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, insight-porn
2018-12-152019-02-18 finished certainty: highly likely importance: 5


On­line & main­stream me­dia and so­cial net­work­ing have be­come in­creas­ingly mis­lead­ing as to the state of the world by fo­cus­ing on ‘sto­ries’ and ‘events’ rather than trends and av­er­ages. This is be­cause as the global pop­u­la­tion in­creases and the scope of me­dia in­creas­es, me­di­a’s urge for nar­ra­tive fo­cuses on the most ex­treme out­lier dat­a­points—but such dat­a­points are, at a global scale, deeply mis­lead­ing as they are dri­ven by un­usual processes such as the men­tally ill or hoax­ers.

At a global scale, any­thing that can hap­pen will hap­pen a small but nonzero times: this has been epit­o­mized as “Lit­tle­wood’s Law: in the course of any nor­mal per­son’s life, mir­a­cles hap­pen at a rate of roughly one per month.” This must now be ex­tended to a global scale for a hy­per­-net­worked global me­dia cov­er­ing anom­alies from 8 bil­lion peo­ple—all co­in­ci­dences, hoax­es, men­tal ill­ness­es, psy­cho­log­i­cal odd­i­ties, ex­tremes of con­tin­u­ums, mis­takes, mis­un­der­stand­ings, ter­ror­ism, un­ex­plained phe­nom­ena etc. Hence, there will be enough ‘mir­a­cles’ that all me­dia cov­er­age of events can po­ten­tially be com­posed of noth­ing but ex­treme out­liers, even though it would seem like an ‘ex­tra­or­di­nary’ claim to say that all me­di­a-re­ported events may be flukes.

This cre­ates an epis­temic en­vi­ron­ment deeply hos­tile to un­der­stand­ing re­al­i­ty, one which is ded­i­cated to find­ing ar­bi­trary amounts of and am­pli­fy­ing the least rep­re­sen­ta­tive dat­a­points.

Given this, it is im­por­tant to main­tain ex­treme skep­ti­cism of any in­di­vid­ual anec­dotes or sto­ries which are se­lec­tively re­ported but still claimed (often im­plic­it­ly) to be rep­re­sen­ta­tive of a gen­eral trend or fact about the world. Stan­dard tech­niques like crit­i­cal think­ing, em­pha­siz­ing trends & av­er­ages, and de­mand­ing orig­i­nal sources can help fight the bi­as­ing effect of news.

The para­dox of news is that by de­sign, the more you read, the less you might know, by ac­cu­mu­lat­ing an ever greater ar­se­nal of facts and ex­am­ples which are (usu­al­ly) true, but whose in­ter­pre­ta­tion bears ever less re­sem­blance to re­al­i­ty. This was al­ways true, but online/mainstream me­dia and so­cial net­work­ing, which turn over much seem have be­come in­creas­ingly mis­lead­ing as to the state of the world by fo­cus­ing on ‘sto­ries’ and ‘events’ rather than trends and av­er­ages, which come and go in the “is­sue-at­ten­tion cy­cle” (/) be­fore slower fol­lowup re­port­ing or fac­t-check­ers or fail­ures to repli­cate can catch up (and the cy­cle may be —who can re­mem­ber last mon­th’s out­rage, much less 12-month­s-ago’s cri­sis?). As an ex­am­ple of this, Scott Alexan­der in March 2017 pointed out an anom­aly in the nar­ra­tive in the fol­lowup to a news story (which got far less press than did the orig­i­nal):

Re­mem­ber how every­one was talk­ing about how Trump must have 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.1

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. Lit­tle­wood’s law is it­self a spe­cial-case of “the Law of Truly Large Num­bers”:

The Law of Truly Large Num­bers. Suc­cinctly put, the law of truly large num­bers states: With a large enough sam­ple, any out­ra­geous thing is likely to hap­pen. The point is that truly rare events, say events that oc­cur only once in a mil­lion [as the math­e­mati­cian Lit­tle­wood (1953) re­quired for an event to be sur­pris­ing] are bound to be plen­ti­ful in a pop­u­la­tion of 250 mil­lion peo­ple. If a co­in­ci­dence oc­curs to one per­son in a mil­lion each day, then we ex­pect 250 oc­cur­rences a day and close to 100,000 such oc­cur­rences a year.

Go­ing from a year to a life­time and from the pop­u­la­tion of the United States to that of the world (5 bil­lion at this writ­ing), we can be ab­solutely sure that we will see in­cred­i­bly re­mark­able events. When such events oc­cur, they are often noted and record­ed. If they hap­pen to us or some­one we know, it is hard to es­cape that spooky feel­ing.

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

Politics

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. The prob­lem is, there need not be any suffi­cient rea­sons. In ac­counts of con artists, one of the most con­sis­tent themes is how un­der­stand­able their schemes are when you ap­pre­ci­ate how much good faith we as­sume and take on faith, and how oth­er­wise mis­er­ably & pa­thet­i­cally un­der­stand­able they and their mal­ice is (bor­row­ing & steal­ing wealth & power to fill the empty void within them­selves); while in ac­counts of forg­ers, hoax­es, and fab­ri­ca­tors, the most con­sis­tent theme is that the in­ves­ti­ga­tor, after ex­haust­ing all av­enues, ex­am­in­ing all mi­nor con­tribut­ing fac­tors, un­con­vinc­ingly lay­ing out all sen­si­ble mo­ti­va­tions like ca­reer ad­vance­ment, fre­quently in­ter­view­ing them at length only to be baffled by de­flec­tions, and lies, is fi­nally left in si­lence. Why did they do it? No one knows.

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 & 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 ashamed of them­selves for such a lack of in­tel­lec­tual hon­esty & fla­grantly par­ti­san bias.

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.”2 (One of the other cul­prits for the an­ti-se­mitic bomb threats, in­ci­den­tal­ly, was .)

Or con­sider the by Nasim Na­jafi Agh­dam, un­usual for be­ing a mass shoot­ing per­pe­trated by a wom­an, but also bizarre in that by the self­-de­scribed “first Per­sian fe­male ve­gan body­builder”3 was ap­par­ently YouTube re­mov­ing ads from her pro-ve­g­an­ism & ex­er­cise videos pop­u­lar in Iran. Or how about that Eng­lish kid who con­vinced his friend to mur­der him on the or­ders of British in­tel­li­gence? Or the col­lec­tive­ly.

Technology

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 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 . 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 can have any­where from 1 to 48 bits‽”).

Science

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 post-WWII, 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 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 (), 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, . 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 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 (, but for bi­as­es).

Media

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, , but the orig­i­nal pho­to­graph ed­i­tor at the re­spected firm did­n’t in­tend to ‘forge’ any­thing: it was sim­ply some po­lit­i­cal hu­mor, part of a set of 3 edited pho­tographs along with (sit­ting on an ele­phant) and (don­key), which was dredged up and re­pur­posed for In­ter­net memes. (S­peak­ing of ele­phants, you may have seen an ele­phant at an Irish riot c.1970—pho­to­shopped for an amus­ing se­ries of Irish satires, but sub­se­quently taken for re­al.) More re­cently 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’? (How about or­gan har­vest­ing video hoax­es?) 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. Snopes is chock­-a-block with these. When it comes to me­dia, .

Tails at Scales

“‘What did the Men of old use them [the palan­tír] for?’ asked Pip­pin, de­lighted and as­ton­ished at get­ting an­swers to so many ques­tions…‘To see far off, and to con­verse in thought with one an­oth­er,’ said Gan­dalf…In the days of his wis­dom Denethor would not pre­sume to use it to chal­lenge Sauron, know­ing the lim­its of his own strength. But his wis­dom failed…He was too great to be sub­dued to the will of the Dark Pow­er, he saw nonethe­less only those things which that Power per­mit­ted him to see. The knowl­edge which he ob­tained was, doubtless, often of ser­vice to him; yet the vi­sion of the great might of Mor­dor that was shown to him fed the de­spair of his heart un­til it over­threw his mind.”

Gan­dalf, The Re­turn of the King

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 —“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 bias4, it is a se­lec­tion bias which gets worse over time.

Coping

’In the au­tumn of 1939, and his young Cam­bridge stu­dent and friend were walk­ing along the river when they saw a news­pa­per ven­dor’s sign an­nounc­ing that the Ger­mans had ac­cused the British gov­ern­ment of in­sti­gat­ing a re­cent at­tempt to as­sas­si­nate Hitler. When Wittgen­stein re­marked that it would­n’t sur­prise him at all if it were true, Mal­colm re­torted that it was im­pos­si­ble be­cause “the British were too civ­i­lized and de­cent to at­tempt any­thing so un­der­hand, and . . . such an act was in­com­pat­i­ble with the British ‘na­tional char­ac­ter’.” Wittgen­stein was fu­ri­ous. Some 5 years lat­er, he wrote to Mal­colm:

“When­ever I thought of you I could­n’t help think­ing of a par­tic­u­lar in­ci­dent which seemed to me very im­por­tant. . . . you made a re­mark about ‘na­tional char­ac­ter’ that shocked me by its prim­i­tive­ness. I then thought: what is the use of study­ing phi­los­o­phy if all that it does for you is to en­able you to talk with some plau­si­bil­ity about some ab­struse ques­tions of log­ic, etc., & if it does not im­prove your think­ing about the im­por­tant ques­tions of every­day life, if it does not make you more con­sci­en­tious than any . . . jour­nal­ist in the use of the dan­ger­ous phrases such peo­ple use for their own ends. You see, I know it’s diffi­cult to think well about ‘cer­tainty’, ‘prob­a­bil­ity’, ‘per­cep­tion’, etc. But it is, if pos­si­ble, still more diffi­cult to think, or try to think, re­ally hon­estly about your life & other peo­ples lives.”5

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 of cov­er­age as your first anec­dote—right?

  • 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 in to­day’s edi­tion, there might be a gi­ant void with a tiny lit­tle 2-line wire ser­vice item for Africa, while the (much small­er) USA sec­tion re­quires a mi­cro­scope to read all the ma­te­r­ial in it.

  • 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 ? 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; take 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 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)6; 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 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.

See Also

Appendix

Origin of “Littlewood’s Law of Miracles”

I try to trace back “Lit­tle­wood’s Law of Mir­a­cles” to its sup­posed source in Lit­tle­wood’s A Math­e­mati­cian’s Mis­cel­lany. It does not ap­pear in that book, and fur­ther in­ves­ti­ga­tion in­di­cates that Lit­tle­wood did not come up with it but that Free­man Dyson coined it in 2004, prob­a­bly based on the ear­lier “Law of Truly Large Num­bers” coined by Di­a­co­nis & Mosteller 1989, in a case of Stigler’s law.

Wikipedia and other sources on “Lit­tle­wood’s Law of Mir­a­cles” all at­tribute it to math­e­mati­cian (best known for his col­lab­o­ra­tions with Hardy & Ra­manu­jan). Cu­ri­ous­ly, no one ever quotes Lit­tle­wood’s orig­i­nal for­mu­la­tion but typ­i­cally a para­phrase by :

Lit­tle­wood’s law of mir­a­cles states that in the course of any nor­mal per­son’s life, mir­a­cles hap­pen at a rate of roughly one per month.

Para­phrases are often wit­tier & more mem­o­rable than the orig­i­nal, but I do like to see the orig­i­nals to see what else they said. WP at­trib­utes the quote to a Lit­tle­wood an­thol­ogy of es­says, Lit­tle­wood’s /Lit­tle­wood’s Mis­cel­lany (1953/1986), with­out spec­i­fy­ing chap­ter or page num­ber. (In­deed, no writer on Lit­tle­wood’s Law spec­i­fies chapter/page num­ber when cit­ing ei­ther ver­sion of A Math­e­mati­cian’s Mis­cel­lany.)

Puz­zling­ly, at no point in the book, ei­ther the 1953 or 1986 edi­tions (which ap­pear near-i­den­ti­cal), does Lit­tle­wood ever de­fine a “law of mir­a­cles” or speak of “one per month”.

The rel­e­vant essay/chapter ap­pears to be “Large Num­bers”, which is a dis­cus­sion of large num­bers such as as­tro­nom­i­cal units, switch­ing over to prob­a­bil­i­ties & co­in­ci­dences. Lit­tle­wood goes through a mis­cel­lany of cal­cu­la­tions in­tended to show that var­i­ous un­likely things would be ex­pected to hap­pen in Eng­land or the world based purely on prob­a­bil­i­ty, and ends with a dis­cus­sion of in­te­ger fac­tor­ing.

This sec­tion is a log­i­cal place for him to de­fine “Lit­tle­wood’s law”, but he never does. The clos­est that he comes is the sec­tion of the sub­chap­ter, “Large Num­bers: Co­in­ci­dences and Im­prob­a­bil­i­ties §12”, where he dis­cusses a sta­tis­ti­cal ther­mo­dy­nam­ics ques­tion of heat (a puz­zle we would prob­a­bly de­scribe as “how likely is it that a snow­ball could sur­vive a week in Hell by ran­dom ther­mal fluc­tu­a­tions?”), where he offhand­edly de­scribes the nec­es­sary enor­mous­ly-im­prob­a­ble macro fluc­tu­a­tion as a “mir­a­cle”. (He ul­ti­mately con­cludes that, if I un­der­stand the units cor­rect­ly, the snow­ball would have a chance of sur­vival of just 1 in .) The word “mil­lion” does not ap­pear, but go­ing back 5 pages to §5, Lit­tle­wood offhand­edly em­ploys the unit 106 (ie 1 mil­lion) as ap­par­ently a kind of cut­off for an im­pres­sive co­in­ci­dence:

§5. Im­prob­a­bil­i­ties are apt to be over­es­ti­mat­ed. It is true that I should have been sur­prised in the past to learn that [athe­ist] Pro­fes­sor Hardy had joined the [Chris­t­ian AA-pre­de­ces­sor] . But one could not say the ad­verse chance was 106 : 1. Math­e­mat­ics is a dan­ger­ous pro­fes­sion; an ap­pre­cia­ble pro­por­tion of us go mad, and then this par­tic­u­lar event would be quite like­ly.

…I some­times ask the ques­tion: what is the most re­mark­able co­in­ci­dence you have ex­pe­ri­enced, and is it, for the most re­mark­able one, re­mark­able? (With a life­time to choose from, 106 : 1 is a mere tri­fle.) This is, of course, a sub­ject made for bores, but I own two, one start­ing at the mo­ment but de­bunk­able, the other gen­uinely re­mark­able…

Searches for “month”/“mil­lion”/“mir­a­cle” all fail­ing and hav­ing reached a dead end with Lit­tle­wood him­self, I turned back to ex­am­ine the Free­man Dyson source more care­fully in the hopes of a quote or ex­act page num­ber.

The source for Dyson’s para­phrase of Lit­tle­wood is a 2004 New York Re­view of Books book re­view “One in a Mil­lion”, re­view­ing a 2004 trans­la­tion of a French book about skep­ti­cism (Charpak & Broch’s De­bunked! ESP, Telekine­sis, and Other Pseu­do­science, trans­lated by Bart K. Hol­land).

Dyson’s re­view is (as usual for the NYRB) be­hind an im­pen­e­tra­ble pay­wall but the re­view was reprinted in 2006 as chap­ter 27 of Dyson’s col­lec­tion The Sci­en­tist as Rebel (ISBN: 1590172167), which is eas­ily ac­ces­si­ble, and the rel­e­vant sec­tions about Lit­tle­wood read:

…The book also has a good chap­ter on “Amaz­ing Co­in­ci­dences.” These are strange events which ap­pear to give ev­i­dence of su­per­nat­ural in­flu­ences op­er­at­ing in every­day life. They are not the re­sult of de­lib­er­ate fraud or trick­ery, but only of the laws of prob­a­bil­i­ty. The para­dox­i­cal fea­ture of the laws of prob­a­bil­ity is that they make un­likely events hap­pen un­ex­pect­edly often. A sim­ple way to state the para­dox is Lit­tle­wood’s law of mir­a­cles. John Lit­tle­wood was a fa­mous math­e­mati­cian who was teach­ing at Cam­bridge Uni­ver­sity when I was a stu­dent. Be­ing a pro­fes­sional math­e­mati­cian, he de­fined mir­a­cles pre­cisely be­fore stat­ing his law about them. He de­fined a mir­a­cle as an event that has spe­cial sig­nifi­cance when it oc­curs, but oc­curs with a prob­a­bil­ity of one in a mil­lion. This de­fi­n­i­tion agrees with our com­mon­sense un­der­stand­ing of the word “mir­a­cle.”

Lit­tle­wood’s law of mir­a­cles states that in the course of any nor­mal per­son’s life, mir­a­cles hap­pen at a rate of roughly one per month. The proof of the law is sim­ple. Dur­ing the time that we are awake and ac­tively en­gaged in liv­ing our lives, roughly for eight hours each day, we see and hear things hap­pen­ing at a rate of about one per sec­ond. So the to­tal num­ber of events that hap­pen to us is about 30,000 per day, or about a mil­lion per month. With few ex­cep­tions, these events are not mir­a­cles be­cause they are in­signifi­cant. The chance of a mir­a­cle is about one per mil­lion events. There­fore we should ex­pect about one mir­a­cle to hap­pen, on the av­er­age, every month. Broch tells sto­ries of some amaz­ing co­in­ci­dences that hap­pened to him and his friends, all of them eas­ily ex­plained as con­se­quences of Lit­tle­wood’s law.

…If this ide­al­ized pic­ture of a telepa­thy ex­per­i­ment were re­al, we should long ago have been able to de­cide whether telepa­thy ex­ists or not. In the real world, the way such ex­per­i­ments are done is very differ­ent, as I know from per­sonal ex­pe­ri­ence. When I was a teenager long ago, para­psy­chol­ogy was fash­ion­able. I bought a deck of and did card-guess­ing ex­per­i­ments with my friends. We spent long hours, tak­ing turns at gaz­ing and guess­ing cards. Un­like Broch, we were strongly mo­ti­vated to find pos­i­tive ev­i­dence of telepa­thy. We con­sid­ered it likely that telepa­thy ex­isted and we wanted to prove our­selves to be tele­path­i­cally gift­ed. When we started our ses­sions, we achieved some spec­tac­u­larly high per­cent­ages of cor­rect guess­es. Then, as time went on, the per­cent­ages de­clined to­ward twenty and our en­thu­si­asm dwin­dled. After a few months of spo­radic efforts, we put the cards away and for­got about them.

Look­ing back on our ex­pe­ri­ence with the cards, we came to un­der­stand that there are three for­mi­da­ble ob­sta­cles to any sci­en­tific study of telepa­thy. The first ob­sta­cle is bore­dom. The ex­per­i­ments are in­suffer­ably bor­ing. In the end we gave up be­cause we could not stand the bore­dom of sit­ting and guess­ing cards for hours on end. The sec­ond ob­sta­cle is in­ad­e­quate con­trols. We never even tried to im­pose rig­or­ous con­trols on com­mu­ni­ca­tion be­tween sender and re­ceiv­er. With­out such con­trols, our re­sults were sci­en­tifi­cally worth­less. But any se­ri­ous sys­tem of con­trols, stop­ping us from chat­ting and jok­ing while we were gaz­ing and guess­ing, would have made the ex­per­i­ments even more in­suffer­ably bor­ing.

The third ob­sta­cle is bi­ased sam­pling. The re­sults of such ex­per­i­ments de­pend cru­cially on when you de­cide to stop. If you de­cide to stop after the ini­tial spec­tac­u­larly high per­cent­ages, the re­sults are strongly pos­i­tive. If you de­cide to stop when you are al­most dy­ing of bore­dom, the re­sults are strongly neg­a­tive. The only way to ob­tain un­bi­ased re­sults is to de­cide in ad­vance when to stop, and this we had not done. We were not dis­ci­plined enough to make a de­ci­sion in ad­vance to do 10,000 guesses and then stop, re­gard­less of the per­cent­age of cor­rect guesses that we might have achieved. We did not suc­ceed in over­com­ing a sin­gle one of the three ob­sta­cles. To reach any sci­en­tifi­cally cred­i­ble con­clu­sions, we would have needed to over­come all three.

The his­tory of the card-guess­ing ex­per­i­ments, car­ried out ini­tially by at Duke Uni­ver­sity and later by many other groups fol­low­ing Rhine’s meth­ods, is a sorry sto­ry. A num­ber of ex­per­i­ments that claimed pos­i­tive re­sults were later proved to be fraud­u­lent. Those that were not fraud­u­lent were plagued by the same three ob­sta­cles that frus­trated our efforts. It is diffi­cult, ex­pen­sive, and te­dious to im­pose con­trols rig­or­ous enough to elim­i­nate the pos­si­bil­ity of fraud. And even after such con­trols have been im­posed, the con­clu­sions of a se­ries of ex­per­i­ments can be strongly bi­ased by se­lec­tive re­port­ing of the re­sults. Lit­tle­wood’s law ap­plies to ex­per­i­men­tal re­sults as well as to the events of daily life. A ses­sion with a no­tice­ably high per­cent­age of cor­rect guesses is a mir­a­cle ac­cord­ing to Lit­tle­wood’s de­fi­n­i­tion. If a large num­ber of ex­per­i­ments are done by var­i­ous groups un­der var­i­ous con­di­tions, mir­a­cles will oc­ca­sion­ally oc­cur. If mir­a­cles are se­lec­tively re­port­ed, they are ex­per­i­men­tally in­dis­tin­guish­able from real oc­cur­rences of telepa­thy.

Dyson 2004 does not at­tribute Lit­tle­wood’s Law to A Math­e­mati­cians Mis­cel­lany and gives no source at all. One might guess that the im­plicit source is the “Amaz­ing Co­in­ci­dences” chap­ter of De­bunked!, but upon check­ing, De­bunked! does not men­tion Lit­tle­wood any­where. (The “Amaz­ing Co­in­ci­dences” chap­ter is, how­ev­er, in the spirit of “Co­in­ci­dences and Im­prob­a­bil­i­ties”, and a more pleas­ant read.)

Dyson’s de­fi­n­i­tion of events hap­pen­ing one per sec­ond seems fairly rea­son­able, and it then fol­lows that dur­ing one’s most ac­tive hours, a mil­lion will hap­pen dur­ing a month. It is un­clear why Dyson de­scribes Lit­tle­wood as hav­ing de­fined “mir­a­cles pre­cisely” as be­ing events with “a prob­a­bil­ity of one in a mil­lion”, since no de­fi­n­i­tion of “mir­a­cle” oc­curs in the pre­sumed source and the only use of the word “mir­a­cle” (in the snow­ball Hell ex­am­ple) refers to a prob­a­bil­ity as­tro­nom­i­cally rar­er, un­less we take Lit­tle­wood’s use of 106 as his de­fi­n­i­tion of a cri­te­ria & are free with putting “mir­a­cle” in Lit­tle­wood’s mouth. But even as­sum­ing this, nowhere in A Math­e­mati­cian’s Mis­cel­lany can I find any­thing like that analy­sis about 8 ac­tive hours a day or things hap­pen­ing one per sec­ond or a mil­lion “events” a month.

Where does ‘month’ keep com­ing from, any­way? I sus­pect that the ap­peal of month as the unit of time, rather than any other unit like minute or hour day or year or decade, re­flects the es­sen­tially memetic as­pect of Lit­tle­wood’s ob­ser­va­tions: he is skep­ti­cally ex­am­in­ing those sto­ries that peo­ple retell end­less­ly. If an ap­pro­pri­ately ‘mirac­u­lous’ story could be turned up every hour, it would quickly lose all nov­el­ty; but one good story every decade, or even year, is too rare, with pen­t-up de­mand, and a mag­a­zine could steal cir­cu­la­tion from more ret­i­cent ri­vals by re­port­ing ex­am­ples more fre­quent­ly, lead­ing to an in­ter­me­di­ate equi­lib­ri­um. Once a week or month sounds about right: a reg­u­lar source of en­ter­tain­ment by the ex­tra­or­di­nary, but not so fre­quent as to wear out its wel­come & won­der and be­come or­di­nary. (S­ince Lit­tle­wood was writ­ing in a less glob­al­ized me­dia en­vi­ron­ment, with a smaller effec­tive pop­u­la­tion size, a thresh­old of one in a mil­lion was ap­pro­pri­ate; but these days, to main­tain an ap­pro­pri­ate click­bait drip rate, a more strin­gent thresh­old may be re­quired, such as one in a bil­lion.) One can see this sort of tem­po­ral limit in out­rage cy­cles on so­cial me­di­a—they can’t hap­pen too often, be­cause par­ti­sans will be­come ex­hausted and top­ics will lose nov­el­ty, but since po­ten­tial out­rages are al­ways hap­pen­ing which can feed the need, quiet pe­ri­ods won’t last too long; thus, there seems to be a pe­ri­od­ic­ity around the week range, rather than, say, hour or year. Per­haps sim­i­lar­ly, in big so­ci­ety-wide is­sues not based on sin­gle in­ci­dents or out­liers, there is the mul­ti­-year “is­sue-at­ten­tion cy­cle”.

Are there any other sources be­sides Dyson?

Check­ing Google Scholar & Google Books for “Lit­tle­wood’s Law” prior to 2004, there are no hits for any­thing like “Lit­tle­wood’s Law of Mir­a­cles”. (There is one hit for an artillery/geometry math­e­mat­i­cal for­mula, and there is an amus­ing crit­i­cism of a math­e­mat­i­cal logic text­book by Boo­los 1986: “[The book] con­stantly vi­o­lates Lit­tle­wood’s law of ex­po­si­tion: Do not omit from the pre­sen­ta­tion of an ar­gu­ment two con­sec­u­tive steps.” But no mir­a­cles or sta­tis­tic­s.) Check­ing sev­eral dozen dis­cus­sions of the Law in gen­eral Google hits, all date after 2004 and ap­pear to trace back to Dyson 2004 or later sources.

The clos­est thing to a pre­de­ces­sor I found was the pa­per “Meth­ods for Study­ing Co­in­ci­dences”, & 1989, which dis­cusses the same topic as Littlewood/Charpak-Broch/Dyson, and in an­a­lyz­ing the same phe­nom­ena of “ex­tra­or­di­nary” events in or­di­nary life and mak­ing some cute analy­ses (like an ex­pla­na­tion of Baader-Mein­hof effects as in a ) coins a law, the :

The Law of Truly Large Num­bers. Suc­cinctly put, the law of truly large num­bers states: With a large enough sam­ple, any out­ra­geous thing is likely to hap­pen. The point is that truly rare events, say events that oc­cur only once in a mil­lion [as the math­e­mati­cian Lit­tle­wood (1953) re­quired for an event to be sur­pris­ing] are bound to be plen­ti­ful in a pop­u­la­tion of 250 mil­lion peo­ple. If a co­in­ci­dence oc­curs to one per­son in a mil­lion each day, then we ex­pect 250 oc­cur­rences a day and close to 100,000 such oc­cur­rences a year.

Go­ing from a year to a life­time and from the pop­u­la­tion of the United States to that of the world (5 bil­lion at this writ­ing), we can be ab­solutely sure that we will see in­cred­i­bly re­mark­able events. When such events oc­cur, they are often noted and record­ed. If they hap­pen to us or some­one we know, it is hard to es­cape that spooky feel­ing.

Di­a­co­nis & Mosteller 1989 an­tic­i­pate Dyson 2004 in defin­ing “one in a mil­lion” as a cri­te­ria for “sur­pris­ing” based on Lit­tle­wood’s in­vo­ca­tions of 106, and puts it in terms of in­di­vid­u­als & days, al­though they do not give any es­ti­mate in­volv­ing sec­onds or months for in­di­vid­u­als. Im­por­tant­ly, de­spite cit­ing Lit­tle­wood 1953, Di­a­co­nis & Mosteller 1989 do not men­tion or give any sign of know­ing any Law.

So, by all avail­able ev­i­dence, “Lit­tle­wood’s Law of Mir­a­cles” did not ex­ist in print be­fore Dyson 2004 coined it.

This sug­gests that Dyson, per­haps as a stu­dent at Cam­bridge Uni­ver­sity as he men­tions (1940–1942, Fel­low 1946–1949), heard an ex­tended or folk­loric ver­sion be­fore Lit­tle­wood 1953, and only men­tioned it 62 years later in print. More like­ly, Dyson is ex­tend­ing Di­a­co­nis & Mosteller 19898 but mis­at­tribut­ing it all to Lit­tle­wood based on a old mem­ory of the book (in a case of ) and ‘re­con­struct­ing’ an es­ti­mate of how often one mil­lion “events” would oc­cur in a kind of which leads to a nice time unit of a month.


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

  2. A pas­sage I like from by :

    “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 (which was a key source for ), al­though the sources for 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 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 (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 Rodolphe Gerol­stein, the hero of his fan­tas­ti­cally pop­u­lar se­r­ial novel (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).

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  3. The diffi­culty of do­ing ve­g­an­ism safe­ly, or its com­pat­i­bil­ity with ath­leti­cism is ap­par­ently a sore point for ve­g­ans, given the on­line pop­u­lar­ity of ve­gan gu­rus claim­ing to do both but who then even­tu­ally are dis­cov­ered to be hyp­ocrites & ex­pelled.↩︎

  4. 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.↩︎

  5. Nor­man Mal­colm, Lud­wig Wittgen­stein: A Mem­oir and a Bi­o­graph­i­cal Sketch by G. H. Von Wright, Sec­ond ed., with Wittgen­stein’s Let­ters to Mal­colm 1984, pg 30, pg35 (em­pha­sis in orig­i­nal).↩︎

  6. 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.)↩︎

  7. And the un­named clus­ter of these in­volv­ing so­cial con­ta­gion.↩︎

  8. Would Dyson have read Di­a­co­nis & Mosteller 1989? En­tirely pos­si­ble. Aside from be­ing an in­ter­est­ing pa­per Dyson might read any­way, while Dyson & Di­a­co­nis do not seem to over­lap at any in­sti­tu­tions, they both have worked on the­ory and eg both were speak­ers at a 2002 work­shop, so that is one way they might be ac­quainted with each oth­er’s work. Di­a­con­is’s ad­vi­sor Fred­er­ick Mosteller has no con­nec­tion with Dyson that I no­ticed al­though as a ma­jor sta­tis­ti­cian, founder of Har­vard’s sta­tis­tics de­part­ment, and pres­i­dent of mul­ti­ple ma­jor aca­d­e­mic or­ga­ni­za­tions, he needs no par­tic­u­lar con­nec­tion to have po­ten­tially in­ter­acted with Dyson many times.↩︎