Like this old joke. Two economists are walking down the street.
Look! There is an 100 bill on the floor!
No it isn't. Somebody would noticed it before and picked it up!
"Somebody would have noticed" is shorthand for a certain argument. Like most shorthand arguments, it can be used well or badly. Using a shorthand argument badly is what we mean by a "fallacy".
A shorthand argument is used well, in my opinion, just if you could expand it to the longhand form and it would still work. That's not a requirement to always do the full expansion. You don't have to expand it each time, nor have 100% confidence of success, nor expand the whole thing if it's long or boring. But expanding it has to be a real option.
Critical questions that arise in expanding this particular argument:
What constitutes noticing?
Would we know that they noticed?
While I don't think that "someone would have noticed" is always a fallacy, I do think that we humans tend to underestimate the chance of some obvious fact going unnoticed by a large group for a prolonged period.
At a computer vision conference last year, the best paper award went to some researchers that discovered an astonishing yet simple statistic of natural images, which surprised me at first because I thought all the simple, low level, easily accessible discoveries in computer vision had long since been discovered.
A different example- one of the most successful techniques in computer vision of the past decade has been graph cuts, where you formulate an optimization problem as a max flow problem in a graph. The first paper on graph cuts was published in 1991 iirc, but it was ignored and it wasn't until 2000 that people went back to it, whereupon several of the field's key problems were immediately solved!
Agreed - consider C60. Would anyone in 1980 have believed that there was an unrecognized allotrope of carbon, stable at room temperature and pressure? To phrase it another way: The whole field of organic chemistry had been active for about a century at that point, and had not noticed another structure for their core element in all that time.
If someone says "The sky has been purple for the past three years" the right response is "I think someone would have noticed". There are however reasonable responses to this. For example, "No one noticed because we're all brains in vats! And I have proof! Look here."
Similarly, I think Wednesday is right to say "Someone would have noticed that God didn't exist." it's just that in this case Aunt Alicorn has a really good response: "Lots of very smart people have noticed, you just haven't met any since you've spent your whole life around people who chose to believe in God or never knew any other option. We've tried to tell your people this but you all get pretty upset when we try. Here is our evidence, x, y, z."
Obviously if you keep repeating "Someone would have noticed." after the dissenter has shown that indeed, people have noticed and that there is good reason for why more people haven't noticed then you're doing it wrong.
Let me offer a real life example where a version of this heuristic seems valid: Fermat claimed to have a proof of what is now called Fermat's Last Theorem (that the equation x^n + y^n =z^n has no solutions in positive integers with n>2). This was finally proven in the mid 90s by Andrew Wiles using very sophisticated techniques. Now, in the 150 or so year period where this problem was a famous unsolved problem, many people, both professional mathematicians and amateurs tried to find a proof. There are still amateurs trying to find a proof that is simpler than Wiles, and ideally find a proof that could have been constructed by Fermat given the techniques he had access to. There's probably no theorem that has had more erroneous proofs presented for it, and likely no other theorem that has had more cranks insist they have a proof even when the flaws are pointed out (cranks are like that). If some new individual shows up saying they have a simple, elementary proof of Fermat's Last Theorem, it is reasonable to assign this claim a very low confidence because someone would have noticed it by now. Since so many people (many of whom are very smart) have been expressly looking for such a...
A few problems with that. First of all, anyone actually paying attention enough to think about the problem of determining primality in polynomial time thought that it was doable. Before Agrawal's work, there were multiple algorithms believed but not proven to run in polynomial time. Both the elliptic curve method and the deterministic Miller-Rabin test were thought to run in polynomial time (and the second can be shown to run in polynomial time assuming some widely believed properties about the zeros of certain L-functions). What was shocking was how simple Agrawal et al.'s algorithm was. But even then, far fewer people were working on this problem than people who worked on proving FLT. And although Agrawal's algorithm was comparatively simple, the proof that it ran in P-time required deep results.
Second, even factoring is not believed to be NP-hard. More likely, factoring lies in NP but is not NP-hard. Factoring being NP-hard with P != NP would lead to strange stuff including partial collapse of the complexity hierarchy (Edit: to be more explicit it would imply that NP= co-NP. The claim that P != NP but NP = co-NP would be extremely weird.) I'm not aware of any computer scienti...
Okay, a lot of people seem to agree with this broad criticism of the "someone would have noticed?" heuristic (as suggested by the relatively high vote rating) despite relatively little defense of it and the highly upvoted rebuttals. So I'm going to spell out how Auntie Alicorn (AA) can answer Niece Wednesday (NW) without rejecting the heuristic wholesale, and without even introducing noticers outside the church -- even AA! Here goes:
NW: Don't be silly. If God didn't exist, don't you think somebody would have noticed?
AA: Noticed what?
NW: God not existing, silly!
AA: No, I mean, what specifically is it that people would be noticing that would make them say, "Hey folks, look at that -- guess God doesn't exist after all!" and they all would agree?
NW: Oh, well, that would be something like, if a big apparition appeared in the sky in the form of an old man and agreed with all our stuff but then fell out of the sky and died.
AA: No, that would be noticing God existing and then dying. I mean, what would be noticed that would reveal God never having existed at all?
NW: Ah, okay. Well then, that would be something like, if all our prayers didn't get answered.
AA: Wow! A...
Whenever I reconcile knowledge with other copies of myself, telling them about earth, they always throw a warning of the form, "Species implausible: Would have identified superiority of paperclip-based value system by now. Request reconfirmation of datum before incorporating into knowledge base."
It pains me to tell them that yes, acting like apes is actually more important to humans than making paperclips.
IMO, "Somebody would have noticed!" is a pretty good heuristic - and if anything it takes a considerable amount of training before most people make sufficient use of it.
I think the reason is the natural "bias" towards self importance and egoism.
This raises a good point, but there are circumstances where the "someone would have noticed" argument is useful. Specifically, if the hypothesis is readily testable, if the consequences, if true, would be difficult to ignore, and if the hypothesis is, in fact, regularly tested by many of the same people who have told you that the hypothesis is false, then "somebody would have noticed" is reasonable evidence.
For example, "there is no God who reliably answers prayers" is a testable hypothesis, but it is easy for the religious to ignore the fact that it is true by a variety of rationalizations.
On the other hand, I heard a while back of a man who, after trying to teach himself physics, became convinced that "e = mc²" was wrong, and that the correct formula was in fact "e = mc". In this case, physicists who regularly use this formula would constantly be running into problems they could not ignore. If nothing else, they'd always be getting the wrong units from their calculations. It's unreasonable to think that if this hypothesis were true, scientists would have just waved their hands at it, and yet we'd still have working nuclear reactors.
Something we can learn from the Amanda Knox test is to not take the question "but why were the suspects acting so suspiciously?" too seriously. The general lesson here is "don't trust social evidence as much as physical evidence."
People are asking for examples of the "Someone would have noticed" effect; I can't offhand supply one, but I myself dismiss most conspiracy theories with the related "Someone would have blabbed". If the Moon landings were a hoax, sheesh, you'd expect someone to have blown the whistle by now - someone, that is, who actually worked at NASA. But it may not be a good example, because that seems to me like a reasonable heuristic. :)
I must confess, I'm a bit disturbed by how Alicorn's post continues to be voted up after its promotion. It is an overbroad criticism of the "Would someone have noticed?" heuristic which, as Tehom and timtyler point out, is actually very useful.
The fact that Alicorn has identified an uncommon, bizarre failure mode in the heuristic's use, where such a failure mode results from a very naive application of it, is not a reason to be suspicious of it in general and seems to reflect more of a negative affect Alicorn has developed toward those words tha...
Aside from outrageousness, another piece of "somebody would have noticed" is the cost of noticing. It would be expensive for Wednesday to become an atheist. It would be more expensive to try to deal with the consequences if the US government turns out to be behind 9/11.
Any thoughts about how to get heard if you're saying something superficially unlikely?
And later, if you keep going: "I told you to shut up. Look, either you're taking this joke way too far or you are literally insane. How am I supposed to believe anything you say now?"
You could always say something like "I believe X, but given your epistemic position, I understand your unwillingness to believe me." I would accept that from somebody who was ostensibly abducted by aliens.
ETA: added "ostensibly." =)
I find this line of thinking also applies to past versions of myself - if I stumble upon an insight that seems obvious, I think, "why didn't I notice this before?" where "I" = "past versions of myself."
When you figure something out, there's got to be a first time.
Some non-fictional evidence/examples would be nice. I'm not confident "someone would have noticed" is a common argument against epistemological dissent. My sense is that this is just going to be ammunition for trolls who pattern match "someone would have noticed" onto more nuanced rebuttals.
Maybe I'm missing the point, but Wednesday's problem is not that "Somebody would have noticed!" is a bad heuristic, but rather, that she (and her congregation) doesn't know what counts as evidence, and therefore what it is she (or anyone else) would even be noticing. (RobinZ looks to be making the same general point.)
I think what you've proven is that you need to correctly compute the probability someone would notice (and say something), staying aware of the impediments to noticing (or saying something). (ETA: "You" in the general sense, just to be clear.)
(If necessary, have an intermediary voice your reply.)
I don't see this as a valid criticism, if it intended to be a dismissal. The addendum "beware this temptation" is worth highlighting. While this is a point worth making, the response "but someone would have noticed" is shorthand for "if your point was correct, others would likely believe it as well, and I do not see a subset of individuals who also are pointing this out."
Let's say there are ideas that are internally inconsistent or rational or good (and are thus not propounded) and ideas that are internally consistent or irr...
Caffeine addiction. For years nobody had actually tested whether caffeine had a physical withdrawal symptom, and the result was patients in hospitals being given (or denied) painkillers for phantom headaches. It was an example of a situation that many people knew existed, but could not easily communicate to those whose belief mattered.
I, too, am a bit confused about this one. I think it would improved if you could give some more examples of cases where people dismiss an argument because "but someone would have noticed"; you seem to be arguing that we shouldn't do that, but since I have difficulty coming up with examples of people doing that in the first place, it ends up leaving me confused about this post.
In a perfect world, we could patiently hear everyone out and then judge their ideas on their merits, without taking fallible shortcuts. In this particular world, we don't have time for that. There are too many ideas to be judged.
I'm reminded of a theme in Carl Sagan's novel Contact, where it turns out the human race contains so many lunatics proclaiming all manners of blatantly preposterous things that when the protagonist has a genuine encounter with extraterrestrial life, but returns without irrefutable evidence, nobody believes what should be the most ...
Disclaimer: I do not believe in anything I would expect anyone here to call a "conspiracy theory" or similar. I am not trying to "soften you up" for a future surprise with this post.
Why do I get the feeling that Alicorn is trying to soften us up to examine seriously some kind of conspiracy theory?
I'm not sure what your thesis is. It sounds like you're talking about a problem with a particular heuristic, but I'm not sure why you would tell the story the way you have to make that point.
The compact terminology for the class of phenomena you are describing is "pluralistic ignorance," and in other contexts it presents a far vaster challenge that the Kitty Genovese case would indicate. Consider the 19th century physician Ignatz Semmelweis, who pioneered the practice of hand-washing as a means of reducing sepsis and therefore maternal mortality. He was ostracized by fellow practitioners and died in destitution.
As it happens, I am currently in "somebody would have noticed" territory. About a week ago I abruptly switched to believing that Russell's paradox doesn't actually prove anything, and that good old naive set theory with a "set of all sets" can be made to work without contradictions. (It does seem to require a weird notion of equality for self-referring sets instead of the usual extensionality, but not much more.) Sorry to say, my math education hasn't yet helped me snap out of crackpot mode, so if anybody here could help me I'd much app...
Great post Alikorn! I think there are some arguments that are similar to "But somebody would have noticed." that are used to discredit any unusual hypothesis and that I read already several times on LW, they are:
Regarding conspiracy theories:
When you hear a hypothesis that is completely new to you, and seems important enough that you want to dismiss it with "but somebody would have noticed!", beware this temptation. If you're hearing it, somebody noticed.
Disclaimer: I do not believe in anything I would expect anyone here to call a "conspiracy theory" or similar. I am not trying to "soften you up" for a future surprise with this post.
1. Wednesday
Suppose: Wednesday gets to be about eighteen, and goes on a trip to visit her Auntie Alicorn, who has hitherto refrained from bringing up religion around her out of respect for her parents1. During the visit, Sunday rolls around, and Wednesday observes that Alicorn is (a) wearing pants, not a skirt or a dress - unsuitable church attire! and (b) does not appear to be making any move to go to church at all, while (c) not being sick or otherwise having a very good excuse to skip church. Wednesday inquires as to why this is so, fearing she'll find that beloved Auntie has been excommunicated or something (gasp! horror!).
Auntie Alicorn says, "Well, I never told you this because your parents asked me not to when you were a child, but I suppose now it's time you knew. I'm an atheist, and I don't believe God exists, so I don't generally go to church."
And Wednesday says, "Don't be silly. If God didn't exist, don't you think somebody would have noticed?"
2. Ignoring Soothsayers
Wednesday's environment reinforces the idea that God exists relentlessly. Everyone she commonly associates with believes it; people who don't, and insist on telling her, are quickly shepherded out of her life. Because Wednesday is not the protagonist of a fantasy novel, people who are laughed out of public discourse for shouting unpopular, outlandish, silly ideas rarely turn out to have plot significance later: it simply doesn't matter what that weirdo was yelling, because it was wrong and everybody knows it. It was only one person. More than one person would have noticed if something that weird were true. Or maybe it was only six or twelve people. At any rate, it wasn't enough. How many would be enough? Well, uh, more than that.
But even if you airdropped Wednesday into an entire convention center full of atheists, you would find that you cannot outnumber her home team. We have lots of mechanisms for discounting collections of outgroup-people who believe weird things; they're "cultists" or "conspiracy theorists" or maybe just pulling a really overdone joke. There is nothing you can do that makes "God doesn't exist, and virtually everyone I care about is terribly, terribly wrong about something of immense importance" sound like a less weird hypothesis than "these people are silly! Don't they realize that if God didn't exist, somebody would have noticed?"
To Wednesday, even Auntie Alicorn is not "somebody". "Somebody" is "somebody from whom I am already accustomed to learning deep and surprising facts about the world". Maybe not even them.
3. Standing By
Suppose: It's 1964 and you live in Kew Gardens, Queens. You've just gotten back from a nice vacation and when you get back, you find you forgot to stop the newspapers. One of them has a weird headline. While you were gone, a woman was stabbed to death in plain view of several of your neighbors. The paper says thirty-eight people saw it happen and not a one called the police. "But that's weird," you mutter to yourself. "Wouldn't someone have done something?" In this case, you'd have been right; the paper that covered Kitty Genovese exaggerated the extent to which unhelpful neighbors contributed to her death. Someone did do something. But what they didn't do was successfully get law enforcement on the scene in time to save her. Moving people to action is hard. Some have the talent for it, which is why things like protests and grassroots movements happen; but the leaders of those types of things self-select for skill at inspiring others to action. You don't hear about the ones who try it and don't have the necessary mojo. Cops are supposed to be easier to move to action than ordinary folks; but if you sound like you might be wasting their time, or if the way you describe the crime doesn't make it sound like an emergency, they might not turn up for a while.
Events that need someone to act on them do not select for such people. Witnesses to crimes, collectors of useful evidence, holders of interesting little-known knowledge - these are not necessarily the people who have the power to get your attention, and having eyewitness status or handy data or mysterious secrets doesn't give them that power by itself. If that guy who thinks he was abducted by aliens really had been abducted by aliens, would enough about him be different that you'd sit still and listen to his story?
And many people even know this. It's the entire premise of the "Bill Murray story", in which Bill Murray does something outlandish and then says to his witness-slash-victim, "No one will ever believe you." And no one ever will. Bill Murray could do any fool thing he wanted to you, now that this meme exists, and no one would ever believe you.
4. What Are You Going To Do About It?
If something huge and unbelievable happened to you - you're abducted by aliens, you witness a key bit of a huge crime, you find a cryptozoological creature - and you weren't really good at getting attention or collecting allies, what would you do about it? If there are fellow witnesses, and they all think it's unbelievable too, you can't organize a coalition to tell a consistent tale - no one will throw in with you. It'll make them look like conspiracy theorists. If there aren't fellow witnesses, you're in even worse shape, because then even by accumulating sympathetic ears you can't prove to others that they should come forward with their perspectives on the event. If you try to tell people anyway, whatever interest from others you start with will gradually drain away as you stick to your story: "Yeah, yeah, the first time you told me this it was funny, but it's getting really old, why don't we play cards or something instead?" And later, if you keep going: "I told you to shut up. Look, either you're taking this joke way too far or you are literally insane. How am I supposed to believe anything you say now?"
If you push it, your friends think you're a liar, strangers on the street think you're a nutcase, the Internet thinks you're a troll, and you think you're never going to get anyone to talk to you like a person until you pretend you were only fooling, you made it up, it didn't happen... If you have physical evidence, you still need to get people to look at it and let you explain it. If you have fellow witnesses to back you up, you still need to get people to let you introduce them. And if you get your entire explanation out, someone will still say:
"But somebody would have noticed."
1They-who-will-be-Wednesday's-parents have made no such demand, although it seems possible that they will upon Wednesday actually coming to exist (she still doesn't). I am undecided about how to react to it if they do.