The Importance of Sidekicks
[Reposted from my personal blog.]
Mindspace is wide and deep. “People are different” is a truism, but even knowing this, it’s still easy to underestimate.
I spent much of my initial engagement with the rationality community feeling weird and different. I appreciated the principle and project of rationality as things that were deeply important to me; I was pretty pro-self improvement, and kept tsuyoku naritai as my motto for several years. But the rationality community, the people who shared this interest of mine, often seemed baffled by my values and desires. I wasn’t ambitious, and had a hard time wanting to be. I had a hard time wanting to be anything other than a nurse.
It wasn’t until this August that I convinced myself that this wasn’t a failure in my rationality, but rather a difference in my basic drives. It’s around then, in the aftermath of the 2014 CFAR alumni reunion, that I wrote the following post.
I don’t believe in life-changing insights (that happen to me), but I think I’ve had one–it’s been two weeks and I’m still thinking about it, thus it seems fairly safe to say I did.
At a CFAR Monday test session, Anna was talking about the idea of having an “aura of destiny”–it’s hard to fully convey what she meant and I’m not sure I get it fully, but something like seeing yourself as you’ll be in 25 years once you’ve saved the world and accomplished a ton of awesome things. She added that your aura of destiny had to be in line with your sense of personal aesthetic, to feel “you.”
I mentioned to Kenzi that I felt stuck on this because I was pretty sure that the combination of ambition and being the locus of control that “aura of destiny” conveyed to me was against my sense of personal aesthetic.
Kenzi said, approximately [I don't remember her exact words]: “What if your aura of destiny didn’t have to be those things? What if you could be like…Samwise, from Lord of the Rings? You’re competent, but most importantly, you’re *loyal* to Frodo. You’re the reason that the hero succeeds.”
I guess this isn’t true for most people–Kenzi said she didn’t want to keep thinking of other characters who were like this because she would get so insulted if someone kept comparing her to people’s sidekicks–but it feels like now I know what I am.
So. I’m Samwise. If you earn my loyalty, by convincing me that what you’re working on is valuable and that you’re the person who should be doing it, I’ll stick by you whatever it takes, and I’ll *make sure* you succeed. I don’t have a Frodo right now. But I’m looking for one.
It then turned out that quite a lot of other people recognized this, so I shifted from “this is a weird thing about me” to “this is one basic personality type, out of many.” Notably, Brienne wrote the following comment:
Sidekick” doesn’t *quite* fit my aesthetic, but it’s extremely close, and I feel it in certain moods. Most of the time, I think of myself more as what TV tropes would call a “dragon”. Like the Witch-king of Angmar, if we’re sticking of LOTR. Or Bellatrix Black. Or Darth Vader. (It’s not my fault people aren’t willing to give the good guys dragons in literature.)
For me, finding someone who shared my values, who was smart and rational enough for me to trust him, and who was in a much better position to actually accomplish what I most cared about than I imagined myself ever being, was the best thing that could have happened to me.
She also gave me what’s maybe one of the best and most moving compliments I’ve ever received.
In Australia, something about the way you interacted with people suggested to me that you help people in a completely free way, joyfully, because it fulfills you to serve those you care about, and not because you want something from them… I was able to relax around you, and ask for your support when I needed it while I worked on my classes. It was really lovely… The other surprising thing was that you seemed to act that way with everyone. You weren’t “on” all the time, but when you were, everybody around you got the benefit. I’d never recognized in anyone I’d met a more diffuse service impulse, like the whole human race might be your master. So I suddenly felt like I understood nurses and other people in similar service roles for the first time.
Sarah Constantin, who according to a mutual friend is one of the most loyal people who exists, chimed in with some nuance to the Frodo/Samwise dynamic: “Sam isn’t blindly loyal to Frodo. He makes sure the mission succeeds even when Frodo is fucking it up. He stands up to Frodo. And that’s important too.”
Kate Donovan, who also seems to share this basic psychological makeup, added “I have a strong preference for making the lives of the lead heroes better, and very little interest in ever being one.”
Meanwhile, there were doubts from others who didn’t feel this way. The “we need heroes, the world needs heroes” narrative is especially strong in the rationalist community. And typical mind fallacy abounds. It seems easy to assume that if someone wants to be a support character, it’s because they’re insecure–that really, if they believed in themselves, they would aim for protagonist.
I don’t think this is true. As Kenzi pointed out: “The other thing I felt like was important about Samwise is that his self-efficacy around his particular mission wasn’t a detriment to his aura of destiny – he did have insecurities around his ability to do this thing – to stand by Frodo – but even if he’d somehow not had them, he still would have been Samwise – like that kind of self-efficacy would have made his essence *more* distilled, not less.”
Brienne added: “Becoming the hero would be a personal tragedy, even though it would be a triumph for the world if it happened because I surpassed him, or discovered he was fundamentally wrong.”
Why write this post?
Usually, “this is a true and interesting thing about humans” is enough of a reason for me to write something. But I’ve got a lot of other reasons, this time.
I suspect that the rationality community, with its “hero” focus, drives away many people who are like me in this sense. I’ve thought about walking away from it, for basically that reason. I could stay in Ottawa and be a nurse for forty years; it would fulfil all my most basic emotional needs, and no one would try to change me. Because oh boy, have people tried to do that. It’s really hard to be someone who just wants to please others, and to be told, basically, that you’re not good enough–and that you owe it to the world to turn yourself ambitious, strategic, Slytherin.
Firstly, this is mean regardless. Secondly, it’s not true.
Samwise was important. So was Frodo, of course. But Frodo needed Samwise. Heroes need sidekicks. They can function without them, but function a lot better with them. Maybe it’s true that there aren’t enough heroes trying to save the world. But there sure as hell aren’t enough sidekicks trying to help them. And there especially aren’t enough talented, competent, awesome sidekicks.
If you’re reading this post, and it resonates with you… Especially if you’re someone who has felt unappreciated and alienated for being different… I have something to tell you. You count. You. Fucking. Count. You’re needed, even if the heroes don’t realize it yet. (Seriously, heroes, you should be more strategic about looking for awesome sidekicks. AFAIK only Nick Bostrom is doing it.) This community could use more of you. Pretty much every community could use more of you.
I’d like, someday, to live in a culture that doesn’t shame this way of being. As Brienne points out, “Society likes *selfless* people, who help everybody equally, sure. It’s socially acceptable to be a nurse, for example. Complete loyalty and devotion to “the hero”, though, makes people think of brainwashing, and I’m not sure what else exactly but bad things.” (And not all subsets of society even accept nursing as a Valid Life Choice.) I’d like to live in a world where an aspiring Samwise can find role models; where he sees awesome, successful people and can say, “yes, I want to grow up to be that.”
Maybe I can’t have that world right away. But at least I know what I’m reaching for. I have a name for it. And I have a Frodo–Ruby and I are going to be working together from here on out. I have a reason not to walk away.
Low Hanging fruit for buying a better life
What can I purchase with $100 that will be the best thing I can buy to make my life better?
I've decided to budget some regular money to improving my life each month. I'd like to start with low hanging fruit for obvious reasons - but when I sat down to think of improvements, I found myself thinking of the same old things I'd already been planning to do anyway... and I'd like out of that rut.
Constraints/more info:
- be concrete. I know - "spend money on experiences" is a good idea - but what experiences are the best option to purchase *first*
- "better" is deliberately left vague - choose how you would define it, so that I'm not constrained just by ways of "being better" that I'd have thought of myself.
- please assume that I have all my basic needs met (eg food, clothing, shelter) and that I have budgeted separately for things like investing for my financial future and for charity.
- apart from the above, assume nothing - Especially don't try and tailor solutions to anything you might know and/or guess about me specifically, because I think this would be a useful resource for others who might have just begun.
- don't constrain yourself to exactly $100 - I could buy 2-3 things for that, or I could save up over a couple of months and buy something more expensive... I picked $100 because it's a round number and easy to imagine.
- it's ok to add "dumb" things - they can help spur great ideas, or just get rid of an elephant in the room.
- try thinking of your top-ten before reading any comments, in order not to bias your initial thinking. Then come back and add ten more once you've been inspired by what everyone else came up with.
Background:
This is a question I recently posed to my local Less Wrong group and we came up with a few good ideas, so I thought I'd share the discussion with the wider community and see what we can come up with. I'll add the list we came up with later on in the comments...
It'd be great to have a repository of low-hanging fruit for things that can be solved with (relatively affordable) amounts of money. I'd personally like to go through the list - look at candidates that sound like they'd be really useful to me and then make a prioritised list of what to work on first.
Overpaying for happiness?
Happy New Year, everyone!
In the past few months I've been thinking several thoughts that all seem to point in the same direction:
1) People who live in developed Western countries usually make and spend much more money than people in poorer countries, but aren't that much happier. It feels like we're overpaying for happiness, spending too much money to get a single bit of enjoyment.
2) When you get enjoyment from something, the association between "that thing" and "pleasure" in your mind gets stronger, but at the same time it becomes less sensitive and requires more stimulus. For example if you like sweet food, you can get into a cycle of eating more and more food that's sweeter and sweeter. But the guy next door, who's eating much less and periodically fasting to keep the association fresh, is actually getting more pleasure from food than you are! The same thing happens when you learn to deeply appreciate certain kinds of art, and then notice that the folks who enjoy "low" art are visibly having more fun.
3) People sometimes get unrealistic dreams and endlessly chase them, like trying to "make it big" in writing or sports, because they randomly got rewarded for it at an early age. I wrote a post about that.
I'm not offering any easy answers here. But it seems like too many people get locked in loops where they spend more and more effort to get less and less happiness. The most obvious examples are drug addiction and video gaming, but also "one-itis" in dating, overeating, being a connoisseur of anything, striving for popular success, all these things follow the same pattern. You're just chasing after some Skinner-box thing that you think you "love", but it doesn't love you back.
Sooo... if you like eating, give yourself a break every once in a while? If you like comfort, maybe get a cold shower sometimes? Might be a good idea to make yourself the kind of person that can get happiness cheaply.
Sorry if this post is not up to LW standards, I typed it really quickly as it came to my mind.
"Follow your dreams" as a case study in incorrect thinking
This post doesn't contain any new ideas that LWers don't already know. It's more of an attempt to organize my thoughts and have a writeup for future reference.
Here's a great quote from Sam Hughes, giving some examples of good and bad advice:
"You and your gaggle of girlfriends had a saying at university," he tells her. "'Drink through it'. Breakups, hangovers, finals. I have never encountered a shorter, worse, more densely bad piece of advice." Next he goes into their bedroom for a moment. He returns with four running shoes. "You did the right thing by waiting for me. Probably the first right thing you've done in the last twenty-four hours. I subscribe, as you know, to a different mantra. So we're going to run."
The typical advice given to young people who want to succeed in highly competitive areas, like sports, writing, music, or making video games, is to "follow your dreams". I think that advice is up there with "drink through it" in terms of sheer destructive potential. If it was replaced with "don't bother following your dreams" every time it was uttered, the world might become a happier place.
The amazing thing about "follow your dreams" is that thinking about it uncovers a sort of perfect storm of biases. It's fractally wrong, like PHP, where the big picture is wrong and every small piece is also wrong in its own unique way.
The big culprit is, of course, optimism bias due to perceived control. I will succeed because I'm me, the special person at the center of my experience. That's the same bias that leads us to overestimate our chances of finishing the thesis on time, or having a successful marriage, or any number of other things. Thankfully, we have a really good debiasing technique for this particular bias, known as reference class forecasting, or inside vs outside view. What if your friend Bob was a slightly better guitar player than you? Would you bet a lot of money on Bob making it big like Jimi Hendrix? The question is laughable, but then so is betting the years of your own life, with a smaller chance of success than Bob.
That still leaves many questions unanswered, though. Why do people offer such advice in the first place, why do other people follow it, and what can be done about it?
Survivorship bias is one big reason we constantly hear successful people telling us to "follow our dreams". Successful people doesn't really know why they are successful, so they attribute it to their hard work and not giving up. The media amplifies that message, while millions of failures go unreported because they're not celebrities, even though they try just as hard. So we hear about successes disproportionately, in comparison to how often they actually happen, and that colors our expectations of our own future success. Sadly, I don't know of any good debiasing techniques for this error, other than just reminding yourself that it's an error.
When someone has invested a lot of time and effort into following their dream, it feels harder to give up due to the sunk cost fallacy. That happens even with very stupid dreams, like the dream of winning at the casino, that were obviously installed by someone else for their own profit. So when you feel convinced that you'll eventually make it big in writing or music, you can remind yourself that compulsive gamblers feel the same way, and that feeling something doesn't make it true.
Of course there are good dreams and bad dreams. Some people have dreams that don't tease them for years with empty promises, but actually start paying off in a predictable time frame. The main difference between the two kinds of dream is the difference between positive-sum games, a.k.a. productive occupations, and zero-sum games, a.k.a. popularity contests. Sebastian Marshall's post Positive Sum Games Don't Require Natural Talent makes the same point, and advises you to choose a game where you can be successful without outcompeting 99% of other players.
The really interesting question to me right now is, what sets someone on the path of investing everything in a hopeless dream? Maybe it's a small success at an early age, followed by some random encouragement from others, and then you're locked in. Is there any hope for thinking back to that moment, or set of moments, and making a little twist to put yourself on a happier path? I usually don't advise people to change their desires, but in this case it seems to be the right thing to do.
Non-obvious skills with highly measurable progress?
A lot of my significant personal improvement happened as a result of highly measurable progress and tight feedback loops. For example:
- Project Euler
- Go (the game has a very accurate ranking system)
- Strength training
Harper's Magazine article on LW/MIRI/CFAR and Ethereum
Cover title: “Power and paranoia in Silicon Valley”; article title: “Come with us if you want to live: Among the apocalyptic libertarians of Silicon Valley” (mirrors: 1, 2, 3), by Sam Frank; Harper’s Magazine, January 2015, pg26-36 (~8500 words). The beginning/ending are focused on Ethereum and Vitalik Buterin, so I'll excerpt the LW/MIRI/CFAR-focused middle:
…Blake Masters-the name was too perfect-had, obviously, dedicated himself to the command of self and universe. He did CrossFit and ate Bulletproof, a tech-world variant of the paleo diet. On his Tumblr’s About page, since rewritten, the anti-belief belief systems multiplied, hyperlinked to Wikipedia pages or to the confoundingly scholastic website Less Wrong: “Libertarian (and not convinced there’s irreconcilable fissure between deontological and consequentialist camps). Aspiring rationalist/Bayesian. Secularist/agnostic/ ignostic . . . Hayekian. As important as what we know is what we don’t. Admittedly eccentric.” Then: “Really, really excited to be in Silicon Valley right now, working on fascinating stuff with an amazing team.” I was startled that all these negative ideologies could be condensed so easily into a positive worldview. …I saw the utopianism latent in capitalism-that, as Bernard Mandeville had it three centuries ago, it is a system that manufactures public benefit from private vice. I started CrossFit and began tinkering with my diet. I browsed venal tech-trade publications, and tried and failed to read Less Wrong, which was written as if for aliens.
…I left the auditorium of Alice Tully Hall. Bleary beside the silver coffee urn in the nearly empty lobby, I was buttonholed by a man whose name tag read MICHAEL VASSAR, METAMED research. He wore a black-and-white paisley shirt and a jacket that was slightly too big for him. “What did you think of that talk?” he asked, without introducing himself. “Disorganized, wasn’t it?” A theory of everything followed. Heroes like Elon and Peter (did I have to ask? Musk and Thiel). The relative abilities of physicists and biologists, their standard deviations calculated out loud. How exactly Vassar would save the world. His left eyelid twitched, his full face winced with effort as he told me about his “personal war against the universe.” My brain hurt. I backed away and headed home. But Vassar had spoken like no one I had ever met, and after Kurzweil’s keynote the next morning, I sought him out. He continued as if uninterrupted. Among the acolytes of eternal life, Vassar was an eschatologist. “There are all of these different countdowns going on,” he said. “There’s the countdown to the broad postmodern memeplex undermining our civilization and causing everything to break down, there’s the countdown to the broad modernist memeplex destroying our environment or killing everyone in a nuclear war, and there’s the countdown to the modernist civilization learning to critique itself fully and creating an artificial intelligence that it can’t control. There are so many different - on different time-scales - ways in which the self-modifying intelligent processes that we are embedded in undermine themselves. I’m trying to figure out ways of disentangling all of that. . . .I’m not sure that what I’m trying to do is as hard as founding the Roman Empire or the Catholic Church or something. But it’s harder than people’s normal big-picture ambitions, like making a billion dollars.” Vassar was thirty-four, one year older than I was. He had gone to college at seventeen, and had worked as an actuary, as a teacher, in nanotech, and in the Peace Corps. He’d founded a music-licensing start-up called Sir Groovy. Early in 2012, he had stepped down as president of the Singularity Institute for Artificial Intelligence, now called the Machine Intelligence Research Institute (MIRI), which was created by an autodidact named Eliezer Yudkowsky, who also started Less Wrong. Vassar had left to found MetaMed, a personalized-medicine company, with Jaan Tallinn of Skype and Kazaa, $500,000 from Peter Thiel, and a staff that included young rationalists who had cut their teeth arguing on Yudkowsky’s website. The idea behind MetaMed was to apply rationality to medicine-“rationality” here defined as the ability to properly research, weight, and synthesize the flawed medical information that exists in the world. Prices ranged from $25,000 for a literature review to a few hundred thousand for a personalized study. “We can save lots and lots and lots of lives,” Vassar said (if mostly moneyed ones at first). “But it’s the signal-it’s the ‘Hey! Reason works!’-that matters. . . . It’s not really about medicine.” Our whole society was sick - root, branch, and memeplex - and rationality was the only cure. …I asked Vassar about his friend Yudkowsky. “He has worse aesthetics than I do,” he replied, “and is actually incomprehensibly smart.” We agreed to stay in touch.
One month later, I boarded a plane to San Francisco. I had spent the interim taking a second look at Less Wrong, trying to parse its lore and jargon: “scope insensitivity,” “ugh field,” “affective death spiral,” “typical mind fallacy,” “counterfactual mugging,” “Roko’s basilisk.” When I arrived at the MIRI offices in Berkeley, young men were sprawled on beanbags, surrounded by whiteboards half black with equations. I had come costumed in a Fermat’s Last Theorem T-shirt, a summary of the proof on the front and a bibliography on the back, printed for the number-theory camp I had attended at fifteen. Yudkowsky arrived late. He led me to an empty office where we sat down in mismatched chairs. He wore glasses, had a short, dark beard, and his heavy body seemed slightly alien to him. I asked what he was working on. “Should I assume that your shirt is an accurate reflection of your abilities,” he asked, “and start blabbing math at you?” Eight minutes of probability and game theory followed. Cogitating before me, he kept grimacing as if not quite in control of his face. “In the very long run, obviously, you want to solve all the problems associated with having a stable, self-improving, beneficial-slash-benevolent AI, and then you want to build one.” What happens if an artificial intelligence begins improving itself, changing its own source code, until it rapidly becomes - foom! is Yudkowsky’s preferred expression - orders of magnitude more intelligent than we are? A canonical thought experiment devised by Oxford philosopher Nick Bostrom in 2003 suggests that even a mundane, industrial sort of AI might kill us. Bostrom posited a “superintelligence whose top goal is the manufacturing of paper-clips.” For this AI, known fondly on Less Wrong as Clippy, self-improvement might entail rearranging the atoms in our bodies, and then in the universe - and so we, and everything else, end up as office supplies. Nothing so misanthropic as Skynet is required, only indifference to humanity. What is urgently needed, then, claims Yudkowsky, is an AI that shares our values and goals. This, in turn, requires a cadre of highly rational mathematicians, philosophers, and programmers to solve the problem of “friendly” AI - and, incidentally, the problem of a universal human ethics - before an indifferent, unfriendly AI escapes into the wild.
Among those who study artificial intelligence, there’s no consensus on either point: that an intelligence explosion is possible (rather than, for instance, a proliferation of weaker, more limited forms of AI) or that a heroic team of rationalists is the best defense in the event. That MIRI has as much support as it does (in 2012, the institute’s annual revenue broke $1 million for the first time) is a testament to Yudkowsky’s rhetorical ability as much as to any technical skill. Over the course of a decade, his writing, along with that of Bostrom and a handful of others, has impressed the dangers of unfriendly AI on a growing number of people in the tech world and beyond. In August, after reading Superintelligence, Bostrom’s new book, Elon Musk tweeted, “Hope we’re not just the biological boot loader for digital superintelligence. Unfortunately, that is increasingly probable.” In 2000, when Yudkowsky was twenty, he founded the Singularity Institute with the support of a few people he’d met at the Foresight Institute, a Palo Alto nanotech think tank. He had already written papers on “The Plan to Singularity” and “Coding a Transhuman AI,” and posted an autobiography on his website, since removed, called “Eliezer, the Person.” It recounted a breakdown of will when he was eleven and a half: “I can’t do anything. That’s the phrase I used then.” He dropped out before high school and taught himself a mess of evolutionary psychology and cognitive science. He began to “neuro-hack” himself, systematizing his introspection to evade his cognitive quirks. Yudkowsky believed he could hasten the singularity by twenty years, creating a superhuman intelligence and saving humankind in the process. He met Thiel at a Foresight Institute dinner in 2005 and invited him to speak at the first annual Singularity Summit. The institute’s paid staff grew. In 2006, Yudkowsky began writing a hydra-headed series of blog posts: science-fictionish parables, thought experiments, and explainers encompassing cognitive biases, self-improvement, and many-worlds quantum mechanics that funneled lay readers into his theory of friendly AI. Rationality workshops and Meetups began soon after. In 2009, the blog posts became what he called Sequences on a new website: Less Wrong. The next year, Yudkowsky began publishing Harry Potter and the Methods of Rationality at
fanfiction.net. The Harry Potter category is the site’s most popular, with almost 700,000 stories; of these, HPMoR is the most reviewed and the second-most favorited. The last comment that the programmer and activist Aaron Swartz left on Reddit before his suicide in 2013 was on/r/hpmor. In Yudkowsky’s telling, Harry is not only a magician but also a scientist, and he needs just one school year to accomplish what takes canon-Harry seven. HPMoR is serialized in arcs, like a TV show, and runs to a few thousand pages when printed; the book is still unfinished. Yudkowsky and I were talking about literature, and Swartz, when a college student wandered in. Would Eliezer sign his copy of HPMoR? “But you have to, like, write something,” he said. “You have to write, ‘I am who I am.’ So, ‘I am who I am’ and then sign it.” “Alrighty,” Yudkowsky said, signed, continued. “Have you actually read Methods of Rationality at all?” he asked me. “I take it not.” (I’d been found out.) “I don’t know what sort of a deadline you’re on, but you might consider taking a look at that.” (I had taken a look, and hated the little I’d managed.) “It has a legendary nerd-sniping effect on some people, so be warned. That is, it causes you to read it for sixty hours straight.”The nerd-sniping effect is real enough. Of the 1,636 people who responded to a 2013 survey of Less Wrong’s readers, one quarter had found the site thanks to HPMoR, and many more had read the book. Their average age was 27.4, their average IQ 138.2. Men made up 88.8% of respondents; 78.7% were straight, 1.5% transgender, 54.7 % American, 89.3% atheist or agnostic. The catastrophes they thought most likely to wipe out at least 90% of humanity before the year 2100 were, in descending order, pandemic (bioengineered), environmental collapse, unfriendly AI, nuclear war, pandemic (natural), economic/political collapse, asteroid, nanotech/gray goo. Forty-two people, 2.6 %, called themselves futarchists, after an idea from Robin Hanson, an economist and Yudkowsky’s former coblogger, for reengineering democracy into a set of prediction markets in which speculators can bet on the best policies. Forty people called themselves reactionaries, a grab bag of former libertarians, ethno-nationalists, Social Darwinists, scientific racists, patriarchists, pickup artists, and atavistic “traditionalists,” who Internet-argue about antidemocratic futures, plumping variously for fascism or monarchism or corporatism or rule by an all-powerful, gold-seeking alien named Fnargl who will free the markets and stabilize everything else. At the bottom of each year’s list are suggestive statistical irrelevancies: “every optimizing system’s a dictator and i’m not sure which one i want in charge,” “Autocracy (important: myself as autocrat),” “Bayesian (aspiring) Rationalist. Technocratic. Human-centric Extropian Coherent Extrapolated Volition.” “Bayesian” refers to Bayes’s Theorem, a mathematical formula that describes uncertainty in probabilistic terms, telling you how much to update your beliefs when given new information. This is a formalization and calibration of the way we operate naturally, but “Bayesian” has a special status in the rationalist community because it’s the least imperfect way to think. “Extropy,” the antonym of “entropy,” is a decades-old doctrine of continuous human improvement, and “coherent extrapolated volition” is one of Yudkowsky’s pet concepts for friendly artificial intelligence. Rather than our having to solve moral philosophy in order to arrive at a complete human goal structure, C.E.V. would computationally simulate eons of moral progress, like some kind of Whiggish Pangloss machine. As Yudkowsky wrote in 2004, “In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together.” Yet can even a single human’s volition cohere or compute in this way, let alone humanity’s? We stood up to leave the room. Yudkowsky stopped me and said I might want to turn my recorder on again; he had a final thought. “We’re part of the continuation of the Enlightenment, the Old Enlightenment. This is the New Enlightenment,” he said. “Old project’s finished. We actually have science now, now we have the next part of the Enlightenment project.”
In 2013, the Singularity Institute changed its name to the Machine Intelligence Research Institute. Whereas MIRI aims to ensure human-friendly artificial intelligence, an associated program, the Center for Applied Rationality, helps humans optimize their own minds, in accordance with Bayes’s Theorem. The day after I met Yudkowsky, I returned to Berkeley for one of CFAR’s long-weekend workshops. The color scheme at the Rose Garden Inn was red and green, and everything was brocaded. The attendees were mostly in their twenties: mathematicians, software engineers, quants, a scientist studying soot, employees of Google and Facebook, an eighteen-year-old Thiel Fellow who’d been paid $100,000 to leave Boston College and start a company, professional atheists, a Mormon turned atheist, an atheist turned Catholic, an Objectivist who was photographed at the premiere of Atlas Shrugged II: The Strike. There were about three men for every woman. At the Friday-night meet and greet, I talked with Benja, a German who was studying math and behavioral biology at the University of Bristol, whom I had spotted at MIRI the day before. He was in his early thirties and quite tall, with bad posture and a ponytail past his shoulders. He wore socks with sandals, and worried a paper cup as we talked. Benja had felt death was terrible since he was a small child, and wanted his aging parents to sign up for cryonics, if he could figure out how to pay for it on a grad-student stipend. He was unsure about the risks from unfriendly AI - “There is a part of my brain,” he said, “that sort of goes, like, ‘This is crazy talk; that’s not going to happen’” - but the probabilities had persuaded him. He said there was only about a 30% chance that we could make it another century without an intelligence explosion. He was at CFAR to stop procrastinating. Julia Galef, CFAR’s president and cofounder, began a session on Saturday morning with the first of many brain-as-computer metaphors. We are “running rationality on human hardware,” she said, not supercomputers, so the goal was to become incrementally more self-reflective and Bayesian: not perfectly rational agents, but “agent-y.” The workshop’s classes lasted six or so hours a day; activities and conversations went well into the night. We got a condensed treatment of contemporary neuroscience that focused on hacking our brains’ various systems and modules, and attended sessions on habit training, urge propagation, and delegating to future selves. We heard a lot about Daniel Kahneman, the Nobel Prize-winning psychologist whose work on cognitive heuristics and biases demonstrated many of the ways we are irrational. Geoff Anders, the founder of Leverage Research, a “meta-level nonprofit” funded by Thiel, taught a class on goal factoring, a process of introspection that, after many tens of hours, maps out every one of your goals down to root-level motivations-the unchangeable “intrinsic goods,” around which you can rebuild your life. Goal factoring is an application of Connection Theory, Anders’s model of human psychology, which he developed as a Rutgers philosophy student disserting on Descartes, and Connection Theory is just the start of a universal renovation. Leverage Research has a master plan that, in the most recent public version, consists of nearly 300 steps. It begins from first principles and scales up from there: “Initiate a philosophical investigation of philosophical method”; “Discover a sufficiently good philosophical method”; have 2,000-plus “actively and stably benevolent people successfully seek enough power to be able to stably guide the world”; “People achieve their ultimate goals as far as possible without harming others”; “We have an optimal world”; “Done.” On Saturday night, Anders left the Rose Garden Inn early to supervise a polyphasic-sleep experiment that some Leverage staff members were conducting on themselves. It was a schedule called the Everyman 3, which compresses sleep into three twenty-minute REM naps each day and three hours at night for slow-wave. Anders was already polyphasic himself. Operating by the lights of his own best practices, goal-factored, coherent, and connected, he was able to work 105 hours a week on world optimization. For the rest of us, for me, these were distant aspirations. We were nerdy and unperfected. There was intense discussion at every free moment, and a genuine interest in new ideas, if especially in testable, verifiable ones. There was joy in meeting peers after years of isolation. CFAR was also insular, overhygienic, and witheringly focused on productivity. Almost everyone found politics to be tribal and viscerally upsetting. Discussions quickly turned back to philosophy and math. By Monday afternoon, things were wrapping up. Andrew Critch, a CFAR cofounder, gave a final speech in the lounge: “Remember how you got started on this path. Think about what was the time for you when you first asked yourself, ‘How do I work?’ and ‘How do I want to work?’ and ‘What can I do about that?’ . . . Think about how many people throughout history could have had that moment and not been able to do anything about it because they didn’t know the stuff we do now. I find this very upsetting to think about. It could have been really hard. A lot harder.” He was crying. “I kind of want to be grateful that we’re now, and we can share this knowledge and stand on the shoulders of giants like Daniel Kahneman . . . I just want to be grateful for that. . . . And because of those giants, the kinds of conversations we can have here now, with, like, psychology and, like, algorithms in the same paragraph, to me it feels like a new frontier. . . . Be explorers; take advantage of this vast new landscape that’s been opened up to us in this time and this place; and bear the torch of applied rationality like brave explorers. And then, like, keep in touch by email.” The workshop attendees put giant Post-its on the walls expressing the lessons they hoped to take with them. A blue one read RATIONALITY IS SYSTEMATIZED WINNING. Above it, in pink: THERE ARE OTHER PEOPLE WHO THINK LIKE ME. I AM NOT ALONE.
That night, there was a party. Alumni were invited. Networking was encouraged. Post-its proliferated; one, by the beer cooler, read SLIGHTLY ADDICTIVE. SLIGHTLY MIND-ALTERING. Another, a few feet to the right, over a double stack of bound copies of Harry Potter and the Methods of Rationality: VERY ADDICTIVE. VERY MIND-ALTERING. I talked to one of my roommates, a Google scientist who worked on neural nets. The CFAR workshop was just a whim to him, a tourist weekend. “They’re the nicest people you’d ever meet,” he said, but then he qualified the compliment. “Look around. If they were effective, rational people, would they be here? Something a little weird, no?” I walked outside for air. Michael Vassar, in a clinging red sweater, was talking to an actuary from Florida. They discussed timeless decision theory (approximately: intelligent agents should make decisions on the basis of the futures, or possible worlds, that they predict their decisions will create) and the simulation argument (essentially: we’re living in one), which Vassar traced to Schopenhauer. He recited lines from Kipling’s “If-” in no particular order and advised the actuary on how to change his life: Become a pro poker player with the $100k he had in the bank, then hit the Magic: The Gathering pro circuit; make more money; develop more rationality skills; launch the first Costco in Northern Europe. I asked Vassar what was happening at MetaMed. He told me that he was raising money, and was in discussions with a big HMO. He wanted to show up Peter Thiel for not investing more than $500,000. “I’m basically hoping that I can run the largest convertible-debt offering in the history of finance, and I think it’s kind of reasonable,” he said. “I like Peter. I just would like him to notice that he made a mistake . . . I imagine a hundred million or a billion will cause him to notice . . . I’d like to have a pi-billion-dollar valuation.” I wondered whether Vassar was drunk. He was about to drive one of his coworkers, a young woman named Alyssa, home, and he asked whether I would join them. I sat silently in the back of his musty BMW as they talked about potential investors and hires. Vassar almost ran a red light. After Alyssa got out, I rode shotgun, and we headed back to the hotel.
It was getting late. I asked him about the rationalist community. Were they really going to save the world? From what? “Imagine there is a set of skills,” he said. “There is a myth that they are possessed by the whole population, and there is a cynical myth that they’re possessed by 10% of the population. They’ve actually been wiped out in all but about one person in three thousand.” It is important, Vassar said, that his people, “the fragments of the world,” lead the way during “the fairly predictable, fairly total cultural transition that will predictably take place between 2020 and 2035 or so.” We pulled up outside the Rose Garden Inn. He continued: “You have these weird phenomena like Occupy where people are protesting with no goals, no theory of how the world is, around which they can structure a protest. Basically this incredibly, weirdly, thoroughly disempowered group of people will have to inherit the power of the world anyway, because sooner or later everyone older is going to be too old and too technologically obsolete and too bankrupt. The old institutions may largely break down or they may be handed over, but either way they can’t just freeze. These people are going to be in charge, and it would be helpful if they, as they come into their own, crystallize an identity that contains certain cultural strengths like argument and reason.” I didn’t argue with him, except to press, gently, on his particular form of elitism. His rationalism seemed so limited to me, so incomplete. “It is unfortunate,” he said, “that we are in a situation where our cultural heritage is possessed only by people who are extremely unappealing to most of the population.” That hadn’t been what I’d meant. I had meant rationalism as itself a failure of the imagination. “The current ecosystem is so totally fucked up,” Vassar said. “But if you have conversations here”-he gestured at the hotel-“people change their mind and learn and update and change their behaviors in response to the things they say and learn. That never happens anywhere else.” In a hallway of the Rose Garden Inn, a former high-frequency trader started arguing with Vassar and Anna Salamon, CFAR’s executive director, about whether people optimize for hedons or utilons or neither, about mountain climbers and other high-end masochists, about whether world happiness is currently net positive or negative, increasing or decreasing. Vassar was eating and drinking everything within reach. My recording ends with someone saying, “I just heard ‘hedons’ and then was going to ask whether anyone wants to get high,” and Vassar replying, “Ah, that’s a good point.” Other voices: “When in California . . .” “We are in California, yes.”
…Back on the East Coast, summer turned into fall, and I took another shot at reading Yudkowsky’s Harry Potter fanfic. It’s not what I would call a novel, exactly, rather an unending, self-satisfied parable about rationality and trans-humanism, with jokes.
…I flew back to San Francisco, and my friend Courtney and I drove to a cul-de-sac in Atherton, at the end of which sat the promised mansion. It had been repurposed as cohousing for children who were trying to build the future: start-up founders, singularitarians, a teenage venture capitalist. The woman who coined the term “open source” was there, along with a Less Wronger and Thiel Capital employee who had renamed himself Eden. The Day of the Idealist was a day for self-actualization and networking, like the CFAR workshop without the rigor. We were to set “mega goals” and pick a “core good” to build on in the coming year. Everyone was a capitalist; everyone was postpolitical. I squabbled with a young man in a Tesla jacket about anti-Google activism. No one has a right to housing, he said; programmers are the people who matter; the protesters’ antagonistic tactics had totally discredited them.
…Thiel and Vassar and Yudkowsky, for all their far-out rhetoric, take it on faith that corporate capitalism, unchecked just a little longer, will bring about this era of widespread abundance. Progress, Thiel thinks, is threatened mostly by the political power of what he calls the “unthinking demos.”
Pointer thanks to /u/Vulture.
Anthropic signature: strange anti-correlations
Imagine that the only way that civilization could be destroyed was by a large pandemic that occurred at the same time as a large recession, so that governments and other organisations were too weakened to address the pandemic properly.
Then if we looked at the past, as observers in a non-destroyed civilization, what would we expect to see? We could see years with no pandemics or no recessions; we could see mild pandemics, mild recessions, or combinations of the two; we could see large pandemics with no or mild recessions; or we could see large recessions with no or mild pandemics. We wouldn't see large pandemics combined with large recessions, as that would have caused us to never come into existence. These are the only things ruled out by anthropic effects.
Assume that pandemics and recessions are independent (at least, in any given year) in terms of "objective" (non-anthropic) probabilities. Then what would we see? We would see that pandemics and recessions appear to be independent when either of them are of small intensity. But as the intensity rose, they would start to become anti-correlated, with a large version of one completely precluding a large version of the other.
The effect is even clearer if we have a probabilistic relation between pandemics, recessions and extinction (something like: extinction risk proportional to product of recession size times pandemic size). Then we would see an anti-correlation rising smoothly with intensity.
Thus one way of looking for anthropic effects in humanity's past is to look for different classes of incidents that are uncorrelated at small magnitude, and anti-correlated at large magnitudes. More generally, to look for different classes of incidents where the correlation changes at different magnitudes - without any obvious reasons. Than might be the signature of an anthropic disaster we missed - or rather, that missed us.
Roles are Martial Arts for Agency
A long time ago I thought that Martial Arts simply taught you how to fight – the right way to throw a punch, the best technique for blocking and countering an attack, etc. I thought training consisted of recognizing these attacks and choosing the correct responses more quickly, as well as simply faster/stronger physical execution of same. It was later that I learned that the entire purpose of martial arts is to train your body to react with minimal conscious deliberation, to remove “you” from the equation as much as possible.
The reason is of course that conscious thought is too slow. If you have to think about what you’re doing, you’ve already lost. It’s been said that if you had to think about walking to do it, you’d never make it across the room. Fighting is no different. (It isn’t just fighting either – anything that requires quick reaction suffers when exposed to conscious thought. I used to love Rock Band. One day when playing a particularly difficult guitar solo on expert I nailed 100%… except “I” didn’t do it at all. My eyes saw the notes, my hands executed them, and no where was I involved in the process. It was both exhilarating and creepy, and I basically dropped the game soon after.)
You’ve seen how long it takes a human to learn to walk effortlessly. That's a situation with a single constant force, an unmoving surface, no agents working against you, and minimal emotional agitation. No wonder it takes hundreds of hours, repeating the same basic movements over and over again, to attain even a basic level of martial mastery. To make your body react correctly without any thinking involved. When Neo says “I Know Kung Fu” he isn’t surprised that he now has knowledge he didn’t have before. He’s amazed that his body now reacts in the optimal manner when attacked without his involvement.
All of this is simply focusing on pure reaction time – it doesn’t even take into account the emotional terror of another human seeking to do violence to you. It doesn’t capture the indecision of how to respond, the paralysis of having to choose between outcomes which are all awful and you don’t know which will be worse, and the surge of hormones. The training of your body to respond without your involvement bypasses all of those obstacles as well.
This is the true strength of Martial Arts – eliminating your slow, conscious deliberation and acting while there is still time to do so.
Roles are the Martial Arts of Agency.
When one is well-trained in a certain Role, one defaults to certain prescribed actions immediately and confidently. I’ve acted as a guy standing around watching people faint in an overcrowded room, and I’ve acted as the guy telling people to clear the area. The difference was in one I had the role of Corporate Pleb, and the other I had the role of Guy Responsible For This Shit. You know the difference between the guy at the bar who breaks up a fight, and the guy who stands back and watches it happen? The former thinks of himself as the guy who stops fights. They could even be the same guy, on different nights. The role itself creates the actions, and it creates them as an immediate reflex. By the time corporate-me is done thinking “Huh, what’s this? Oh, this looks bad. Someone fainted? Wow, never seen that before. Damn, hope they’re OK. I should call 911.” enforcer-me has already yelled for the room to clear and whipped out a phone.
Roles are the difference between Hufflepuffs gawking when Neville tumbles off his broom (Protected), and Harry screaming “Wingardium Leviosa” (Protector). Draco insulted them afterwards, but it wasn’t a fair insult – they never had the slightest chance to react in time, given the role they were in. Roles are the difference between Minerva ordering Hagrid to stay with the children while she forms troll-hunting parties (Protector), and Harry standing around doing nothing while time slowly ticks away (Protected). Eventually he switched roles. But it took Agency to do so. It took time.
Agency is awesome. Half this site is devoted to becoming better at Agency. But Agency is slow. Roles allow real-time action under stress.
Agency has a place of course. Agency is what causes us to decide that Martial Arts training is important, that has us choose a Martial Art, and then continue to train month after month. Agency is what lets us decide which Roles we want to play, and practice the psychology and execution of those roles. But when the time for action is at hand, Agency is too slow. Ensure that you have trained enough for the next challenge, because it is the training that will see you through it, not your agenty conscious thinking.
As an aside, most major failures I’ve seen recently are when everyone assumed that someone else had the role of Guy In Charge If Shit Goes Down. I suggest that, in any gathering of rationalists, they begin the meeting by choosing one person to be Dictator In Extremis should something break. Doesn’t have to be the same person as whoever is leading. Would be best if it was someone comfortable in the role and/or with experience in it. But really there just needs to be one. Anyone.
cross-posted from my blog
Why the tails come apart
[I'm unsure how much this rehashes things 'everyone knows already' - if old hat, feel free to downvote into oblivion. My other motivation for the cross-post is the hope it might catch the interest of someone with a stronger mathematical background who could make this line of argument more robust]
[Edit 2014/11/14: mainly adjustments and rewording in light of the many helpful comments below (thanks!). I've also added a geometric explanation.]
Many outcomes of interest have pretty good predictors. It seems that height correlates to performance in basketball (the average height in the NBA is around 6'7"). Faster serves in tennis improve one's likelihood of winning. IQ scores are known to predict a slew of factors, from income, to chance of being imprisoned, to lifespan.
What's interesting is what happens to these relationships 'out on the tail': extreme outliers of a given predictor are seldom similarly extreme outliers on the outcome it predicts, and vice versa. Although 6'7" is very tall, it lies within a couple of standard deviations of the median US adult male height - there are many thousands of US men taller than the average NBA player, yet are not in the NBA. Although elite tennis players have very fast serves, if you look at the players serving the fastest serves ever recorded, they aren't the very best players of their time. It is harder to look at the IQ case due to test ceilings, but again there seems to be some divergence near the top: the very highest earners tend to be very smart, but their intelligence is not in step with their income (their cognitive ability is around +3 to +4 SD above the mean, yet their wealth is much higher than this) (1).
The trend seems to be that even when two factors are correlated, their tails diverge: the fastest servers are good tennis players, but not the very best (and the very best players serve fast, but not the very fastest); the very richest tend to be smart, but not the very smartest (and vice versa). Why?
Too much of a good thing?
One candidate explanation would be that more isn't always better, and the correlations one gets looking at the whole population doesn't capture a reversal at the right tail. Maybe being taller at basketball is good up to a point, but being really tall leads to greater costs in terms of things like agility. Maybe although having a faster serve is better all things being equal, but focusing too heavily on one's serve counterproductively neglects other areas of one's game. Maybe a high IQ is good for earning money, but a stratospherically high IQ has an increased risk of productivity-reducing mental illness. Or something along those lines.
I would guess that these sorts of 'hidden trade-offs' are common. But, the 'divergence of tails' seems pretty ubiquitous (the tallest aren't the heaviest, the smartest parents don't have the smartest children, the fastest runners aren't the best footballers, etc. etc.), and it would be weird if there was always a 'too much of a good thing' story to be told for all of these associations. I think there is a more general explanation.
The simple graphical explanation
[Inspired by this essay from Grady Towers]
Suppose you make a scatter plot of two correlated variables. Here's one I grabbed off google, comparing the speed of a ball out of a baseball pitchers hand compared to its speed crossing crossing the plate:

It is unsurprising to see these are correlated (I'd guess the R-square is > 0.8). But if one looks at the extreme end of the graph, the very fastest balls out of the hand aren't the very fastest balls crossing the plate, and vice versa. This feature is general. Look at this data (again convenience sampled from googling 'scatter plot') of this:

Or this:

Or this:

Given a correlation, the envelope of the distribution should form some sort of ellipse, narrower as the correlation goes stronger, and more circular as it gets weaker: (2)

The thing is, as one approaches the far corners of this ellipse, we see 'divergence of the tails': as the ellipse doesn't sharpen to a point, there are bulges where the maximum x and y values lie with sub-maximal y and x values respectively:

So this offers an explanation why divergence at the tails is ubiquitous. Providing the sample size is largeish, and the correlation not too tight (the tighter the correlation, the larger the sample size required), one will observe the ellipses with the bulging sides of the distribution. (3)
Hence the very best basketball players aren't the very tallest (and vice versa), the very wealthiest not the very smartest, and so on and so forth for any correlated X and Y. If X and Y are "Estimated effect size" and "Actual effect size", or "Performance at T", and "Performance at T+n", then you have a graphical display of winner's curse and regression to the mean.
An intuitive explanation of the graphical explanation
It would be nice to have an intuitive handle on why this happens, even if we can be convinced that it happens. Here's my offer towards an explanation:
The fact that a correlation is less than 1 implies that other things matter to an outcome of interest. Although being tall matters for being good at basketball, strength, agility, hand-eye-coordination matter as well (to name but a few). The same applies to other outcomes where multiple factors play a role: being smart helps in getting rich, but so does being hard working, being lucky, and so on.
For a toy model, pretend that wealth is wholly explained by two factors: intelligence and conscientiousness. Let's also say these are equally important to the outcome, independent of one another and are normally distributed. (4) So, ceteris paribus, being more intelligent will make one richer, and the toy model stipulates there aren't 'hidden trade-offs': there's no negative correlation between intelligence and conscientiousness, even at the extremes. Yet the graphical explanation suggests we should still see divergence of the tails: the very smartest shouldn't be the very richest.
The intuitive explanation would go like this: start at the extreme tail - +4SD above the mean for intelligence, say. Although this gives them a massive boost to their wealth, we'd expect them to be average with respect to conscientiousness (we've stipulated they're independent). Further, as this ultra-smart population is small, we'd expect them to fall close to the average in this other independent factor: with 10 people at +4SD, you wouldn't expect any of them to be +2SD in conscientiousness.
Move down the tail to less extremely smart people - +3SD say. These people don't get such a boost to their wealth from their intelligence, but there should be a lot more of them (if 10 at +4SD, around 500 at +3SD), this means one should expect more variation in conscientiousness - it is much less surprising to find someone +3SD in intelligence and also +2SD in conscientiousness, and in the world where these things were equally important, they would 'beat' someone +4SD in intelligence but average in conscientiousness. Although a +4SD intelligence person will likely be better than a given +3SD intelligence person (the mean conscientiousness in both populations is 0SD, and so the average wealth of the +4SD intelligence population is 1SD higher than the 3SD intelligence people), the wealthiest of the +4SDs will not be as good as the best of the much larger number of +3SDs. The same sort of story emerges when we look at larger numbers of factors, and in cases where the factors contribute unequally to the outcome of interest.
When looking at a factor known to be predictive of an outcome, the largest outcome values will occur with sub-maximal factor values, as the larger population increases the chances of 'getting lucky' with the other factors:

So that's why the tails diverge.
A parallel geometric explanation
There's also a geometric explanation. The R-square measure of correlation between two sets of data is the same as the cosine of the angle between them when presented as vectors in N-dimensional space (explanations, derivations, and elaborations here, here, and here). (5) So here's another intuitive handle for tail divergence:

Grant a factor correlated with an outcome, which we represent with two vectors at an angle theta, the inverse cosine equal the R-squared. 'Reading off the expected outcome given a factor score is just moving along the factor vector and multiplying by cosine theta to get the distance along the outcome vector. As cos theta is never greater than 1, we see regression to the mean. The geometrical analogue to the tails coming apart is the absolute difference in length along factor versus length along outcome|factor scales with the length along the factor; the gap between extreme values of a factor and the less extreme values of the outcome grows linearly as the factor value gets more extreme. For concreteness (and granting normality), an R-square of 0.5 (corresponding to an angle of sixty degrees) means that +4SD (~1/15000) on a factor will be expected to be 'merely' +2SD (~1/40) in the outcome - and an R-square of 0.5 is remarkably strong in the social sciences, implying it accounts for half the variance.(6) The reverse - extreme outliers on outcome are not expected to be so extreme an outlier on a given contributing factor - follows by symmetry.
Endnote: EA relevance
I think this is interesting in and of itself, but it has relevance to Effective Altruism, given it generally focuses on the right tail of various things (What are the most effective charities? What is the best career? etc.) It generally vindicates worries about regression to the mean or winner's curse, and suggests that these will be pretty insoluble in all cases where the populations are large: even if you have really good means of assessing the best charities or the best careers so that your assessments correlate really strongly with what ones actually are the best, the very best ones you identify are unlikely to be actually the very best, as the tails will diverge.
This probably has limited practical relevance. Although you might expect that one of the 'not estimated as the very best' charities is in fact better than your estimated-to-be-best charity, you don't know which one, and your best bet remains your estimate (in the same way - at least in the toy model above - you should bet a 6'11" person is better at basketball than someone who is 6'4".)
There may be spread betting or portfolio scenarios where this factor comes into play - perhaps instead of funding AMF to diminishing returns when its marginal effectiveness dips below charity #2, we should be willing to spread funds sooner.(6) Mainly, though, it should lead us to be less self-confident.
1. Given income isn't normally distributed, using SDs might be misleading. But non-parametric ranking to get a similar picture: if Bill Gates is ~+4SD in intelligence, despite being the richest man in america, he is 'merely' in the smartest tens of thousands. Looking the other way, one might look at the generally modest achievements of people in high-IQ societies, but there are worries about adverse selection.
2. As nshepperd notes below, this depends on something like multivariate CLT. I'm pretty sure this can be weakened: all that is needed, by the lights of my graphical intuition, is that the envelope be concave. It is also worth clarifying the 'envelope' is only meant to illustrate the shape of the distribution, rather than some boundary that contains the entire probability density: as suggested by homunq: it is an 'pdf isobar' where probability density is higher inside the line than outside it.
3. One needs a large enough sample to 'fill in' the elliptical population density envelope, and the tighter the correlation, the larger the sample needed to fill in the sub-maximal bulges. The old faithful case is an example where actually you do get a 'point', although it is likely an outlier.
![]()
4. It's clear that this model is fairly easy to extend to >2 factor cases, but it is worth noting that in cases where the factors are positively correlated, one would need to take whatever component of the factors which are independent of one another.
5. My intuition is that in cartesian coordinates the R-square between correlated X and Y is actually also the cosine of the angle between the regression lines of X on Y and Y on X. But I can't see an obvious derivation, and I'm too lazy to demonstrate it myself. Sorry!
6. Another intuitive dividend is that this makes it clear why you can by R-squared to move between z-scores of correlated normal variables, which wasn't straightforwardly obvious to me.
7. I'd intuit, but again I can't demonstrate, the case for this becomes stronger with highly skewed interventions where almost all the impact is focused in relatively low probability channels, like averting a very specified existential risk.
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d)