[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.

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

[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.

I once asked a room full of about 100 neuroscientists whether willpower depletion was a thing, and there was widespread disagreement with the idea. (A propos, this is a great way to quickly gauge consensus in a field.) Basically, for a while some researchers believed that willpower depletion "is" glucose depletion in the prefrontal cortex, but some more recent experiments have failed to replicate this, e.g. by finding that the mere taste of sugar is enough to "replenish" willpower faster than the time it takes blood to move from the mouth to the brain:

Carbohydrate mouth-rinses activate dopaminergic pathways in the striatum–a region of the brain associated with responses to reward (Kringelbach, 2004)–whereas artificially-sweetened non-carbohydrate mouth-rinses do not (Chambers et al., 2009). Thus, the sensing of carbohydrates in the mouth appears to signal the possibility of reward (i.e., the future availability of additional energy), which could motivate rather than fuel physical effort.

-- Molden, D. C. et al, The Motivational versus Metabolic Effects of Carbohydrates on Self-Control. Psychological Science.

Stanford's Carol Dweck and Greg Walden even found that hinting to people that using willpower is energizing might actually make them less depletable:

When we had people read statements that reminded them of the power of willpower like, “Sometimes, working on a strenuous mental task can make you feel energized for further challenging activities,” they kept on working and performing well with no sign of depletion. They made half as many mistakes on a difficult cognitive task as people who read statements about limited willpower. In another study, they scored 15 percent better on I.Q. problems.

-- Dweck and Walden, Willpower: It’s in Your Head? New York Times.

While these are all interesting empirical findings, there’s a very similar phenomenon that’s much less debated and which could explain many of these observations, but I think gets too little popular attention in these discussions:

Willpower is distractible.

Indeed, willpower and working memory are both strongly mediated by the dorsolateral prefontal cortex, so “distraction” could just be the two functions funging against one another. To use the terms of Stanovich popularized by Kahneman in Thinking: Fast and Slow, "System 2" can only override so many "System 1" defaults at any given moment.

So what’s going on when people say "willpower depletion"? I’m not sure, but even if willpower depletion is not a thing, the following distracting phenomena clearly are:

• Thirst
• Hunger
• Sleepiness
• Physical fatigue (like from running)
• Physical discomfort (like from sitting)
• That specific-other-thing you want to do
• Anxiety about willpower depletion
• Indignation at being asked for too much by bosses, partners, or experimenters...

... and "willpower depletion" might be nothing more than mental distraction by one of these processes. Perhaps it really is better to think of willpower as power (a rate) than energy (a resource).

If that’s true, then figuring out what processes might be distracting us might be much more useful than saying “I’m out of willpower” and giving up. Maybe try having a sip of water or a bit of food if your diet permits it. Maybe try reading lying down to see if you get nap-ish. Maybe set a timer to remind you to call that friend you keep thinking about.

The last two bullets,

• Anxiety about willpower depletion
• Indignation at being asked for too much by bosses, partners, or experimenters...

are also enough to explain why being told willpower depletion isn’t a thing might reduce the effects typically attributed to it: we might simply be less distracted by anxiety or indignation about doing “too much” willpower-intensive work in a short period of time.

Of course, any speculation about how human minds work in general is prone to the "typical mind fallacy". Maybe my willpower is depletable and yours isn’t. But then that wouldn’t explain why you can cause people to exhibit less willpower depletion by suggesting otherwise. But then again, most published research findings are false. But then again the research on the DLPFC and working memory seems relatively old and well established, and distraction is clearly a thing...

All in all, more of my chips are falling on the hypothesis that willpower “depletion” is often just willpower distraction, and that finding and addressing those distractions is probably a better a strategy than avoiding activities altogether in order to "conserve willpower".

I think people who are not made happier by having things either have the wrong things, or have them incorrectly.  Here is how I get the most out of my stuff.

Money doesn't buy happiness.  If you want to try throwing money at the problem anyway, you should buy experiences like vacations or services, rather than purchasing objects.  If you have to buy objects, they should be absolute and not positional goods; positional goods just put you on a treadmill and you're never going to catch up.

Supposedly.

I think getting value out of spending money, owning objects, and having positional goods are all three of them skills, that people often don't have naturally but can develop.  I'm going to focus mostly on the middle skill: how to have things correctly¹.

Related to: The Apologist and the Revolutionary, Dreams with Damaged Priors

Several years ago, I posted about V.S. Ramachandran's 1996 theory explaining anosognosia through an "apologist" and a "revolutionary".

Anosognosia, a condition in which extremely sick patients mysteriously deny their sickness, occurs during right-sided brain injury but not left-sided brain injury. It can be extraordinarily strange: for example, in one case, a woman whose left arm was paralyzed insisted she could move her left arm just fine, and when her doctor pointed out her immobile arm, she claimed that was her daughter's arm even though it was obviously attached to her own shoulder. Anosognosia can be temporarily alleviated by squirting cold water into the patient's left ear canal, after which the patient suddenly realizes her condition but later loses awareness again and reverts back to the bizarre excuses and confabulations.

Ramachandran suggested that the left brain is an "apologist", trying to justify existing theories, and the right brain is a "revolutionary" which changes existing theories when conditions warrant. If the right brain is damaged, patients are unable to change their beliefs; so when a patient's arm works fine until a right-brain stroke, the patient cannot discard the hypothesis that their arm is functional, and can only use the left brain to try to fit the facts to their belief.

In the almost twenty years since Ramachandran's theory was published, new research has kept some of the general outline while changing many of the specifics in the hopes of explaining a wider range of delusions in neurological and psychiatric patients. The newer model acknowledges the left-brain/right-brain divide, but adds some new twists based on the Mind Projection Fallacy and the brain as a Bayesian reasoner.

This is the completed article that Luke wrote the first half of. My thanks go to the following for reading, editing, and commenting; Luke Muehlhauser, Louie Helm, Benjamin Noble, and Francelle Wax.

People disagree about things. Some say that television makes you dumber; other say it makes you smarter. Some scientists believe life must exist elsewhere in the universe; others believe it must not. Some say that complicated financial derivatives are essential to a modern competitive economy; others think a nation's economy will do better without them. It's hard to know what is true.

And it's hard to know how to figure out what is true. Some argue that you should assume the things you are most certain about and then deduce all other beliefs from your original beliefs. Others think you should accept at face value the most intuitive explanations of personal experience. Still others think you should generally agree with the scientific consensus until it is disproved.

Wouldn't it be nice if determining what is true was like baking a cake? What if there was a recipe for finding out what is true? All you'd have to do is follow the written directions exactly, and after the last instruction you'd inevitably find yourself with some sweet, tasty truth!

In this tutorial, we'll explain the closest thing we’ve found so far to a recipe for finding truth: Solomonoff induction.

There are some qualifications to make. To describe just one: roughly speaking, you don't have time to follow the recipe. To find the truth to even a simple question using this recipe would require you to follow one step after another until long after the heat death of the universe, and you can't do that.

But we can find shortcuts. Suppose you know that the exact recipe for baking a cake asks you to count out one molecule of H₂O at a time until you have exactly 0.5 cups of water. If you did that, you might not finish the cake before the heat death of the universe. But you could approximate that part of the recipe by measuring out something very close to 0.5 cups of water, and you'd probably still end up with a pretty good cake.

Similarly, once we know the exact recipe for finding truth, we can try to approximate it in a way that allows us to finish all the steps sometime before the sun burns out.

This tutorial explains that best-we've-got-so-far recipe for finding truth, Solomonoff induction. Don’t worry, we won’t be using any equations, just qualitative descriptions.

Like Eliezer Yudkowsky's Intuitive Explanation of Bayes' Theorem and Luke Muehlhauser's Crash Course in the Neuroscience of Human Motivation, this tutorial is long. You may not have time to read it; that's fine. But if you do read it, we recommend that you read it in sections.