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This is an essay describing some of my motivation to be an effective altruist. It is crossposted from my blog. Many of the ideas here are quite similar to others found in the sequences. I have a slightly different take, and after adjusting for the typical mind fallacy I expect that this post may contain insights that are new to many.
I'm not very good at feeling the size of large numbers. Once you start tossing around numbers larger than 1000 (or maybe even 100), the numbers just seem "big".
Consider Sirius, the brightest star in the night sky. If you told me that Sirius is as big as a million earths, I would feel like that's a lot of Earths. If, instead, you told me that you could fit a billion Earths inside Sirius… I would still just feel like that's a lot of Earths.
The feelings are almost identical. In context, my brain grudgingly admits that a billion is a lot larger than a million, and puts forth a token effort to feel like a billion-Earth-sized star is bigger than a million-Earth-sized star. But out of context — if I wasn't anchored at "a million" when I heard "a billion" — both these numbers just feel vaguely large.
I feel a little respect for the bigness of numbers, if you pick really really large numbers. If you say "one followed by a hundred zeroes", then this feels a lot bigger than a billion. But it certainly doesn't feel (in my gut) like it's 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 times bigger than a billion. Not in the way that four apples intenally feels like twice as many as two apples. My brain can't even begin to wrap itself around this sort of magnitude differential.
This phenomena is related to scope insensitivity, and it's important to me because I live in a world where sometimes the things I care about are really really numerous.
For example, billions of people live in squalor, with hundreds of millions of them deprived of basic needs and/or dying from disease. And though most of them are out of my sight, I still care about them.
The loss of a human life with all is joys and all its sorrows is tragic no matter what the cause, and the tragedy is not reduced simply because I was far away, or because I did not know of it, or because I did not know how to help, or because I was not personally responsible.
Knowing this, I care about every single individual on this planet. The problem is, my brain is simply incapable of taking the amount of caring I feel for a single person and scaling it up by a billion times. I lack the internal capacity to feel that much. My care-o-meter simply doesn't go up that far.
And this is a problem.
Followup to: Announcing the 2014 program equilibrium iterated PD tournament
In August, I announced an iterated prisoner's dilemma tournament in which bots can simulate each other before making a move. Eleven bots were submitted to the tournament. Today, I am pleased to announce the final standings and release the source code and full results.
All of the source code submitted by the competitors and the full results for each match are available here. See here for the full set of rules and tournament code.
Before we get to the final results, here's a quick rundown of the bots that competed:
AnderBot follows a simple tit-for-tat-like algorithm that eschews simulation:
- On the first turn, Cooperate.
- For the next 10 turns, play tit-for-tat.
- For the rest of the game, Defect with 10% probability or Defect if the opposing bot has defected more times than AnderBot.
Many people have an incorrect view of the Future of Humanity Institute's funding situation, so this is a brief note to correct that; think of it as a spiritual successor to this post. As John Maxwell puts it, FHI is "one of the three organizations co-sponsoring LW [and] a group within the University of Oxford's philosophy department that tackles important, large-scale problems for humanity like how to go about reducing existential risk." (If you're not familiar with our work, this article is a nice, readable introduction, and our director, Nick Bostrom, wrote Superintelligence.) Though we are a research institute in an ancient and venerable institution, this does not guarantee funding or long-term stability.
I sometimes let imaginary versions of myself make decisions for me.
(I also sometimes imagine what Anna would do, and then do that. I call it "Annajitsu".)
Is intelligence hard to evolve? Well, we're intelligent, so it must be easy... except that only an intelligent species would be able to ask that question, so we run straight into the problem of anthropics. Any being that asked that question would have to be intelligent, so this can't tell us anything about its difficulty (a similar mistake would be to ask "is most of the universe hospitable to life?", and then looking around and noting that everything seems pretty hospitable at first glance...).
Instead, one could point at the great apes, note their high intelligence, see that intelligence arises separately, and hence that it can't be too hard to evolve.
One could do that... but one would be wrong. The key test is not whether intelligence can arise separately, but whether it can arise independently. Chimpanzees, Bonobos and Gorillas and such are all "on our line": they are close to common ancestors of ours, which we would expect to be intelligent because we are intelligent. Intelligent species tend to have intelligent relatives. So they don't provide any extra information about the ease or difficulty of evolving intelligence.
To get independent intelligence, we need to go far from our line. Enter the smart and cute icon on many student posters: the dolphin.
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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
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[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]
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 is interesting is the strength of these relationships appear to deteriorate as you advance far along the right tail. Although 6'7" is very tall, is 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 although we know the predictors are correlated with the outcome, freakishly extreme outcomes do not go together with similarly freakishly extreme predictors. 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 quiz time versus test score:
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:
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 to tight (the tighter the correlation, the larger the sample size required), one will observe the ellipses with the bulging sides of the distribution (2).
Hence the very best basketball players aren't the tallest (and vice versa), the very wealthiest not the 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 these height, strength, agility and hand-eye-coordination are independent of one another, gaussian, and additive towards the outcome of basketball ability with equal weight.(3) So, ceritus paribus, being taller will make one better at basketball, and the toy model stipulates there aren't 'hidden trade-offs': there's no negative correlation between height and the other attributes, even at the extremes. Yet the graphical explanation suggests we should still see divergence of the tails: the very tallest shouldn't be the very best.
The intuitive explanation would go like this: Start at the extreme tail - +4SD above the mean for height. Although their 'basketball-score' gets a massive boost from their height, we'd expect them to be average with respect to the other basketball relevant abilities (we've stipulated they're independent). Further, as this ultra-tall population is small, this population won't have a very high variance: with 10 people at +4SD, you wouldn't expect any of them to be +2SD in another factor like agility.
Move down the tail to slightly less extreme values - +3SD say. These people don't get such a boost to their basketball score for their height, but there should be a lot more of them (if 10 at +4SD, around 500 at +3SD), this means there is a lot more expected variance in the other basketball relevant activities - it is much less surprising to find someone +3SD in height and also +2SD in agility, and in the world where these things were equally important, they would 'beat' someone +4SD in height but average in the other attributes. Although a +4SD height person will likely be better than a given +3SD height person, the best of the +4SDs will not be as good as the best of the much larger number of +3SDs
The trade-off will vary depending on the exact weighting of the factors, which explain more of the variance, but the point seems to hold in the general case: 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.
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.(4) Mainly, though, it should lead us to be less self-confident.
1. One might look at the generally modest achievements of people in high-IQ societies as further evidence, but there are worries about adverse selection.
2. 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.
3. If you want to apply it to cases where the factors are positively correlated - which they often are - just use the components of the other factors that are independent of the factor of interest. I think, but I can't demonstrate, the other stipulations could also be relaxed.
4. 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.
Through a series of diagrams, this article will walk through key concepts in Nick Bostrom’s Superintelligence. The book is full of heavy content, and though well written, its scope and depth can make it difficult to grasp the concepts and mentally hold them together. The motivation behind making these diagrams is not to repeat an explanation of the content, but rather to present the content in such a way that the connections become clear. Thus, this article is best read and used as a supplement to Superintelligence.
Note: Superintelligence is now available in the UK. The hardcover is coming out in the US on September 3. The Kindle version is already available in the US as well as the UK.
Roadmap: there are two diagrams, both presented with an accompanying description. The two diagrams are combined into one mega-diagram at the end.
Figure 1: Pathways to Superintelligence
Figure 1 displays the five pathways toward superintelligence that Bostrom describes in chapter 2 and returns to in chapter 14 of the text. According to Bostrom, brain-computer interfaces are unlikely to yield superintelligence. Biological cognition, i.e., the enhancement of human intelligence, may yield a weak form of superintelligence on its own. Additionally, improvements to biological cognition could feed back into driving the progress of artificial intelligence or whole brain emulation. The arrows from networks and organizations likewise indicate technologies feeding back into AI and whole brain emulation development.
Artificial intelligence and whole brain emulation are two pathways that can lead to fully realized superintelligence. Note that neuromorphic is listed under artificial intelligence, but an arrow connects from whole brain emulation to neuromorphic. In chapter 14, Bostrom suggests that neuromorphic is a potential outcome of incomplete or improper whole brain emulation. Synthetic AI includes all the approaches to AI that are not neuromorphic; other terms that have been used are algorithmic or de novo AI.
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