The correct response to uncertainty is *not* half-speed
Related to: Half-assing it with everything you've got; Wasted motion; Say it Loud.
Once upon a time (true story), I was on my way to a hotel in a new city. I knew the hotel was many miles down this long, branchless road. So I drove for a long while.

After a while, I began to worry I had passed the hotel.

So, instead of proceeding at 60 miles per hour the way I had been, I continued in the same direction for several more minutes at 30 miles per hour, wondering if I should keep going or turn around.

- I wasn't sure if I was a good enough writer to write a given doc myself, or if I should try to outsource it. So, I sat there kind-of-writing it while also fretting about whether the task was correct.
- (Solution: Take a minute out to think through heuristics. Then, either: (1) write the post at full speed; or (2) try to outsource it; or (3) write full force for some fixed time period, and then pause and evaluate.)
- I wasn't sure (back in early 2012) that CFAR was worthwhile. So, I kind-of worked on it.
- An old friend came to my door unexpectedly, and I was tempted to hang out with her, but I also thought I should finish my work. So I kind-of hung out with her while feeling bad and distracted about my work.
- A friend of mine, when teaching me math, seems to mumble specifically those words that he doesn't expect me to understand (in a sort of compromise between saying them and not saying them)...
- Duncan reports that novice Parkour students are unable to safely undertake certain sorts of jumps, because they risk aborting the move mid-stream, after the actual last safe stopping point (apparently kind-of-attempting these jumps is more dangerous than either attempting, or not attempting the jumps)
- It is said that start-up founders need to be irrationally certain that their startup will succeed, lest they be unable to do more than kind-of work on it...

[Link] 10 Tips from CFAR: My Business Insider article
My Business Insider article titled 10 tips from a Silicon Valley bootcamp that aims to make smart, successful people more productive.
Mental representation and the is-ought distinction
I'm reading Thinking, Fast and Slow. In appendix B I came across the following comment. Emphasis mine:
Studies of language comprehension indicate that people quickly recode much of what they hear into an abstract representation that no longer distinguishes whether the idea was expressed in an active or in a passive form and no longer discriminates what was actually said from what was implied, presupposed, or implicated (Clark and Clark 1977).
My first thought on seeing this is: holy crap, this explains why people insist on seeing relevance claims in my statements that I didn't put there. If the brain doesn't distinguish statement from implicature, and my conversational partner believes that A implies B when I don't, then of course I'm going to be continually running into situations where people model me as saying and believing B when I actually only said A. At a minimum this will happen any time I discuss any question of seemingly-morally-relevant fact with someone who hasn't trained themselves to make the is-ought distinction. Which is most people.
The next thought my brain jumped to: This process might explain the failure to make the is-ought distinction in the first place. That seems like much more of a leap, though. I looked up the Clark and Clark cite. Unfortunately it's a fairly long book that I'm not entirely sure I want to wade through. Has anyone else read it? Can someone offer more details about exactly what findings Kahneman is referencing?
If you can see the box, you can open the box
First post here, and I'm disagreeing with something in the main sequences. Hubris acknowledged, here's what I've been thinking about. It comes from the post "Are your enemies innately evil?":
On September 11th, 2001, nineteen Muslim males hijacked four jet airliners in a deliberately suicidal effort to hurt the United States of America. Now why do you suppose they might have done that? Because they saw the USA as a beacon of freedom to the world, but were born with a mutant disposition that made them hate freedom?
Realistically, most people don't construct their life stories with themselves as the villains. Everyone is the hero of their own story. The Enemy's story, as seen by the Enemy, is not going to make the Enemy look bad. If you try to construe motivations that would make the Enemy look bad, you'll end up flat wrong about what actually goes on in the Enemy's mind.
If I'm misreading this, please correct me, but the way I am reading this is:
1) People do not construct their stories so that they are the villains,
therefore
2) the idea that Al Qaeda is motivated by a hatred of American freedom is false.
Reading the Al Qaeda document released after the attacks called Why We Are Fighting You you find the following:
What are we calling you to, and what do we want from you?
1. The first thing that we are calling you to is Islam.
A. The religion of tahwid; of freedom from associating partners with Allah Most High , and rejection of such blasphemy; of complete love for Him, the Exalted; of complete submission to his sharia; and of the discarding of all the opinions, orders, theories, and religions that contradict with the religion He sent down to His Prophet Muhammad. Islam is the religion of all the prophets and makes no distinction between them.
It is to this religion that we call you …
2. The second thing we call you to is to stop your oppression, lies, immorality and debauchery that has spread among you.
A. We call you to be a people of manners, principles, honor and purity; to reject the immoral acts of fornication, homosexuality, intoxicants, gambling and usury.
We call you to all of this that you may be freed from the deceptive lies that you are a great nation, which your leaders spread among you in order to conceal from you the despicable state that you have obtained.
B. It is saddening to tell you that you are the worst civilization witnessed in the history of mankind:
i. You are the nation who, rather than ruling through the sharia of Allah, chooses to invent your own laws as you will and desire. You separate religion from you policies, contradicting the pure nature that affirms absolute authority to the Lord your Creator….
ii. You are the nation that permits usury…
iii. You are a nation that permits the production, spread, and use of intoxicants. You also permit drugs, and only forbid the trade of them, even though your nation is the largest consumer of them.
iv. You are a nation that permits acts of immorality, and you consider them to be pillars of personal freedom.
"Freedom" is of course one of those words. It's easy enough to imagine an SS officer saying indignantly: "Of course we are fighting for freedom! For our people to be free of Jewish domination, free from the contamination of lesser races, free from the sham of democracy..."
If we substitute the symbol with the substance though, what we mean by freedom - "people to be left more or less alone, to follow whichever religion they want or none, to speak their minds, to try to shape society's laws so they serve the people" - then Al Qaeda is absolutely inspired by a hatred of freedom. They wouldn't call it "freedom", mind you, they'd call it "decadence" or "blasphemy" or "shirk" - but the substance is what we call "freedom".
Returning to the syllogism at the top, it seems to be that there is an unstated premise. The conclusion "Al Qaeda cannot possibly hate America for its freedom because everyone sees himself as the hero of his own story" only follows if you assume that What is heroic, what is good, is substantially the same for all humans, for a liberal Westerner and an Islamic fanatic.
(for Americans, by "liberal" here I mean the classical sense that includes just about everyone you are likely to meet, read or vote for. US conservatives say they are defending the American revolution, which was broadly in line with liberal principles - slavery excepted, but since US conservatives don't support that, my point stands).
When you state the premise baldly like that, you can see the problem. There's no contradiction in thinking that Muslim fanatics think of themselves as heroic precisely for being opposed to freedom, because they see their heroism as trying to extend the rule of Allah - Shariah - across the world.
Now to the point - we all know the phrase "thinking outside the box". I submit that if you can recognize the box, you've already opened it. Real bias isn't when you have a point of view you're defending, but when you cannot imagine that another point of view seriously exists.
That phrasing has a bit of negative baggage associated with it, that this is just a matter of pigheaded close-mindedness. Try thinking about it another way. Would you say to someone with dyscalculia "You can't get your head around the basics of calculus? You are just being so close minded!" No, that's obviously nuts. We know that different peoples minds work in different ways, that some people can see things others cannot.
Orwell once wrote about the British intellectuals inability to "get" fascism, in particular in his essay on H.G. Wells. He wrote that the only people who really understood the nature and menace of fascism were either those who had felt the lash on their backs, or those who had a touch of the fascist mindset themselves. I suggest that some people just cannot imagine, cannot really believe, the enormous power of faith, of the idea of serving and fighting and dying for your god and His prophet. It is a kind of thinking that is just alien to many.
Perhaps this is resisted because people think that "Being able to think like a fascist makes you a bit of a fascist". That's not really true in any way that matters - Orwell was one of the greatest anti-fascist writers of his time, and fought against it in Spain.
So - if you can see the box you are in, you can open it, and already have half-opened it. And if you are really in the box, you can't see the box. So, how can you tell if you are in a box that you can't see versus not being in a box?
The best answer I've been able to come up with is not to think of "box or no box" but rather "open or closed box". We all work from a worldview, simply because we need some knowledge to get further knowledge. If you know you come at an issue from a certain angle, you can always check yourself. You're in a box, but boxes can be useful, and you have the option to go get some stuff from outside the box.
The second is to read people in other boxes. I like steelmanning, it's an important intellectual exercise, but it shouldn't preclude finding actual Men of Steel - that is, people passionately committed to another point of view, another box, and taking a look at what they have to say.
Now you might say: "But that's steelmanning!" Not quite. Steelmanning is "the art of addressing the best form of the other person’s argument, even if it’s not the one they presented." That may, in some circumstances, lead you to make the mistake of assuming that what you think is the best argument for a position is the same as what the other guy thinks is the best argument for his position. That's especially important if you are addressing a belief held by a large group of people.
Again, this isn't to run down steelmanning - the practice is sadly limited, and anyone who attempts it has gained a big advantage in figuring out how the world is. It's just a reminder that the steelman you make may not be quite as strong as the steelman that is out to get you.
[EDIT: Link included to the document that I did not know was available online before now]
The Truth About Mathematical Ability
There's widespread confusion about the nature of mathematical ability, for a variety of reasons:
- Most people don't know what math is.
- Most people don't know enough statistics to analyze the question properly.
- Most mathematicians are not very metacognitive.
- Very few people have more than a casual interest in the subject.
If the nature of mathematical ability were exclusively an object of intellectual interest, this would be relatively inconsequential. For example, many people are confused about Einstein’s theory of relativity, but this doesn’t have much of an impact on their lives. But in practice, people’s misconceptions about the nature of mathematical ability seriously interfere with their own ability to learn and do math, something that hurts them both professionally and emotionally.
I have a long standing interest in the subject, and I’ve found myself in the unusual position of being an expert. My experiences include:
- Completing a PhD in pure math at University of Illinois.
- Four years of teaching math at the high school and college levels (precalculus, calculus, multivariable calculus and linear algebra)
- Personal encounters with some of the best mathematicians in the world, and a study of great mathematicians’ biographies.
- A long history of working with mathematically gifted children: as a counselor at MathPath for three summers, through one-on-one tutoring, and as an instructor at Art of Problem Solving.
- Studying the literature on IQ and papers from the Study of Exceptional Talent as a part of my work for Cognito Mentoring.
- Training as a full-stack web developer at App Academy.
- Doing a large scale data science project where I applied statistics and machine learning to make new discoveries in social psychology.
I’ve thought about writing about the nature of mathematical ability for a long time, but there was a missing element: I myself had never done genuinely original and high quality mathematical research. After completing much of my data science project, I realized that this had changed. The experience sharpened my understanding of the issues.
This is a the first of a sequence of posts where I try to clarify the situation. My main point in this post is:
There are several different dimensions to mathematical ability. Common measures rarely assess all of these dimensions, and can paint a very incomplete picture of what somebody is capable of.
Intrapersonal comparisons: you might be doing it wrong.
Nothing weighty or profound today, but I noticed a failure mode in myself which other people might plausibly suffer from so I thought I'd share it.
Basically, I noticed that sometimes when I discovered a more effective way of doing something -- say, going from conventional flashcards to Anki -- I found myself getting discouraged.
I realized that it was because each time I found such a technique, I automatically compared my current self to a version of me that had had access to the technique the whole time. Realizing that I wasn't as far along as I could've been resulted in a net loss of motivation.
Now, I deliberately compare two future versions of myself, one armed with the technique I just discovered and one without. Seeing how much farther along I will be results in a net gain of motivation.
A variant of this exercise is taking any handicap you might have and wildly exaggerating it. I suffer from mild Carpal Tunnel (or something masquerading as CT) which makes progress in programming slow. When I feel down about this fact I imagine how hard programming would be without hands.
Sometimes I go as far as to plan out what I might do if I woke up tomorrow with a burning desire to program and nothing past my wrists. Well, I'd probably figure out a way to code by voice and then practice mnemonics because I wouldn't be able to write anything down. Since these solutions exist I can implement one or both of them the moment my carpal tunnel gets bad enough.
With this realization comes a boost in motivation knowing I can go a different direction if required.
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.
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.
A vote against spaced repetition
LessWrong seems to be a big fan of spaced-repetition flashcard programs like Anki, Supermemo, or Mnemosyne. I used to be. After using them religiously for 3 years in medical school, I now categorically advise against using them for large volumes of memorization.
[A caveat before people get upset: I think they appropriate in certain situations, and I have not tried to use them to learn a language, which seems its most popular use. More at the bottom.]
A bit more history: I and 30 other students tried using Mnemosyne (and some used Anki) for multiple tests. At my school, we have a test approximately every 3 weeks, and each test covers about 75 pages of high-density outline-format notes. Many stopped after 5 or so such tests, citing that they simply did not get enough returns from their time. I stuck with it longer and used them more than anyone else, using them for 3 years.
Incidentally, I failed my first year and had to repeat.
By the end of that third year (and studying for my Step 1 boards, a several-month process), I lost faith in spaced-repetition cards as an effective tool for my memorization demands. I later met with a learning-skills specialist, who felt the same way, and had better reasons than my intuition/trial-and-error:
- Flashcards are less useful to learning the “big picture”
- Specifically, if you are memorizing a large amount of information, there is often a hierarchy, organization, etc that can make leaning the whole thing easier, and you loose the constant visual reminder of the larger context when using flashcards.
- Flashcards do not take advantage of spatial, mapping, or visual memory, all of which the human mind is much better optimized for. It is not so well built to memorize pairs between seemingly arbitrary concepts with few to no intuitive links. My preferred methods are, in essence, hacks that use your visual and spatial memory rather than rote.
Here are examples of the typical kind of things I memorize every day and have found flashcards to be surprisingly worthless for:
- The definition of Sjögren's syndrome
- The contraindications of Metronidazole
- The significance of a rise in serum αFP
Here is what I now use in place of flashcards:
- Ven diagrams/etc, to compare and contrast similar lists. (This is more specific to medical school, when you learn subtly different diseases.)
- Mnemonic pictures. I have used this myself for years to great effect, and later learned it was taught by my study-skills expert, though I'm surprised I haven't found them formally named and taught anywhere else. The basic concept is to make a large picture, where each detail on the picture corresponds to a detail you want to memorize.
- Memory palaces. I recently learned how to properly use these, and I'm a true believer. When I only had the general idea to “pair things you want to memorize with places in your room” I found it worthless, but after I was taught a lot of do's and don'ts, they're now my favorite way to memorize any list of 5+ items. If there's enough demand on LW I can write up a summary.
Spaced repetition is still good for knowledge you need to retrieve immediately, when a 2-second delay would make it useless. I would still consider spaced-repetition to memorize some of the more rarely-used notes on the treble and bass clef, if I ever decide to learn to sight-read music properly. I make no comment on it's usefulness to learn a foreign language, as I haven't tried it, but if I were to pick one up I personally would start with a rosetta-stone-esque program.
Your mileage may vary, but after seeing so many people try and reject them, I figured it was enough data to share. Mnemonic pictures and memory palaces are slightly time consuming when you're learning them. However, if someone has the motivation and discipline to make a stack of flashcards and study them every day indefinitely, then I believe learning and using those skills is a far better use of time.
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