Littlewood's Law and the Global Media

Selection effects in media become increasingly strong as populations and media increase, meaning that rare datapoints driven by unusual processes such as the mentally ill or hoaxers are increasingly unreliable as evidence of anything at all and must be ignored. At scale, anything that can happen will happen a small but nonzero times. (politics, psychology, sociology, statistics, philosophy)
created: 15 Dec 2018; modified: 19 Jan 2019; status: finished; confidence: highly likely; importance: 5

Scott Alexander in March 2017 noted a followup to a news story which got much less press than did the original news story:

Remember how everyone was talking about how Trump must have inspired an anti-Semitic crime wave among his supporters? And remember how some of the incidents were traced to an anti-Trump socialist working at a leftist magazine? Well, the rest of them seem to be the fault of an Israeli Jew who may have a personality-altering brain tumor. The Atlantic has a pretty good postmortem of the whole affair.

(His autism/brain tumor defense did not succeed, and he was ultimately convicted & sentenced to 10 years.)

Littlewood’s Law

This is an interesting one because it illustrates a version of Littlewood’s Law of Miracles: in a world with ~8 billion people, one which is increasingly networked and mobile and wealthy at that, a one-in-billion event will happen 8 times a month.

Human extremes are not only weirder than we suppose, they are weirder than we can suppose.


Hate crimes, and Anti-Semitic attacks are pretty rare in any absolute sense in the USA (a country of >325m people), so it doesn’t require a common cause to account for such rare effects. A surprising number of hate crimes turn out to be hoaxes, perpetrated by a member of the targeted group; it might seem crazy for, say, a black person to fake a burning cross on their lawn or a hanging noose, but apparently every once in a while, a black person has sufficient reason to do so. If someone said, I don’t really believe these anti-semitic hoaxes are real in the sense of a bunch of anti-Semites have been emboldened by Trump’s election, I think there’s something else going on, like maybe an employee made them up to drum up donations, you would probably think that was excuse-making; if they had said, I don’t believe them, maybe they’re actually fake because some schizophrenic or crazy Jew with a brain cancer and a flair for VoIP pranks did them all themselves, you would definitely think they were desperately coming up with excuses & denying facts, and to not put too fine a point on it, that they should be thoroughly ashamed of themselves for such a despicable lack of intellectual honesty.

Yet, there you have it! It is apparently a real thing, that a (self-hating?) Jew halfway across the world in Israel decided to spend all his spare time hoaxing over the Internet dozens of Jewish institutions with hate-crimes in the US post-Trump-election in part because he is an anti-social & autistic criminal, who may be driven in part by a brain tumor causing a severe personality disorder. It sounds absurdly implausible and made up - yet, among ~8 billion people, there turns out to be at least one evil brain-tumor phreaker Jew, and we all got to hear about his handiwork. My, Earth really is full of things.1 (One of the other culprits for the anti-semitic bomb threats, incidentally, was a liberal journalist.)

Or consider the YouTube headquarters shooting by Nasim Najafi Aghdam, unusual for being a mass shooting perpetrated by a woman, but also bizarre in that the motivation for the shooting by the self-described first Persian female vegan bodybuilder was apparently YouTube removing ads from her pro-veganism & exercise videos popular in Iran. Or the Darwin Awards collectively.


Industrial accidents are similar. In industrial accidents, post-mortems often detail a long series of unlucky chances and interacting failures which all combine to lead to the final explosion. the swiss cheese model imagines each layer of systems as being like a slice of Swiss cheese and only when the holes of 6 or 7 layers line up, can anything fall through: The systems were always failing to some degree, but are so redundant that a total failure is avoided, until it happens, and one marvels that 7 different things all went wrong simultaneously. Precisely because airplanes are so safe, planes no longer crash for boringly plausible reasons like the propeller fell off the plane or the pilot couldn’t see the ground in the fog, and the remaining aviation incidents now tend to be astonishing in some way; the Germanwings suicide required not just a suicidal pilot who wanted to take a whole plane with him but also abuse of post-9/11 security mechanisms intended to prevent hijacking airplanes & crashing them, or the remarkable idiocy of the co-pilot of Air France 447, or… whatever it was that happened to MH-370. In technology, software engineers who work on global-scale systems (sometimes called hyperscalers) are forced to confront the fact that at scale just about anything that can happen will happen eventually - only very rarely, to be sure (otherwise they’d’ve been fixed long before) but a nonzero number of times, and that may be enough to trigger a new failure mode and damage or even collapse computer systems (which remain rather fragile compared to all other systems). These anomalies triggering bugs make fun war stories, but also make a more important point about reality exceeding the imagination of designers, when systems fail in ways or datapoints arise that people didn’t realize was even possible (what do you mean, a byte can have anywhere from 1 to 48 bits‽).


Think about scientific papers. Imagine the ideal scenario in which models are always correct, all plans are pre-registered, etc. Because of the massive exponential expansion of the academic-industrial complex worldwide, there’s something like 1 million papers published each year; assuming (unfortunately) fairly normal research practices of testing out a few configurations on a few subsets and using a few covariates and eyeballing the data beforehand to decide on statistical approach, each paper has the equivalent of hundreds or thousands of NHST tests; thus, it is entirely possible to legitimately see a p=(1 in 1 billion) or p<0.00000005 just when the null is true (which it never is), and if you consider just the most recent set of papers from the past decade or so, you could see p<0.0000000005. All with the null hypothesis being true. Of course, in practice, things are far worse than that. Throw in the low but non-zero base rate of fraud, questionable research practices, incorrect parametric modeling assumptions, endemic publication bias, odd phenomenon like the lizardman constant in surveys (where a tiny fraction of respondents will always just answer at random or give the troll answer), etc, and there’s a point at which no matter how many studies there are on a particular effect, you still don’t have particularly strong belief in it because the data may simply be measuring ever more precisely the level of crud in that field rather than the substantive effect you want interpret to it as (Duhem-Quine, but for biases).


Can we trust film or photographs because they look real? After all, no hoaxer would be able to or be able to afford to make such a realistic video, right? Of course not. Not because of Deep Fakes, but because humanity has devoted itself with extreme assiduity to churning out millions of highly sophisticated fake news, applying its utmost ingenuity and considerable resources to… making fictional depictions of fake events, such as Hollywood movies. Many hoaxes or fakes are of high quality simply because they are recycled from commercial media, special effects, mockumentaries, etc, which have the highest standards and often are deliberately designed to erase any hints of being fiction. To give an example, likely hundreds of thousands of people were convinced by a video of a school cafeteria spiked with laxatives, with students soiling themselves; after all, the prank’s so realistic, with its cellphone footage and so many different students affected by vomiting/pooping, certainly no random Internet troll with Photoshop could possibly have faked it - and the hoaxers didn’t, because it was from a multi-season Netflix mockumentary series. Which series? Well, one you’ve almost certainly never heard of (much less watched), inasmuch as thanks to Netflix & other trends there are now >400 scripted TV series annually in the USA alone. No one could ever have heard of more than a minute fraction of these US series, but every year there is more accumulated high-quality fictional video available to be weaponized. Fortunately, a laxative prank does not matter, but imagine at some point a bright-eyed young liberal director decides to make a mockumentary of the Trump administration, complete with pee tape? Nor does there need to be a hoaxer, per se: these can be emergent (a stand alone complex?) - perhaps someone saw a clip and didn’t notice the metadata, or posted it with no metadata and a viewer assumes it’s real and reshares it, and that is how the viral hoax comes into being.

Tails at Scales

As time passes, it becomes increasingly hard to believe rare events at face value, and one has to simply defy the data. Sure, that video looks real, but it probably isn’t; it’s bizarre that anyone would run all those bomb hoaxes, but maybe someone did and it wasn’t a vast anti-semitic terrorism wave; and maybe the co-pilot just decided to crash the plane and it wasn’t an ISIS attack after all. At some point, you may have to simply start ignoring all anecdotes & individual datapoints because they border on zero evidence and a priori may simply be fake.

This is life in a big world, and it’s only getting bigger as the global population grows, wealth & leisure grow, and technologies advance. (If you thought humans could think & do weird things and fail in weird ways, just wait until everyone gets their hands on good AI tech!) There are billions of people out there, and anything that can go weird, will. The totalitarian principle - Everything not forbidden is compulsory.

Epistemological implications

Nevertheless, it all adds up to normality!

Because weirdness, however weird or often reported, increasingly tells us nothing about the world at large. If you lived in a small village of 100 people and you heard 10 anecdotes about bad behavior, the extremes are not that extreme, and you can learn from them (they may even give a good idea of what humans in general are like); if you live in a global village of 10 billion people and hear 10 anecdotes, you learn… nothing, really, because those few extreme anecdotes represent extraordinary flukes which are the confluence of countless individual flukes, which will never happen again in precisely that way (an expat Iranian fitness instructor is never going to shoot up YouTube HQ again, we can safely say), and offer no lessons applicable to the billions of other people. One could live a thousand lifetimes without encountering such extremes first-hand, rather than vicariously.

This is not due to whipping boys like social media or Russian trolls - all of this would be a problem regardless. The media can report with perfect accuracy on each (genuine) incident, but the mere fact of reporting on them and us learning about such vanishingly weird incidents is itself the problem - we can’t put the proper psychological weight on it. This is not just a selection bias2, it is a selection bias which gets worse over time.


What can we do in self-defense?

We could start trying to structure our communications in a way which embodies the true proportions, and builds in the weighting we are unable to do.

  • Crime and crime rates are an easy one - falls in the crime rate should get as much space as the total of individual crimes; if a murder gets a headline, then a year with 50 fewer murders should get 50 headlines about the that reduction’s 50 non-murders (because surely avoiding a murder is as good news as a murder is bad news?).
  • Perhaps in one format, discussion could be weighted similar to a meta-analytic weighting of effect sizes: you are allowed to discuss both anecdotes and studies, but the number of words about a anecdote or study must be weighted by sample size.

    So if you write 1 page about someone who claims X cured their dandruff, you must then write 100 pages about the study of n=100 showing that X doesn’t cure dandruff. That’s only fair, since that study is made of 100 anecdotes, so to speak, and they are as deserving of 1 page as the first anecdote.
  • Weighting could be applied to costs & benefits as well: in a discussion of clinical trial design and bioethics of randomized experiments and whether it can be ethical to run a RCT, one could allow discussion of the Tuskegee syphilis experiment (affecting 399 men) but only if one then has proportionately much discussion of the estimates of the number of people hurt by small underpowered incorrect or delayed randomized trials (usually estimated in the millions), which might require some advanced typographic innovations.
  • A proportional newspaper might allocate space by geographic region populations, so there’s a giant void with a tiny little 2-line wire item for Africa, while the (much smaller) USA section requires a microscope.
  • What if one wrote movie or book summaries in a strict scaling of 100 words per X minutes/pages, instead of relying on fading memories or a few points? After all, that’s how one has to consume them, at 1 second per second, and what the experience actually is.

    It seems peculiar that reviews will describe hours of material in a few sentences, and then a 30 second scene might get a loving multi-page description and analysis, since that is not how one watches the movie, and that gives a misleading view of the movie’s pacing, if nothing else. What if social media stopped prioritizing recent short items and instead gave visual real estate in proportion to how old something is?
  • Weight by age: If someone is rereading a 50-year-old essay, that should be given more proportionally more emphasis on a social media stream than a 5-minute old Tumblr post.

More immediately, you should keep your eye on the ball: ask yourself regularly how useful news consumption has really been, and if you justify it as entertainment, how it makes you feel (do you feel entertained or refreshed afterwards?), and if you should spend as much time on it as you do; try to cut back or ignore recent news (perhaps replace a daily newspaper subscription with a weekly periodical like The Economist and especially stop watching cable news!); shift focus to topics of long-term importance rather than high-frequency noise (eg scientific rather than polling or stock market articles); don’t rely on self-selected convenience samples of news/opinions/responses/anecdotes brought to you by other people, but make your own convenience sample which will at least have different biases and be less extreme (ie don’t go off 10 comments online, ask 10 of your followers instead, or read 10 random stories instead of the top 10 trending stories); insist on following back & getting fulltext sources (if you don’t have time to trace something back to its source, then your followers collectively don’t have time to spend reading it)3; read articles to the end (many newspapers, like the New York Times, have a nasty habit of including critical caveats - at the end, where most readers won’t bother to read to); discount things which are too good to be true; focus on immediate utility; try to reduce reliance on anecdotes & stories; consider epistemological analogues of robust statistics like simply throwing out the top and bottom percentiles of data; and pay attention to the trends, the big picture, the central tendency, not outliers.

The world is only getting bigger.

  1. A passage I like from The Shadow of the Torturer by Gene Wolfe:

    How many people do you think there are in Nessus?

    I have no idea.

    No more do I, Torturer. No more does anyone. Every attempt to count them has failed, as has every attempt to tax them systematically. The city grows and changes every night, like writing chalked on a wall. Houses are built in the streets by clever people who take up the cobbles in the dark and claim the ground - did you know that? The exultant Talarican, whose madness manifested itself as a consuming interest in the lowest aspects of human existence, claimed that the persons who live by devouring the garbage of others number two gross thousands. That there are ten thousand begging acrobats, of whom nearly half are women. That if a pauper were to leap from the parapet of this bridge each time we draw breath, we should live forever, because the city breeds and breaks men faster than we respire.

    I have wondered if Wolfe was alluding to Henry Mayhew’s London Labour and the London Poor (which was a key source for Tim Powers’s The Anubis Gates), although the sources for Robb’s The Discovery of France are also plausible (perhaps conflating Alexandre Privat d’Anglemont with his quondam patron Lord Henry Seymour):

    Every town and village was a living encyclopedia of crafts and trades. In 1886, most of the eight hundred and twenty-four inhabitants of the little town of Saint-Étienne-d’Orthe, on a low hill near the river Adour, were farmers and their dependents. Of the active population of two hundred and eleven, sixty-two had another trade: there were thirty-three seamstresses and weavers, six carpenters, five fishermen, four innkeepers, three cobblers, two shepherds, two blacksmiths, two millers, two masons, one baker, one rempailleur (upholsterer or chair-bottomer) and one witch (potentially useful in the absence of a doctor), but no butcher and no storekeeper other than two grocers. In addition to the local industries and the services provided by itinerant traders (see p. 146), most places also had snake collectors, rat catchers with trained ferrets and mole catchers who either set traps or lay in wait with a spade. There were rebilhous, who called out the hours of the night, cinderellas, who collected and sold ashes used for laundering clothes, men called tétaïres, who performed the function of a breast-pump by sucking mothers’ breasts to start the flow of milk, and all the other specialists that the census listed under trades unknown and without trade, which usually meant gypsies, prostitutes and beggars…

    As the Breton peasant Déguignet discovered to other people’s cost, begging was a profession in its own right. Beggar women sold their silence to respectable people by making lewd and compromising remarks about them in the street. They borrowed children who were diseased or deformed. They manufactured realistic sores from egg yolk and dried blood, working the yolk into a scratch to produce the full crusty effect. A judge at Rennes in 1787 reported a bogus old man with a fake hump and a club foot, another man who succeeded in blacking out one eye to give a terrible, dramatic impression of blindness, and yet another who could mimic all the symptoms of epilepsy. ’Idle beggar was a contradiction in terms. As Déguignet insisted in his memoirs, it was no simple task to hide behind a hedgerow and to fabricate a stump or a hideously swollen leg covered with rotten flesh.

    These rustic trades were also found in cities. In the 1850s, one of the first amateur anthropologists of Paris, the Caribbean writer [Alexandre] Privat d’Anglemont, set out to explain [in Paris anecdoté (1854)/Paris Inconnu (1861); no English translations available] how seventy thousand Parisians began the day without knowing how they would survive and yet somehow end up managing to eat, more or less. The result was a valuable compendium of little-known trades. He found a man who bred maggots for anglers by collecting dead cats and dogs in his attic, women who worked as human alarm clocks (a speedy woman in a densely populated quartier could serve up to twenty clients), guardian angels who were paid by restaurants to guide their drunken clients home, a former bear-hunter from the Pyrenees who exterminated cats, and a goatherd from the Limousin who kept a herd of goats on the fifth floor of a tenement in the Latin Quarter.

    To expand a little more from Jullien 2009:

    His books are filled with tales of quaint encounters, and describe the bizarre trades of old Paris. The reader is introduced to a killer of cats, who sells the skins as sable and the flesh as rabbit (113), a painter of turkey feet, expert at giving them the glossy look of freshly killed fowl (50), a breeder of maggots for the many fishermen of Paris (23), a retailer of used bread crusts to feed rabbits (52), a guardian angel who escorts drunks back home safely (66), a maker of artificial rooster crests (116), a renter of leeches to patients who cannot afford to buy them (121), and - strangest of all - even a lyric poet who makes a living with his poetry (139). The list goes on.

    Milord l’Arsouille, a.k.a Lord Henry Seymour (1801-1859), the eccentric English millionaire who held court in the Paris slums, haunts the final pages of the book (228-240). Although Privat never met him in person, but only heard of him, he is the benign ghost who provides the author with a kind of aristocratic patronage. Milord l’Arsouille, often emulated (but never surpassed) by young and wealthy Parisians, became a legend for the poor people, a real-life replica of Eugène Sue’s Rodolphe Gerolstein, the hero of his fantastically popular serial novel Les Mystèresde Paris (1843)…Like Prince Rudolph, Milord L’Arsouille is a protector of the weak and punisher of the evil, and outrageous anecdotes proliferate around him (239-240).

  2. Describing the news or media as having a selection bias problem is a bit odd, and like describing bombs as having a mortality problem; arguably, the sole function of the news is to be a giant global selection bias.

  3. Not that any source is 100% reliable, but at least tracing it back eliminates the many serious distortions which happen along the way. I can’t count how many times I’ve found leprechauns when I traced back a claim or story to its original source or paper, and discovered that a major caveat had been left out, the original was fake or otherwise worthless, or the original actually said the opposite of what had finally been relayed to me. (And often the best & most interesting version is the original, anyway.)