Stuff That Makes Stuff Happen

Fol­lowup to: Causal­ity: The Fabric of Real Things

Pre­vi­ous med­i­ta­tion:

“You say that a uni­verse is a con­nected fabric of causes and effects. Well, that’s a very Western view­point—that it’s all about mechanis­tic, de­ter­minis­tic stuff. I agree that any­thing else is out­side the realm of sci­ence, but it can still be real, you know. My cousin is psy­chic—if you draw a card from his deck of cards, he can tell you the name of your card be­fore he looks at it. There’s no mechanism for it—it’s not a causal thing that sci­en­tists could study—he just does it. Same thing when I com­mune on a deep level with the en­tire uni­verse in or­der to re­al­ize that my part­ner truly loves me. I agree that purely spiritual phe­nom­ena are out­side the realm of causal pro­cesses that can be stud­ied by ex­per­i­ments, but I don’t agree that they can’t be real.

Re­ply:

Fun­da­men­tally, a causal model is a way of fac­tor­iz­ing our un­cer­tainty about the uni­verse. One way of view­ing a causal model is as a struc­ture of de­ter­minis­tic func­tions plus un­cor­re­lated sources of back­ground un­cer­tainty.

Let’s use the Obe­sity-Ex­er­cise-In­ter­net model (re­minder: which is to­tally made up) as an ex­am­ple again:

We can also view this as a set of de­ter­minis­tic func­tions Fi, plus un­cor­re­lated back­ground sources of un­cer­tainty Ui:

This says is that the value x3 - how much some­one ex­er­cises—is a func­tion of how obese they are (x1), how much time they spend on the In­ter­net (x2), plus some other back­ground fac­tors U3 which don’t cor­re­late to any­thing else in the di­a­gram, all of which col­lec­tively de­ter­mine, when com­bined by the mechanism F3, how much time some­one spends ex­er­cis­ing.

There might be any num­ber of differ­ent real fac­tors in­volved in the pos­si­ble states of U3 - like whether some­one has a per­sonal taste for jog­ging, whether they’ve ever been to a tram­poline park and liked it, whether they have some gene that af­fects ex­er­cise en­dor­phins. Th­ese are all differ­ent un­known back­ground facts about a per­son, which might af­fect whether or not they ex­er­cise, above and be­yond obe­sity and In­ter­net use.

But from the per­spec­tive of some­body build­ing a causal model, so long as we don’t have any­thing else in our causal graph that cor­re­lates with these fac­tors, we can sum them up into a sin­gle fac­tor of sub­jec­tive un­cer­tainty, our un­cer­tainty U3 about all the other things that might add up to a force for or against ex­er­cis­ing. Once we know that some­one isn’t over­weight and that they spend a lot of time on the In­ter­net, all our un­cer­tainty about those other back­ground fac­tors gets summed up with those two known fac­tors and turned into a 38% con­di­tional prob­a­bil­ity that the per­son ex­er­cises fre­quently.

And the key con­di­tion on a causal graph is that if you’ve prop­erly de­scribed your be­liefs about the con­nec­tive mechanisms Fi, all your re­main­ing un­cer­tainty Ui should be con­di­tion­ally in­de­pen­dent:

or more generally

And then plug­ging those prob­a­ble Ui into the strictly de­ter­minis­tic Fi should give us back out our whole causal model—the same joint prob­a­bil­ity table over the ob­serv­able Xi.

Hence the idea that a causal model fac­tor­izes un­cer­tainty. It fac­tor­izes out all the mechanisms that we be­lieve con­nect vari­ables, and all re­main­ing un­cer­tainty should be un­cor­re­lated so far as we know.

To put it an­other way, if we our­selves knew about a cor­re­la­tion be­tween two Ui that wasn’t in the causal model, our own ex­pec­ta­tions for the joint prob­a­bil­ity table couldn’t match the model’s product

and all the the­o­rems about causal in­fer­ence would go out the win­dow. Tech­ni­cally, the idea that the Ui are un­cor­re­lated is known as the causal Markov con­di­tion.

What if you re­al­ize that two vari­ables ac­tu­ally are cor­re­lated more than you thought? What if, to make the di­a­gram cor­re­spond to re­al­ity, you’d have to hack it to make some Ua and Ub cor­re­lated?

Then you draw an­other ar­row from Xa to Xb, or from Xb to Xa; or you make a new node rep­re­sent­ing the cor­re­lated part of Ua and Ub, Xc, and draw ar­rows from Xc to Xa and Xb.

vs. vs.

(Or you might have to draw some ex­tra causal ar­rows some­where else; but those three changes are the ones that would solve the prob­lem most di­rectly.)

There was ap­par­ently at one point—I’m not sure if it’s still go­ing on or not—this big de­bate about the true mean­ing of ran­dom­iza­tion in ex­per­i­ments, and what counts as ‘truly ran­dom’. Is your ran­dom­ized ex­per­i­ment in­val­i­dated, if you use a merely pseudo-ran­dom al­gorithm in­stead of a ther­mal noise gen­er­a­tor? Is it okay to use pseudo-ran­dom al­gorithms? Is it okay to use shoddy pseudo-ran­dom­ness that a pro­fes­sional cryp­tog­ra­pher would sneer at? Clearly, us­ing 1-0-1-0-1-0 on a list of pa­tients in alpha­bet­i­cal or­der isn’t ran­dom enough… or is it? What if you pair off pa­tients in alpha­bet­i­cal or­der, and flip a coin to as­sign one mem­ber of each pair to the ex­per­i­men­tal group and the con­trol? How ran­dom is ran­dom?

Un­der­stand­ing that causal mod­els fac­tor­ize un­cer­tainty leads to the re­al­iza­tion that “ran­dom­iz­ing” an ex­per­i­men­tal vari­able means us­ing ran­dom­ness, a Ux for the as­sign­ment, which doesn’t cor­re­late with your un­cer­tainty about any other Ui. Our un­cer­tainty about a ther­mal noise gen­er­a­tor seems strongly guaran­teed to be un­cor­re­lated with our un­cer­tainty about a sub­ject’s eco­nomic sta­tus, their up­bring­ing, or any­thing else in the uni­verse that might af­fect how they re­act to Drug A...

...un­less some­body wrote down the out­put of the ther­mal noise gen­er­a­tor, and then used it in an­other ex­per­i­ment on the same group of sub­jects to test Drug B. It doesn’t mat­ter how “in­trin­si­cally ran­dom” that out­put was—whether it was the XOR of a ther­mal noise source, a quan­tum noise source, a hu­man be­ing’s so-called free will, and the world’s strongest cryp­to­graphic al­gorithm—once it ends up cor­re­lated to any other un­cer­tain back­ground fac­tor, any other Ui, you’ve in­val­i­dated the ran­dom­iza­tion. That’s the im­plicit prob­lem in the XKCD car­toon above.

But pick­ing a strong ran­dom­ness source, and us­ing the out­put only once, is a pretty solid guaran­tee this won’t hap­pen.

Un­less, ya know, you start out with a list of sub­jects sorted by in­come, and the ran­dom­ness source ran­domly hap­pens to put out 111111000000. Where­upon, as soon as you look at the out­put and are no longer un­cer­tain about it, you might ex­pect cor­re­la­tion and trou­ble. But that’s a differ­ent and much thornier is­sue in Bayesi­anism vs. fre­quen­tism.

If we take fre­quen­tist ideas about ran­dom­iza­tion at face value, then the key re­quire­ment for the­o­rems about ex­per­i­men­tal ran­dom­iza­tion to be ap­pli­ca­ble, is for your un­cer­tainty about pa­tient ran­dom­iza­tion to not cor­re­late with any other back­ground facts about the pa­tients. A dou­ble-blinded study (where the doc­tors don’t know pa­tient sta­tus) en­sures that pa­tient sta­tus doesn’t cor­re­late with the doc­tor’s be­liefs about a pa­tient lead­ing them to treat pa­tients differ­ently. Even plug­ging in the fixed string “1010101010” would be suffi­ciently ran­dom if that pat­tern wasn’t cor­re­lated to any­thing im­por­tant; the trou­ble is that such a sim­ple pat­tern could very eas­ily cor­re­late with some back­ground effect, and we can be­lieve in this pos­si­ble cor­re­la­tion even if we’re not sure what the ex­act cor­re­la­tion would be.

(It’s worth not­ing that the Cen­ter for Ap­plied Ra­tion­al­ity ran the June mini­camp ex­per­i­ment us­ing a stan­dard but un­usual statis­ti­cal method of sort­ing ap­pli­cants into pairs that seemed of roughly matched prior abil­ity /​ prior ex­pected out­come, and then flip­ping a coin to pick one mem­ber of each pair to be ad­mit­ted or not ad­mit­ted that year. This pro­ce­dure means you never ran­domly im­prob­a­bly get an ex­per­i­men­tal group that would, once you ac­tu­ally looked at the ran­dom num­bers, seem much more promis­ing or much worse than the con­trol group in ad­vance—where the fre­quen­tist guaran­tee that you used an ex­per­i­men­tal pro­ce­dure where this usu­ally doesn’t hap­pen ‘in the long run’, might be cold com­fort if it ob­vi­ously had hap­pened this time once you looked at the ran­dom num­bers. Roughly, this choice re­flects a differ­ence be­tween fre­quen­tist ideas about pro­ce­dures that make it hard for sci­en­tists to ob­tain re­sults un­less their the­o­ries are true, and then not car­ing about the ac­tual ran­dom num­bers so long as it’s still hard to get fake re­sults on av­er­age; ver­sus a Bayesian goal of try­ing to get the max­i­mum ev­i­dence out of the up­date we’ll ac­tu­ally have to perform af­ter look­ing at the re­sults, in­clud­ing how the ran­dom num­bers turned out on this par­tic­u­lar oc­ca­sion. Note that fre­quen­tist ethics are still be­ing obeyed—you can’t game the ex­pected statis­ti­cal sig­nifi­cance of ex­per­i­men­tal vs. con­trol re­sults by pick­ing bad pairs, so long as the coin­flips them­selves are fair!)


Okay, let’s look at that med­i­ta­tion again:

“You say that a uni­verse is a con­nected fabric of causes and effects. Well, that’s a very Western view­point—that it’s all about mechanis­tic, de­ter­minis­tic stuff. I agree that any­thing else is out­side the realm of sci­ence, but it can still be real, you know. My cousin is psy­chic—if you draw a card from his deck of cards, he can tell you the name of your card be­fore he looks at it. There’s no mechanism for it—it’s not a causal thing that sci­en­tists could study—he just does it. Same thing when I com­mune on a deep level with the en­tire uni­verse in or­der to re­al­ize that my part­ner truly loves me. I agree that purely spiritual phe­nom­ena are out­side the realm of causal pro­cesses that can be stud­ied by ex­per­i­ments, but I don’t agree that they can’t be real.

Well, you know, you can stand there all day, shout­ing all you like about how some­thing is out­side the realm of sci­ence, but if a pic­ture of the world has this...

...then we’re ei­ther go­ing to draw an ar­row from the top card to the pre­dic­tion; an ar­row from the pre­dic­tion to the top card (the pre­dic­tion makes it hap­pen!); or ar­rows from a third source to both of them (aliens are pick­ing the top card and us­ing telepa­thy on your cousin… or some­thing; there’s no rule you have to la­bel your nodes).

More gen­er­ally, for me to ex­pect your be­liefs to cor­re­late with re­al­ity, I have to ei­ther think that re­al­ity is the cause of your be­liefs, ex­pect your be­liefs to al­ter re­al­ity, or be­lieve that some third fac­tor is in­fluenc­ing both of them.

This is the more gen­eral ar­gu­ment that “To draw an ac­cu­rate map of a city, you have to open the blinds and look out the win­dow and draw lines on pa­per cor­re­spond­ing to what you see; sit­ting in your liv­ing-room with the blinds closed, mak­ing stuff up, isn’t go­ing to work.”

Cor­re­la­tion re­quires causal in­ter­ac­tion; and ex­pect­ing be­liefs to be true means ex­pect­ing the map to cor­re­late with the ter­ri­tory. To open your eyes and look at your shoelaces is to let those shoelaces have a causal effect on your brain—in gen­eral, look­ing at some­thing, gain­ing in­for­ma­tion about it, re­quires let­ting it causally af­fect you. Learn­ing about X means let­ting your brain’s state be causally de­ter­mined by X’s state. The first thing that hap­pens is that your shoelace is un­tied; the next thing that hap­pens is that the shoelace in­ter­acts with your brain, via light and eyes and the vi­sual cor­tex, in a way that makes your brain be­lieve your shoelace is un­tied.

p(Shoelace=tied, Belief=”tied”) 0.931
p(Shoelace=tied, Belief=”un­tied”) 0.003
p(Shoelace=un­tied, Belief=”un­tied”) 0.053
p(Shoelace=un­tied, Belief=”tied”) 0.012

This is re­lated in spirit to the idea seen ear­lier on LW that hav­ing knowl­edge ma­te­ri­al­ize from nowhere di­rectly vi­o­lates the sec­ond law of ther­mo­dy­nam­ics be­cause mu­tual in­for­ma­tion counts as ther­mo­dy­namic ne­gen­tropy. But the causal form of the proof is much deeper and more gen­eral. It ap­plies even in uni­verses like Con­way’s Game of Life where there’s no equiv­a­lent of the sec­ond law of ther­mo­dy­nam­ics. It ap­plies even if we’re in the Ma­trix and the aliens can vi­o­late physics at will. Even when en­tropy can go down, you still can’t learn about things with­out be­ing causally con­nected to them.


The fun­da­men­tal ques­tion of ra­tio­nal­ity, “What do you think you know and how do you think you know it?”, is on its strictest level a re­quest for a causal model of how you think your brain ended up mir­ror­ing re­al­ity—the causal pro­cess which ac­counts for this sup­posed cor­re­la­tion.

You might not think that this would be a use­ful ques­tion to ask—that when your brain has an ir­ra­tional be­lief, it would au­to­mat­i­cally have ir­ra­tional be­liefs about pro­cess.

But “the hu­man brain is not illog­i­cally om­ni­scient”, we might say. When our brain un­der­goes mo­ti­vated cog­ni­tion or other fal­la­cies, it of­ten ends up strongly be­liev­ing in X, with­out the un­con­scious ra­tio­nal­iza­tion pro­cess hav­ing been so­phis­ti­cated enough to also in­vent a causal story ex­plain­ing how we know X. “How could you pos­si­bly know that, even if it was true?” is a more skep­ti­cal form of the same ques­tion. If you can suc­cess­fully stop your brain from ra­tio­nal­iz­ing-on-the-spot, there ac­tu­ally is this use­ful thing you can some­times catch your­self in, wherein you go, “Oh, wait, even if I’m in a world where AI does get de­vel­oped on March 4th, 2029, there’s no lawful story which could ac­count for me know­ing that in ad­vance—there must’ve been some other pres­sure on my brain to pro­duce that be­lief.”


Since it illus­trates an im­por­tant gen­eral point, I shall now take a mo­ment to re­mark on the idea that sci­ence is merely one mag­is­terium, and there’s other mag­is­te­ria which can’t be sub­jected to stan­dards of mere ev­i­dence, be­cause they are spe­cial. That see­ing a ghost, or know­ing some­thing be­cause God spoke to you in your heart, is an ex­cep­tion to the or­di­nary laws of episte­mol­ogy.

That ex­cep­tion would be con­ve­nient for the speaker, per­haps. But causal­ity is more gen­eral than that; it is not ex­cepted by such hy­pothe­ses. “I saw a ghost”, “I mys­te­ri­ously sensed a ghost”, “God spoke to me in my heart”—there’s no difficulty draw­ing those causal di­a­grams.

The meth­ods of sci­ence—even so­phis­ti­cated meth­ods like the con­di­tions for ran­dom­iz­ing a trial—aren’t just about atoms, or quan­tum fields.

They’re about stuff that makes stuff hap­pen, and hap­pens be­cause of other stuff.

In this world there are well-paid pro­fes­sional mar­keters, in­clud­ing philo­soph­i­cal and the­olog­i­cal mar­keters, who have thou­sands of hours of prac­tice con­vinc­ing cus­tomers that their be­liefs are be­yond the reach of sci­ence. But those mar­keters don’t know about causal mod­els. They may know about—know how to lie per­sua­sively rel­a­tive to—the episte­mol­ogy used by a Tra­di­tional Ra­tion­al­ist, but that’s crude by the stan­dards of to­day’s ra­tio­nal­ity-with-math. Highly Ad­vanced Episte­mol­ogy hasn’t diffused far enough for there to be ex­plicit anti-episte­mol­ogy against it.

And so we shouldn’t ex­pect to find any­one with a back­ground story which would jus­tify evad­ing sci­ence’s skep­ti­cal gaze. As a mat­ter of cog­ni­tive sci­ence, it seems ex­tremely likely that the hu­man brain na­tively rep­re­sents some­thing like causal struc­ture—that this na­tive rep­re­sen­ta­tion is how your own brain knows that “If the ra­dio says there was an earth­quake, it’s less likely that your bur­glar alarm go­ing off im­plies a bur­glar.” Peo­ple who want to evade the gaze of sci­ence haven’t read Judea Pearl’s book; they don’t know enough about for­mal causal­ity to not au­to­mat­i­cally rea­son this way about things they claim are in sep­a­rate mag­is­te­ria. They can say words like “It’s not mechanis­tic”, but they don’t have the math­e­mat­i­cal fluency it would take to de­liber­ately de­sign a sys­tem out­side Judea Pearl’s box.

So in all prob­a­bil­ity, when some­body says, “I com­muned holis­ti­cally and in a purely spiritual fash­ion with the en­tire uni­verse—that’s how I know my part­ner loves me, not be­cause of any mechanism”, their brain is just rep­re­sent­ing some­thing like this:

Part­ner loves Uni­verse knows I hear uni­verse %
p u h 0.44
p u ¬h 0.023
p ¬u h 0.01
p ¬u ¬h 0.025
¬p u h 0.43
¬p u ¬h 0.023
¬p ¬u h 0.015
¬p ¬u ¬h 0.035

True, false, or mean­ingless, this be­lief isn’t be­yond in­ves­ti­ga­tion by stan­dard ra­tio­nal­ity.

Be­cause causal­ity isn’t a word for a spe­cial, re­stricted do­main that sci­en­tists study. ‘Causal pro­cess’ sounds like an im­pres­sive for­mal word that would be used by peo­ple in lab coats with doc­torates, but that’s not what it means.

‘Cause and effect’ just means “stuff that makes stuff hap­pen and hap­pens be­cause of other stuff”. Any time there’s a noun, a verb, and a sub­ject, there’s causal­ity. If the uni­verse spoke to you in your heart—then the uni­verse would be mak­ing stuff hap­pen in­side your heart! All the stan­dard the­o­rems would still ap­ply.

What­ever peo­ple try to imag­ine that sci­ence sup­pos­edly can’t an­a­lyze, it just ends up as more “stuff that makes stuff hap­pen and hap­pens be­cause of other stuff”.


Main­stream sta­tus.

Part of the se­quence Highly Ad­vanced Episte­mol­ogy 101 for Beginners

Next post: “Causal Refer­ence

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