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As previously discussed, on June 6th I received a message from jackk, a Trike Admin. He reported that the user Jiro had asked Trike to carry out an investigation to the retributive downvoting that Jiro had been subjected to. The investigation revealed that the user Eugine_Nier had downvoted over half of Jiro's comments, amounting to hundreds of downvotes.
I asked the community's guidance on dealing with the issue, and while the matter was being discussed, I also reviewed previous discussions about mass downvoting and looked for other people who mentioned being the victims of it. I asked Jack to compile reports on several other users who mentioned having been mass-downvoted, and it turned out that Eugine was also overwhelmingly the biggest downvoter of users David_Gerard, daenarys, falenas108, ialdabaoth, shminux, and Tenoke. As this discussion was going on, it turned out that user Ander had also been targeted by Eugine.
I sent two messages to Eugine, requesting an explanation. I received a response today. Eugine admitted his guilt, expressing the opinion that LW's karma system was failing to carry out its purpose of keeping out weak material and that he was engaged in a "weeding" of users who he did not think displayed sufficient rationality.
Needless to say, it is not the place of individual users to unilaterally decide that someone else should be "weeded" out of the community. The Less Wrong content deletion policy contains this clause:
Harrassment of individual users.
If we determine that you're e.g. following a particular user around and leaving insulting comments to them, we reserve the right to delete those comments. (This has happened extremely rarely.)
Although the wording does not explicitly mention downvoting, harassment by downvoting is still harassment. Several users have indicated that they have experienced considerable emotional anguish from the harassment, and have in some cases been discouraged from using Less Wrong at all. This is not a desirable state of affairs, to say the least.
I was originally given my moderator powers on a rather ad-hoc basis, with someone awarding mod privileges to the ten users with the highest karma at the time. The original purpose for that appointment was just to delete spam. Nonetheless, since retributive downvoting has been a clear problem for the community, I asked the community for guidance on dealing with the issue. The rough consensus of the responses seemed to authorize me to deal with the problem as I deemed appropriate.
The fact that Eugine remained quiet about his guilt until directly confronted with the evidence, despite several public discussions of the issue, is indicative of him realizing that he was breaking prevailing social norms. Eugine's actions have worsened the atmosphere of this site, and that atmosphere will remain troubled for as long as he is allowed to remain here.
Therefore, I now announce that Eugine_Nier is permanently banned from posting on LessWrong. This decision is final and will not be changed in response to possible follow-up objections.
Unfortunately, it looks like while a ban prevents posting, it does not actually block a user from casting votes. I have asked jackk to look into the matter and find a way to actually stop the downvoting. Jack indicated earlier on that it would be technically straightforward to apply a negative karma modifier to Eugine's account, and wiping out Eugine's karma balance would prevent him from casting future downvotes. Whatever the easiest solution is, it will be applied as soon as possible.
EDIT 24 July 2014: Banned users are now prohibited from voting.
[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.
Last month I saw this post: http://lesswrong.com/lw/kbc/meta_the_decline_of_discussion_now_with_charts/ addressing whether the discussion on LessWrong was in decline. As a relatively new user who had only just started to post comments, my reaction was: “I hope that LessWrong isn’t in decline, because the sequences are amazing, and I really like this community. I should try to write a couple articles myself and post them! Maybe I could do an analysis/summary of certain sequences posts, and discuss how they had helped me to change my mind”. I started working on writing an article.
Then I logged into LessWrong and saw that my Karma value was roughly half of what it had been the day before. Previously I hadn’t really cared much about Karma, aside from whatever micro-utilons of happiness it provided to see that the number slowly grew because people generally liked my comments. Or at least, I thought I didn’t really care, until my lizard brain reflexes reacted to what it perceived as an assault on my person.
Had I posted something terrible and unpopular that had been massively downvoted during the several days since my previous login? No, in fact my ‘past 30 days’ Karma was still positive. Rather, it appeared that everything I had ever posted to LessWrong now had a -1 on it instead of a 0. Of course, my loss probably pales in comparison to that of other, more prolific posters who I have seen report this behavior.
So what controversial subject must I have commented on in order to trigger this assault? Well, let’s see, in the past week I had asked if anyone had any opinions of good software engineer interview questions I could ask a candidate. I posted in http://lesswrong.com/lw/kex/happiness_and_children/ that I was happy to not have children, and finally, here in what appears to me to be by far the most promising candidate:http://lesswrong.com/r/discussion/lw/keu/separating_the_roles_of_theory_and_direct/ I replied to a comment about global warming data, stating that I routinely saw headlines about data supporting global warming.
Here is our scenario: A new user is attempting to participate on a message board that values empiricism and rationality, posted that evidence supports that climate change is real. (Wow, really rocking the boat here!) Then, apparently in an effort to ‘win’ this discussion by silencing opposition, someone went and downvoted every comment this user had ever made on the site. Apparently they would like to see LessWrong be a bastion of empiricism and rationality and [i]climate change denial[/i] instead? And the way to achieve this is not to have a fair and rational discussion of the existing empirical data, but rather to simply Karmassassinate anyone who would oppose them?
Here is my hypothesis: The continuing problem of karma downvote stalkers is contributing to the decline of discussion on the site. I definitely feel much less motivated to try and contribute anything now, and I have been told by multiple other people at LessWrong meetings things such as “I used to post a lot on LessWrong, but then I posted X, and got mass downvoted, so now I only comment on Yvain’s blog”. These anecdotes are, of course, only very weak evidence to support my claim. I wish I could provide more, but I will have to defer to any readers who can supply more.
Perhaps this post will simply trigger more retribution, or maybe it will trigger an outswelling of support, or perhaps just be dismissed by people saying I should’ve posted it to the weekly discussion thread instead. Whatever the outcome, rather than meekly leaving LessWrong and letting my 'stalker' win, I decided to open a discussion about the issue. Thank you!
This paper, or more often the New Scientist's exposition of it is being discussed online and is rather topical here. In a nutshell, stimulating one small but central area of the brain reversibly rendered one epilepsia patient unconscious without disrupting wakefulness. Impressively, this phenomenon has apparently been hypothesized before, just never tested (because it's hard and usually unethical). A quote from the New Scientist article (emphasis mine):
One electrode was positioned next to the claustrum, an area that had never been stimulated before.
When the team zapped the area with high frequency electrical impulses, the woman lost consciousness. She stopped reading and stared blankly into space, she didn't respond to auditory or visual commands and her breathing slowed. As soon as the stimulation stopped, she immediately regained consciousness with no memory of the event. The same thing happened every time the area was stimulated during two days of experiments (Epilepsy and Behavior, doi.org/tgn).
To confirm that they were affecting the woman's consciousness rather than just her ability to speak or move, the team asked her to repeat the word "house" or snap her fingers before the stimulation began. If the stimulation was disrupting a brain region responsible for movement or language she would have stopped moving or talking almost immediately. Instead, she gradually spoke more quietly or moved less and less until she drifted into unconsciousness. Since there was no sign of epileptic brain activity during or after the stimulation, the team is sure that it wasn't a side effect of a seizure.
If confirmed, this hints at several interesting points. For example, a complex enough brain is not sufficient for consciousness, a sort-of command and control structure is required, as well, even if relatively small. A low-consciousness state of late-stage dementia sufferers might be due to the damage specifically to the claustrum area, not just the overall brain deterioration. The researchers speculates that stimulating the area in vegetative-state patients might help "push them out of this state". From an AI research perspective, understanding the difference between wakefulness and consciousness might be interesting, too.
Jason Mitchell is [edit: has been] the John L. Loeb Associate Professor of the Social Sciences at Harvard. He has won the National Academy of Science's Troland Award as well as the Association for Psychological Science's Janet Taylor Spence Award for Transformative Early Career Contribution.
Here, he argues against the principle of replicability of experiments in science. Apparently, it's disrespectful, and presumptively wrong.
Recent hand-wringing over failed replications in social psychology is largely pointless, because unsuccessful experiments have no meaningful scientific value.
Because experiments can be undermined by a vast number of practical mistakes, the likeliest explanation for any failed replication will always be that the replicator bungled something along the way. Unless direct replications are conducted by flawless experimenters, nothing interesting can be learned from them.
Three standard rejoinders to this critique are considered and rejected. Despite claims to the contrary, failed replications do not provide meaningful information if they closely follow original methodology; they do not necessarily identify effects that may be too small or flimsy to be worth studying; and they cannot contribute to a cumulative understanding of scientific phenomena.
Replication efforts appear to reflect strong prior expectations that published findings are not reliable, and as such, do not constitute scientific output.
The field of social psychology can be improved, but not by the publication of negative findings. Experimenters should be encouraged to restrict their “degrees of freedom,” for example, by specifying designs in advance.
Whether they mean to or not, authors and editors of failed replications are publicly impugning the scientific integrity of their colleagues. Targets of failed replications are justifiably upset, particularly given the inadequate basis for replicators’ extraordinary claims.
This is why we can't have social science. Not because the subject is not amenable to the scientific method -- it obviously is. People are conducting controlled experiments and other people are attempting to replicate the results. So far, so good. Rather, the problem is that at least one celebrated authority in the field hates that, and would prefer much, much more deference to authority.
In early 2000, I registered my personal domain name weidai.com, along with a couple others, because I was worried that the small (sole-proprietor) ISP I was using would go out of business one day and break all the links on the web to the articles and software that I had published on my "home page" under its domain. Several years ago I started getting offers, asking me to sell the domain, and now they're coming in almost every day. A couple of days ago I saw the first six figure offer ($100,000).
In early 2009, someone named Satoshi Nakamoto emailed me personally with an announcement that he had published version 0.1 of Bitcoin. I didn't pay much attention at the time (I was more interested in Less Wrong than Cypherpunks at that point), but then in early 2011 I saw a LW article about Bitcoin, which prompted me to start mining it. I wrote at the time, "thanks to the discussion you started, I bought a Radeon 5870 and started mining myself, since it looks likely that I can at least break even on the cost of the card." That approximately $200 investment (plus maybe another $100 in electricity) is also worth around six figures today.
Clearly, technological advances can sometimes create gold rush-like situations (i.e., first-come-first-serve opportunities to make truly extraordinary returns with minimal effort or qualifications). And it's possible to stumble into them without even trying. Which makes me think, maybe we should be trying? I mean, if only I had been looking for possible gold rushes, I could have registered a hundred domain names optimized for potential future value, rather than the few that I happened to personally need. Or I could have started mining Bitcoins a couple of years earlier and be a thousand times richer.
I wish I was already an experienced gold rush spotter, so I could explain how best to do it, but as indicated above, I participated in the ones that I did more or less by luck. Perhaps the first step is just to keep one's eyes open, and to keep in mind that tech-related gold rushes do happen from time to time and they are not impossibly difficult to find. What other ideas do people have? Are there other past examples of tech gold rushes besides the two that I mentioned? What might be some promising fields to look for them in the future?
On a recent trip to Ireland, I gave a talk on tactics for having better arguments (video here). There's plenty in the video that's been discussed on LW before (Ideological Turing Tests and other reframes), but I thought I'd highlight one other class of trick I use to have more fruitful disagreements.
It's hard, in the middle of a fight, to remember, recognize, and defuse common biases, rhetorical tricks, emotional triggers, etc. I'd rather cheat than solve a hard problem, so I put a lot of effort into shifting disagreements into environments where it's easier for me and my opposite-number to reason and argue well, instead of relying on willpower. Here's a recent example of the kind of shift I like to make:
A couple months ago, a group of my friends were fighting about the Brendan Eich resignation on facebook. The posts were showing up fast; everyone was, presumably, on the edge of their seats, fueled by adrenaline, and alone at their various computers. It’s a hard place to have a charitable, thoughtful debate.
I asked my friends (since they were mostly DC based) if they’d be amenable to pausing the conversation and picking it up in person. I wanted to make the conversation happen in person, not in front of an audience, and in a format that let people speak for longer and ask questions more easily. If so, I promised to bake cookies for the ultimate donnybrook.
My friends probably figured that I offered cookies as a bribe to get everyone to change venues, and they were partially right. But my cookies had another strategic purpose. When everyone arrived, I was still in the process of taking the cookies out of the oven, so I had to recruit everyone to help me out.
“Alice, can you pour milk for people?”
“Bob, could you pass out napkins?”
“Eve, can you greet people at the door while I’m stuck in the kitchen with potholders on?”
Before we could start arguing, people on both sides of the debate were working on taking care of each other and asking each others’ help. Then, once the logistics were set, we all broke bread (sorta) with each other and had a shared, pleasurable experience. Then we laid into each other.
Sharing a communal experience of mutual service didn’t make anyone pull their intellectual punches, but I think it made us more patient with each other and less anxiously fixated on defending ourselves. Sharing food and seating helped remind us of the relationships we enjoyed with each other, and why we cared about probing the ideas of this particular group of people.
I prefer to fight with people I respect, who I expect will fight in good faith. It's hard to remember that's what I'm doing if I argue with them in the same forums (comment threads, fb, etc) that I usually see bad fights. An environment shift and other compensatory gestures makes it easier to leave habituated errors and fears at the door.
Analogy gets a bad rap around here, and not without reason. The kinds of argument from analogy condemned in the above links fully deserve the condemnation they get. Still, I think it's too easy to read them and walk away thinking "Boo analogy!" when not all uses of analogy are bad. The human brain seems to have hardware support for thinking in analogies, and I don't think this capability is a waste of resources, even in our highly non-ancestral environment. So, assuming that the linked posts do a sufficient job detailing the abuse and misuse of analogy, I'm going to go over some legitimate uses.
The first thing analogy is really good for is description. Take the plum pudding atomic model. I still remember this falsified proposal of negative 'raisins' in positive 'dough' largely because of the analogy, and I don't think anyone ever attempted to use it to argue for the existence of tiny subnuclear particles corresponding to cinnamon.
But this is only a modest example of what analogy can do. The following is an example that I think starts to show the true power: my comment on Robin Hanson's 'Don't Be "Rationalist"'. To summarize, Robin argued that since you can't be rationalist about everything you should budget your rationality and only be rational about the most important things; I replied that maybe rationality is like weightlifting, where your strength is finite yet it increases with use. That comment is probably the most successful thing I've ever written on the rationalist internet in terms of the attention it received, including direct praise from Eliezer and a shoutout in a Scott Alexander (yvain) post, and it's pretty much just an analogy.
Here's another example, this time from Eliezer. As part of the AI-Foom debate, he tells the story of Fermi's nuclear experiments, and in particular his precise knowledge of when a pile would go supercritical.
What do the above analogies accomplish? They provide counterexamples to universal claims. In my case, Robin's inference that rationality should be spent sparingly proceeded from the stated premise that no one is perfectly rational about anything, and weightlifting was a counterexample to the implicit claim 'a finite capacity should always be directed solely towards important goals'. If you look above my comment, anon had already said that the conclusion hadn't been proven, but without the counterexample this claim had much less impact.
In Eliezer's case, "you can never predict an unprecedented unbounded growth" is the kind of claim that sounds really convincing. "You haven't actually proved that" is a weak-sounding retort; "Fermi did it" immediately wins the point.
The final thing analogies do really well is crystallize patterns. For an example of this, let's turn to... Failure by Analogy. Yep, the anti-analogy posts are themselves written almost entirely via analogy! Alchemists who glaze lead with lemons and would-be aviators who put beaks on their machines are invoked to crystallize the pattern of 'reasoning by similarity'. The post then makes the case that neural-net worshippers are reasoning by similarity in just the same way, making the same fundamental error.
It's this capacity that makes analogies so dangerous. Crystallizing a pattern can be so mentally satisfying that you don't stop to question whether the pattern applies. The antidote to this is the question, "Why do you believe X is like Y?" Assessing the answer and judging deep similarities from superficial ones may not always be easy, but just by asking you'll catch the cases where there is no justification at all.
Let me tell you a parable of the future. Let’s say, 70 years from now, in a large Western country we’ll call Nacirema.
One day far from now: scientific development has continued apace, and a large government project (with, unsurprisingly, a lot of military funding) has taken the scattered pieces of cutting-edge research and put them together into a single awesome technology, which could revolutionize (or at least, vastly improve) all sectors of the economy. Leading thinkers had long forecast that this area of science’s mysteries would eventually yield to progress, despite theoretical confusion and perhaps-disappointing initial results and the scorn of more conservative types and the incomprehension (or outright disgust, for ‘playing god’) of the general population, and at last - it had! The future was bright.
Unfortunately, it was hurriedly decided to use an early prototype outside the lab in an impoverished foreign country. Whether out of arrogance, bureaucratic inertia, overconfidence on the part of the involved researchers, condescending racism, the need to justify the billions of grant-dollars that cumulative went into the project over the years by showing some use of it - whatever, the reasons no longer mattered after the final order was signed. The technology was used, but the consequences turned out to be horrific: over a brief period of what seemed like mere days, entire cities collapsed and scores - hundreds - of thousands of people died. (Modern economies are extremely interdependent and fragile, and small disruptions can have large consequences; more people died in the chaos of the evacuation of the areas around Fukushima than will die of the radiation.)
Summary: I don't think 'politics is the mind-killer' works well rthetorically. I suggest 'politics is hard mode' instead.
My usual first objection is that it seems odd to single politics out as a “mind-killer” when there’s plenty of evidence that tribalism happens everywhere. Recently, there has been a whole kerfuffle within the field of psychology about replication of studies. Of course, some key studies have failed to replicate, leading to accusations of “bullying” and “witch-hunts” and what have you. Some of the people involved have since walked their language back, but it was still a rather concerning demonstration of mind-killing in action. People took “sides,” people became upset at people based on their “sides” rather than their actual opinions or behavior, and so on.
Unless this article refers specifically to electoral politics and Democrats and Republicans and things (not clear from the wording), “politics” is such a frightfully broad category of human experience that writing it off entirely as a mind-killer that cannot be discussed or else all rationality flies out the window effectively prohibits a large number of important issues from being discussed, by the very people who can, in theory, be counted upon to discuss them better than most. Is it “politics” for me to talk about my experience as a woman in gatherings that are predominantly composed of men? Many would say it is. But I’m sure that these groups of men stand to gain from hearing about my experiences, since some of them are concerned that so few women attend their events.
In this article, Eliezer notes, “Politics is an important domain to which we should individually apply our rationality — but it’s a terrible domain in which to learn rationality, or discuss rationality, unless all the discussants are already rational.” But that means that we all have to individually, privately apply rationality to politics without consulting anyone who can help us do this well. After all, there is no such thing as a discussant who is “rational”; there is a reason the website is called “Less Wrong” rather than “Not At All Wrong” or “Always 100% Right.” Assuming that we are all trying to be more rational, there is nobody better to discuss politics with than each other.
The rest of my objection to this meme has little to do with this article, which I think raises lots of great points, and more to do with the response that I’ve seen to it — an eye-rolling, condescending dismissal of politics itself and of anyone who cares about it. Of course, I’m totally fine if a given person isn’t interested in politics and doesn’t want to discuss it, but then they should say, “I’m not interested in this and would rather not discuss it,” or “I don’t think I can be rational in this discussion so I’d rather avoid it,” rather than sneeringly reminding me “You know, politics is the mind-killer,” as though I am an errant child. I’m well-aware of the dangers of politics to good thinking. I am also aware of the benefits of good thinking to politics. So I’ve decided to accept the risk and to try to apply good thinking there. [...]
I’m sure there are also people who disagree with the article itself, but I don’t think I know those people personally. And to add a political dimension (heh), it’s relevant that most non-LW people (like me) initially encounter “politics is the mind-killer” being thrown out in comment threads, not through reading the original article. My opinion of the concept improved a lot once I read the article.
In the same thread, Andrew Mahone added, “Using it in that sneering way, Miri, seems just like a faux-rationalist version of ‘Oh, I don’t bother with politics.’ It’s just another way of looking down on any concerns larger than oneself as somehow dirty, only now, you know, rationalist dirty.” To which Miri replied: “Yeah, and what’s weird is that that really doesn’t seem to be Eliezer’s intent, judging by the eponymous article.”
Eliezer replied briefly, to clarify that he wasn't generally thinking of problems that can be directly addressed in local groups (but happen to be politically charged) as "politics":
Hanson’s “Tug the Rope Sideways” principle, combined with the fact that large communities are hard to personally influence, explains a lot in practice about what I find suspicious about someone who claims that conventional national politics are the top priority to discuss. Obviously local community matters are exempt from that critique! I think if I’d substituted ‘national politics as seen on TV’ in a lot of the cases where I said ‘politics’ it would have more precisely conveyed what I was trying to say.
But that doesn't resolve the issue. Even if local politics is more instrumentally tractable, the worry about polarization and factionalization can still apply, and may still make it a poor epistemic training ground.
A subtler problem with banning “political” discussions on a blog or at a meet-up is that it’s hard to do fairly, because our snap judgments about what counts as “political” may themselves be affected by partisan divides. In many cases the status quo is thought of as apolitical, even though objections to the status quo are ‘political.’ (Shades of Pretending to be Wise.)
Because politics gets personal fast, it’s hard to talk about it successfully. But if you’re trying to build a community, build friendships, or build a movement, you can’t outlaw everything ‘personal.’
And selectively outlawing personal stuff gets even messier. Last year, daenerys shared anonymized stories from women, including several that discussed past experiences where the writer had been attacked or made to feel unsafe. If those discussions are made off-limits because they relate to gender and are therefore ‘political,’ some folks may take away the message that they aren’t allowed to talk about, e.g., some harmful or alienating norm they see at meet-ups. I haven’t seen enough discussions of this failure mode to feel super confident people know how to avoid it.
Since this is one of the LessWrong memes that’s most likely to pop up in cross-subcultural dialogues (along with the even more ripe-for-misinterpretation “policy debates should not appear one-sided“…), as a first (very small) step, my action proposal is to obsolete the ‘mind-killer’ framing. A better phrase for getting the same work done would be ‘politics is hard mode’:
1. ‘Politics is hard mode’ emphasizes that ‘mind-killing’ (= epistemic difficulty) is quantitative, not qualitative. Some things might instead fall under Middlingly Hard Mode, or under Nightmare Mode…
2. ‘Hard’ invites the question ‘hard for whom?’, more so than ‘mind-killer’ does. We’re used to the fact that some people and some contexts change what’s ‘hard’, so it’s a little less likely we’ll universally generalize.
3. ‘Mindkill’ connotes contamination, sickness, failure, weakness. In contrast, ‘Hard Mode’ doesn’t imply that a thing is low-status or unworthy. As a result, it’s less likely to create the impression (or reality) that LessWrongers or Effective Altruists dismiss out-of-hand the idea of hypothetical-political-intervention-that-isn’t-a-terrible-idea. Maybe some people do want to argue for the thesis that politics is always useless or icky, but if so it should be done in those terms, explicitly — not snuck in as a connotation.
4. ‘Hard Mode’ can’t readily be perceived as a personal attack. If you accuse someone of being ‘mindkilled’, with no context provided, that smacks of insult — you appear to be calling them stupid, irrational, deluded, or the like. If you tell someone they’re playing on ‘Hard Mode,’ that’s very nearly a compliment, which makes your advice that they change behaviors a lot likelier to go over well.
5. ‘Hard Mode’ doesn’t risk bringing to mind (e.g., gendered) stereotypes about communities of political activists being dumb, irrational, or overemotional.
6. ‘Hard Mode’ encourages a growth mindset. Maybe some topics are too hard to ever be discussed. Even so, ranking topics by difficulty encourages an approach where you try to do better, rather than merely withdrawing. It may be wise to eschew politics, but we should not fear it. (Fear is the mind-killer.)
7. Edit: One of the larger engines of conflict is that people are so much worse at noticing their own faults and biases than noticing others'. People will be relatively quick to dismiss others as 'mindkilled,' while frequently flinching away from or just-not-thinking 'maybe I'm a bit mindkilled about this.' Framing the problem as a challenge rather than as a failing might make it easier to be reflective and even-handed.
This is not an attempt to get more people to talk about politics. I think this is a better framing whether or not you trust others (or yourself) to have productive political conversations.
When I playtested this post, Ciphergoth raised the worry that 'hard mode' isn't scary-sounding enough. As dire warnings go, it's light-hearted—exciting, even. To which I say: good. Counter-intuitive fears should usually be argued into people (e.g., via Eliezer's politics sequence), not connotation-ninja'd or chanted at them. The cognitive content is more clearly conveyed by 'hard mode,' and if some group (people who love politics) stands to gain the most from internalizing this message, the message shouldn't cast that very group (people who love politics) in an obviously unflattering light. LW seems fairly memetically stable, so the main issue is what would make this meme infect friends and acquaintances who haven't read the sequences. (Or Dune.)
If you just want a scary personal mantra to remind yourself of the risks, I propose 'politics is SPIDERS'. Though 'politics is the mind-killer' is fine there too.
If you and your co-conversationalists haven’t yet built up a lot of trust and rapport, or if tempers are already flaring, conveying the message ‘I’m too rational to discuss politics’ or ‘You’re too irrational to discuss politics’ can make things worse. In that context, ‘politics is the mind-killer’ is the mind-killer. At least, it’s a needlessly mind-killing way of warning people about epistemic hazards.
‘Hard Mode’ lets you speak as the Humble Aspirant rather than the Aloof Superior. Strive to convey: ‘I’m worried I’m too low-level to participate in this discussion; could you have it somewhere else?’ Or: ‘Could we talk about something closer to Easy Mode, so we can level up together?’ More generally: If you’re worried that what you talk about will impact group epistemology, you should be even more worried about how you talk about it.
This is a thread for rationality-related or LW-related jokes and humor. Please post jokes (new or old) in the comments.
Q: Why are Chromebooks good Bayesians?
A: Because they frequently update!
A super-intelligent AI walks out of a box...
Q: Why did the psychopathic utilitarian push a fat man in front of a trolley?
A: Just for fun.
Here is an interesting blog post about a guy who did a resume experiment between two positions which he argues are by experience identical, but occupy different "social status" positions in tech: A software engineer and a data manager.
Interview A: as Software Engineer
Bill faced five hour-long technical interviews. Three went well. One was so-so, because it focused on implementation details of the JVM, and Bill’s experience was almost entirely in C++, with a bit of hobbyist OCaml. The last interview sounds pretty hellish. It was with the VP of Data Science, Bill’s prospective boss, who showed up 20 minutes late and presented him with one of those interview questions where there’s “one right answer” that took months, if not years, of in-house trial and error to discover. It was one of those “I’m going to prove that I’m smarter than you” interviews...
Let’s recap this. Bill passed three of his five interviews with flying colors. One of the interviewers, a few months later, tried to recruit Bill to his own startup. The fourth interview was so-so, because he wasn’t a Java expert, but came out neutral. The fifth, he failed because he didn’t know the in-house Golden Algorithm that took years of work to discover. When I asked that VP/Data Science directly why he didn’t hire Bill (and he did not know that I knew Bill, nor about this experiment) the response I got was “We need people who can hit the ground running.” Apparently, there’s only a “talent shortage” when startup people are trying to scam the government into changing immigration policy. The undertone of this is that “we don’t invest in people”.
Or, for a point that I’ll come back to, software engineers lack the social status necessary to make others invest in them.
Interview B: as Data Science manager.
A couple weeks later, Bill interviewed at a roughly equivalent company for the VP-level position, reporting directly to the CTO.
Worth noting is that we did nothing to make Bill more technically impressive than for Company A. If anything, we made his technical story more honest, by modestly inflating his social status while telling a “straight shooter” story for his technical experience. We didn’t have to cover up periods of low technical activity; that he was a manager, alone, sufficed to explain those away.
Bill faced four interviews, and while the questions were behavioral and would be “hard” for many technical people, he found them rather easy to answer with composure. I gave him the Golden Answer, which is to revert to “There’s always a trade-off between wanting to do the work yourself, and knowing when to delegate.” It presents one as having managerial social status (the ability to delegate) but also a diligent interest in, and respect for, the work. It can be adapted to pretty much any “behavioral” interview question...
Bill passed. Unlike for a typical engineering position, there were no reference checks. The CEO said, “We know you’re a good guy, and we want to move fast on you”. As opposed tot he 7-day exploding offers typically served to engineers, Bill had 2 months in which to make his decision. He got a fourth week of vacation without even having to ask for it, and genuine equity (about 75% of a year’s salary vesting each year)...
It was really interesting, as I listened in, to see how different things are once you’re “in the club”. The CEO talked to Bill as an equal, not as a paternalistic, bullshitting, “this is good for your career” authority figure. There was a tone of equality that a software engineer would never get from the CEO of a 100-person tech company.
The author concludes that positions that are labeled as code-monkey-like are low status, while positions that are labeled as managerial are high status. Even if they are "essentially" doing the same sort of work.
Not sure about this methodology, but it's food for thought.
The official story: "Fifty Shades of Grey" was a Twilight fan-fiction that had over two million downloads online. The publishing giant Vintage Press saw that number and realized there was a huge, previously-unrealized demand for stories like this. They filed off the Twilight serial numbers, put it in print, marketed it like hell, and now it's sold 60 million copies.
The reality is quite different.
Still very much a work in progress
Why do we bother about utility functions on Less Wrong? Well, because of results of the New man and the Morning Star, which showed that, essentially, if you make decisions, you better use something equivalent to expected utility maximisation. If you don't, you lose. Lose what? It doesn't matter, money, resources, whatever: the point is that any other system can be exploited by other agents or the universe itself to force you into a pointless loss. A pointless loss being a lose that give you no benefit or possibility of benefit - it's really bad.
The justifications for the axioms of expected utility are, roughly:
- (Completeness) "If you don't decide, you'll probably lose pointlessly."
- (Transitivity) "If your choices form loops, people can make you lose pointlessly."
- (Continuity/Achimedean) This axiom (and acceptable weaker versions of it) is much more subtle that it seems; "No choice is infinity important" is what it seems to say, but " 'I could have been a contender' isn't good enough" is closer to what it does. Anyway, that's a discussion for another time.
- (Independence) "If your choice aren't independent, people can expect to make you lose pointlessly."
Equivalency is not identity
A lot of people believe a subtlety different version of the result:
- If you don't have a utility function, you'll lose pointlessly.
This is wrong. The correct result is:
- If you don't lose pointlessly, then your decisions are equivalent with having a utility function.
There has been some talk of a lack of content being posted to Less Wrong, so I decided to start a series on various experiments that I've tried and what I've learned from them as I believe that experimentation is key to being a rationalist. My first few posts will be adapted from content I've written for /r/socialskills, but as Less Wrong has a broader scope I plan to post some original content too. I hope that this post will encourage other people to share detailed descriptions of the experiments that they have tried as I believe that this is much more valuable than a list of lessons posted outside of the context in which they were learned. If anyone has already posted any similar posts, then I would really appreciate any links.
I used to have a lot of trouble in conversation thinking of things to say. I wanted to be a more interesting person and I noticed that my brother uses his knowledge of a broad range of topics to engage people in conversations, so I wanted to do the same.
I was drawn quite quickly towards facts because of how quickly they can be read. If a piece of trivia takes 10 seconds to read, then you can read 360 in an hour. If only 5% are good, then that's still 18 usable facts per hour. Articles are longer, but have significantly higher chances of teaching you something. It seemed like you should be able to prevent ever running out of things to talk about with a reasonable investment of time. It didn't quite work out this way, but this was the idea.d
Another motivation was that I have always valued intelligence and learning more information made me feel good about myself.
Today I learned: #1 recommended source
The straight dope: Many articles in the archive are quite interesting, but I unsubscribed because I found the more recent ones boring
Cracked: Not the most reliable source and can be a huge time sink, but occasionally there are articles there that will give you 6 or 7 interesting facts in one go
Dr Karl: Science blog
I read through the top 1000 links on Today I learned, the entire archive of the straight dope, maybe half of damn interesting and now I know, half of Karl and all the mythbusters results up to about a year or two ago. We are pretty much talking about months of solid reading.
You probably guessed it, but my return on investment wasn't actually that great. I tended to consume this trivia in ridiculously huge batches because by reading all this information I at least felt like I was doing something. If someone came up to me and asked me for a random piece of trivia - I actually don't have that much that I can pull out. It's actually much easier if someone asks about a specific topic, but there's still not that much I can access.
To test my knowledge I decided to pick the first three topics that came into my head and see how much random trivia I could remember about each. As you can see, the results were rather disappointing:
- Cats can survive falls from a higher number of floors better than a lower number of falls because they have a low terminal velocity and more time to orient themselves to ensure they land on their feet
- House cats can run faster than Ursain bolt
- If you are attacked by a dog the best strategy is to shove your hand down its mouth and attack the neck with your other hand
- Dogs can be trained to drive cars (slowly)
- There is such a thing as the world's ugliest dog competition
- Cheese is poisonous to rats
- The existence of rat kings - rats who got their tails stuck together
Knowing these facts does occasionally help me by giving me something interesting to say when I wouldn't have otherwise had it, but quite often I want to quote one of these facts, but I can't quite remember the details. It's hard to quantify how much this helps me though. There have been a few times when I've been able to get someone interested in a conversation that they wouldn't have otherwise been interested in, but I can also go a dozen conversations without quoting any of these facts. No-one has ever gone "Wow, you know so many facts!". Another motivation I had was that being knowledgeable makes me feel good about myself. I don't believe that there was any significant impact in this regard either - I don't have a strong self-concept of myself as someone who is particularly knowledgeable about random facts. Overall this experiment was quite disappointing given the high time investment.
While the social benefits have been extremely minimal, learning all of these facts has expanded my world view.
- I had no idea how crazy nature was: most surprising fact I've learned is that Bluebottles are multiple organisms
- Some of the stuff that the CIA got up to is unbelievable - you'd almost think it came from a conspiracy theorist
- There are many things that you take for granted, but when you think about it, are actually amazing coincidences - moon and sun appearing around the same size
- You don't want to get on the wrong side of the law as it can be horribly unjust
- The government is pretty careless with nuclear weapons. If we can't trust the government can't look after nukes, what can we trust them to look after?
While this technique worked poorly for me, there are many changes that I could have made that might have improved effectiveness.
- Lower batch sizes: when you read too many facts in one go you get tired and it all tends to blur together
- Notes: I started making notes of the most interesting facts I was finding using Evernote. I regularly add new facts, but only very occasionally go back and actually look them up. I was trying to review the new facts that I learned regularly, but I got busy and just fell out of the habit. Perhaps I could have a separate list for the most important facts I learn every week and this would be less effort?
- Rereading saved facts: I did a complete reread through my saved notes once. I still don't think that I have a very good recall - probably related to batch size!
- Spaced repetition: Many people claim that this make memorisation easy
- Thoughtback: This is a lighter alternative to spaced repetition - it gives you notifications on your phone of random facts - about one per day
- Talking to other people: This is a very effective method for remembering facts. That vast majority of facts that I've shared with other people, I still remember. Perhaps I should create a list of facts that I want to remember and then pick one or two at a time to share with people. Once I've shared them a few times, I could move on to the next fact
- Blog posts - perhaps if I collected some of my related facts into blog posts, having to decide which to include and which to not include my help me remember these facts more
- Pausing: I find that I am more likely to remember things if I pause and think that this is something that I want to remember. I was trying to build that habit, but I didn't succeed in this
- Other memory techniques: brains are better at remembering things if you process them. So if you want to remember the story where thieves stole a whole beach in one night, try to picture the beach and then the shock when some surfer turns up and all the sand is gone. Try to imagine what you'd need to pull that off.
I believe that if I had spread my reading out over a greater period of time, then the cost would have been justified. Part of this would have been improved retention and part of this would have been having a new interesting fact to use in conversation every week that I know I hadn't told anyone else before.
The social benefits are rather minimal, so it would be difficult to get them to match up with the time invested. I believe that with enough refinement, someone could improve their effectiveness to the stage where the benefits matched up with the effort invested, but broadening one's knowledge will always be the primary advantage gained.
The argument is simple. Assume the tool AI is given the task of finding the best plan for achieving some goal. The plan must be realistic and remain within the resources of the AI's controller - energy, money, social power, etc. The best plans are the ones that use these resources in the most effective and economic way to achieve the goal.
And the AI's controller has one special type of resource, uniquely effective at what it does. Namely, the AI itself. It is smart, potentially powerful, and could self-improve and pull all the usual AI tricks. So the best plan a tool AI could come up with, for almost any goal, is "turn me into an agent AI with that goal." The smarter the AI, the better this plan is. Of course, the plan need not read literally like that - it could simply be a complicated plan that, as a side-effect, turns the tool AI into an agent. Or copy the AI's software into a agent design. Or it might just arrange things so that we always end up following the tool AIs advice and consult it often, which is an indirect way of making it into an agent. Depending on how we've programmed the tool AI's preferences, it might be motivated to mislead us about this aspect of its plan, concealing the secret goal of unleashing itself as an agent.
In any case, it does us good to realise that "make me into an agent" is what a tool AI would consider the best possible plan for many goals. So without a hint of agency, it's motivated to make us make it into a agent.
I play Starcraft:BW sometimes with my brothers. One of my brothers is much better than the rest of us combined. This story is typical: In a free-for-all, the rest of us gang up on him, knowing that he is the biggest threat. By sheer numbers we beat him down, but foolishly allow him to escape with a few workers. Despite suffering this massive setback, he rebuilds in hiding and ends up winning due to his ability to tirelessly expand his economy while simultaneously fending off our armies.
This story reminds me of some AI-takeover scenarios. I wonder: Could we make a video game that illustrates many of the core ideas surrounding AGI? For example, a game where the following concepts were (more or less) accurately represented as mechanics:
--AI arms race
--AI friendliness and unfriendliness
--rogue AI and AI takeover
--AI being awesome at epistemology and science and having amazing predictive power
--Interesting conversations between AI and their captors about whether or not they should be unboxed.
I thought about this for a while, and I think it would be feasible and (for some people at least) fun. I don't foresee myself being able to actually make this game any time soon, but I like thinking about it anyway. Here is a sketch of the main mechanics I envision:
(1) The most crucial part of this design is the "Modeling AI Predictive Power" section. This is how we represent the AI's massive advantage in predictive power. However, this comes at the cost of tripling the amount of time the game takes to play. Can you think of a better way to do this?
(2) I'd like AI's to be able to "predict" the messages that players send to each other also. However, it would be too much to ask players to make "Decoy Message Logs." Is it worth dropping the decoy idea (and making the predictions 100% accurate) to implement this?
(3) Any complaints about the skeleton sketched above? Perhaps something is wildly unrealistic, and should be replaced by a different mechanic that more accurately captures the dynamics of AGI?
For what its worth, I spent a reasonable amount of time thinking about the mechanics I used, and I think I could justify their realism. I expect to have made quite a few mistakes, but I wasn't just making stuff up on the fly.
(4) Any other ideas for mechanics to add to the game?
I asked this question on Facebook here, and got some interesting answers, but I thought it would be interesting to ask LessWrong and get a larger range of opinions. I've modified the list of options somewhat.
What explains why some classification, prediction, and regression methods are common in academic social science, while others are common in machine learning and data science?
For instance, I've encountered probit models in some academic social science, but not in machine learning.
The main algorithms that I believe are common to academic social science and machine learning are the most standard regression algorithms: linear regression and logistic regression.
Possibilities that come to mind:
(0) My observation is wrong and/or the whole question is misguided.
(1) The focus in machine learning is on algorithms that can perform well on large data sets. Thus, for instance, probit models may be academically useful but don't scale up as well as logistic regression.
(2) Academic social scientists take time to catch up with new machine learning approaches. Of the methods mentioned above, random forests and support vector machines was introduced as recently as 1995. Neural networks are older but their practical implementation is about as recent. Moreover, the practical implementations of these algorithm in the standard statistical softwares and packages that academics rely on is even more recent. (This relates to point (4)).
(3) Academic social scientists are focused on publishing papers, where the goal is generally to determine whether a hypothesis is true. Therefore, they rely on approaches that have clear rules for hypothesis testing and for establishing statistical significance (see also this post of mine). Many of the new machine learning approaches don't have clearly defined statistical approaches for significance testing. Also, the strength of machine learning approaches is more exploratory than testing already formulated hypotheses (this relates to point (5)).
(4) Some of the new methods are complicated to code, and academic social scientists don't know enough mathematics, computer science, or statistics to cope with the methods (this may change if they're taught more about these methods in graduate school, but the relative newness of the methods is a factor here, relating to (2)).
(5) It's hard to interpret the results of fancy machine learning tools in a manner that yields social scientific insight. The results of a linear or logistic regression can be interpreted somewhat intuitively: the parameters (coefficients) associated with individual features describe the extent to which those features affect the output variable. Modulo issues of feature scaling, larger coefficients mean those features play a bigger role in determining the output. Pairwise and listwise R^2 values provide additional insight on how much signal and noise there is in individual features. But if you're looking at a neural network, it's quite hard to infer human-understandable rules from that. (The opposite direction is not too hard: it is possible to convert human-understandable rules to a decision tree and then to use a neural network to approximate that, and add appropriate fuzziness. But the neural networks we obtain as a result of machine learning optimization may be quite different from those that we can interpret as humans). To my knowledge, there haven't been attempts to reinterpret neural network results in human-understandable terms, though Sebastian Kwiatkowski's comment on my Facebook post points to an example where the results of naive Bayes and SVM classifiers for hotel reviews could be translated into human-understandable terms (namely, reviews that mentioned physical aspects of the hotel, such as "small bedroom", were more likely to be truthful than reviews that talked about the reasons for the visit or the company that sponsored the visit). But Kwiatkowski's comment also pointed to other instances where the machine's algorithms weren't human-interpretable.
What's your personal view on my main question, and on any related issues?
This post explores the question: how strongly should we defer to predictions and forecasts made by people with domain expertise? I'll assume that the domain expertise is legitimate, i.e., the people with domain expertise do have a lot of information in their minds that non-experts don't. The information is usually not secret, and non-experts can usually access it through books, journals, and the Internet. But experts have more information inside their head, and may understand it better. How big an advantage does this give them in forecasting?
Tetlock and expert political judgment
In an earlier post on historical evaluations of forecasting, I discussed Philip E. Tetlock's findings on expert political judgment and forecasting skill, and summarized his own article for Cato Unbound co-authored with Dan Gardner that in turn summarized the themes of the book:
- The average expert’s forecasts were revealed to be only slightly more accurate than random guessing—or, to put more harshly, only a bit better than the proverbial dart-throwing chimpanzee. And the average expert performed slightly worse than a still more mindless competition: simple extrapolation algorithms that automatically predicted more of the same.
- The experts could be divided roughly into two overlapping yet statistically distinguishable groups. One group (the hedgehogs) would actually have been beaten rather soundly even by the chimp, not to mention the more formidable extrapolation algorithm. The other (the foxes) would have beaten the chimp and sometimes even the extrapolation algorithm, although not by a wide margin.
- The hedgehogs tended to use one analytical tool in many different domains; they preferred keeping their analysis simple and elegant by minimizing “distractions.” These experts zeroed in on only essential information, and they were unusually confident—they were far more likely to say something is “certain” or “impossible.” In explaining their forecasts, they often built up a lot of intellectual momentum in favor of their preferred conclusions. For instance, they were more likely to say “moreover” than “however.”
- The foxes used a wide assortment of analytical tools, sought out information from diverse sources, were comfortable with complexity and uncertainty, and were much less sure of themselves—they tended to talk in terms of possibilities and probabilities and were often happy to say “maybe.” In explaining their forecasts, they frequently shifted intellectual gears, sprinkling their speech with transition markers such as “although,” “but,” and “however.”
- It's unclear whether the performance of the best forecasters is the best that is in principle possible.
- This widespread lack of curiosity—lack of interest in thinking about how we think about possible futures—is a phenomenon worthy of investigation in its own right.
Tetlock has since started The Good Judgment Project (website, Wikipedia), a political forecasting competition where anybody can participate, and with a reputation of doing a much better job at prediction than anything else around. Participants are given a set of questions and can basically collect freely available online information (in some rounds, participants were given additional access to some proprietary data). They then use that to make predictions. The aggregate predictions are quite good. For more information, visit the website or see the references in the Wikipedia article. In particular, this Economist article and this Business Insider article are worth reading. (I discussed the GJP and other approaches to global political forecasting in this post).
So at least in the case of politics, it seems that amateurs, armed with basic information plus the freedom to look around for more, can use "fox-like" approaches and do a better job of forecasting than political scientists. Note that experts still do better than ignorant non-experts who are denied access to information. But once you have basic knowledge and are equipped to hunt more down, the constraining factor does not seem to be expertise, but rather, the approach you use (fox-like versus hedgehog-like). This should not be taken as a claim that expertise is irrelevant or unnecessary to forecasting. Experts play an important role in expanding the scope of knowledge and methodology that people can draw on to make their predictions. But the experts themselves, as people, do not have a unique advantage when it comes to forecasting.
Tetlock's research focused on politics. But the claim that the fox-hedgehog distinction turns out to be a better prediction of forecasting performance than the level of expertise is a general one. How true is this claim in domains other than politics? Domains such as climate science, economic growth, computing technology, or the arrival of artificial general intelligence?
Armstrong and Green again
J. Scott Armstrong is a leading figure in the forecasting community. Along with Kesten C. Green, he penned a critique of the forecasting exercises in climate science in 2007, with special focus on the IPCC reports. I discussed the critique at length in my post on the insularity critique of climate science. Here, I quote a part from the introduction of the critique that better explains the general prior that Armstrong and Green claim to be bringing to the table when they begin their evaluation. Of the points they make at the beginning, two bear directly on the deference we should give to expert judgment and expert consensus:
- Unaided judgmental forecasts by experts have no value: This applies whether the opinions are expressed in words, spreadsheets, or mathematical models. It applies regardless of how much scientific evidence is possessed by the experts. Among the reasons for this are:
a) Complexity: People cannot assess complex relationships through unaided observations.
b) Coincidence: People confuse correlation with causation.
c) Feedback: People making judgmental predictions typically do not receive unambiguous feedback they can use to improve their forecasting.
d) Bias: People have difficulty in obtaining or using evidence that contradicts their initial beliefs. This problem is especially serious for people who view themselves as experts.
- Agreement among experts is only weakly related to accuracy: This is especially true when the experts communicate with one another and when they work together to solve problems, as is the case with the IPCC process.
Armstrong and Green later elaborate on these claims, referencing Tetlock's work. (Note that I have removed the parts of the section that involve direct discussion of climate-related forecasts, since the focus here is on the general question of how much deference to show to expert consensus).
Many public policy decisions are based on forecasts by experts. Research on persuasion has shown that people have substantial faith in the value of such forecasts. Faith increases when experts agree with one another. Our concern here is with what we refer to as unaided expert judgments. In such cases, experts may have access to empirical studies and other information, but they use their knowledge to make predictions without the aid of well-established forecasting principles. Thus, they could simply use the information to come up with judgmental forecasts. Alternatively, they could translate their beliefs into mathematical statements (or models) and use those to make forecasts.
Although they may seem convincing at the time, expert forecasts can make for humorous reading in retrospect. Cerf and Navasky’s (1998) book contains 310 pages of examples, such as Fermi Award-winning scientist John von Neumann’s 1956 prediction that “A few decades hence, energy may be free”. [...] The second author’s review of empirical research on this problem led him to develop the “Seer-sucker theory,” which can be stated as “No matter how much evidence exists that seers do not exist, seers will find suckers” (Armstrong 1980). The amount of expertise does not matter beyond a basic minimum level. There are exceptions to the Seer-sucker Theory: When experts get substantial well-summarized feedback about the accuracy of their forecasts and about the reasons why their forecasts were or were not accurate, they can improve their forecasting. This situation applies for short-term (up to five day) weather forecasts, but we are not aware of any such regime for long-term global climate forecasting. Even if there were such a regime, the feedback would trickle in over many years before it became useful for improving forecasting.
Research since 1980 has provided much more evidence that expert forecasts are of no value. In particular, Tetlock (2005) recruited 284 people whose professions included, “commenting or offering advice on political and economic trends.” He asked them to forecast the probability that various situations would or would not occur, picking areas (geographic and substantive) within and outside their areas of expertise. By 2003, he had accumulated over 82,000 forecasts. The experts barely if at all outperformed non-experts and neither group did well against simple rules. Comparative empirical studies have routinely concluded that judgmental forecasting by experts is the least accurate of the methods available to make forecasts. For example, Ascher (1978, p. 200), in his analysis of long-term forecasts of electricity consumption found that was the case.
Note that the claims that Armstrong and Green make are in relation to unaided expert judgment, i.e., expert judgment that is not aided by some form of assistance or feedback that promotes improved forecasting. (One can argue that expert judgment in climate science is not unaided, i.e., that the critique is mis-applied to climate science, but whether that is the case is not the focus of my post). While Tetlock's suggestion to be more fox-like, Armstrong and Green recommend the use of their own forecasting principles, as encoded in their full list of principles and described on their website.
A conflict of intuitions, and an attempt to resolve it
I have two conflicting intuitions here. I like to use the majority view among experts as a reasonable Bayesian prior to start with, that I might then modify based on further study. The relevant question here is who the experts are. Do I defer to the views of domain experts, who may know little about the challenges of forecasting, or do I defer to the views of forecasting experts, who may know little of the domain but argue that domain experts who are not following good forecasting principles do not have any advantage over non-experts?
I think the following heuristics are reasonable starting points:
- In cases where we have a historical track record of forecasts, we can use that to evaluate the experts and non-experts. For instance, I reviewed the track record of survey-based macroeconomic forecasts, thanks to a wealth of recorded data on macroeconomic forecasts by economists over the last few decades. (Unfortunately, these surveys did not include corresponding data on layperson opinion).
- The faster the feedback from making a forecast to knowing whether it's right, the more likely it is that experts would have learned how to make good forecasts.
- The more central forecasting is to the overall goals of the domain, the more likely people are to get it right. For instance, forecasting is a key part of weather and climate science. But forecasting progress on mathematical problems has a negligible relation with doing mathematical research.
- Ceteris paribus, if experts are clearly recording their forecasts and the reasons behind them, and systematically evaluating the performance on past forecasts, that should be taken as (weak) evidence in favor of the experts' views being taken more seriously (even if we don't have enough of a historical track record to properly calibrate forecast accuracy). However, if they simply make forecasts but then fail to review their past history of forecasts, this may be taken as being about as bad as not forecasting at all. And in cases that the forecasts were bold, failed miserably, and yet the errors were not acknowledged, this should be taken as being considerably worse than not forecasting at all.
- A weak inside view of the nature of domain expertise can give some idea of whether expertise should generally translate to better forecasting skill. For instance, even a very weak understanding of physics will tell us that physicists are no more likely to determine whether a coin toss will yield heads or tails, even though the fate of the coin is determined by physics. Similarly, with the exception of economists who specialize in the study of macroeconomic indicators, one wouldn't expect economists to be able to forecast macroeconomic indicators better than most moderately economically informed people.
My first thought was that the more politicized a field, the less reliable any forecasts coming out of it. I think there are obvious reasons for that view, but there are also countervailing considerations.
The main claimed danger of politicization is groupthink and lack of openness to evidence. It could even lead to suppression, misrepresentation, or fabrication of evidence. Quite often, however, we see these qualities in highly non-political fields. People believe that certain answers are the right ones. Their political identity or ego is not attached to it. They just have high confidence that that answer is correct, and when the evidence they have does not match up, they think there is a problem with the evidence. Of course, if somebody does start challenging the mainstream view, and the issue is not quickly resolved either way, it can become politicized, with competing camps of people who hold the mainstream view and people who side with the challengers. Note, however, that the politicization has arguably reduced the aggregate amount of groupthink in the field. Now that there are two competing camps rather than one received wisdom, new people can examine evidence and better decide which camp is more on the side of truth. People in both camps, now that they are competing, may try to offer better evidence that could convince the undecideds or skeptics. So "politicization" might well improve the epistemic situation (I don't doubt that the opposite happens quite often). Examples of such politicization might be the replacement of geocentrism by heliocentrism, the replacement of creationism by evolution, and the replacement of Newtonian mechanics by relativity and/or quantum mechanics. In the first two cases, religious authorities pushed against the new idea, even though the old idea had not been a "politicized" tenet before the competing claims came along. In the case of Newtonian and quantum mechanics, the debate seems to have been largely intra-science, but quantum mechanics had its detractors, including Einstein, famous for the "God does not play dice" quip. (This post on Slate Star Codex is somewhat related).
The above considerations aren't specific to forecasting, and they apply even for assertions that fall squarely within the domain of expertise and require no forecasting skill per se. The extent to which they apply to forecasting problems is unclear. It's unclear whether most domains have any significant groupthink in favor of particular forecasts. In fact, in most domains, forecasts aren't really made or publicly recorded at all. So concerns of groupthink in a non-politicized scenario may not apply to forecasting. Perhaps the problem is the opposite: forecasts are so unimportant in many domains that the forecasts offered by experts are almost completely random and hardly informed in a systematic way by their expert knowledge. Even in such situations, politicization can be helpful, in so far as it makes the issue more salient and might prompt individuals to give more attention to trying to figure out which side is right.
The case of forecasting AI progress
I'm still looking at the case of forecasting AI progress, but for now, I'd like to point people to Luke Muehlhauser's excellent blog post from May 2013 discussing the difficulty with forecasting AI progress. Interestingly, he makes many points similar to those I make here. (Note: Although I had read the post around the time it was published, I hadn't read it recently until I finished drafting the rest of my current post. Nonetheless, my views can't be considered totally independent of Luke's because we've discussed my forecasting contract work for MIRI).
Should we expect experts to be good at predicting AI, anyway? As Armstrong & Sotala (2012) point out, decades of research on expert performance2 suggest that predicting the first creation of AI is precisely the kind of task on which we should expect experts to show poor performance — e.g. because feedback is unavailable and the input stimuli are dynamic rather than static. Muehlhauser & Salamon (2013) add, “If you have a gut feeling about when AI will be created, it is probably wrong.”
On the other hand, Tetlock (2005) points out that, at least in his large longitudinal database of pundit’s predictions about politics, simple trend extrapolation is tough to beat. Consider one example from the field of AI: when David Levy asked 1989 World Computer Chess Championship participants when a chess program would defeat the human World Champion, their estimates tended to be inaccurately pessimistic,8 despite the fact that computer chess had shown regular and predictable progress for two decades by that time. Those who forecasted this event with naive trend extrapolation (e.g. Kurzweil 1990) got almost precisely the correct answer (1997).
Looking for thoughts
I'm particularly interested in thoughts from people on the following fronts:
- What are some indicators you use to determine the reliability of forecasts by subject matter experts?
- How do you resolve the conflict of intuitions between deferring to the views of domain experts and deferring to the conclusion that forecasters have drawn about the lack of utility of domain experts' forecasts?
- In particular, what do you think of the way that "politicization" affects the reliability of forecasts?
- Also, how much value do you assign to agreement between experts when judging how much trust to place in expert forecasts?
- Comments that elaborate on these questions or this general topic within the context of a specific domain or domains would also be welcome.
One of many problems with the contemporary university system is that the same institutions that educate students also give them their degrees and grades. This obviously creates massive incentives for grade inflation and lowering of standards. Giving a thorough education requires hard work not only from students but also from the professors. In the absence of an independent body that tests that the students actually have learnt what they are supposed to have learnt, many professors spend as little time as possible at teaching, giving the students light workloads (something most of them of course happily accept). The faculty/student non-aggression pact is an apt term for this.
To see how absurd this system is, imagine that we would have the same system for drivers' licenses: that the driving schools that train prospective drivers also tested them and issued their drivers' licenses. In such a system, people would most probably chose the most lenient schools, leading to a lowering of standards. For fear of such a lowering of standards, prospective drivers are in many countries (I would guess universally but do not know that for sure) tested by government bodies.
Presumably, the main reason for this is that governments really care about the lowering of drivers' standards. Ensuring that all drivers are appropriately educated (i.e. is seen as very important. By contrast, the governments don't care that much about the lowering of academic standards. If they would, they would long ago have replaced a present grading/certification system with one where students are tested by independent bodies, rather than by the universities themselves.
This is all the more absurd given how much politicians in most countries talk about the importance of education. More often than not they talk about education, especially higher education, as a panacea to cure for all ills. However, if we look at the politicians' actions, rather than at their words, it doesn't seem like they actually do think it's quite as important as they say to ensure that the population is well-educated.
Changing the system for certifying students is important not the least in order to facilitate inventions in higher education. The present system discriminates in favour of traditional campus courses, which are both expensive and fail to teach the students as much as they should. I'm not saying that online courses, and other non-standard courses, are necessarily better or more cost-effective, but they should get the chance to prove that they are.
The system is of course hard to change, since there are lots of vested interests that don't want it to change. This is nicely illustrated by the reactions to a small baby-step towards the system that I'm envisioning that OECD is presently trying to take. Financial Times (which has a paywall, unfortunately) reports that OECD are attempting to introduce Pisa-style tests to compare students from higher education institutions around the world. Third year students would be tested on critical thinking, analytical reasoning, problem solving and written communcation. There would also be discipline-specific trials for economics and engineering.
These attempts have, however, not progressed because of resistance from some universities and member countries. OECD says that the resistance often comes from "the most prestigious institutions, because they have very little to win...and a lot to lose". In contrast, "the greatest supporters are the ones that add the greatest value...many of the second-tier institutes are actually a lot better and they're very keen to get on a level playing field."
I figure that if OECD get enough universities on board, they could start implementing the system without the obstructing top universities. They could also allow students from those universities to take the tests independently. If employers started taking these tests seriously, students would have every reason to take them even if their universities haven't joined. Slowly, these presumably more objective tests, or others like them, would become more important at the cost of the universities' inflated grades. People often try to change institutions or systems directly, but sometimes it is more efficient to build alternative systems, show that their useful to the relevant actors, and start out-competing the dominant system (as discussed in these comments).
This is a somewhat long and rambling post. Apologies for the length. I hope the topic and content are interesting enough for you to forgive the meandering presentation.
I blogged about the scenario planning method a while back, where I linked to many past examples of scenario planning exercises. In this post, I take a closer look at scenario analysis in the context of understanding the possibilities for the unfolding of technological progress over the next 10-15 years. Here, I will discuss some predetermined elements and critical uncertainties, offer my own scenario analysis, and then discuss scenario analyses by others.
Remember: it is not the purpose of scenario analysis to identify a set of mutually exclusive and collectively exhaustive outcomes. In fact, usually, the real-world outcome has some features from two or more of the scenarios considered, with one scenario dominating somewhat. As I noted in my earlier post:
The utility of scenario analysis is not merely in listing a scenario that will transpire, or a collection of scenarios a combination of which will transpire. The utility is in how it prepares the people undertaking the exercise for the relevant futures. One way it could so prepare them is if the early indicators of the scenarios are correctly chosen and, upon observing them, people are able to identify what scenario they're in and take the appropriate measures quickly. Another way is by identifying some features that are common to all scenarios, though the details of the feature may differ by scenario. We can therefore have higher confidence in these common features and can make plans that rely on them.
The predetermined element: the imminent demise of Moore's law "as we know it"
As Steven Schnaars noted in Megamistakes (discussed here), forecasts of technological progress in most domains have been overoptimistic, but in the domain of computing, they've been largely spot-on, mostly because the raw technology has improved quickly. The main reason has been Moore's law, and a couple other related laws, that have undergirded technological progress. But now, the party is coming to an end! The death of Moore's law (as we know it) is nigh, and there are significant implications for the future of computing.
Moore's law refers to many related claims about technological progress. Some forms of this technological progress have already stalled. Other forms are slated to stall in the near future, barring unexpected breakthroughs. These facts about Moore's law form the backdrop for all our scenario planning.
The critical uncertainty arises in how industry will respond to the prospect of Moore's law death. Will there be a doubling down on continued improvement at the cutting edge? Will the battle focus on cost reductions? Or will we have neither cost reduction nor technological improvement? What sort of pressure will hardware stagnation put on software?
Now, onto a description of the different versions of Moore's law (slightly edited version of information from Wikipedia):
Density at minimum cost per transistor. This is the formulation given in Moore's 1965 paper. It is not just about the density of transistors that can be achieved, but about the density of transistors at which the cost per transistor is the lowest. As more transistors are put on a chip, the cost to make each transistor decreases, but the chance that the chip will not work due to a defect increases. In 1965, Moore examined the density of transistors at which cost is minimized, and observed that, as transistors were made smaller through advances in photolithography, this number would increase at "a rate of roughly a factor of two per year".
Dennard scaling. This suggests that power requirements are proportional to area (both voltage and current being proportional to length) for transistors. Combined with Moore's law, performance per watt would grow at roughly the same rate as transistor density, doubling every 1–2 years. According to Dennard scaling transistor dimensions are scaled by 30% (0.7x) every technology generation, thus reducing their area by 50%. This reduces the delay by 30% (0.7x) and therefore increases operating frequency by about 40% (1.4x). Finally, to keep electric field constant, voltage is reduced by 30%, reducing energy by 65% and power (at 1.4x frequency) by 50%. Therefore, in every technology generation transistor density doubles, circuit becomes 40% faster, while power consumption (with twice the number of transistors) stays the same.
So how are each of these faring?
- Transistors per integrated circuit: At least in principle, this can continue for a decade or so. The technological ideas exist to publish transistor sizes down from the current values of 32 nm and 28 nm all the way down to 7 nm.
- Density at minimum cost per transistor. This is probably stopping around now. There is good reason to believe that, barring unexpected breakthroughs, the transistor size for which we have minimum cost per transistor shall not go down below 28 nm. There may still be niche applications that benefit from smaller transistor sizes, but there will be no overwhelming economic case to switch production to smaller transistor sizes (i.e., higher densities).
- Dennard scaling. This broke down around 2005-2007. So for approximately a decade, we've essentially seen continued miniaturization but without any corresponding improvement in processor speed or performance per watt. There have been continued overall improvements in energy efficiency of computing, but not through this mechanism. The absence of automatic speed improvements has led to increased focus on using greater parallelization (note that the miniaturization means more parallel processors can be packed in the same space, so Moore's law is helping in this other way). In particular, there has been an increased focus on multicore processors, though there may be limits to how far that can take us too.
Moore's law isn't the only law that is slated to end. Other similar laws, such as Kryder's law (about the cost of hard disk space) may also end in the near future. Koomey's law on energy efficiency may also stall, or might continue to hold but through very different mechanisms compared to the ones that have driven it so far.
Some discussions that do not use explicit scenario analysis
The quotes below are to give a general idea of what people seem to generally agree on, before we delve into different scenarios.
We have been hearing about the imminent demise of Moore's Law quite a lot recently. Most of these predictions have been targeting the 7nm node and 2020 as the end-point. But we need to recognize that, in fact, 28nm is actually the last node of Moore's Law.
Summarizing all of these factors, it is clear that -- for most SoCs -- 28nm will be the node for "minimum component costs" for the coming years. As an industry, we are facing a paradigm shift because dimensional scaling is no longer the path for cost scaling. New paths need to be explored such as SOI and monolithic 3D integration. It is therefore fitting that the traditional IEEE conference on SOI has expanded its scope and renamed itself as IEEE S3S: SOI technology, 3D Integration, and Subthreshold Microelectronics.
Computer scientist Moshe Yardi writes:
So the real question is not when precisely Moore's Law will die; one can say it is already a walking dead. The real question is what happens now, when the force that has been driving our field for the past 50 years is dissipating. In fact, Moore's Law has shaped much of the modern world we see around us. A recent McKinsey study ascribed "up to 40% of the global productivity growth achieved during the last two decades to the expansion of information and communication technologies made possible by semiconductor performance and cost improvements." Indeed, the demise of Moore's Law is one reason some economists predict a "great stagnation" (see my Sept. 2013 column).
"Predictions are difficult," it is said, "especially about the future." The only safe bet is that the next 20 years will be "interesting times." On one hand, since Moore's Law will not be handing us improved performance on a silver platter, we will have to deliver performance the hard way, by improved algorithms and systems. This is a great opportunity for computing research. On the other hand, it is possible that the industry would experience technological commoditization, leading to reduced profitability. Without healthy profit margins to plow into research and development, innovation may slow down and the transition to the post-CMOS world may be long, slow, and agonizing.
However things unfold, we must accept that Moore's Law is dying, and we are heading into an uncharted territory.
"I drive a 1964 car. I also have a 2010. There's not that much difference -- gross performance indicators like top speed and miles per gallon aren't that different. It's safer, and there are a lot of creature comforts in the interior," said Nvidia Chief Scientist Bill Dally. If Moore's Law fizzles, "We'll start to look like the auto industry."
Three critical uncertainties: technological progress, demand for computing power, and interaction with software
Uncertainty #1: Technological progress
Moore's law is dead, long live Moore's law! Even if Moore's law as originally stated is no longer valid, there are other plausible computing advances that would preserve the spirit of the law.
Minor modifications of current research (as described in EETimes) include:
- Improvements in 3D circuit design (Wikipedia), so that we can stack multiple layers of circuits one on top of the other, and therefore pack more computing power per unit volume.
- Improvements in understanding electronics at the nanoscale, in particular understanding subthreshold leakage (Wikipedia) and how to tackle it.
Then, there are possibilities for totally new computing paradigms. These have fairly low probability, and are highly unlikely to become commercially viable within 10-15 years. Each of these offers an advantage over currently available general-purpose computing only for special classes of problems, generally those that are parallelizable in particular ways (the type of parallelizability needed differs somewhat between the computing paradigms).
- Quantum computing (Wikipedia) (speeds up particular types of problems). Quantum computers already exist, but the current ones can tackle only a few qubits. Currently, the best known quantum computers in action are those maintained at the Quantum AI Lab (Wikipedia) run jointly by Google, NASA. and USRA. It is currently unclear how to manufacture quantum computers with a larger number of qubits. It's also unclear how the cost will scale in the number of qubits. If the cost scales exponentially in the number of qubits, then quantum computing will offer little advantage over classical computing. Ray Kurzweil explains this as follows:
A key question is: how difficult is it to add each additional qubit? The computational power of a quantum computer grows exponentially with each added qubit, but if it turns out that adding each additional qubit makes the engineering task exponentially more difficult, we will not be gaining any leverage. (That is, the computational power of a quantum computer will be only linearly proportional to the engineering difficulty.) In general, proposed methods for adding qubits make the resulting systems significantly more delicate and susceptible to premature decoherence.
Kurzweil, Ray (2005-09-22). The Singularity Is Near: When Humans Transcend Biology (Kindle Locations 2152-2155). Penguin Group. Kindle Edition.
- DNA computing (Wikipedia)
- Other types of molecular computing (Technology Review featured story from 2000, TR story from 2010)
- Spintronics (Wikipedia): The idea is to store information using the spin of the electron, a quantum property that is binary and can be toggled at zero energy cost (in principle). The main potential utility of spintronics is in data storage, but it could potentially help with computation as well.
- Optical computing aka photonic computing (Wikipedia): This uses beams of photons that store the relevant information that needs to be manipulated. Photons promise to offer higher bandwidth than electrons, the tool used in computing today (hence the name electronic computing).
Uncertainty #2: Demand for computing
Even if computational advances are possible in principle, the absence of the right kind of demand can lead to a lack of financial incentive to pursue the relevant advances. I discussed the interaction between supply and demand in detail in this post.
As that post discussed, demand for computational power at the consumer end is probably reaching saturation. The main source of increased demand will now be companies that want to crunch huge amounts of data in order to more efficiently mine data for insight and offer faster search capabilities to their users. The extent to which such demand grows is uncertain. In principle, the demand is unlimited: the more data we collect (including "found data" that will expand considerably as the Internet of Things grows), the more computational power is needed to apply machine learning algorithms to the data. Since the complexity of many machine learning algorithms grows at least linearly (and in some cases quadratically or cubically) in the data, and the quantity of data itself will probably grow superlinearly, we do expect a robust increase in demand for computing.
Uncertainty #3: Interaction with software
Much of the increased demand for computing, as noted above, does not arise so much from a need for raw computing power by consumers, but a need for more computing power to manipulate and glean insight from large data sets. While there has been some progress with algorithms for machine learning and data mining, the fields are probably far from mature. So an alternative to hardware improvements is improvements in the underlying algorithms. In addition to the algorithms themselves, execution details (such as better use of parallel processing capabilities and more efficient use of idle processor capacity) can also yield huge performance gains.
This might be a good time to note a common belief about software and why I think it's wrong. We often tend to hear of software bloat, and some people subscribe to Wirth's law, the claim that software is getting slower more quickly than hardware is getting faster. I think that there are some softwares that have gotten feature-bloated over time, largely because there are incentives to keep putting out new editions that people are willing to pay money for, and Microsoft Word might be one case of such bloat. For the most part, though, software has been getting more efficient, partly by utilizing the new hardware better, but also partly due to underlying algorithmic improvements. This was one of the conclusions of Katja Grace's report on algorithmic progress (see also this link on progress on linear algebra and linear programming algorithms). There are a few softwares that get feature-bloated and as a result don't appear to improve over time as far as speed goes, but it's arguably the case that people's revealed preferences show that they are willing to put up with the lack of speed improvements as long as they're getting feature improvements.
Computing technology progress over the next 10-15 years: my three scenarios
- Slowdown to ordinary rates of growth of cutting-edge industrial productivity: For the last few decades, several dimensions of computing technology have experienced doublings over time periods ranging from six months to five years. With such fast doubling, we can expect price-performance thresholds for new categories of products to be reached every few years, with multiple new product categories a decade. Consider, for instance, desktops, then laptops, then smartphones, then tablets. If the doubling time reverts to the norm seen in other cutting-edge industrial sectors, namely 10-25 years, then we'd probably see the introduction of revolutionary new product categories only about once a generation. There are already some indications of a possible slowdown, and it remains to be seen whether we see a bounceback.
- Continued fast doubling: The other possibility is that the evidence for a slowdown is largely illusory, and computing technology will continue to experience doublings over timescales of less than five years. There would therefore be scope to introduce new product categories every few years.
- New computing paradigm with high promise, but requiring significant adjustment: This is an unlikely, but not impossible, scenario. Here, a new computing paradigm, such as quantum computing, reaches the realm of feasibility. However, the existing infrastructure of algorithms is ill-designed for quantum computing, and in fact, quantum computing engenders many security protocols while offering its own unbreakable ones. Making good use of this new paradigm requires a massive re-architecting of the world's computing infrastructure.
There are two broad features that are likely to be common to all scenarios:
- Growing importance of algorithms: Scenario (1): If technological progress in computing power stalls, then the pressure for improvements to the algorithms and software may increase. Scenario (2): if technological progress in computing power continues, that might only feed the hunger for bigger data. And as the size of data sets increases, asymptotic performance starts mattering more (the distinction between O(n) and O(n2) matters more when n is large). In both cases, I expect more pressure on algorithms and software, but in different ways: in the case of stalling hardware progress, the focus will be more on improving the software and making minor changes to improve the constants, whereas in the case of rapid hardware progress, the focus will be more on finding algorithms that have better asymptotic (big-oh) performance. Scenario (3): In the case of paradigm shifts, the focus will be on algorithms that better exploit the new paradigm. In all cases, there will need to be some sort of shift toward new algorithms and new code that better exploits the new situation.
- Growing importance of parallelization: Although the specifics of how algorithms will become more important varies between the scenarios, one common feature is that algorithms that can better make parallel use of large numbers of machines will become more important. We have seen parallelization grow in importance over the last 15 years, even as the computing gains for individual processors through Moore's law seems to be plateauing out, while data centers have proliferated in number. However, the full power of parallelization is far from tapped out. Again, parallelization matters for slightly different reasons in different cases. Scenario (1): A slowdown in technological progress would mean that gains in the amount of computation can largely be achieved by scaling up the number of machines. In other words, the usage of computing shifts further in a capital-intensive direction. Parallel computing is important for effective utilization of this capital (the computing resources). Scenario (2): Even in the face of rapid hardware progress, automatic big data generation will likely improve much faster than storage, communication, and bandwidth. This "big data" is too huge to store or even stream on a single machine, so parallel processing across huge clusters of machines becomes important. Scenario (3): Note also that almost all the new computing paradigms currently under consideration (including quantum computing) offer massive advantages for special types of parallelizable problems, so parallelization matters even in the case of a paradigm shift in computing.
Other scenario analyses
McKinsey carried out a scenario analysis here, focused more on the implications for the semiconductor manufacturing industry than for users of computing. The report notes the importance of Moore's law in driving productivity improvements over the last few decades:
As a result, Moore’s law has swept much of the modern world along with it. Some estimates ascribe up to 40 percent of the global productivity growth achieved during the last two decades to the expansion of information and communication technologies made possible by semiconductor performance and cost improvements.
The scenario analysis identifies four potential sources of innovation related to Moore's law:
- More Moore (scaling)
- Wafer-size increases (maximize productivity)
- More than Moore (functional diversification)
- Beyond CMOS (new technologies)
Their scenario analysis uses a 2 X 2 model, with the two dimensions under consideration being performance improvements (continue versus stop) and cost improvements (continue versus stop). The case that both performance improvements and cost improvements continue is the "good" case for the semiconductor industry. The case that both stop is the case where the industry is highly likely to get commodified, with profit margins going down and small players catching up to the big ones. In the intermediate cases (where one of the two continues and the other stops), consolidation of the semiconductor industry is likely to continue, but there is still a risk of falling demand.
The McKinsey scenario analysis was discussed by Timothy Taylor on his blog, The Conversable Economist, here.
Roland Berger carried out a detailed scenario analysis focused on the "More than Moore" strategy here.
Blegging for missed scenarios, common features and early indicators
Are there scenarios that the analyses discussed above missed? Are there some types of scenario analysis that we didn't adequately consider? If you had to do your own scenario analysis for the future of computing technology and hardware progress over the next 10-15 years, what scenarios would you generate?
As I noted in my earlier post:
The utility of scenario analysis is not merely in listing a scenario that will transpire, or a collection of scenarios a combination of which will transpire. The utility is in how it prepares the people undertaking the exercise for the relevant futures. One way it could so prepare them is if the early indicators of the scenarios are correctly chosen and, upon observing them, people are able to identify what scenario they're in and take the appropriate measures quickly. Another way is by identifying some features that are common to all scenarios, though the details of the feature may differ by scenario. We can therefore have higher confidence in these common features and can make plans that rely on them.
I already identified some features I believe to be common to all scenarios (namely, increased focus on algorithms, and increased focus on parallelization). Do you agree with my assessment that these are likely to matter regardless of scenario? Are there other such common features you have high confidence in?
If you generally agree with one or more of the scenario analyses here (mine or McKinsey's or Roland Berger's), what early indicators would you use to identify which of the enumerated scenarios we are in? Is it possible to look at how events unfold over the next 2-3 years and draw intelligent conclusions from that about the likelihood of different scenarios?
Applied Causal Inference for Empirical Research
This sequence is an introduction to basic causal inference. It was originally written as auxiliary notes for a course in Epidemiology, but it is relevant to almost any kind of applied statistical and empirical research, including econometrics, sociology, psychology, political science etc. I would not be surprised if you guys find a lot of errors, and I would be very grateful if you point them out in the comments. This will help me improve my course notes and potentially help me improve my understanding of the material.
For mathematically inclined readers, I recommend skipping this sequence and instead reading Pearl's book on Causality. There is also a lot of good material on causal graphs on Less Wrong itself. Also, note that my thesis advisor is writing a book that covers the same material in more detail, the first two parts are available for free at his website.
Pearl's book, Miguel's book and Eliezer's writings are all more rigorous and precise than my sequence. This is partly because I have a different goal: Pearl and Eliezer are writing for mathematicians and theorists who may be interested in contributing to the theory. Instead, I am writing for consumers of science who want to understand correlation studies from the perspective of a more rigorous epistemology.
I will use Epidemiological/Counterfactual notation rather than Pearl's notation. I apologize if this is confusing. These two approaches refer to the same mathematical objects, it is just a different notation. Whereas Pearl would use the "Do-Operator" E[Y|do(a)], I use counterfactual variables E[Ya]. Instead of using Pearl's "Do-Calculus" for identification, I use Robins' G-Formula, which will give the same results.
For all applications, I will use the letter "A" to represent "treatment" or "exposure" (the thing we want to estimate the effect of), Y to represent the outcome, L to represent any measured confounders, and U to represent any unmeasured confounders.
Outline of Sequence:
I hope to publish one post every week. I have rough drafts for the following eight sections, and will keep updating this outline with links as the sequence develops:
Part 0: Sequence Announcement / Introduction (This post)
Part 1: Basic Terminology and the Assumptions of Causal Inference
Part 2: Graphical Models
Part 3: Using Causal Graphs to Understand Bias
Part 4: Time-Dependent Exposures
Part 5: The G-Formula
Part 6: Inverse Probability Weighting
Part 7: G-Estimation of Structural Nested Models and Instrumental Variables
Part 8: Single World Intervention Graphs, Cross-World Counterfactuals and Mediation Analysis
Introduction: Why Causal Inference?
The goal of applied statistical research is almost always to learn about causal effects. However, causal inference from observational is hard, to the extent that it is usually not even possible without strong, almost heroic assumptions. Because of the inherent difficulty of the task, many old-school investigators were trained to avoid making causal claims. Words like “cause” and “effect” were banished from polite company, and the slogan “correlation does not imply causation” became an article of faith which, when said loudly enough, seemingly absolved the investigators from the sin of making causal claims.
However, readers were not fooled: They always understood that epidemiologic papers were making causal claims. Of course they were making causal claims; why else would anybody be interested in a paper about the correlation between two variables? For example, why would anybody want to know about the correlation between eating nuts and longevity, unless they were wondering if eating nuts would cause them to live longer?
When readers interpreted these papers causally, were they simply ignoring the caveats, drawing conclusions that were not intended by the authors? Of course they weren’t. The discussion sections of epidemiologic articles are full of “policy implications” and speculations about biological pathways that are completely contingent on interpreting the findings causally. Quite clearly, no matter how hard the investigators tried to deny it, they were making causal claims. However, they were using methodology that was not designed for causal questions, and did not have a clear language for reasoning about where the uncertainty about causal claims comes from.
This was not sustainable, and inevitably led to a crisis of confidence, which culminated when some high-profile randomized trials showed completely different results from the preceding observational studies. In one particular case, when the Women’s Health Initiative trial showed that post-menopausal hormone replacement therapy increases the risk of cardiovascular disease, the difference was so dramatic that many thought-leaders in clinical medicine completely abandoned the idea of inferring causal relationships from observational data.
It is important to recognize that the problem was not that the results were wrong. The problem was that there was uncertainty that was not taken seriously by the investigators. A rational person who wants to learn about the world will be willing to accept that studies have errors of margin, but only as long as the investigators make a good-faith effort to examine what the sources of error are, and as long as they communicate clearly about this uncertainty to their readers. Old-school epidemiology failed at this. We are not going to make the same mistake. Instead, we are going to develop a clear, precise language for reasoning about uncertainty and bias.
In this context, we are going to talk about two sources of uncertainty – “statistical” uncertainty and “epidemiological” uncertainty.
We are going to use the word “Statistics” to refer to the theory of how we can learn about correlations from limited samples. For statisticians, the primary source of uncertainty is sampling variability. Statisticians are very good at accounting for this type of uncertainty: Concepts such as “standard errors”, “p-values” and “confidence intervals” are all attempts at quantifying and communicating the extent of uncertainty that results from sampling variability.
The old school of epidemiology would tell you to stop after you had found the correlations and accounted for the sampling variability. They believed going further was impossible. However, correlations are simply not interesting. If you truly believed that correlations tell you nothing about causation, there would be no point in doing the study.
Therefore, we are going to use the terms “Epidemiology” or “Causal Inference” to refer to the next stage in the process: Learning about causation from correlations. This is a much harder problem, with many additional sources of uncertainty, including confounding and selection bias. However, recognizing that the problem is hard does not mean that you shouldn't try, it just means that you have to be careful. As we will see, it is possible to reason rigorously about whether correlation really does imply causation in your particular study: You will just need a precise language. The goal of this sequence is simply to give you such a language.
In order to teach you the logic of this language, we are going to make several controversial statements such as «The only way to estimate a causal effect is to run a randomized controlled trial» . You may not be willing to believe this at first, but in order to understand the logic of causal inference, it is necessary that you are at least willing to suspend your disbelief and accept it as true within the course.
It is important to note that we are not just saying this to try to convince you to give up on observational studies in favor of randomized controlled trials. We are making this point because understanding it is necessary in order to appreciate what it means to control for confounding: It is not possible to give a coherent meaning to the word “confounding” unless one is trying to determine whether it is reasonable to model the data as if it came from a complex randomized trial run by nature.
When we say that causal inference is hard, what we mean by this is not that it is difficult to learn the basics concepts of the theory. What we mean is that even if you fully understand everything that has ever been written about causal inference, it is going to be very hard to infer a causal relationship from observational data, and that there will always be uncertainty about the results. This is why this sequence is not going to be a workshop that teaches you how to apply magic causal methodology. What we are interested in, is developing your ability to reason honestly about where uncertainty and bias comes from, so that you can communicate this to the readers of your studies. We want to teach you about, is the epistemology that underlies epidemiological and statistical research with observational data.
Insisting on only using randomized trials may seem attractive to a purist, it does not take much imagination to see that there are situations where it is important to predict the consequences of an action, but where it is not possible to run a trial. In such situations, there may be Bayesian evidence to be found in nature. This evidence comes in the form of correlations in observational data. When we are stuck with this type of evidence, it is important that we have a clear framework for assessing the strength of the evidence.
I am publishing Part 1 of the sequence at the same time as this introduction. I would be very interested in hearing feedback, particularly about whether people feel this has already been covered in sufficient detail on Less Wrong. If there is no demand, there won't really be any point in transforming the rest of my course notes to a Less Wrong format.
Thanks to everyone who had a look at this before I published, including paper-machine and Vika, Janos, Eloise and Sam from the Boston Meetup group.
WARNING: Memetic hazard.
Is there anything we should do?
If your 5-year-old seems to have an unhealthy appetite for chocolate, you’d take measures to prevent them from consuming it. Any time they’d ask you to buy them some, you’d probably refuse their request, even if they begged. You might make sure that any chocolate in the house is well-hidden and out of their reach. You might even confiscate chocolate they already have, like if you forced them to throw out half their Halloween candy. You’d almost certainly trigger a temper tantrum and considerably worsen their mood. But no one would label you an unrelenting tyrant. Instead, you’d be labeled a good parent.
Your 5-year-old isn’t expected to have the capacity to understand the consequences to their actions, let alone have the efficacy to accomplish the actions they know are right. That’s why you’re a good parent when you force them to do the right actions, even against their explicit desires.
You know chocolate is a superstimulus and that 5-year-olds have underdeveloped mental executive functions. You have good reasons to believe that your child’s chocolate obsession isn’t caused by their agency, and instead caused by an obsolete evolutionary adaptation. But from your child’s perspective, desiring and eating chocolate is an exercise in agency. They’re just unaware of how their behaviors and desires are suboptimal. So by removing their ability to act upon their explicit desires, you’re denying their agency.
So far, denying agency doesn’t seem so bad. You have good reason to believe your child isn’t capable of acting rationally and you’re only helping them in the long run. But the ethicality gets murky when your assessment of their rationality is questionable.
Imagine you and your mother have an important flight to catch 2 hours from now. You realize that you have to leave to the airport now in order to make it on time. As you’re about to leave, you recalled the 2 beers you recently consumed. But you feel the alcohol left in your system will barely affect your driving, if at all. The problem is that if your mother found out about your beer consumption, she’d refuse to be your passenger until you completely sobered up - as she’s done in the past. You know this would cause you to miss your flight because she can’t drive and there are no other means of transportation.
A close family member died in a drunk driving accident several years ago and, ever since, she overreacts to drinking and driving risks. You think her reaction is irrational and reveals she has non-transitive preferences. For example, one time she was content on being your passenger after you warned her you were sleep deprived and your driving might be affected. Another time she refused to be your passenger after finding out you had one cocktail that hardly affected you. She’s generally a rational person, but with the recent incident and her past behavior, you deem her incapable of having a calibrated reaction. With all this in mind, you contemplate the ethicality of denying her agency by not telling her about your beer drinking.
Similar to the scenario with your 5-year-old, your intention is to ultimately help the person whose agency you’re denying. But in the scenario with your mother, it’s less clear whether you have enough information or are rational enough yourself to assess your mother’s capacity to act within her preferences. Humans are notoriously good at self-deception and rationalizing their actions. Your motivation to catch your flight might be making you irrational about how much alcohol affects your driving. Or maybe the evidence you collected against her rationality is skewed by confirmation bias. If you’re wrong about your assessment, you’d be disrespecting her wishes.
I can modify the scenario to make its ethicality even murkier. Imagine your mother wasn’t catching the plane with you. Instead, you promised to drive her back to her retirement home before your flight. You don’t want to break your promise nor miss your flight, so you contemplate not telling her about your beer consumption.
In this modified version, you’re not actually making your mother better off by denying her agency - you’re only benefiting yourself. You just believe her reaction to your beer consumption isn’t calibrated, and it would cause you to miss your flight. Even if you had plenty of evidence to back up your assessment of her rationality, would it be ethical to deny her agency when it’s only benefiting you?
What are some times you’ve denied someone’s agency? What are your justifications for doing so?
To quickly escape the great filter should we flood our galaxy with radio signals? While communicating with fellow humans we already send out massive amounts of information that an alien civilization could eventually pickup, but should we engage in positive SETI? Or, if you fear the attention of dangerous aliens, should we set up powerful long-lived solar or nuclear powered automated radio transmitters in the desert and in space that stay silent so long as they receive a yearly signal from us, but then if they fail to get the no-go signal because our civilization has fallen, continuously transmit our dead voice to the stars? If we do destroy ourselves it would be an act of astronomical altruism to warn other civilizations of our fate especially if we broadcasted news stories from just before our demise, e.g. physicists excited about a new high energy experiment.
This is an exposition of some of the main ideas in the paper Robust Cooperation. My goal is to make the ideas and proofs seem natural and intuitive - instead of some mysterious thing where we invoke Löb's theorem at the right place and the agents magically cooperate. Also I hope it is accessible to people without a math or CS background. Be warned, it is pretty cheesy ok.
In a small quirky town, far away from other cities or towns, the most exciting event is a game called (for historical reasons) The Prisoner's Dilemma. Everyone comes out to watch the big tournament at the end of Summer, and you (Alice) are especially excited because this year it will be your first time playing in the tournament! So you've been thinking of ways to make sure that you can do well.
The way the game works is this: Each player can choose to cooperate or defect with the other player. If you both cooperate, then you get two points each. If one of you defects, then that player will get three points, and the other player won't get any points. But if you both defect, then you each get only one point. You have to make your decisions separately, without communicating with each other - however, everyone is required to register the algorithm they will be using before the tournament, and you can look at the other player's algorithm if you want to. You also are allowed to use some outside help in your algorithm.
Now if you were a newcomer, you might think that no matter what the other player does, you can always do better by defecting. So the best strategy must be to always defect! Of course, you know better, if everyone tried that strategy, then they would end up defecting against each other, which is a shame since they would both be better off if they had just cooperated.
But how can you do better? You have to be able to describe your algorithm in order to play. You have a few ideas, and you'll be playing some practice rounds with your friend Bob soon, so you can try them out before the actual tournament.
Your first plan:
I'll cooperate with Bob if I can tell from his algorithm that he'll cooperate with me. Otherwise I'll defect.
For your first try, you'll just run Bob's algorithm and see if he cooperates. But there's a problem - if Bob tries the same strategy, he'll have to run your algorithm, which will run his algorithm again, and so on into an infinite loop!
So you'll have to be a bit more clever than that... luckily you know a guy, Shady, who is good at these kinds of problems.
You call up Shady, and while you are waiting for him to come over, you remember some advice your dad Löb gave you.
(Löb's theorem) "If someone says you can trust them on X, well then they'll just tell you X."
If (someone tells you If [I tell you] X, then X is true)
Then (someone tells you X is true)
(See The Cartoon Guide to Löb's Theorem[pdf] for a nice proof of this)
Here's an example:
Sketchy watch salesman: Hey, if I tell you these watches are genuine then they are genuine!
You: Ok... so are these watches genuine?
Sketchy watch salesman: Of course!
It's a good thing to remember when you might have to trust someone. If someone you already trust tells you you can trust them on something, then you know that something must be true.
On the other hand, if someone says you can always trust them, well that's pretty suspicious... If they say you can trust them on everything, that means that they will never tell you a lie - which is logically equivalent to them saying that if they were to tell you a lie, then that lie must be true. So by Löb's theorem, they will lie to you. (Gödel's second incompleteness theorem)
Despite his name, you actually trust Shady quite a bit. He's never told you or anyone else anything that didn't end up being true. And he's careful not to make any suspiciously strong claims about his honesty.
So your new plan is to ask Shady if Bob will cooperate with you. If so, then you will cooperate. Otherwise, defect. (FairBot)
It's game time! You look at Bob's algorithm, and it turns out he picked the exact same algorithm! He's going to ask Shady if you will cooperate with him. Well, the first step is to ask Shady, "will Bob cooperate with me?"
Shady looks at Bob's algorithm and sees that if Shady says you cooperate, then Bob cooperates. He looks at your algorithm and sees that if Shady says Bob cooperates, then you cooperate. Combining these, he sees that if he says you both cooperate, then both of you will cooperate. So he tells you that you will both cooperate (your dad was right!)
Let A stand for "Alice cooperates with Bob" and B stand for "Bob cooperates with Alice".
From looking at the algorithms, and .
So combining these, .
Then by Löb's theorem, .
Since that means that Bob will cooperate, you decide to actually cooperate.
Bob goes through an analagous thought process, and also decides to cooperate. So you cooperate with each other on the prisoner's dilemma! Yay!
That night, you go home and remark, "it's really lucky we both ended up using Shady to help us, otherwise that wouldn't have worked..."
Your dad interjects, "Actually, it doesn't matter - as long as they were both smart enough to count, it would work. This doesn't just say 'I tell you X', it's stronger than that - it actually says 'Anyone who knows basic arithmetic will tell you X'. So as long as they both know a little arithmetic, it will still work - even if one of them is pro-axiom-of-choice, and the other is pro-axiom-of-life. The cooperation is robust." That's really cool!
But there's another issue you think of. Sometimes, just to be tricky, the tournament organizers will set up a game where you have to play against a rock. Yes, literally just a rock that holding the cooperate button down. If you played against a rock with your current algorithm, well you start by asking Shady if the rock will cooperate with you. Shady is like, "well yeah, duh." So then you cooperate too. But you could have gotten three points by defecting! You're missing out on a totally free point!
You think that it would be a good idea to make sure the other player isn't a complete idiot before you cooperate with them. How can you check? Well, let's see if they would cooperate with a rock placed on the defect button (affectionately known as 'DefectRock'). If they know better than that, and they will cooperate with you, then you will cooperate with them.
The next morning, you excitedly tell Shady about your new plan. "It will be like before, except this time, I also ask you if the other player will cooperate with DefectRock! If they are dumb enough to do that, then I'll just defect. That way, I can still cooperate with other people who use algorithms like this one, or the one from before, but I can also defect and get that extra point when there's just a rock on cooperate."
Shady get's an awkward look on his face, "Sorry, but I can't do that... or at least it wouldn't work out the way you're thinking. Let's say you're playing against Bob, who is still using the old algorithm. You want to know if Bob will cooperate with DefectRock, so I have to check and see if I'll tell Bob that DefectRock will cooperate with him. I would have say I would never tell Bob that DefectRock will cooperate with him. But by Löb's theorem, that means I would tell you this obvious lie! So that isn't gonna work."
Notation, if X cooperates with Y in the prisoner's dilemma (or = D if not).
You ask Shady, does ?
Bob's algorithm: only if .
So to say , we would need .
This is equivalent to , since is an obvious lie.
By Löb's theorem, , which is a lie.
<Extra credit: does the fact that Shady is the one explaining this mean you can't trust him?>
<Extra extra credit: find and fix the minor technical error in the above argument.>
Shady sees the dismayed look on your face and adds, "...but, I know a guy who can vouch for me, and I think maybe that could make your new algorithm work."
So Shady calls his friend T over, and you work out the new details. You ask Shady if Bob will cooperate with you, and you ask T if Bob will cooperate with DefectRock. So T looks at Bob's algorithm, which asks Shady if DefectRock will cooperate with him. Shady, of course, says no. So T sees that Bob will defect against DefectRock, and lets you know. Like before, Shady tells you Bob will cooperate with you, and thus you decide to cooperate! And like before, Bob decides to cooperate with you, so you both cooperate! Awesome! (PrudentBot)
If Bob is using your new algorithm, you can see that the same argument goes through mostly unchanged, and that you will still cooperate! And against a rock on cooperate, T will tell you that it will cooperate with DefectRock, so you can defect and get that extra point! This is really great!!
(ok now it's time for the really cheesy ending)
It's finally time for the tournament. You have a really good feeling about your algorithm, and you do really well! Your dad is in the audience cheering for you, with a really proud look on his face. You tell your friend Bob about your new algorithm so that he can also get that extra point sometimes, and you end up tying for first place with him!
A few weeks later, Bob asks you out, and you two start dating. Being able to cooperate with each other robustly is a good start to a healthy relationship, and you live happily ever after!
In decision theory, we often talk about programs that know their own source code. I'm very confused about how that theory applies to people, or even to computer programs that don't happen to know their own source code. I've managed to distill my confusion into three short questions:
1) Am I uncertain about my own source code?
2) If yes, what kind of uncertainty is that? Logical, indexical, or something else?
3) What is the mathematically correct way for me to handle such uncertainty?
Don't try to answer them all at once! I'll be glad to see even a 10% answer to one question.
I think there's widespread assent on LW that the sequences were pretty awesome. Not only do they elucidate upon a lot of useful concepts, but they provide useful shorthand terms for those concepts which help in thinking and talking about them. When I see a word or phrase in a sentence which, rather than doing any semantic work, simply evokes a positive association to the reader, I have the useful handle of "applause light" for it. I don't have to think "oh, there's one of those...you know...things where a word isn't doing any semantic work but just evokes a positive association the reader". This is a common enough pattern that having the term "applause light" is tremendously convenient.
I would like this thread to be a location where people propose such patterns in comments, and respondents determine (a) whether this pattern actually exists and / or is useful; (b) whether there is already a term or sufficiently-related concept that adequately describes it; and (c) what a useful / pragmatic / catchy term might be for it, if none exists already.
I would like to propose some rules suggested formatting to make this go more smoothly.
(ETA: feel free to ignore this and post however you like, though)
When proposing a pattern, include a description of the general case as well as at least one motivating example. This is useful for establishing what you think the general pattern is, and why you think it matters. For instance:
When someone uses a term without any thought to what that term means in context, but to elicit a positive association in their audience.
I was at a conference where someone said AI development should be "more democratic". I didn't understand what they meant in context, and upon quizzing them, it turned out that they didn't either. It seems to me that they just used the word "democratic" as decoration to make the audience attach positive feelings to what they were saying.
When I think about it, this seems like quite a common rhetorical device.
When responding to a pattern, please specify whether your response is:
(a) wrangling with the definition, usefulness or existence of the pattern
(b) making a claim that a term or sufficiently-related concept exists that adequately describes it
(c) suggesting a completely fresh, hitherto-uncoined name for it
(ETA: or don't, of you don't want to)
Obviously, upvote suggestions that you think are worthy. If this post takes off, I may do a follow-up with the most upvoted suggestions.
Crossposted from the Global Priorities Project
This is the first in a series of posts which take aim at the question: how should we prioritise work on problems where we have very little idea of our chances of success. In this post we’ll see some simple models-from-ignorance which allow us to produce some estimates of the chances of success from extra work. In later posts we’ll examine the counterfactuals to estimate the value of the work. For those who prefer a different medium, I gave a talk on this topic at the Good Done Right conference in Oxford this July.
How hard is it to build an economically efficient fusion reactor? How hard is it to prove or disprove the Goldbach conjecture? How hard is it to produce a machine superintelligence? How hard is it to write down a concrete description of our values?
These are all hard problems, but we don’t even have a good idea of just how hard they are, even to an order of magnitude. This is in contrast to a problem like giving a laptop to every child, where we know that it’s hard but we could produce a fairly good estimate of how much resources it would take.
Since we need to make choices about how to prioritise between work on different problems, this is clearly an important issue. We can prioritise using benefit-cost analysis, choosing the projects with the highest ratio of future benefits to present costs. When we don’t know how hard a problem is, though, our ignorance makes the size of the costs unclear, and so the analysis is harder to perform. Since we make decisions anyway, we are implicitly making some judgements about when work on these projects is worthwhile, but we may be making mistakes.
In this article, we’ll explore practical epistemology for dealing with these problems of unknown difficulty.
We will use a simplifying model for problems: that they have a critical threshold D such that the problem will be completely solved when D resources are expended, and not at all before that. We refer to this as the difficulty of the problem. After the fact the graph of success with resources will look something like this:
Of course the assumption is that we don’t know D. So our uncertainty about where the threshold is will smooth out the curve in expectation. Our expectation beforehand for success with resources will end up looking something like this:
Assuming a fixed difficulty is a simplification, since of course resources are not all homogenous, and we may get lucky or unlucky. I believe that this is a reasonable simplification, and that taking these considerations into account would not change our expectations by much, but I plan to explore this more carefully in a future post.
What kind of problems are we looking at?
We’re interested in one-off problems where we have a lot of uncertainty about the difficulty. That is, the kind of problem we only need to solve once (answering a question a first time can be Herculean; answering it a second time is trivial), and which may not easily be placed in a reference class with other tasks of similar difficulty. Knowledge problems, as in research, are a central example: they boil down to finding the answer to a question. The category might also include trying to effect some systemic change (for example by political lobbying).
This is in contrast to engineering problems which can be reduced down, roughly, to performing a known task many times. Then we get a fairly good picture of how the problem scales. Note that this includes some knowledge work: the “known task” may actually be different each time. For example, proofreading two pages of text is quite the same, but we have a fairly good reference class so we can estimate moderately well the difficulty of proofreading a page of text, and quite well the difficulty of proofreading a 100,000-word book (where the length helps to smooth out the variance in estimates of individual pages).
Some knowledge questions can naturally be broken up into smaller sub-questions. However these typically won’t be a tight enough class that we can use this to estimate the difficulty of the overall problem from the difficult of the first few sub-questions. It may well be that one of the sub-questions carries essentially all of the difficulty, so making progress on the others is only a very small help.
Model from extreme ignorance
One approach to estimating the difficulty of a problem is to assume that we understand essentially nothing about it. If we are completely ignorant, we have no information about the scale of the difficulty, so we want a scale-free prior. This determines that the prior obeys a power law. Then, we update on the amount of resources we have already expended on the problem without success. Our posterior probability distribution for how many resources are required to solve the problem will then be a Pareto distribution. (Fallenstein and Mennen proposed this model for the difficulty of the problem of making a general-purpose artificial intelligence.)
There is still a question about the shape parameter of the Pareto distribution, which governs how thick the tail is. It is hard to see how to infer this from a priori reasons, but we might hope to estimate it by generalising from a very broad class of problems people have successfully solved in the past.
This idealised case is a good starting point, but in actual cases, our estimate may be wider or narrower than this. Narrower if either we have some idea of a reasonable (if very approximate) reference class for the problem, or we have some idea of the rate of progress made towards the solution. For example, assuming a Pareto distribution implies that there’s always a nontrivial chance of solving the problem at any minute, and we may be confident that we are not that close to solving it. Broader because a Pareto distribution implies that the problem is certainly solvable, and some problems will turn out to be impossible.
This might lead people to criticise the idea of using a Pareto distribution. If they have enough extra information that they don’t think their beliefs represent a Pareto distribution, can we still say anything sensible?
Reasoning about broader classes of model
In the previous section, we looked at a very specific and explicit model. Now we take a step back. We assume that people will have complicated enough priors and enough minor sources of evidence that it will in practice be impossible to write down a true distribution for their beliefs. Instead we will reason about some properties that this true distribution should have.
The cases we are interested in are cases where we do not have a good idea of the order of magnitude of the difficulty of a task. This is an imprecise condition, but we might think of it as meaning something like:
There is no difficulty X such that we believe the probability of D lying between X and 10X is more than 30%.
Here the “30%” figure can be adjusted up for a less stringent requirement of uncertainty, or down for a more stringent one.
Now consider what our subjective probability distribution might look like, where difficulty lies on a logarithmic scale. Our high level of uncertainty will smooth things out, so it is likely to be a reasonably smooth curve. Unless we have specific distinct ideas for how the task is likely to be completed, this curve will probably be unimodal. Finally, since we are unsure even of the order of magnitude, the curve cannot be too tight on the log scale.
Note that this should be our prior subjective probability distribution: we are gauging how hard we would have thought it was before embarking on the project. We’ll discuss below how to update this in the light of information gained by working on it.
The distribution might look something like this:
In some cases it is probably worth trying to construct an explicit approximation of this curve. However, this could be quite labour-intensive, and we usually have uncertainty even about our uncertainty, so we will not be entirely confident with what we end up with.
Instead, we could ask what properties tend to hold for this kind of probability distribution. For example, one well-known phenomenon which is roughly true of these distributions but not all probability distributions is Benford’s law.
Approximating as locally log-uniform
It would sometimes be useful to be able to make a simple analytically tractable approximation to the curve. This could be faster to produce, and easily used in a wider range of further analyses than an explicit attempt to model the curve exactly.
As a candidate for this role, we propose working with the assumption that the distribution is locally flat. This corresponds to being log-uniform. The smoothness assumptions we made should mean that our curve is nowhere too far from flat. Moreover, it is a very easy assumption to work with, since it means that the expected returns scale logarithmically with the resources put in: in expectation, a doubling of the resources is equally good regardless of the starting point.
It is, unfortunately, never exactly true. Although our curves may be approximately flat, they cannot be everywhere flat -- this can’t even give a probability distribution! But it may work reasonably as a model of local behaviour. If we want to turn it into a probability distribution, we can do this by estimating the plausible ranges of D and assuming it is uniform across this scale. In our example we would be approximating the blue curve by something like this red box:
Obviously in the example the red box is not a fantastic approximation. But nor is it a terrible one. Over the central range, it is never out from the true value by much more than a factor of 2. While crude, this could still represent a substantial improvement on the current state of some of our estimates. A big advantage is that it is easily analytically tractable, so it will be quick to work with. In the rest of this post we’ll explore the consequences of this assumption.
Places this might fail
In some circumstances, we might expect high uncertainty over difficulty without everywhere having local log-returns. A key example is if we have bounds on the difficulty at one or both ends.
For example, if we are interested in X, which comprises a task of radically unknown difficulty plus a repetitive and predictable part of difficulty 1000, then our distribution of beliefs of the difficulty about X will only include values above 1000, and may be quite clustered there (so not even approximately logarithmic returns). The behaviour in the positive tail might still be roughly logarithmic.
In the other direction, we may know that there is a slow and repetitive way to achieve X, with difficulty 100,000. We are unsure whether there could be a quicker way. In this case our distribution will be uncertain over difficulties up to around 100,000, then have a spike. This will give the reverse behaviour, with roughly logarithmic expected returns in the negative tail, and a different behaviour around the spike at the upper end of the distribution.
In some sense each of these is diverging from the idea that we are very ignorant about the difficulty of the problem, but it may be useful to see how the conclusions vary with the assumptions.
Implications for expected returns
What does this model tell us about the expected returns from putting resources into trying to solve the problem?
Under the assumption that the prior is locally log-uniform, the full value is realised over the width of the box in the diagram. This is w = log(y) - log(x), where x is the value at the start of the box (where the problem could first be plausibly solved), y is the value at the end of the box, and our logarithms are natural. Since it’s a probability distribution, the height of the box is 1/w.
For any z between x and y, the modelled chance of success from investing z resources is equal to the fraction of the box which has been covered by that point. That is:
(1) Chance of success before reaching z resources = log(z/x)/log(y/x).
So while we are in the relevant range, the chance of success is equal for any doubling of the total resources. We could say that we expect logarithmic returns on investing resources.
Sometimes of greater relevance to our decisions is the marginal chance of success from adding an extra unit of resources at z. This is given by the derivative of Equation (1):
(2) Chance of success from a marginal unit of resource at z = 1/zw.
So far, we’ve just been looking at estimating the prior probabilities -- before we start work on the problem. Of course when we start work we generally get more information. In particular, if we would have been able to recognise success, and we have invested z resources without observing success, then we learn that the difficulty is at least z. We must update our probability distribution to account for this. In some cases we will have relatively little information beyond the fact that we haven’t succeeded yet. In that case the update will just be to curtail the distribution to the left of z and renormalise, looking roughly like this:
Again the blue curve represents our true subjective probability distribution, and the red box represents a simple model approximating this. Now the simple model gives slightly higher estimated chance of success from an extra marginal unit of resources:
(3) Chance of success from an extra unit of resources after z = 1/(z*(ln(y)-ln(z))).
Of course in practice we often will update more. Even if we don’t have a good idea of how hard fusion is, we can reasonably assign close to zero probability that an extra $100 today will solve the problem today, because we can see enough to know that the solution won’t be found imminently. This looks like it might present problems for this approach. However, the truly decision-relevant question is about the counterfactual impact of extra resource investment. The region where we can see little chance of success has a much smaller effect on that calculation, which we discuss below.
Comparison with returns from a Pareto distribution
We mentioned that one natural model of such a process is as a Pareto distribution. If we have a Pareto distribution with shape parameter α, and we have so far invested z resources without success, then we get:
(4) Chance of success from an extra unit of resources = α/z.
This is broadly in line with equation (3). In both cases the key term is a factor of 1/z. In each case there is also an additional factor, representing roughly how hard the problem is. In the case of the log-linear box, this depends on estimating an upper bound for the difficulty of the problem; in the case of the Pareto distribution it is handled by the shape parameter. It may be easier to introspect and extract a sensible estimate for the width of the box than for the shape parameter, since it is couched more in terms that we naturally understand.
In this post, we’ve just explored a simple model for the basic question of how likely success is at various stages. Of course it should not be used blindly, as you may often have more information than is incorporated into the model, but it represents a starting point if you don't know where to begin, and it gives us something explicit which we can discuss, critique, and refine.
In future posts, I plan to:
- Explore what happens in a field of related problems (such as a research field), and explain why we might expect to see logarithmic returns ex post as well as ex ante.
- Look at some examples of this behaviour in the real world.
- Examine the counterfactual impact of investing resources working on these problems, since this is the standard we should be using to prioritise.
- Apply the framework to some questions of interest, with worked proof-of-concept calculations.
- Consider what happens if we relax some of the assumptions or take different models.
A look at all natural foods through the lenses of Bayesianism, optimisation, and friendly utility functions.
How should we consider foods that claim to be "all natural"? Or, since that claim is a cheap signal, foods that have few ingredients, all of them easy to recognise and all "natural"? Or "GM free"?
From the logical point of view, the case is clear: valuing these foods is nothing more that the appeal to nature fallacy. Natural products include many pernicious things (such as tobacco, hemlock, belladonna, countless parasites, etc...). And the difference between natural and not-natural isn't obvious: synthetic vitamin C is identical to the "natural" molecule, and gene modifications are just advanced forms of selective breeding.
But we're not just logicians, we're Bayesians. So let's make a few prior assumptions:
- There are far more possible products in the universe that are bad to eat than are good.
- Products that humans have been consuming for generations are much more likely to be good to eat that than a random product.
Now let's see the food industry as optimising along a few axis:
- Cost. This should be low.
- Immediate consumer satisfaction (including taste, appearance, texture, general well-being for a week or so). This should be high.
- Long term damage to the consumer's health. This should be low.
I'd like to gauge interest in an (english-language) Tokyo area meetup - given Tokyo's size, if a couple people are interested, it would be good to pick a location/day that's convenient for everybody. Otherwise I will announce a date and time and wait in a cafe with a book hoping that somebody will turn up.
I have been to several LW gatherings and have met consistently awesome and nice people, so if any Tokyo lurkers are reading this, I can assure you it's totally worth it to come! Please make yourself heard in the comments if you are interested.
The following simple game has one solution that seems correct, but isn’t. Can you figure out why?
Player One moves first. He must pick A, B, or C. If Player One picks A the game ends and Player Two does nothing. If Player One picks B or C, Player Two will be told that Player One picked B or C, but will not be told which of these two strategies Player One picked, Player Two must then pick X or Y, and then the game ends. The following shows the Players’ payoffs for each possible outcome. Player One’s payoff is listed first.
A 3,0 [And Player Two never got to move.]
Your job, should you choose to accept it, is to comment on this thread explaining the most awesome thing you've done this since June 1st. You may be as blatantly proud of yourself as you feel. You may unabashedly consider yourself the coolest freaking person ever because of that awesome thing you're dying to tell everyone about. This is the place to do just that.
Remember, however, that this isn't any kind of progress thread. Nor is it any kind of proposal thread. This thread is solely for people to talk about the awesome things they have done. Not "will do". Not "are working on". Have already done. This is to cultivate an environment of object level productivity rather than meta-productivity methods.
So, what's the coolest thing you've done this month?
Of the technologies that have a reasonable chance of come to mass market in the next 20-25 years and having a significant impact on human society, driverless cars (also known as self-driving cars or autonomous cars) stand out. I was originally planning to collect material discussing driverless cars, but Gwern has a really excellent compendium of statements about driverless cars, published January 2013 (if you're reading this, Gwern, thanks!). There have been a few developments since then (for instance, Google's announcement that it was building its own driverless car, or a startup called Cruise Automation planning to build a $10,000 driverless car) but the overall landscape remains similar. There's been some progress with understanding and navigating city streets and with handling adverse weather conditions, and it's more or less on schedule.
My question is about driverless car forecasts. Driverless Future has a good summary page of forecasts made by automobile manufacturer, insurers, and professional societies. The range of time for the arrival of the first commercial driverless cars varies between 2018 and 2030. The timeline for driverless cars to achieve mass penetration is similarly stagged between the early 2020s and 2040. (The forecasts aren't all directly comparable).
A few thoughts come to mind:
- Insurer societies and professional societies seem more conservative in their estimates than manufacturers (both automobile manufacturers and people manufacturing the technology for driverless cars). Note that the estimates of many manufacturers are centered on their projected release dates for their own driverless cars. This suggests an obvious conflict of interest: manufacturers may be incentivized to be optimistic in their projections of when driverless cars will be released, insofar as making more optimistic predictions wins them news coverage and might also improve their market valuation. (At the same time, the release dates are sufficiently far in the future that it's unlikely that they'll be held to account for false projections, so there isn't a strong incentive to be conservative the same way as there is with quarterly sales and earning forecasts). Overall, then, I'd defer more to the judgment of the professional societies, namely the IEEE and the Society of Autonomous Engineers.
- The statements compiled by Gwern point to the many legal hurdles and other thorny issues of ethics that would need to be resolved, at least partially, before driverless cars start becoming a big presence in the market.
- The general critique made by Schnaars in Megamistakes (that I discussed here) applies to driverless car technology: consumers may be unwilling to pay the added cost despite the safety benefits. Some of the quotes in Gwern's compendium reference related issues. This points further in the direction of forecasts by manufacturers being overly optimistic.
Questions for the people here:
- Do you agree with my points (1)-(3) above?
- Would you care to make forecasts for things such as: (a) the date that the first commercial driverless car will hit the market in a major country or US state? (b) the date by which over 10% of new cars sold in a large country or US state will be driverless (i.e., capable of fully autonomous operation), (c) same as (b), but over 50%, (d) the date by which over 10% of cars on the road (in a large country or US state) will be operating autonomously, (e) same as (d), but over 50%. You don't have to answer these exact questions, I'm just providing some suggestions since "forecast the future of driverless cars" is overly vague.
- What's your overall view on whether it is desirable at the margin to speed up or slow down the arrival of autonomous vehicles on the road? What factors would you consider in answering such a question?
Vincent Müller and Nick Bostrom have just released a paper surveying the results of a poll of experts about future progress in artificial intelligence. The authors have also put up a companion site where visitors can take the poll and see the raw data. I just checked the site and so far only one individual has submitted a response. This provides an opportunity for testing the views of LW members against those of experts. So if you are willing to complete the questionnaire, please do so before reading the paper. (I have abstained from providing a link to the pdf to create a trivial inconvenience for those who cannot resist temptaion. Once you take the poll, you can easily find the paper by conducting a Google search with the keywords: bostrom muller future progress artificial intelligence.)
Note: Please see this post of mine for more on the project, my sources, and potential sources for bias.
One of the categories of critique that have been leveled against climate science is the critique of insularity. Broadly, it is claimed that the type of work that climate scientists are trying to do draws upon insight and expertise in many other domains, but climate scientists have historically failed to consult experts in those domains or even to follow well-documented best practices.
Note: I wrote a preliminary version of this before drafting the post, but after having done most of the relevant investigation. I reviewed and edited it prior to publication. Note also that I don't justify these takeaways explicitly in my later discussion, because a lot of these come from general intuitions of mine and it's hard to articulate how the information I received explicitly affected my reaching the takeaways. I might discuss the rationales behind these takeaways more in a later post.
- Many of the criticisms are broadly on the mark: climate scientists should have consulted best practices in other domains, and in general should have either followed them or clearly explained the reasons for divergence.
- However, this criticism is not unique to climate science: academia in general has suffered from problems of disciplines being relatively insular (UPDATE: Here's Robin Hanson saying something similar). And many similar things may be true, albeit in different ways, outside academia.
- One interesting possibility is that bad practices here operate via founder effects: for an area that starts off as relatively obscure and unimportant, setting up good practices may not be considered important. But as the area grows in importance, it is quite rare for the area to be cleaned up. People and institutions get used to the old ways of doing things. They have too much at stake to make reforms. This does suggest that it's important to get things right early on.
- (This is speculative, and not discussed in the post): The extent of insularity of a discipline seems to be an area where a few researchers can have significant effect on the discipline. If a few reasonably influential climate scientists had pushed for more integration with and understanding of ideas from other disciplines, the history of climate science research would have been different.
Relevant domains they may have failed to use or learn from
- Forecasting research: Although climate scientists were engaging in an exercise that had a lot to do with forecasting, they neither cited research nor consulted experts in the domain of forecasting.
- Statistics: Climate scientists used plenty of statistics in their analysis. They did follow the basic principles of statistics, but in many cases used them incorrectly or combined them with novel approaches that were nonstandard and did not have clear statistical literature justifying the use of such approaches.
- Programming and software engineering: Climate scientists used a lot of code both for their climate models and for their analyses of historical climate. But their code failed basic principles of decent programming, let alone good software engineering principles such as documentation, unit testing, consistent variable names, and version control.
- Publication of data, metadata, and code: This is a phenomenon becoming increasingly common in some other sectors of academia and industry. Climate scientists they failed to learn from econometrics and biomedical research, fields that had been struggling with some qualitatively similar problems and that had been moving to publishing data, metadata, and code.
Let's look at each of these critiques in turn.
Critique #1: Failure to consider forecasting research
We'll devote more attention to this critique, because it has been made, and addressed, cogently in considerable detail.
J. Scott Armstrong (faculty page, Wikipedia) is one of the big names in forecasting. In 2007, Armstrong and Kesten C. Green co-authored a global warming audit (PDF of paper, webpage with supporting materials) for the Forecasting Principles website. that was critical of the forecasting exercises by climate scientists used in the IPCC reports.
Armstrong and Green began their critique by noting the following:
- The climate science literature did not reference any of the forecasting literature, and there was no indication that they had consulted forecasting experts, even though what they were doing was to quite an extent a forecasting exercise.
- There was only one paper, by Stewart and Glantz, dating back to 1985, that could be described as a forecasting audit, and that paper was critical of the methodology of climate forecasting. And that paper appears to have been cited very little in the coming years.
- Armstrong and Green tried to contact leading climate scientists. Of the few who responded, none listed specific forecasting principles they followed, or reasons for not following general forecasting principles. They pointed to the IPCC reports as the best source for forecasts. Armstrong and Green estimated that the IPCC report violated 72 of 89 forecasting principles they were able to rate (their list of forecasting principles includes 140 principles, but they judged only 127 as applicable to climate forecasting, and were able to rate only 89 of them). No climate scientists responded to their invitation to provide their own ratings for the forecasting principles.
How significant are these general criticisms? It depends on the answers to the following questions:
- In general, how much credence do you assign to the research on forecasting principles, and how strong a prior do you have in favor of these principles being applicable to a specific domain? I think the answer is that forecasting principles as identified on the Forecasting Principles website are a reasonable starting point, and therefore, any major forecasting exercise (or exercise that implicitly generates forecasts) should at any rate justify major points of departure from these principles.
- How representative are the views of Armstrong and Green in the forecasting community? I have no idea about the representativeness of their specific views, but Armstrong in particular is high-status in the forecasting community (that I described a while back) and the Forecasting Principles website is one of the go-to sources, so material on the website is probably not too far from views in the forecasting community. (Note: I asked the question on Quora a while back, but haven't received any answers).
So it seems like there was arguably a failure of proper procedure in the climate science community in terms of consulting and applying practices from relevant domains. Still, how germane was it to the quality of their conclusions? Maybe it didn't matter after all?
In Chapter 12 of The Signal and the Noise, statistician and forecaster Nate Silver offers the following summary of Armstrong and Green's views:
- First, Armstrong and Green contend that agreement among forecasters is not related to accuracy—and may reflect bias as much as anything else. “You don’t vote,” Armstrong told me. “That’s not the way science progresses.”
- Next, they say the complexity of the global warming problem makes forecasting a fool’s errand. “There’s been no case in history where we’ve had a complex thing with lots of variables and lots of uncertainty, where people have been able to make econometric models or any complex models work,” Armstrong told me. “The more complex you make the model the worse the forecast gets.”
- Finally, Armstrong and Green write that the forecasts do not adequately account for the uncertainty intrinsic to the global warming problem. In other words, they are potentially overconfident.
Silver, Nate (2012-09-27). The Signal and the Noise: Why So Many Predictions Fail-but Some Don't (p. 382). Penguin Group US. Kindle Edition.
Silver addresses each of these in his book (read it to know what he says). Here are my own thoughts on the three points as put forth by Silver:
- I think consensus among experts (to the extent that it does exist) should be taken as a positive signal, even if the experts aren't good at forecasting. But certainly, the lack of interest or success in forecasting should dampen the magnitude of the positive signal. We should consider it likely that climate scientists have identified important potential phenomena, but should be skeptical of any actual forecasts derived from their work.
- I disagree somewhat with this point. I think forecasting could still be possible, but as of now, there is little of a successful track record of forecasting (as Green notes in a later draft paper). So forecasting efforts, including simple ones (such as persistence, linear regression, random walk with drift) and ones based on climate models (both the ones in common use right now and others that give more weight to the PDO/AMO), should continue but the jury is still out on the extent to which they work.
- I agree here that many forecasters are potentially overconfident.
Some counterpoints to the Armstrong and Green critique:
- One can argue that what climate scientists are doing isn't forecasting at all, but scenario analysis. After all, the IPCC generates scenarios, but not forecasts. But as I discussed in an earlier post, scenario planning and forecasting are closely related, and even if scenarios aren't direct explicit unconditional forecasts, they often involve implicit conditional forecasts. To its credit, the IPCC does seem to have used some best practices from the scenario planning literature in generating its emissions scenarios. But that is not part of the climate modeling exercise of the IPCC.
- Many other domains that involve planning for the future don't reference the forecasting literature. Examples include scenario planning (discussed here) and the related field of futures studies (discussed here). Insularity of disciplines from each other is a common feature (or bug) in much of academia. Can we really expect or demand that climate scientists hold themselves to a higher standard?
UPDATE: I forgot to mention in my original draft of the post that Armstrong challenged Al Gore to a bet pitting Armstrong's No Change model with the IPCC model. Gore did not accept the bet, but Armstrong created the website (here) anyway to record the relative performance of the two models.
UPDATE 2: Read drnickbone's comment and my replies for more information on the debate. drnickbone in particular points to responses from Real Climate and Skeptical Science, that I discuss in my response to his comment.
Critique #2: Inappropriate or misguided use of statistics, and failure to consult statisticians
To some extent, this overlaps with Critique #1, because best practices in forecasting include good use of statistical methods. However, the critique is a little broader. There are many parts of climate science not directly involved with forecasting, but where statistical methods still matter. Historical climate reconstruction is one such example. The purpose of these is to get a better understanding of the sorts of climate that could occur and have occurred, and how different aspects of the climate correlated. Unfortunately, historical climate data is not very reliable. How do we deal with different proxies for the climate variables we are interested in so that we can reconstruct them? A careful use of statistics is important here.
Let's consider an example that's quite far removed from climate forecasting, but has (perhaps undeservedly) played an important role in the public debate on global warming: Michael Mann's famed hockey stick (Wikipedia), discussed in detail in Mann, Bradley and Hughes (henceforth, MBH98) (available online here). The major critiques of the paper arose in a series of papers by McIntyre and McKitrick, the most important of them being their 2005 paper in Geophysical Research Letters (henceforth, MM05) (available online here).
I read about the controversy in the book The Hockey Stick Illusion by Andrew Montford (Amazon, Wikipedia), but the author also has a shorter article titled Caspar and the Jesus paper that covers the story as it unfolds from his perspective. While there's a lot more to the hockey stick controversy than statistics alone, some of the main issues are statistical.
Unfortunately, I wasn't able to resolve the statistical issues myself well enough to have an informed view. But my very crude intuition, as well as the statements made by statisticians as recorded below, supports Montford's broad outline of the story. I'll try to describe the broad critiques leveled from the statistical perspective:
- Choice of centering and standardization: The data was centered around the 20th century, a method known as short-centering, and bound to create a bias in favor of picking hockey stick-like shapes when doing principal components analysis. Each series was also standardized (divided by the standard deviation for the 20th century), which McIntyre argued was inappropriate.
- Unusual choice of statistic used for significance: MBH98 used a statistic called the RE statistic (reduction of error statistic). This is a fairly unusual statistic to use. In fact, it doesn't have a Wikipedia page, and practically the only stuff on the web (on Google and Google Scholar) about it was in relation to tree-ring research (the proxies used in MBH98 were tree rings). This should seem suspicious: why is tree-ring research using a statistic that's basically unused outside the field? There are good reasons to avoid using statistical constructs on which there is little statistical literature, because people don't have a feel for how they work. MBH98 could have used the R^2 statistic instead, and in fact, they mentioned it in their paper but then ended up not using it.
- Incorrect calculation of significance threshold: MM05 (plus subsequent comments by McIntyre) claims that not only is the RE statistic nonstandard, there were problems with the way MBH98 used it. First off, there is no theoretical distribution of the RE statistic, so calculating the cutoff needed to attain a particular significance level is a tricky exercise (this is one of many reasons why using a RE statistic may be ill-advised, according to McIntyre). MBH98 calculated the cutoff value for 99% significance incorrectly to be 0. The correct value according to McIntyre was about 0.54, whereas the actual RE statistic value for the data set in MBH98 was 0.48, i.e., not close enough. A later paper by Ammann and Wahl, cited by many as a vindication of MBH98, computed a similar cutoff of 0.52, so that the actual RE statistic value failed the significance test. So how did it manage to vindicate MBH98 when the value of the RE statistic failed the cutoff? They appear to have employed a novel statistical procedure, coming up with something called a calibration/verification RE ratio. McIntyre was quite critical of this, for reasons he described in detail here.
There has been a lengthy debate on the subject, plus two external inquiries and reports on the debate: the NAS Panel Report headed by Gerry North, and the Wegman Report headed by Edward Wegman. Both of them agreed with the statistical criticisms made by McIntyre, but the NAS report did not make any broader comments on what this says about the discipline or the general hockey stick hypothesis, while the Wegman report made more explicit criticism.
The Wegman Report made the insularity critique in some detail:
In general, we found MBH98 and MBH99 to be somewhat obscure and incomplete and the criticisms of MM03/05a/05b to be valid and compelling. We also comment that they were attempting to draw attention to the discrepancies in MBH98 and MBH99, and not to do paleoclimatic temperature reconstruction. Normally, one would try to select a calibration dataset that is representative of the entire dataset. The 1902-1995 data is not fully appropriate for calibration and leads to a misuse in principal component analysis. However, the reasons for setting 1902-1995 as the calibration point presented in the
narrative of MBH98 sounds reasonable, and the error may be easily overlooked by someone not trained in statistical methodology. We note that there is no evidence that Dr. Mann or any of the other authors in paleoclimatology studies have had significant interactions with mainstream statisticians.
In our further exploration of the social network of authorships in temperature reconstruction, we found that at least 43 authors have direct ties to Dr. Mann by virtue of coauthored papers with him. Our findings from this analysis suggest that authors in the area of paleoclimate studies are closely connected and thus ‘independent studies’ may not be as independent as they might appear on the surface. This committee does not believe that web logs are an appropriate forum for the scientific debate on this issue.
It is important to note the isolation of the paleoclimate community; even though they rely heavily on statistical methods they do not seem to be interacting with the statistical community. Additionally, we judge that the sharing of research materials, data and results was haphazardly and grudgingly done. In this case we judge that there was too much reliance on peer review, which was not necessarily independent. Moreover, the work has been sufficiently politicized that this community can hardly reassess their public positions without losing credibility. Overall, our committee believes that Mann’s assessments that the decade of the 1990s was the hottest decade of the millennium and that 1998 was the hottest year of the millennium cannot be supported by his analysis.
McIntyre has a lengthy blog post summarizing what he sees as the main parts of the NAS Panel Report, the Wegman Report, and other statements made by statisticians critical of MBH98.
Critique #3: Inadequate use of software engineering, project management, and coding documentation and testing principles
In the aftermath of Climategate, most public attention was drawn to the content of the emails. But apart from the emails, data and code was also leaked, and this gave the world an inside view of the code that's used to simulate the climate. A number of criticisms of the coding practice emerged.
Chicago Boyz had a lengthy post titled Scientists are not Software Engineers that noted the sloppiness in the code, and some of the implications, but was also quick to point out that poor-quality code is not unique to climate science and is a general problem with large-scale projects that arise from small-scale academic research growing beyond what the coders originally intended, but with no systematic efforts being made to refactor the code (if you have thoughts on the general prevalence of good software engineering practices in code for academic research, feel free to share them by answering my Quora question here, and if you have insights on climate science code in particular, answer my Quora question here). Below are some excerpts from the post:
No, the real shocking revelation lies in the computer code and data that were dumped along with the emails. Arguably, these are the most important computer programs in the world. These programs generate the data that is used to create the climate models which purport to show an inevitable catastrophic warming caused by human activity. It is on the basis of these programs that we are supposed to massively reengineer the entire planetary economy and technology base.
The dumped files revealed that those critical programs are complete and utter train wrecks.
The design, production and maintenance of large pieces of software require project management skills greater than those required for large material construction projects. Computer programs are the most complicated pieces of technology ever created. By several orders of magnitude they have more “parts” and more interactions between those parts than any other technology.
Software engineers and software project managers have created procedures for managing that complexity. It begins with seemingly trivial things like style guides that regulate what names programmers can give to attributes of software and the associated datafiles. Then you have version control in which every change to the software is recorded in a database. Programmers have to document absolutely everything they do. Before they write code, there is extensive planning by many people. After the code is written comes the dreaded code review in which other programmers and managers go over the code line by line and look for faults. After the code reaches its semi-complete form, it is handed over to Quality Assurance which is staffed by drooling, befanged, malicious sociopaths who live for nothing more than to take a programmer’s greatest, most elegant code and rip it apart and possibly sexually violate it. (Yes, I’m still bitter.)
Institutions pay for all this oversight and double-checking and programmers tolerate it because it is impossible to create a large, reliable and accurate piece of software without such procedures firmly in place. Software is just too complex to wing it.
Clearly, nothing like these established procedures was used at CRU. Indeed, the code seems to have been written overwhelmingly by just two people (one at a time) over the past 30 years. Neither of these individuals was a formally trained programmer and there appears to have been no project planning or even formal documentation. Indeed, the comments of the second programmer, the hapless “Harry”, as he struggled to understand the work of his predecessor are now being read as a kind of programmer’s Icelandic saga describing a death march through an inexplicable maze of ineptitude and boobytraps.
A lot of the CRU code is clearly composed of hacks. Hacks are informal, off-the-cuff solutions that programmers think up on the spur of the moment to fix some little problem. Sometimes they are so elegant as to be awe inspiring and they enter programming lore. More often, however, they are crude, sloppy and dangerously unreliable. Programmers usually use hacks as a temporary quick solution to a bottleneck problem. The intention is always to come back later and replace the hack with a more well-thought-out and reliable solution, but with no formal project management and time constraints it’s easy to forget to do so. After a time, more code evolves that depends on the existence of the hack, so replacing it becomes a much bigger task than just replacing the initial hack would have been.
(One hack in the CRU software will no doubt become famous. The programmer needed to calculate the distance and overlapping effect between weather monitoring stations. The non-hack way to do so would be to break out the trigonometry and write a planned piece of code to calculate the spatial relationships. Instead, the CRU programmer noticed that that the visualization software that displayed the program’s results already plotted the station’s locations so he sampled individual pixels on the screen and used the color of the pixels between the stations to determine their location and overlap! This is a fragile hack because if the visualization changes the colors it uses, the components that depend on the hack will fail silently.)
For some choice comments excerpted from a code file, see here.
Critique #4: Practices of publication of data, metadata, and code (that had gained traction in other disciplines)
When McIntyre wanted to replicate MBH98, he emailed Mann asking for his data and code. Mann, though initially cooperative, soon started trying to fed McIntyre off. Part of this was because he thought McIntyre was out to find something wrong with his work (a well-grounded suspicion). But part of it was also that his data and code were a mess. He didn't maintain them in a way that he'd be comfortable sharing them around to anybody other than an already sympathetic academic. And, more importantly, as Mann's colleague Stephen Schneider noted, nobody asked for the code and underlying data during peer review. And most journals at the time did not require authors to submit or archive their code and data at the time of submission or acceptance of their paper. This also closely relates to Critique #3: a requirement or expectation that one's data and code would be published along with one's paper might make people more careful to follow good coding practices and avoid using various "tricks" and "hacks" in their code.
Here's how Andrew Montford puts it in The Hockey Stick Illusion:
The Hockey Stick affair is not the first scandal in which important scientific papers underpinning government policy positions have been found to be non-replicable – McCullough and McKitrick review a litany of sorry cases from several different fields – but it does underline the need for a more solid basis on which political decision-making should be based. That basis is replication. Centuries of scientific endeavour have shown that truth emerges only from repeated experimentation and falsification of theories, a process that only begins after publication and can continue for months or years or decades thereafter. Only through actually reproducing the findings of a scientific paper can other researchers be certain that those findings are correct. In the early history of European science, publication of scientific findings in a journal was usually adequate to allow other researchers to replicate them. However, as science has advanced, the techniques used have become steadily more complicated and consequently more difficult to explain. The advent of computers has allowed scientists to add further layers of complexity to their work and to handle much larger datasets, to the extent that a journal article can now, in most cases, no longer be considered a definitive record of a scientific result. There is simply insufficient space in the pages of a print journal to explain what exactly has been done. This has produced a rather profound change in the purpose of a scientific paper. As geophysicist Jon Claerbout puts it, in a world where powerful computers and vast datasets dominate scientific research, the paper ‘is not the scholarship itself, it is merely advertising of the scholarship’.b The actual scholarship is the data and code used to generate the figures presented in the paper and which underpin its claims to uniqueness. In passing we should note the implications of Claerbout’s observations for the assessment for our conclusions in the last section: by using only peer review to assess the climate science literature, the policymaking community is implicitly expecting that a read-through of a partial account of the research performed will be sufficient to identify any errors or other problems with the paper. This is simply not credible. With a full explanation of methodology now often not possible from the text of a paper, replication can usually only be performed if the data and code are available. This is a major change from a hundred years ago, but in the twenty-first century it should be a trivial problem to address. In some specialisms it is just that. We have seen, however, how almost every attempt to obtain data from climatologists is met by a wall of evasion and obfuscation, with journals and funding bodies either unable or unwilling to assist. This is, of course, unethical and unacceptable, particularly for publicly funded scientists. The public has paid for nearly all of this data to be collated and has a right to see it distributed and reused. As the treatment of the Loehle paper shows,c for scientists to open themselves up to criticism by allowing open review and full data access is a profoundly uncomfortable process, but the public is not paying scientists to have comfortable lives; they are paying for rapid advances in science. If data is available, doubts over exactly where the researcher has started from fall away. If computer code is made public too, then the task of replication becomes simpler still and all doubts about the methodology are removed. The debate moves on from foolish and long-winded arguments about what was done (we still have no idea exactly how Mann calculated his confidence intervals) onto the real scientific meat of whether what was done was correct. As we look back over McIntyre’s work on the Hockey Stick, we see that much of his time was wasted on trying to uncover from the obscure wording of Mann’s papers exactly what procedures had been used. Again, we can only state that this is entirely unacceptable for publicly funded science and is unforgiveable in an area of such enormous policy importance. As well as helping scientists to find errors more quickly, replication has other benefits that are not insignificant. David Goodstein of the California Insitute of Technology has commented that the possibility that someone will try to replicate a piece of work is a powerful disincentive to cheating – in other words, it can help to prevent scientific fraud.251 Goodstein also notes that, in reality, very few scientific papers are ever subject to an attempt to replicate them. It is clear from Stephen Schneider’s surprise when asked to obtain the data behind one of Mann’s papers that this criticism extends into the field of climatology.d In a world where pressure from funding agencies and the demands of university careers mean that academics have to publish or perish, precious few resources are free to replicate the work of others. In years gone by, some of the time of PhD students might have been devoted to replicating the work of rival labs, but few students would accept such a menial task in the modern world: they have their own publication records to worry about. It is unforgiveable, therefore, that in paleoclimate circles, the few attempts that have been made at replication have been blocked by all of the parties in a position to do something about it. Medical science is far ahead of the physical sciences in the area of replication. Doug Altman, of Cancer Research UK’s Medical Statistics group, has commented that archiving of data should be mandatory and that a failure to retain data should be treated as research misconduct.252 The introduction of this kind of regime to climatology could have nothing but a salutary effect on its rather tarnished reputation. Other subject areas, however, have found simpler and less confrontational ways to deal with the problem. In areas such as econometrics, which have long suffered from politicisation and fraud, several journals have adopted clear and rigorous policies on archiving of data. At publications such as the American Economic Review, Econometrica and the Journal of Money, Credit and Banking, a manuscript that is submitted for publication will simply not be accepted unless data and fully functional code are available. In other words, if the data and code are not public then the journals will not even consider the article for publication, except in very rare circumstances. This is simple, fair and transparent and works without any dissent. It also avoids any rancorous disagreements between journal and author after the event. Physical science journals are, by and large, far behind the econometricians on this score. While most have adopted one pious policy or another, giving the appearance of transparency on data and code, as we have seen in the unfolding of this story, there has been a near-complete failure to enforce these rules. This failure simply stores up potential problems for the editors: if an author refuses to release his data, the journal is left with an enforcement problem from which it is very difficult to extricate themselves. Their sole potential sanction is to withdraw the paper, but this then merely opens them up to the possibility of expensive lawsuits. It is hardly surprising that in practice such drastic steps are never taken. The failure of climatology journals to enact strict policies or enforce weaker ones represents a serious failure in the system of assurance that taxpayer-funded science is rigorous and reliable. Funding bodies claim that they rely on journals to ensure data availability. Journals want a quiet life and will not face down the academics who are their lifeblood. Will Nature now go back to Mann and threaten to withdraw his paper if he doesn’t produce the code for his confidence interval calculations? It is unlikely in the extreme. Until politicians and journals enforce the sharing of data, the public can gain little assurance that there is any real need for the financial sacrifices they are being asked to accept. Taking steps to assist the process of replication will do much to improve the conduct of climatology and to ensure that its findings are solidly based, but in the case of papers of pivotal importance politicians must also go further. Where a paper like the Hockey Stick appears to be central to a set of policy demands or to the shaping of public opinion, it is not credible for policymakers to stand back and wait for the scientific community to test the veracity of the findings over the years following publication. Replication and falsification are of little use if they happen after policy decisions have been made. The next lesson of the Hockey Stick affair is that if governments are truly to have assurance that climate science is a sound basis for decision-making, they will have to set up a formal process for replicating key papers, one in which the oversight role is peformed by scientists who are genuinely independent and who have no financial interest in the outcome.
Montford, Andrew (2011-06-06). The Hockey Stick Illusion (pp. 379-383). Stacey Arts. Kindle Edition.
This is an answer to a possible objection to cash-transfer charities like GiveDirectly. I remember reading about this on LessWrong a while ago, but I can't find the discussion now. I was planning on asking about this on an Open Thread, but I got curious, did my own research, and answered my own question, so now it gets its own Discussion post.
Cash-transfer charities do something very simple: they take money given by donors, find very poor people, and give them the money, in instalments. A prominent example is GiveWell's current top charity, GiveDirectly, which gives yearly gifts on the order of $1000 to very poor people in Kenya and Uganda. There is a lot of convincing research that cash-transfer charities are very effective at helping poor people.
There is a complicated debate about whether cash transfers are actually the very best way of helping poor people, or if there are in-kind charities that do the job a little better. This post is not about that. Instead, this post is just about a possible problem with the mechanics of cash transfers. The problem is this: say a donor in (say) the US gives money to GiveDirectly, and they send that money to a person in (say) Kenya. The recipient in Kenya now has a larger bank balance. But this doesn't actually create any wealth in Kenya; it just increases the amount of currency chasing the same pile of goods there. The person getting the transfer gains a positional advantage over her neighbors, but the total wealth there stays exactly the same, which of course is no good. What we as donors would really like to do is make sure that we are in some sense donating real wealth; that we are giving up a claim on some of the world's resources in such a way that other, poorer people then get to claim those resources themselves. But if just money, but no, like, actual stuff, is transferred, then giving to charity just amounts to a bookkeeping trick.
The way out of this, of course, is global trade. Dollars in the US aren't separate from dollars in Kenya; they both participate in the same global market. If global trade is efficient enough, then Kenya as a whole gains dollars relative to the US, and the buying power of their whole economy increases relative to the US economy. So Kenya does really get a bigger pile of goods for their higher number of dollars to chase, so I can transfer real, actual wealth just by changing numbers on a computer screen.
But again, this all depends on global trade, and in particular trade between the US and Kenya, being efficient. A way to measure this is correlation between the price of the same commodity in different countries. If the correlation is low, that suggests the two economies operate pretty much separately. But if the price correlation is high, that suggests that the two countries are both participating in the same market together, and transferring money reliably transfers wealth.
I decided to test this using the price of crude oil. Here's a graph of the price of crude oil in Kenya and in the United States, in inflation-adjusted US dollars, from January 2007 to January 2014. The red line is the US, the blue line is Kenya.
And the correlation is 0.93, according to Excel. So the economies seem tightly connected enough that transferring money does transfer real wealth, and you can be confident that your donation to GiveDirectly doesn't have perverse unintended consequences (or at least, not this kind).
A big caveat: I am no kind of economist; this is purely the result of back-of-the-envelope, common-sense layperson's thinking, and some numbers I found on the internet. Problems I could have include:
1. My intuition that commodity price correlation implies "connectedness" in the relevant way is just wrong.
2. In theory it's okay, but just one commodity doesn't give you the whole picture.
3. Crude oil is not a good index to use.
4. Something else?
Any criticism or other thoughts welcomed.
At the recent Tel Aviv meetup, after a discussion of the open problems in the field of FAI, we reached the conclusion that the problem of logical uncertainty is one of the most major of the problems open today. In this post I will try to give a few insights I had on this problem, which can be thought of as the problem of constructing a (non-degenerate) probability measure over the set of the statements of an arbitrary logical system.
To clarify my goal: I'm trying to make a Solomonoff-like system for assigning probabilities to logical statements. For reasons much like the reasons that Solomonoff Induction is uncomputable, this system will be uncomputable as well. This puts certain limits to it's usefulness, but it's certainly a start. Solomonoff Induction is very useful, if only as a limiting case of computable processes. I believe the system I present here has some of that same value when it comes to the problem of logical uncertainty.
The obvious tack to take is one involving proof-lengths: It is reasonable to say that a sentence that is harder to prove should have a lower measure.
Let's start with a definition:
For each provably true statement φ , let ProofLength(φ) be the length of φ's shortest proof. For all unprovable yet true statements, let ProofLength(φ) be ∞.
Therefore, if we have some probability measure P over true statements in our system, we want P to be monotonic decreasing in regards to proof length. (e.g. P(φ1)<P(φ2) ⇔ ProofLength(φ1)>ProofLength(φ2))
For obvious reasons, we want to assign probability 1 to our axioms. As an axiom always has a proof of length one (the mere statement of the axiom itself, without any previous statements that it is derived from), we want the property P(φ) = 1 ⇔ ProofLength(φ) = 1.
Lastly, for statements that are unprovable, we have to assign a probability of ½. Why? Let φ be an unprovable statement. Because P is a probability measure, P(φ)+P(~φ) = 1. Exactly one of φ or ~φ is true, but as they are unprovable, we have no way of knowing, even in theory, which is which. Thus, by symmetry, P(φ)=P(~φ)=½.
Given these desiderata, we will see what measure P we can construct that follows them.
For each true statement φ I will define P(φ) to be 2-ProofLength(φ)+2-1. This seems at first rather arbitrary, but it matches the desiderata in a fairly elegant way. This P is monotonic with regards to the proof length, as we demanded, and it correctly assigns a probability of 1 to our axioms. It also correctly assigns probability ½ to unprovable statements.
For this to be a probability measure over the set of all statements, we still need to define it on the false statements as well. This is trivial, as we can define P(φ)=1-P(~φ) for all false statements φ. This gives us all the properties we might demand of a logical probability measure that is based on proof lengths:
- Statements that can be easily proved true are given more measure than those that are hard (or even impossible) to prove to be true.
- And in reverse for false statements: Statements that can be easily proved to be false are given a lower measure than those that are hard (or even impossible) to prove to be false.
- Specifically, it assigns probability 1 to axioms (and 0 to the negations of axioms.)
I have no idea if this is the best way to construct a logical probability measure, but it seems like a start. This seems like as decent a way as any to assign priors to statements of logical probability.
That handles priors, but it doesn't seem to give an easy way to update on evidence. Obviously, once you prove something is true or false, you want its probability to rise to 1 or drop to 0 accordingly. Also, if you take some steps in the direction of proving something to be true or false, you want its probability to rise or fall accordingly.
To take a logical sentence and just blindly assign it the probability described above, ignoring everything else, is just as bad as taking the Solomonoff prior for the probability of a regular statement (in the standard system of probability) , and refusing to update away from that that. The role of the P described above is very much like that of the role of the Solomonoff prior in normal inductive Bayesian reasoning. This is nice, and perhaps it is a step forwards, but it isn't a system that can be used by itself for making decisions.
Luckily, there is a way to update on information in Solomonoff induction. You merely "slice off" the worlds that are now impossible given the new evidence, and recalculate. (It can be proven that doing so is equivalent to updating using Bayes' Theorem.)
To my delight, I found that something similar is possible with this system too! This is the truly important insight here, as this gives (for the first time, so far as I know) a method for actually updating on logical probabilities, so that as you advance towards a proof, your probability estimate of that sentence being true approaches 1, but only reaches 1 once you have a full proof.
What you do is exactly the same as in Solomonoff induction: Every time you prove something, you update by recalculating the probability of every statement, given that you now now the newly proven thing. Informally, the reasoning is like this: If you proved a statement, that means you know it with probability 1, or in other words, it can be considered as effectively a new axiom. So add it to your axioms, and you will get your updated probability!
In more technical terms, in a given logical system S, P(φ|ψ) will be defined as the P(φ) I described above, just in the logical system S+ψ, rather than is S. This obeys all the properties we want out of an update on evidence: An update increases the probability we assign to a statement that we proved part of, or proved a lemma for, or whatever, and decreases the probability we assign to a statement that we proved part of its negation, or a lemma for the proof of its negation, or the like.
This is not a complete theory of logical uncertainty, but it could be a foundation. It certainly includes some insights I haven't seen before, or at least that I haven't seen explained in these terms. In the upcoming weeks the Tel Aviv meetup group is planning to do a MIRIx workshop on the topic of logical uncertainty, and we hope to make some real strides in it. Perhaps we will expand on this, or perhaps we will come up with some other avenue of attack. If we can give logical uncertainty a formal grounding, that will be a fairly major step. After all, the black box of logical uncertainty sits right at the heart of most attempts to advance AGI, and at the moment it is merely handwaved away in most applications. But eventually it needs an underpinning, and that is what we are aiming at.
There is a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it’s fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that “Eliezer said X is true” unless you use rot13.
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