angels of our Nature) with Yuvah Noah Harari’s theory of civilization’s woes (Sapiens). We could have them compare so-and-so’s account of human history as an ever-expanding unlatching of energy sources with Robert Wright’s account of human history as unlatching more and more positive-sum games (Nonzero). What role could the lure of certainty play? To help them grow their skills at finding anomalies, we might help them work through pseudo-histories and conspiracy theories. Q: Conspiracy theories! Oh, come now, you’re playing with fire. Well, the world is on fire. Our students will spend the rest of their lives encountering terrible-but-beguiling arguments about how the world works; if we don’t prepare them for those, what have we been doing? So we should introduce arguments that the Moon landing was a hoax, that the Illuminati founded America, that aliens built the pyramids, and so on. At no point can we demean students for falling for any of these theories — the job of a teacher at this stage, Egan writes, is to support students in their reasoning even when their beliefs are offensive and stupid, gradually offering anomalies. There’s no way out of bad theories except through them. By the time students graduate, we want them to have wrestled with terrible ideas and — for a while — lost. They need to experience what it’s like to change their minds about something they felt strongly about. They need to viscerally realize, in Feynman’s famous phrase, “The first principle is that you must not fool yourself and you are the easiest person to fool.” High school natural science How could entering the big fights reinvent high school science? At present, so much of the high school science curriculum — especially “honors” classes — is oriented toward helping amass details. (The same is true of 100-level university classes, which famously “survey” the field to prepare for more advanced studies. I always thought this was stupid — of the huge lecture hall of students in my Geology 100 class, how many went on to take even a second course?) The meaty debates that propel science forward are held back. Egan complains: “The more general and speculative theories in any discipline are treated like an unconventional and disreputable relation who, even though the children find her exciting and entertaining, must be kept hidden from view, her very existence denied as long as possible”. This is a stupid approach — students with an adventurous bent are convinced that science isn’t for them. Egan proposes, simply, that we flip this, and organize high school science classes around the big debates. We shouldn’t be ashamed at how, well, adolescent this might look: “the dramatic, speculative, and contentious theories will be up-front in the early years of the [high school] curriculum”. What might those be? Egan doesn’t give a list, but we can spitball some: instead of explaining what “matter” is from the top down, a physics class could problematize “matter” by following the debates over the nature of dark matter and dark energy, and by becoming familiarized with the various interpretations of quantum mechanics
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Greece was a backwater on the periphery of the Persian Empire — but in a historical instant it was transformed into an intellectual and cultural powerhouse: philosophers like Plato, and Aristotle revolutionized Western thought; mathematicians like Pythagoras and Euclid revolutionized math; playwrights like Aeschylus and Sophocles revolutionized drama.
Highlights From The Comments On Tegmark's Mathematical Universe
February 21, 2025 · Original source
I find this kind of thing annoying too, sorry. “Oh, this new idea is basically just reinventing Plato. And also Descartes and Leibniz. And Pythagoras. All of whom were just reinventing each other, or whatever.”