# Meditations on Momentum

Cross-posted and lightly-ed­ited from The Deep Dish.

Epistemic sta­tus: de­scribing a gen­eral phe­nomenon; may not be cor­rect on ev­ery spe­cific point. may have used sci­en­tific terms in an an­noy­ing metaphor­i­cal fash­ion. el­e­ments of point­ing out the bleed­ing ob­vi­ous, hope­fully framed in a novel way.

tl;dr: pos­i­tive feed­back loops are a thing, think­ing in sys­tems/​ex­po­nen­tially is hard, in­ter­sec­tion­al­ity is un­der­rated.

“For to ev­ery­one who has, more will be given, and he will have an abun­dance. But from the one who has not, even what he has will be taken away.”
—MATTHEW 25:29

In 2013, un­known au­thor Robert Galbraith pub­lished his de­but novel… to crick­ets.

The first print run of The Cuckoo’s Cal­ling was 1500 copies. It’s not clear how many ac­tu­ally sold. The book oc­cu­pied 4709th place on Ama­zon’s best­sel­ler charts.

And there, per­haps it would have stayed, if the cuckoo in the nest had re­mained undis­cov­ered. The se­cret un­rav­el­led af­ter a few months: ex-mil­i­tary se­cu­rity con­trac­tor Galbraith was a pseudonym for J.K. Rowl­ing. As soon as the news broke, The Cuckoo’s Cal­ling soared to the num­ber one spot on Ama­zon. Sales in­creased by 150,000 per cent overnight. Copies from that first ne­glected print run are now worth thou­sands of dol­lars.

What’s the differ­ence be­tween Robert Galbraith and J.K. Rowl­ing? Clearly, be­ing a tal­ented writer is nec­es­sary, but not suffi­cient. Rowl­ing has mo­men­tum on her side. At this point, she could pub­lish the con­tents of a bowl of alpha­bet soup, and it would still sell bet­ter than 99 per cent of nov­els by hope­ful first-time au­thors.

This is a ‘no duh’ ex­am­ple, de­signed to get you nod­ding your head along. But mo­men­tum is ev­ery­where, and it’s rarely in plain sight. Without be­ing con­sciously aware of do­ing so, I’ve writ­ten about it in four do­mains:

#### 1. Popularity

Pop­u­lar things of­ten get their start through what amounts to good luck. The rapid as­cent is driven by some­thing even more pow­er­ful than rocket fuel: so­cial con­ta­gion. Our opinions and prefer­ences cluster to­gether, but it’s not be­cause we’ve care­fully eval­u­ated them on their mer­its. We just want to feel close to our fel­low so­cial apes, and have some­thing to gos­sip about around the wa­ter cooler.
In other words, pop­u­lar­ity is a lot like her­pes. After catch­ing a lucky ini­tial break, it man­ages to spread to a few hosts, then rides the ex­po­nen­tial growth curve un­til it has planted its gen­tle, blistery kiss on 60 per cent of the pop­u­la­tion.

With enough time on his side, [Fry’s] 93 cents trans­forms into $4.3 billion. If your gut in­stincts are scream­ing that this is stag­ger­ingly, ridicu­lously, wrong—well, you’re not alone. As Mark Zucker­berg put it: “Hu­mans don’t un­der­stand ex­po­nen­tial growth. If you fold a pa­per 50 times, it goes to the moon and back.” This is a deli­cious ex­am­ple, not only be­cause the imagery is so jar­ring—whoa, a tiny sheet of pa­per can do that?—but be­cause the Zuck him­self got it wrong. If you fold a piece of pa­per 50 times over, it doesn’t make a paltry re­turn trip to the moon—it goes all the way to the freakin’ sun. Hu­mans don’t un­der­stand ex­po­nen­tial growth, in­deed. #### 3. Entrepreneurship Some­thing idea-based can be sold over and over again with al­most no ex­tra time or effort. It’s in­finitely scal­able. Your de­but album might sell 10 copies (three of which your mum bought) or 10 mil­lion, but the amount of work that went into record­ing it was the same. Scal­able ca­reers don’t fol­low a nor­mal dis­tri­bu­tion, with a clear re­la­tion­ship be­tween effort and re­ward. In­stead, they pro­duce grotesque in­equal­ities. It doesn’t nec­es­sar­ily mat­ter how good you are, or how hard you work: a se­lect few peo­ple cap­ture al­most all the re­wards, while ev­ery­one else gets next to noth­ing. #### 4. Health What’s life like for a mod­er­ately fit and mus­cu­lar per­son? Well, ev­ery­thing works in your fa­vor. The wind is at your back. You’ve got mo­men­tum. The fit­ter you are, the bet­ter your hor­monal and metabolic health, the lower your body­fat, the more re­laxed you can be with your diet, the more fun life is, the more mo­ti­va­tion you have to train, the cooler feats you can perform, the deeper the habit is in­grained, and so on, in an end­less pos­i­tive feed­back loop. In fact, it’s even bet­ter than that. Al­most all these fac­tors are mu­tu­ally re­in­forc­ing. If you do screw up, and drunk­enly de­vour an en­tire box of ce­real, or take a week off from the gym to clock a new video game, it’s no big­gie. Any one link can seize up for a while, and the cy­cle will keep on turn­ing with­out it. …and a few more ex­am­ples I’ve col­lected, but haven’t writ­ten about: #### 5. Academia So­ciol­o­gist Robert Mer­ton coined the term ‘The Matthew Effect’, af­ter the parable of the tal­ents line quoted up top. Mer­ton no­ticed that fa­mous sci­en­tists of­ten get cred­ited for dis­cov­er­ies made by lesser-known re­searchers or grad stu­dents toiling in ob­scu­rity. Similarly, the suc­cess of any given pa­per of­ten de­pends on the promi­nence of the au­thor, and how many early cita­tions it hap­pens to re­ceive: So great is this prob­lem that we are tempted to turn again to the Scrip­tures to des­ig­nate the sta­tus-en­hance­ment and sta­tus-sup­pres­sion com­po­nents of the Matthew effect. We can de­scribe it as the Ec­cle­si­as­ti­cus com­po­nent, from the fa­mil­iar in­junc­tion ‘Let us now praise fa­mous men’. #### 6. Reading Psy­chol­o­gists have dis­cov­ered the same effect in ed­u­ca­tion. The longer it takes kids to learn how to read, the slower the de­vel­op­ment of their other cog­ni­tive skills and perfor­mance: The longer this de­vel­op­men­tal se­quence is al­lowed to con­tinue, the more gen­er­al­ized the defic­its will be­come, seep­ing into more and more ar­eas of cog­ni­tion and be­hav­ior. Or to put it more sim­ply – and sadly – in the words of a tear­ful nine-year-old, already fal­ling frus­trat­ingly be­hind his peers in read­ing progress, “Read­ing af­fects ev­ery­thing you do.” #### 7. Mar­ket prices For most in­tents and pur­poses, the effi­cient mar­kets hy­poth­e­sis is cor­rect. But even the No­bel prize-win­ning EMH cre­ator, Eu­gene Fama, has ad­mit­ted there is one ma­jor anomaly: mo­men­tum, which he de­scribes as the “biggest em­bar­rass­ment to the the­ory”. Here’s Fama’s old ad­vi­sor, Benoit Man­delbrot, on the long mem­ory of mar­ket pric­ing: What a com­pany does to­day—a merger, a spin-off, a crit­i­cal product launch—shapes what the com­pany will look like a decade hence; in the same way, its stock-price move­ments to­day will in­fluence move­ments to­mor­row. …a bot­tom line emerges. Stock prices are not in­de­pen­dent. To­day’s ac­tion can, at least slightly, af­fect to­mor­row’s ac­tion. The stan­dard model is, again, wrong. Had enough? There’s also the height of trees, the colour, bright­ness, and life­time of stars, the pro­lifer­a­tion of species, the halo and horns effect, af­fec­tive death spirals, and the ex­is­tence of life it­self. The prin­ci­ple of cu­mu­la­tive ad­van­tage spans physics, biol­ogy, psy­chol­ogy, eco­nomics, and cul­ture. It al­most seems like some un­der­ly­ing fea­ture of the uni­verse. Here’s Man­delbrot again: “Can you se­ri­ously com­pare the wind to a fi­nan­cial mar­ket, a gale to a rally, a hur­ri­cane to a crash? In terms of the un­der­ly­ing causes, cer­tainly not. But math­e­mat­i­cally, yes. It is an ex­traor­di­nary fea­ture of sci­ence that the most di­verse, seem­ingly un­re­lated, phe­nom­ena can be de­scribed with the same math­e­mat­i­cal tools.” On the macro scale of the uni­verse—the birth of stars, com­plex life boot­strapped from mud—mo­men­tum is kind of mirac­u­lous. For a brief can­dle-flicker, we get to re­sist the re­lentless march of en­tropy; cre­ate defi­ant bas­tions of or­der and beauty amongst the chaos. On the micro scale of in­di­vi­d­ual hu­man af­fairs—wealth, waistlines, pop­u­lar­ity, power—mo­men­tum is kind of ter­rify­ing. It makes us, and it breaks us. The 1 per cent con­trol al­most half of the world’s wealth, a small num­ber of star­tups suc­ceed as­tro­nom­i­cally, most books are sold by the J.K Rowl­ings of the world. Mo­men­tum leaves be­hind a dis­tinc­tive call­ing card, which looks some­thing like this: If this graph was drawn to scale, the tail would ex­tend sev­eral kilo­me­tres off your com­puter screen. For self-pub­lished ebooks, it’s worse: the me­dian num­ber of sales is zero. You will know these var­i­ous pat­terns as the ‘80/​20 rule’, power laws, long-tails, and Pareto dis­tri­bu­tions. The economist Vilfredo Pareto de­voted years to the pat­tern which now bears his name. Surely he has some kind words to say about his curvy wife? At the bot­tom of the [curve], men and women starve and chil­dren die young. In the broad mid­dle of the curve all is tur­moil and mo­tion: peo­ple ris­ing and fal­ling, climb­ing by tal­ent or luck and fal­ling by al­co­holism, tu­ber­cu­lo­sis and other kinds of un­fit­ness. At the very top sit the elite of the elite, who con­trol wealth and power for a time — un­til they are un­seated through rev­olu­tion or up­heaval by a new aris­to­cratic class. Yikes! If each in­stance of the Matthew effect stayed in its own lane, that would be un­fair enough. But as Pareto points out, they’re all hope­lessly en­tan­gled. Each of these do­mains – money, op­por­tu­nity, health, ed­u­ca­tion, tal­ent, pres­tige – not only com­pounds on it­self; but spills over into the other buck­ets too. Some in­ter­ac­tions are ob­vi­ous: a suc­cess­ful au­thor will al­most by defi­ni­tion make more money. Others are less so: a fit and healthy per­son might get pro­moted over an equally-qual­ified over­weight per­son, for no good rea­son at all. And that’s the pos­i­tive side of the ledger… ### The Down­ward Spiral My dear, here we must run as fast as we can, just to stay in place. And if you wish to go any­where you must run twice as fast as that. —Lewis Carroll Mo­men­tum also works in re­verse. Imag­ine your part­ner breaks up with you. You start drink­ing more. The drink­ing af­fects your work. You be­come iso­lated from friends and fam­ily. You stop ex­er­cis­ing and look­ing af­ter your­self. Even­tu­ally, you lose your job. Now you have money prob­lems, on top of your de­clin­ing phys­i­cal and men­tal health, and to­tal lack of sup­port net­work. Things don’t tend to de­te­ri­o­rate in a lin­ear fash­ion: you spiral down­wards faster and faster, un­til you fall off a cliff. The fur­ther down you slip, the harder it is to re­gain lost ground. I had a lit­tle taste of this re­cently. A se­ries of bad things came along in quick suc­ces­sion. Each of them would have been OK in iso­la­tion; to­gether, they put me into a tailspin. I pride my­self on be­ing put-to­gether, but I un­rav­el­led dis­turbingly quickly. Order begets or­der; chaos begets chaos. It was an un­com­fortable re­minder that ev­ery­one is always only a few strokes of mis­for­tune away from the abyss: there but for the grace of God go I. ### Fur­ther Down the Spiral Just to make it ex­plicit: the ti­tle of this post is an homage to Scott Alexan­der’s es­say Med­i­ta­tions on Moloch. As Scott points out in his epic close-read­ing of an Allen Gins­berg poem, there are ob­vi­ous things we could do to make the world a bet­ter place, but some in­visi­ble force stymies our efforts: If ev­ery­one hates the cur­rent sys­tem, who per­pet­u­ates it? And Gins­berg an­swers: “Moloch”. It’s pow­er­ful not be­cause it’s cor­rect – no­body liter­ally thinks an an­cient Carthag­i­nian de­mon causes ev­ery­thing – but be­cause think­ing of the sys­tem as an agent throws into re­lief the de­gree to which the sys­tem isn’t an agent. The same alien ‘oth­er­ness’ ap­plies to mo­men­tum. A hand­ful of A-list ac­tors are in­un­dated with roles, when tens of thou­sands of tal­ented hope­fuls would jump at the chance to eat the scraps from their table. One per cent of ev­ery­one owns half the wealth, while billions of oth­ers are des­per­ately poor. In ev­ery area of life, the peo­ple who are least in need of fur­ther ad­van­tage are most likely to re­ceive it. Al­most ev­ery­one is un­happy with this dis­tri­bu­tion of out­comes, but blam­ing ‘cap­i­tal­ism’ or ‘the gov­ern­ment’ or whichever tribe you hap­pen to hate might be miss­ing the point. If there is some blind force of na­ture op­er­at­ing be­hind the scenes, then the ex­act same pat­tern will con­tinue to per­sist (which might ex­plain why so­cial­ist utopias don’t tend to go ex­actly as planned). Back to Pareto, for more cheer­ful words of en­courage­ment: “There is no progress in hu­man his­tory. Democ­racy is a fraud. Hu­man na­ture is prim­i­tive, emo­tional, un­y­ield­ing. The smarter, abler, stronger, and shrewder take the lion’s share. The weak starve, lest so­ciety be­come de­gen­er­ate: One can com­pare the so­cial body to the hu­man body, which will promptly per­ish if pre­vented from elimi­nat­ing tox­ins.” As­sume we are deal­ing with some kind of all-per­va­sive force of na­ture. Moloch works tire­lessly to de­stroy ev­ery­thing hu­mans hold dear. The Matthew Effect/​mo­men­tum is more like the blind, alien god of evolu­tion—re­spon­si­ble for cre­at­ing ev­ery­thing hu­mans hold dear, but in the same mind­less fash­ion, smites en­tire species into oblivion. The uni­verse is nei­ther hos­tile nor benev­olent; it’s ut­terly in­differ­ent. What to do? ### The Lord Giveth, and The Lord Taketh Away The parable of the tal­ents says: you bet­ter use it or lose it. Get some mo­men­tum be­hind you. Start sav­ing money as early as pos­si­ble. Re­duce debt ag­gres­sively. Build be­havi­ours that com­pound, and nip bad habits in the bud as soon as pos­si­ble. Stay the hell away from the abyss. Sav­ing that first$100,000, as Char­lie Munger put it, is a bitch. You have to be the lit­tle rocket try­ing to es­cape the Earth’s grav­i­ta­tional pull, with all your en­g­ines on full thrust. Then you can take your foot off the gas a lit­tle, but don’t get com­pla­cent. If you lose your mo­men­tum, you’ll drift back to earth, slowly at first, then faster and faster, un­til you slam into the ground at 200 kph.

You have to fight tooth and claw to get some mo­men­tum, and then stay up there just as long as you pos­si­bly can.

This moral sounds sus­pi­ciously de­monic. But un­like Moloch’s favourite games, which are zero or nega­tive-sum, climb­ing the pyra­mid doesn’t always in­volve stamp­ing on the fingers of those be­low you.

Im­prov­ing your own health and fit­ness doesn’t make any­one else sickly. Mak­ing a con­sis­tent habit of read­ing, or learn­ing new skills, doesn’t make other peo­ple dumber. Con­trary to pop­u­lar be­lief, get­ting richer doesn’t nec­es­sar­ily make other peo­ple poorer. And of course, one of the best ways of get­ting rich in the first place is re­fus­ing to pay a pre­mium for pop­u­lar things that are pop­u­lar only be­cause they are pop­u­lar.

### Ex­tend­ing a Helping Hand

If you help your­self with­out hurt­ing any­one, that’s great, but it still leaves loads of peo­ple stuck at the bot­tom of the curve.

Three en­courag­ing ob­ser­va­tions: First, even if the over­all pat­tern never changes, at least the in­di­vi­d­ual data-points can move around.

We know this hap­pens, be­cause even mighty em­pires top­ple. Gen­er­a­tional wealth doesn’t last for­ever. Celebri­ties burn out or fade away. Trees get struck by light­ning. Stars im­plode. In dy­namic so­cieties, ev­ery­one gets their turn at the top.

The sec­ond en­courag­ing ob­ser­va­tion is that mo­men­tum reaches a point of diminish­ing re­turns.

Some­times there are hard phys­i­cal limits: a red­wood can only grow so tall be­fore it takes more en­ergy to pump wa­ter up from its roots than its new nee­dles can har­vest through pho­to­syn­the­sis. After a cer­tain point, a fit per­son has to train harder and harder to eke out smaller and smaller gains, and so on.

Even where there are no phys­i­cal limits, there’s a rapid drop-off in marginal util­ity. A fa­mous per­son re­ceives more offers and op­por­tu­ni­ties than they know what to do with. The same goes for wealth. After the first cou­ple mil­lion bucks, Bill Gates tells us, it’s the same ham­burger.

If you take these two ob­ser­va­tions to­gether, it makes a lot of sense to ex­tend a helping hand up, rather than keep push­ing for smaller and smaller gains. The pat­tern per­sists, but you cre­ate a lot more mo­bil­ity up and down the curve.

### Above and Beyond

Maybe Pareto was wrong.

The third en­courag­ing ob­ser­va­tion is that mo­bil­ity might be in­creas­ing, with­out a bloody rev­olu­tion. [EDIT: had an­other look, I don’t think the data ac­tu­ally sup­ports me here. damn!]

Hu­man na­ture is prim­i­tive and emo­tional, but not un­y­ield­ing. Even though we strug­gle to wrap our mon­key-minds around com­pound in­ter­est—much less so­cial con­ta­gion and non-lin­ear causal­itywe’re get­ting less bad at it.

It’s pretty cool that J.K. Rowl­ing de­liber­ately tried to play life on hard-mode again. It’s much more ex­cit­ing that more than 100 billion­aires have pledged to give away most (or all) of their for­tunes. And that thou­sands of or­di­nary peo­ple have made a life­time com­mit­ment to give at least 10 per cent of their in­come to the most effec­tive char­i­ties.

The parable of the tal­ents is pretty cut-throat. My guess is that it’s meant to be de­scrip­tive, not nor­ma­tive. And lots of peo­pleeven those at the top aren’t OK with it.

Sure, it’s the nat­u­ral or­der of things. But na­ture also gave us strych­nine, par­a­sitic wasps, and cud­dly meerkats that sys­tem­at­i­cally mur­der their in­fants. Na­ture is not to be trusted.

What’s the moral of the story? As far as I can see:

1. work your butt off to get some mo­men­tum be­hind you,

2. keep a watch­ful eye out for any signs of en­tropy creep­ing in,

3. once you hit the point of diminish­ing re­turns, fo­cus your efforts on helping other peo­ple up.

John Wesley, the founder of Method­ism, de­liv­ered a fa­mous ser­mon on this topic in the 18th cen­tury. I think he summed it up more pithily:

“Hav­ing, First, gained all you can, and, Se­condly saved all you can, Then give all you can.”
• Num­ber 4 is even worse than that. Phys­i­cal health is deeply en­tan­gled with men­tal health. Many never get the gen­er­a­tor spin­ning be­cause the first 6-18 months can have fairly illeg­ible feed­back loops de­pend­ing on where you start. And it can be stupid stuff. I only man­aged to start run­ning once I got re­ally frus­trated and tried 12 pairs of shoes to find some that didn’t bother my feet. It was a has­sle, but it per­ma­nently solved the prob­lem since I now know what pa­ram­e­ters to look for. Com­pound­ing small per­ma­nent wins doesn’t look all that im­pres­sive un­til you hit the knee of the curve and then it goes from famine to feast. Get­ting those suc­cess spirals ramp­ing up is why Peter­son is tel­ling peo­ple to clean their room and why Marie Kondo’s book bills it as Life Chang­ing Magic. If you in­ter­nal­ize the meta pat­tern in­stead of think­ing it’s just about clean­ing your room you’re off to the races. (IFS is KonMarie for the in­side of your head)

I’ve also referred to this as in­stan­ti­at­ing the spoon rein­vest­ment act. Deter­min­ing to rein­vest a por­tion of any gained spoons in spoon gen­er­at­ing ac­tivi­ties. See also, slack: https://​​thezvi.word­press.com/​​2017/​​09/​​30/​​slack/​​

• Ab­solutely. Another way of think­ing about it is a punc­tu­ated equil­ibrium: in some do­mains it feels like noth­ing is hap­pen­ing for the longest time, then you sud­denly ex­pe­rience ‘overnight’ suc­cess. I have no­ticed that I find pro­jects with de­layed or noisy feed­back loops su­per stress­ful, even if I know there’s a solid ex­pected pay­off wait­ing in the wings.

I am a fan of Marie Kondo and Peter­son for the ex­act rea­son you de­scribe, and enough peo­ple have men­tioned IFS now that I’ll have to check it out. What’s the ‘spoon’ thing in refer­ence to? This seems to be one of those LW-isms that I’ve missed some­how.

• Pro­moted to cu­rated: I think this was a bit over­looked by other read­ers, and so I think is par­tic­u­larly valuable to pro­mote. It also serves as maybe the best sys­tem-1 in­tro­duc­tion to at­tach­ment-effects/​mo­men­tum/​heavy-tail dis­tri­bu­tions that I’ve seen so far, and as such I am quite con­fi­dent I will re­fer to it mul­ti­ple times in the fu­ture.

Over­all the post is well writ­ten, and I par­tic­u­larly ap­pre­ci­ate the heavy use of quo­ta­tions and con­crete ex­am­ples, which make the post a lot live­lier than I think it would have been oth­er­wise.

I do think some of the op­ti­mism is un­war­ranted, and I think you tried to be a bit too “call-to-ac­tiony” at the end, in a way that I think wasn’t fully epistem­i­cally jus­tified by the rest of your post. I think a more muted end­ing, or maybe more jus­tifi­ca­tion for your recom­men­da­tions would help the post. But over­all I still re­ally en­joyed it and found it quite valuable.

• Thanks for the feed­back—much ap­pre­ci­ated! I agree that the end isn’t well sup­ported (at least, in the post). I write for a gen­eral au­di­ence who want clear, ac­tion­able take­aways. If I cross-post some­thing in the fu­ture, I’ll think about edit­ing it more heav­ily to fit the LW norms (i.e. ex­plain rather than per­suade).

• The post cre­ates un­nec­es­sary con­fu­sion by lump­ing “mo­men­tum” , “ex­po­nen­tial growth”, “com­pound in­ter­est”, and “heavy tail dis­tri­bu­tions”. Con­flat­ing these con­cepts to­gether on sys­tem-1 level into some vague un­differ­en­ti­ated pos­i­tive mess is likely harm­ful for to any­one as­piring to think about sys­tems clearly.

• It seems like it’s pretty con­sis­tently talk­ing about at­tach­ment style effects, do you have an ex­am­ple of where it con­flates that causal mechanism with some­thing else? (I.e. it pretty con­sis­tently talks about the phe­nomenon “hav­ing more of X gives you even more of X” which can hap­pen for a va­ri­ety of rea­sons, but seems like a com­mon enough phe­nom­ena to have a com­mon ab­strac­tion for)

• I don’t know what you mean by at­tach­ment style, but some ex­am­ples of the con­fla­tion...

Mo­men­tum is this: even if JK Rowl­ing’s next book is to­tal crap, it will still sell a lot of copies. Be­cause peo­ple have be­liefs, and be­cause they en­joyed her pre­vi­ous books, they have a prior that they will en­joy also the next one. It would take them sev­eral crap book to up­date.

Power laws are ubiquitous. This should be un­sur­pris­ing—power laws are the sim­plest func­tional form in the log­a­r­ith­mic pic­ture. If we use some sort of sim­plic­ity prior, we are guaran­teed to find them. If we use first terms of Tay­lor ex­pan­sion, we will find them. Log pic­ture is as nat­u­ral as the lin­ear one. Some­one should write a Med­i­ta­tion on Ben­ford’s law—you have an asymp­tot­i­cally straight line in log-log pic­ture of the prob­a­bil­ity than a num­ber starts with some digits (in al­most any real-life set of nu­mer­i­cal val­ues mea­sured in units; you can see this must be the case be­cause of in­var­i­ance to unit scal­ing)

This is maybe worth em­pha­siz­ing: no­body should be sur­prised to find power laws. No­body should pro­pose uni­ver­sal causal mechanism for power laws, it is as stupid as propos­ing one causal mechanism for straight lines in lin­ear pic­ture.

They are of­ten the re­sult of other power-law dis­tributed quan­tities. To take one ex­am­ple from the op… ini­tial dis­tri­bu­tion of masses for an ini­tail pop­u­la­tion of new stars is a trun­cated power law. I don’t know why, but the pro­posed mechanisms for this is for ex­am­ple tur­bu­lent frag­men­ta­tion of the ini­tial cloud, where the power law can come from the power spec­trum of su­per–sonic tur­bu­lence.

• Sure, but where does the post talk about power laws? It only talks about mo­men­tum-like effects, and there is a large liter­a­ture on how prefer­en­tial at­tach­ment can give rise to power-laws, so it has some re­la­tion, but I don’t see the ar­ti­cle talk­ing about power-laws in iso­la­tion. I brought up power-laws in the cu­ra­tion no­tice, be­cause they fre­quently show up in situ­a­tions with in­creas­ing marginal re­turns and mul­ti­plica­tive feed­back loops, but I don’t see how the ar­ti­cle en­courages any kind of con­fla­tion in this area given that it prac­ti­cally makes no refer­ence to it.

I also think you vastly over­state the case for power-laws. Most power-laws are much bet­ter fit by a log-nor­mal dis­tri­bu­tion. See this pa­per for more de­tails. I think the prior for log-nor­mal should be higher than the prior for power-law, be­cause of the mul­ti­plica­tive equiv­a­lent of the cen­tral limit the­o­rem.

• I’m still con­fused what you mean by mo­men­tum-like effects. Mo­men­tum is a very beau­tiful and crisp con­cept - the dual (canon­i­cal con­ju­gate) of po­si­tion, with all kinds of deep con­nec­tions to ev­ery­thing. You can view the whole uni­verse in the dual mo­men­tum space.

If the in­ten­tion is to have a con­cept ca in the shape of “all kinds of dy­nam­ics which can be rounded to dx=a.x” I agree it may be valuable to have a word for that, but why over­load mo­men­tum?

You asked for an ex­am­ple of where it con­flates that causal mechanism with some­thing else. I picked one ex­am­ple from this paragraph

There’s also the height of trees, the colour, bright­ness, and life­time of stars, the pro­lifer­a­tion of species, the halo and horns effect, af­fec­tive death spirals, and the ex­is­tence of life it­self.

So, as I un­der­stand it, I gave you an ex­am­ple (the dis­tri­bu­tion of star masses) which quite likely does not have any use­ful con­nec­tion to prefer­en­tial at­tach­ment or ex­po­nen­tial grow. I’m re­ally con­fused af­ter your last re­ply what is the state of our dis­agree­ment on this.

I’m ac­tu­ally scared to change the topic of the dis­cus­sion what sim­plic­ity means, but the ar­gu­ment is roughly this: if you have ar­bi­trary well be­haved func­tion, in the lin­ear pic­ture, you can ap­prox­i­mate it lo­cally by a straight line (the first term in the Tay­lor se­ries, etc.). And yes, you get bet­ter ap­prox­i­ma­tion by in­clud­ing more terms from the Tay­lor se­ries ex­pan­sion, or by non-lin­ear re­gres­sion, etc. Now, if you trans­late this to the log-log pic­ture, you will find out that power law is in some sense the sim­plest lo­cal ap­prox­i­ma­tion of any­thing. This is also the rea­son why peo­ple of­ten mis­tak­enly use power laws in­stead of log­nor­mal and other dis­tri­bu­tions—if you trun­cate the log­nor­mal and look just on part of the tail you can fit it with power law. Btw you nicely demon­strate this effect your­self—prefer­en­tial at­tach­ment of­ten ac­tu­ally leads to Yule-Si­mon dis­tri­bu­tion, and not a power law … but as usu­ally you can ap­prox­i­mate it.

• Oh, I as­sumed the au­thor was refer­ring to this ex­pla­na­tion for the dis­tri­bu­tion of star masses:

Here we pro­pose a new ap­proach ex­ploit­ing the tech­niques from the field of net­work sci­ence. We rep­re­sent a sys­tem of dense cores ac­cret­ing gas from the sur­round­ing diffuse in­ter­stel­lar medium (ISM) as a spa­tial net­work grow­ing by prefer­en­tial at­tach­ment and as­sume that the ISM den­sity has a self-similar frac­tal dis­tri­bu­tion fol­low­ing the Kol­mogorov tur­bu­lence the­ory. We effec­tively com­bine gravo­tur­bu­lent and com­pet­i­tive ac­cre­tion ap­proaches and pre­dict the ac­cre­tion rate to be pro­por­tional to the dense core mass: dM/​dt∝M. Then we de­scribe the dense core growth and demon­strate that the power-law core mass func­tion emerges in­de­pen­dently of the ini­tial dis­tri­bu­tion of den­sity fluc­tu­a­tions by mass. Our model yields a power law solely defined by the frac­tal di­men­sion­al­ities of the ISM and ac­cret­ing gas. With a proper choice of the low-mass cut-off, it re­pro­duces ob­ser­va­tions over three decades in mass. We also rule out a low-mass star dom­i­nated “bot­tom-heavy” IMF in a sin­gle star-form­ing re­gion.

I agree that if this is in­deed the case, the au­thor should provide a di­rect link to this the­ory, and ideally men­tion it ex­plic­itly as a the­ory among many.

I ac­tu­ally think the the­ory linked above is likely to be wrong, but don’t have any similar senses for all the other links pro­vided in the same para­graph, which seem to me to pretty ro­bustly be sys­tems in which prefer­en­tial at­tach­ment plays a large role.

I think the case of the star-dis­tri­bu­tion is more likely to be an hon­est er­ror where the au­thor heard about the prefer­en­tial at­tach­ment the­ory for the dis­tri­bu­tion of star-sizes some­where else, and used it as an ex­am­ple here even though it prob­a­bly isn’t the most el­e­gant ex­pla­na­tion of the phe­nom­ena, which I do think should be pointed out.

I agree that if the au­thor wanted to im­ply that “all power-law dis­tri­bu­tions are the re­sult of mo­men­tum as defined in this ar­ti­cle” then that would be bad, but I think the au­thor over­whelm­ingly used ex­am­ples that point to­wards a much nar­rower set of phe­nom­ena that also hap­pen to pro­duce things that look like power-laws (which I agree with you should ap­pear for a lot of differ­ent rea­sons and should not be thought to be much ev­i­dence for any spe­cific un­der­ly­ing causal model).

• 1. Go­ing through two of the ad­ja­cent links in the same para­graph:

With the trees, I only skimmed it, but if I get it cor­rectly, the linked ar­ti­cle pro­poses this new hy­poth­e­sis: To­gether these pieces of ev­i­dence point to a new hy­poth­e­sis: Small-scale, gap-gen­er­at­ing dis­tur­bances main­tain power-func­tion size struc­ture whereas later-suc­ces­sional for­est patches are re­spon­si­ble for de­vi­a­tions in the high tail.

and, also from the paper

Cur­rent the­o­ries ex­plain­ing the con­sis­tency of trop­i­cal for­est size struc­ture are con­tro­ver­sial. Ex­pla­na­tions based on scal­ing up in­di­vi­d­ual metabolic rates are crit­i­cized for ig­nor­ing the im­por­tance of asym­met­ric com­pe­ti­tion for light in caus­ing vari­a­tion in dy­namic rates. Other the­o­ries, which em­brace com­pe­ti­tion and scale in­di­vi­d­ual tree vi­tal rates through an as­sump­tion of de­mo­graphic equil­ibrium, are crit­i­cized for lack­ing par­si­mony, be­cause pre­dic­tions rely on site-level, size-spe­cific parameterization

(I also recom­mend look­ing on the plots with the “power law”, which are of the usual type of ap­prox­i­mat­ing some­thing more com­plex with a straight line in some in­ter­val.)

So, what we ac­tu­ally have in this: ap­par­ently differ­ent re­searchers propos­ing differ­ent hy­poth­e­sis to ex­plain the ob­served power-law-like data. It is far from con­clu­sive what the ac­tual rea­son is. As some­thing like pos­i­tive feed­back loops is quite ob­vi­ous part of the hy­poth­e­sis space if you see power-law-like data, you are al­most guaran­teed to find a pa­per which pro­poses some­thing in that di­rec­tion. How­ever, note that ar­ti­cle ac­tu­ally crit­i­cizes pre­vi­ous ex­pla­na­tions based more on “Matthews effect”, and pro­poses dis­tur­bances as a crit­i­cal part of the ex­pla­na­tion.

(Btw I do not claim any dishon­esty from the au­thor any­thing like that.)

Some­thing similar can be said about the Cam­brian ex­plo­sion which is the next link.

Halo and Horn effects are likely evolu­tion­ary adap­tive effects, track­ing some­thing real (traits like “hav­ing an ugly face” and “hav­ing higher prob­a­bil­ity of end­ing up in trou­ble” are likely cor­re­lated—the com­mon cause can be mu­ta­tion load /​ par­a­site load; you have things like the pos­i­tive man­i­fold).

And so on.

Sorry but I will not dis­sect ev­ery para­graph of the ar­ti­cle in this way. (Also it seems a bit fu­tile, as if I dig into spe­cific ex­am­ples, it will be in­ter­preted as nit-pick­ing)

2. Last at­tempt to ges­ture to­ward whats wrong with this whole. The best ap­prox­i­ma­tion of the cluster of phe­nom­ena the ar­ti­cle is point­ing to­ward is not “prefer­en­tial at­tach­ment” (as you pro­pose), but some­thing broader—“sys­tems with feed­back loops which can be in some ap­prox­i­ma­tion de­scribed by the differ­en­tial equa­tion dx = b.x”.

You can start to see sys­tems like that ev­ery­where, and get a sense of some­thing deep, ex­plain­ing life, uni­verse and ev­ery­thing.

One prob­lem with this: if you have a sys­tem de­scribed by a differ­en­tial equa­tion of the form “dx = f(x,..)”, and the func­tion f() is rea­son­able, you can ap­prox­i­mate it by its Tay­lor se­ries “f(x)=a+b.x+c.x.x+..”. Ob­vi­ously, the first or­der term is b.x. Un­for­tu­nately (?) you can say this even be­fore look­ing on the sys­tem.

So, vaguely speak­ing, when you start think­ing in this way, my in­tu­ition is it puts you in a big dan­ger of con­flat­ing some­thing about how you do ap­prox­i­ma­tions with causal ex­pla­na­tions. (I guess it may be a good deal for many peo­ple who don’t have s-1 in­tu­itions for Tay­lor se­ries or even log() func­tion)

• I ac­tu­ally had some similar alarm bells go off for con­fla­tion of con­cepts in the op, es­pe­cially be­cause the post speci­fi­cally ges­tures at one con­cept and doesn’t give ex­pla­na­tions of the differ­ent ex­am­ples where this might come up.

How­ever, on sec­ond thought I think I do like the con­cept this builds. To phrase it in your for­mal terms, I think it’s very use­ful to no­tice all the sys­tems in which the Tay­lor se­ries for has , ESPECIALLY when it’s com­pa­rably easy to con­trol via rather than just .

In this light, you can view mo­men­tum, ex­po­nen­tial growth, heavy-tails, etc., as all cases where a main com­po­nent of con­trol­ling or pre­dict­ing fu­ture is by pay­ing at­ten­tion to the term, and I claim this is an im­por­tant rev­e­la­tion to have at a va­ri­ety of lev­els.

Per­haps more rele­vant to your ac­tual crux, I also get shud­ders when peo­ple over­load physics terms with other mean­ings, but be­fore they were physics terms they were con­cepts for in­tu­itive things. Given that we view the world through phys­i­cal metaphors, I think it’s quite im­por­tant for us to use the best-fit­ting words for con­cepts. Then we can re­mind peo­ple of the differ­ent var­i­ants when peo­ple run into con­fla­tion­ary trou­ble. If we start off by nam­ing things with poor as­so­ci­a­tions we hold our­selves back more. If you have al­ter­na­tive name to “mo­men­tum” for this that you also think have good con­no­ta­tions though, I’d love to hear them.

• The sec­ond thing first: ”...but be­fore they were physics terms they were con­cepts for in­tu­itive things” is ac­tu­ally not true in this case: mo­men­tum did not mean any­thing, be­fore be­ing coined in physics. Than, it be­come used in a metaphor­i­cal way, but mostly con­gru­ently with the origi­nal physics con­cepts, as some­thing like “mass”x”ve­loc­ity”. It seems to me easy to imag­ine vivid pic­tures based of this metaphor, like ad­vanc­ing army con­quer­ing mile af­ter mile of en­emy ter­ri­tory hav­ing a mo­men­tum, or a scholar go­ing through page af­ter page of a difficult text. How­ever, this con­cept is not tied to the term (which is one of my cruxes).

To me, the origi­nal metaphor­i­cal mean­ing of mo­men­tum makes a lot of sense: you have a lot of sys­tems where you have some­thing like mass (closely con­nected to in­er­tia: you need great force to get some­thing mas­sive to move) and some­thing like ve­loc­ity—di­rec­tion and speed where the sys­tem is head­ing. I would ex­pect most peo­ple have this on some level.

Now, to the first thing sec­ond: I agree that it may be use­ful to no­tice all the sys­tems in which the Tay­lor se­ries for f has b>0, ESPECIALLY when it’s com­pa­rably easy to con­trol f via b∗x rather than just a. How­ever, some of the ex­am­ples in the origi­nal post do not match this pat­tern: some could be just sys­tems where, for ex­am­ple, you in­sert heavy-tailed dis­tri­bu­tion on the in­put, and you get heavy-tailed dis­tri­bu­tion on the out­put, or sys­tems where the term is what you should con­trol, or sys­tems where you should ac­tu­ally un­der­stand more about than the fact that is is has pos­i­tive first deriva­tive at some point.

What should be a good name for I don’t know, some ran­dom pro­saic ideas are snow­bal­ling, com­pound, faenus (from latin in­ter­est on money, gains, profit, ad­van­tage), com­pound in­ter­est. But likely there are is some more po­etic name, similarly to Moloch.

• Ok, we all know it. What are the tricks to get the pos­i­tive mo­men­tum?

Try many times?

Spend a lot of time to cre­ate a perfect memetic virus?

• As far as I can tell:

1. Be born to the right par­ents, in the right cir­cum­stances (not helpful, but im­por­tant to ac­knowl­edge).

2. Ap­ply your­self strate­gi­cally in ar­eas that com­pound (e.g. knowl­edge and skills, sav­ing and in­vest­ing, re­sis­tance train­ing, net­work­ing).

3. Ap­ply your effort wher­ever the yield is high­est. All of these do­mains fol­low an S-shaped curve, with early ex­po­nen­tial growth run­ning into an up­per ceiling of diminish­ing re­turns. At any given point in time, it might make sense to fo­cus pri­mar­ily on ac­cu­mu­lat­ing money, at an­other, skills and knowl­edge, at an­other, health and fit­ness, etc.

4. Choose goals that are com­ple­men­tary, so that each ‘bucket’ also helps to fill the oth­ers, and there’s no sin­gle point of failure (or at the very least, avoid goals which con­flict with one an­other).

5. Keep do­ing 2-4 for­ever. Even if you never hit that knee-shaped curve, a con­sis­tent and cu­mu­la­tive effort over time is pretty pow­er­ful in and of it­self.

• After analysing the cases when I was in up and down mo­men­tum, I con­cluded that there are other ad­di­tional points:

1.A new ac­tivity has ini­tially up mo­men­tum, as it cre­ates new con­nec­tions, peo­ple are in­ter­ested in your new pro­ject and you are in­spired. An old ac­tivity cre­ates down mo­men­tum, even if the qual­ity of the product has im­proved, as peo­ple be­come bored with it. (There are coun­terex­am­ples, e.g. Se­quences).

2. You may learn to “feel” which ac­tion has up mo­men­tum or down mo­men­tum and nav­i­gate ac­cord­ingly.

• I doubt there are tricks. Find and re­in­force the feed­back loops that seem to lead where you want. Look for sur­pris­ing cor­re­la­tions (diet and work perfor­mance, for in­stance). Be lucky in your start­ing po­si­tion and smartlucky in the be­hav­iors you choose to fo­cus on.

Also, rec­og­nize that half of peo­ple _ARE_ be­low me­dian on any mea­sure. In large pop­u­la­tions, there are very close to 0 who are the literal best at any­thing. Make sure your satis­fac­tion level is achiev­able, even as you seek top­ics on which you might ex­cel.

• Find the down hill paths

Also make them. Align the brain to work with and not against the self

• minor er­ror—in the sen­tence “For self-pub­lished ebooks, it’s worse: the me­dian num­ber of sales is zero.”, it should say modal (most com­mon num­ber) in­stead of me­dian (num­ber in the mid­dle of the dis­tri­bu­tion).

• To state it more plainly, the claim “the me­dian num­ber of sales is zero” is equiv­a­lent to the claim “more than half of self-pub­lished ebooks sell zero copies”.

• Which is also equiv­a­lent to say­ing “the modal is equiv­a­lent to 0” (since pre­sum­ably you can’t have nega­tive sales)

(Not dis­agree­ing, just found it in­ter­est­ing that all of these turn out to mean the same in this con­text)

• That’s not true? If there are five au­thors sel­l­ing 0, 0, 1, 2, and 3 books each, then the mode is 0 and the me­dian is 1.

• Woops, “im­plies” is not equal to “is equiv­a­lent to”. My bad.

• How do you know? Do you have a source for th claim that the me­dian isn’t 0?

• You may like to read Thomas piketty—cap­i­tal in the 21st cen­tury for his opinions on mo­bil­ity.

• I don’t agree with him but he cer­tainly has opinions that are loud in a par­tic­u­lar di­rec­tion.

I ap­pre­ci­ate the way he stated his se­lec­tion of facts and then stated the con­clu­sions he drew from those facts.

I don’t agree about the con­clu­sions but it’s in­for­ma­tion to take into ac­count.

• Well, can’t dis­agree with such an ab­stract ap­proach. Must be true some­where.

But I do. The world must look like that if you run a fast strat­egy. From here where I am with a slow strat­egy in the up­per mid­dle of the range where it looks mostly flat and the ends far away and the strat­egy is mostly to keep it that way.

As usual Scott Alexan­der ex­plains it much bet­ter:

https://​​slat­estar­codex.com/​​2018/​​12/​​03/​​book-re­view-evolu­tion­ary-psy­chopathol­ogy/​​