The Tails Coming Apart As Metaphor For Life

By Scott Alexander

[Epistemic status: Pretty good, but I make no claim this is original]

A neglected gem from Less Wrong: Why The Tails Come Apart, by commenter Thrasymachus. It explains why even when two variables are strongly correlated, the most extreme value of one will rarely be the most extreme value of the other. Take these graphs of grip strength vs. arm strength and reading score vs. writing score:

In a pinch, the second graph can also serve as a rough map of Afghanistan

Grip strength is strongly correlated with arm strength. But the person with the strongest arm doesn’t have the strongest grip. He’s up there, but a couple of people clearly beat him. Reading and writing scores are even less correlated, and some of the people with the best reading scores aren’t even close to being best at writing.

Thrasymachus gives an intuitive geometric explanation of why this should be; I can’t beat it, so I’ll just copy it outright:

I thought about this last week when I read this article on happiness research.

The summary: if you ask people to “value their lives today on a 0 to 10 scale, with the worst possible life as a 0 and the best possible life as a 10”, you will find that Scandinavian countries are the happiest in the world.

But if you ask people “how much positive emotion do you experience?”, you will find that Latin American countries are the happiest in the world.

If you check where people are the least depressed, you will find Australia starts looking very good.

And if you ask “how meaningful would you rate your life?” you find that African countries are the happiest in the world.

It’s tempting to completely dismiss “happiness” as a concept at all, but that’s not right either. Who’s happier: a millionaire with a loving family who lives in a beautiful mansion in the forest and spends all his time hiking and surfing and playing with his kids? Or a prisoner in a maximum security jail with chronic pain? If we can all agree on the millionaire – and who wouldn’t? – happiness has to at least sort of be a real concept.

The solution is to understand words as hidden inferences – they refer to a multidimensional correlation rather than to a single cohesive property. So for example, we have the word “strength”, which combines grip strength and arm strength (and many other things). These variables really are heavily correlated (see the graph above), so it’s almost always worthwhile to just refer to people as being strong or weak. I can say “Mike Tyson is stronger than an 80 year old woman”, and this is better than having to say “Mike Tyson has higher grip strength, arm strength, leg strength, torso strength, and ten other different kinds of strength than an 80 year old woman.” This is necessary to communicate anything at all and given how nicely all forms of strength correlate there’s no reason not to do it.

But the tails still come apart. If we ask whether Mike Tyson is stronger than some other very impressive strong person, the answer might very well be “He has better arm strength, but worse grip strength”.

Happiness must be the same way. It’s an amalgam between a bunch of correlated properties like your subjective well-being at any given moment, and the amount of positive emotions you feel, and how meaningful your life is, et cetera. And each of those correlated is also an amalgam, and so on to infinity.

And crucially, it’s not an amalgam in the sense of “add subjective well-being, amount of positive emotions, and meaningfulness and divide by three”. It’s an unprincipled conflation of these that just denies they’re different at all.

Think of the way children learn what happiness is. I don’t actually know how children learn things, but I imagine something like this. The child sees the millionaire with the loving family, and her dad says “That guy must be very happy!”. Then she sees the prisoner with chronic pain, and her mom says “That guy must be very sad”. Repeat enough times and the kid has learned “happiness”.

Has she learned that it’s made out of subjective well-being, or out of amount of positive emotion? I don’t know; the learning process doesn’t determine that. But then if you show her a Finn who has lots of subjective well-being but little positive emotion, and a Costa Rican who has lots of positive emotion but little subjective well-being, and you ask which is happier, for some reason she’ll have an opinion. Probably some random variation in initial conditions has caused her to have a model favoring one definition or the other, and it doesn’t matter until you go out to the tails. To tie it to the same kind of graph as in the original post:

And to show how the individual differences work:

I am sorry about this graph, I really am. But imagine that one person, presented with the scatter plot and asked to understand the concept “happiness” from it, draws it as the thick red line (further towards the top right part of the line = more happiness), and a second person trying to the same task generates the thick green line. Ask the first person whether Finland or Costa Rica is happier, and they’ll say Finland: on the red coordinate system, Finland is at 5, but Costa Rica is at 4. Ask the second person, and they’ll say Costa Rica: on the green coordinate system, Costa Rica is at 5, and Finland is at 4 and a half. Did I mention I’m sorry about the graph?

But isn’t the line of best fit (here more or less y = x = the cyan line) the objective correct answer? Only in this metaphor where we’re imagining positive emotion and subjective well-being are both objectively quantifiable, and exactly equally important. In the real world, where we have no idea how to quantify any of this and we’re going off vague impressions, I would hate to be the person tasked with deciding whether the red or green line was more objectively correct.

In most real-world situations Mr. Red and Ms. Green will give the same answers to happiness-related questions. Is Costa Rica happier than North Korea? “Obviously,” the both say in union. If the tails only come apart a little, their answers to 99.9% of happiness-related questions might be the same, so much so that they could never realize they had slightly different concepts of happiness at all.

(is this just reinventing Quine? I’m not sure. If it is, then whatever, my contribution is the ridiculous graphs.)

Perhaps I am also reinventing the model of categorization discussed in How An Algorithm Feels From The Inside, Dissolving Questions About Disease, and The Categories Were Made For Man, Not Man For The Categories.

But I think there’s another interpretation. It’s not just that “quality of life”, “positive emotions”, and “meaningfulness” are three contributors which each give 33% of the activation to our central node of “happiness”. It’s that we got some training data – the prisoner is unhappy, the millionaire is happy – and used it to build a classifier that told us what happiness was. The training data was ambiguous enough that different people built different classifiers. Maybe one person built a classifier that was based entirely on quality-of-life, and a second person built a classifier based entirely around positive emotions. Then we loaded that with all the social valence of the word “happiness”, which we naively expected to transfer across paradigms.

This leads to (to steal words from Taleb) a Mediocristan resembling the training data where the category works fine, vs. an Extremistan where everything comes apart. And nowhere does this become more obvious than in what this blog post has secretly been about the whole time – morality.

The morality of Mediocristan is mostly uncontroversial. It doesn’t matter what moral system you use, because all moral systems were trained on the same set of Mediocristani data and give mostly the same results in this area. Stealing from the poor is bad. Donating to charity is good. A lot of what we mean when we say a moral system sounds plausible is that it best fits our Mediocristani data that we all agree upon. This is a lot like what we mean when we say that “quality of life”, “positive emotions”, and “meaningfulness” are all decent definitions of happiness; they all fit the training data.

The further we go toward the tails, the more extreme the divergences become. Utilitarianism agrees that we should give to charity and shouldn’t steal from the poor, because Utility, but take it far enough to the tails and we should tile the universe with rats on heroin. Religious morality agrees that we should give to charity and shouldn’t steal from the poor, because God, but take it far enough to the tails and we should spend all our time in giant cubes made of semiprecious stones singing songs of praise. Deontology agrees that we should give to charity and shouldn’t steal from the poor, because Rules, but take it far enough to the tails and we all have to be libertarians.

I have to admit, I don’t know if the tails coming apart is even the right metaphor anymore. People with great grip strength still had pretty good arm strength. But I doubt these moral systems form an ellipse; converting the mass of the universe into nervous tissue experiencing euphoria isn’t just the second-best outcome from a religious perspective, it’s completely abominable. I don’t know how to describe this mathematically, but the terrain looks less like tails coming apart and more like the Bay Area transit system:

Mediocristan is like the route from Balboa Park to West Oakland, where it doesn’t matter what line you’re on because they’re all going to the same place. Then suddenly you enter Extremistan, where if you took the Red Line you’ll end up in Richmond, and if you took the Green Line you’ll end up in Warm Springs, on totally opposite sides of the map.

Our innate moral classifier has been trained on the Balboa Park – West Oakland route. Some of us think morality means “follow the Red Line”, and others think “follow the Green Line”, but it doesn’t matter, because we all agree on the same route.

When people talk about how we should arrange the world after the Singularity when we’re all omnipotent, suddenly we’re way past West Oakland, and everyone’s moral intuitions hopelessly diverge.

But it’s even worse than that, because even within myself, my moral intuitions are something like “Do the thing which follows the Red Line, and the Green Line, and the Yellow Line…you know, that thing!” And so when I’m faced with something that perfectly follows the Red Line, but goes the opposite directions as the Green Line, it seems repugnant even to me, as does the opposite tactic of following the Green Line. As long as creating and destroying people is hard, utilitarianism works fine, but make it easier, and suddenly your Standard Utilitarian Path diverges into Pronatal Total Utilitarianism vs. Antinatalist Utilitarianism and they both seem awful. If our degree of moral repugnance is the degree to which we’re violating our moral principles, and my moral principle is “Follow both the Red Line and the Green Line”, then after passing West Oakland I either have to end up in Richmond (and feel awful because of how distant I am from Green), or in Warm Springs (and feel awful because of how distant I am from Red).

This is why I feel like figuring out a morality that can survive transhuman scenarios is harder than just finding the Real Moral System That We Actually Use. There’s a potentially impossible conceptual problem here, of figuring out what to do with the fact that any moral rule followed to infinity will diverge from large parts of what we mean by morality.

This is only a problem for ethical subjectivists like myself, who think that we’re doing something that has to do with what our conception of morality is. If you’re an ethical naturalist, by all means, just do the thing that’s actually ethical.

When Lovecraft wrote that “we live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far”, I interpret him as talking about the region from Balboa Park to West Oakland on the map above. Go outside of it and your concepts break down and you don’t know what to do. He was right about the island, but exactly wrong about its causes – the most merciful thing in the world is how so far we have managed to stay in the area where the human mind can correlate its contents.