The Power to Make Scientific Breakthroughs

This is Part IV of the Speci­fic­ity Sequence

So far, ev­ery­thing we’ve ac­com­plished with our speci­fic­ity pow­ers has been ad­mit­tedly kind of de­struc­tive: de­mol­ish­ing bad ar­gu­ments, judg­ing startup ideas as be­ing ei­ther definitely bad or only maybe bad… it would be nice to ac­com­plish some­thing more con­struc­tive.

Let’s try ac­ti­vat­ing our speci­fic­ity pow­ers for sci­ence. Be­cause at least in sci­ence, if we de­stroy a cur­rently-ac­cepted the­ory, then it’s a good sign that we’re prob­a­bly on our way to in­vent­ing a bet­ter the­ory!

Choos­ing Where to Zoom In

In The Power to De­mol­ish Bad Ar­gu­ments, we zoomed into generic claims by in­spect­ing spe­cific ex­am­ples of those claims. Ac­tu­ally, “zoom­ing in” is an in­com­plete de­scrip­tion of what we did. There’s a one-to-many re­la­tion­ship be­tween generic claims and spe­cific ex­am­ples. How do you choose the ex­am­ples? How do you choose where to zoom into a claim?

It de­pends if you’re try­ing to check ba­sic co­her­ence or pin­point a con­tra­dic­tion.

Check­ing Ba­sic Coherence

If you’re con­fused about what the claim even means, you can just try zoom­ing in any­where to look for any co­her­ent mean­ing of the claim.

This was our strat­egy for zoom­ing into Steve’s claim that “Uber ex­ploits its drivers by pay­ing them too lit­tle”. We asked Steve to give us any spe­cific ex­am­ple of what he was talk­ing about, and there were none to be found, so the dis­cus­sion came to an abrupt stop.

Some read­ers ac­cused me of hunt­ing for the weak­est part of Steve’s claim, so I ex­plained in a com­ment why it’s re­ally not like that:

I’m not say­ing to hunt for a coun­terex­am­ple that de­mol­ishes a claim. I’m say­ing to ask the per­son mak­ing the claim for a sin­gle spe­cific ex­am­ple that’s con­sis­tent with the gen­eral claim.
Imag­ine that a gen­eral claim has 900 ex­am­ples and 100 coun­terex­am­ples. Then I’m just ask­ing to see one of the 900 ex­am­ples :)

Pin­point­ing a Contradiction

When a gen­eral claim has already shown you plenty of spe­cific ex­am­ples, but it also has some ques­tion­able im­pli­ca­tions that may be con­tra­dic­tory or non­sen­si­cal, that’s when you want to go on the hunt for a coun­terex­am­ple.

This is how we chose where to zoom into Steve’s claim that “Ore­gon’s coastline is too straight. I wish all coastlines were less straight so that they could all have a bay!” We pur­posely chose to zoom in on the most ques­tion­able part of Ore­gon’s coastline, the least straight part, the part that would best con­tra­dict his gen­er­al­iza­tion, in or­der to best help me dis­am­biguate what his point is sup­posed to be.

Similarly, in “Surely You’re Jok­ing, Mr. Feyn­man!” (h/​t Eliezer), Richard Feyn­man talks about his trick to check whether a pro­posed the­o­rem is true by zoom­ing into a spe­cific ex­am­ple de­signed to pin­point a con­tra­dic­tion:

I had a scheme, which I still use to­day when some­body is ex­plain­ing some­thing that I’m try­ing to un­der­stand: I keep mak­ing up ex­am­ples. For in­stance, the math­e­mat­i­ci­ans would come in with a ter­rific the­o­rem, and they’re all ex­cited. As they’re tel­ling me the con­di­tions of the the­o­rem, I con­struct some­thing which fits all the con­di­tions. You know, you have a set (one ball) - dis­joint (two halls). Then the balls turn col­ors, grow hairs, or what­ever, in my head as they put more con­di­tions on. Fi­nally they state the the­o­rem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!”
If it’s true, they get all ex­cited, and I let them go on for a while. Then I point out my coun­terex­am­ple.
“Oh. We for­got to tell you that it’s Class 2 Haus­dorff ho­mo­mor­phic.”
“Well, then,” I say, “It’s triv­ial! It’s triv­ial!”

Note that if Feyn­man were just mak­ing up the sim­plest or most ob­vi­ous ex­am­ples, then the pro­posed the­o­rems would prob­a­bly always come out true about those ex­am­ples, be­cause the math­e­mat­i­ci­ans wouldn’t bother us­ing eas­ily-falsifi­able the­o­rems as challenges. In or­der to suc­cess­fully no­tice when the pro­posed the­ory is false, Feyn­man must always be pick­ing the cra­ziest ex­am­ples he can get away with un­der the math­e­mat­i­ci­ans’ grow­ing list of con­di­tions.

Thought Experiments

In math­e­mat­i­cal logic, there’s a for­mal term for zoom­ing into a the­ory: model-check­ing. Given a col­lec­tion of ax­ioms about sets or num­bers or what­ever, you probe their im­pli­ca­tions by look­ing at spe­cific ex­am­ples of struc­tures that obey those ax­ioms. Eliezer ex­plains:

Sup­pose you want to know whether it’s true that all pos­i­tive in­te­gers less than 5, when mul­ti­plied by 7, are less than 50. If you prove the gen­eral truth that all in­te­gers less than 5, times 7, are less than 35, by ma­nipu­lat­ing the ax­ioms of mul­ti­pli­ca­tion and in­equal­ity, that’s de­duc­tion. If you no­tice that the only pos­i­tive in­te­gers less than 5 are just {1, 2, 3, 4} and enu­mer­ate their prod­ucts {7, 14, 21, 28}, which are all less than 50, that’s model-check­ing.

But if we’re do­ing sci­ence, rather than math­e­mat­i­cal logic, then zoom­ing into a the­ory in or­der to probe its im­pli­ca­tions is called by a differ­ent name: thought ex­per­i­ment.

Say you want to make a rev­olu­tion­ary break­through in hu­man­ity’s un­der­stand­ing of the age-old con­cepts of space, time, light, and mo­tion.

What Albert Ein­stein said was, “Speci­fic­ity pow­ers, ac­ti­vate! Form of: thought ex­per­i­ment!” And he zoomed into the pre­vi­ously-un­der­stood laws of physics so he could get a bet­ter view of why they didn’t hold to­gether.

Ein­stein looked for spe­cific sce­nar­ios that would strain the ex­ist­ing the­o­ries of his time the most. But he was always care­ful to stay within the space of sce­nar­ios that the ex­ist­ing the­o­ries could still rea­son about, care­ful not to break any of a the­ory’s rules or as­sump­tions, but just zoom­ing into the parts that felt to him like loose screws.

He fa­mously de­scribed sce­nar­ios like rid­ing on a beam of light, or rid­ing a fast-mov­ing train and watch­ing for a light­ning flash while other peo­ple stand­ing on the plat­form are watch­ing for it too.

In one fa­mous thought ex­per­i­ment, Ein­stein imag­ined a man in a walled room in the setup shown here, and ob­served that the man wouldn’t be able to dis­t­in­guish whether his room is fixed in place and he’s in a grav­i­ta­tional field that pulls him left­ward (his “down”), or some­one is yank­ing on a rope to ac­cel­er­ate him and the room right­ward (his “up”).

Ein­stein then spent a few years do­ing hard math to figure out how the laws of physics had to work in or­der for those two spe­cific situ­a­tions to be fun­da­men­tally equiv­a­lent, and the an­swer he got was his Gen­eral The­ory of Rel­a­tivity.

What ex­actly is a “thought ex­per­i­ment” and how does it work? Wikipe­dia puts it like this:

As op­posed to phys­i­cal ex­per­i­ments, thought ex­per­i­ments do not re­port new em­piri­cal data. They can only provide con­clu­sions based on de­duc­tive or in­duc­tive rea­son­ing from their start­ing as­sump­tions. Thought ex­per­i­ments in­voke par­tic­u­lars that are ir­rele­vant to the gen­er­al­ity of their con­clu­sions. It is the in­vo­ca­tion of these par­tic­u­lars that give thought ex­per­i­ments their ex­per­i­ment-like ap­pear­ance.

Aha, they don’t work by ca­jol­ing the uni­verse into giv­ing us new data. All they do is give our brains meaty “par­tic­u­lars”—a.k.a. speci­fics — to chew on. Thought ex­per­i­ments are yet an­other demon­stra­tion of how speci­fic­ity makes our brains, and Ein­stein’s brain, work bet­ter.

When I asked Steve about zoom­ing into a strate­gi­cally-cho­sen area of Ore­gon’s coastline and look­ing at an in­dented area full of wa­ter, that was ba­si­cally a sim­ple thought ex­per­i­ment to challenge his “Ore­gon’s coastline is straight” the­ory. Ein­stein’s thought ex­per­i­ments were the same thing: zoom­ing into the pre­vi­ously-un­der­stood the­o­ries of physics so he could get a bet­ter view of why they didn’t hold to­gether.

You might think Steve’s state­ment about Ore­gon’s coastline was hardly a the­ory, and it’s too ridicu­lous to perform a real thought ex­per­i­ment on. But that’s only be­cause we already know that Steve isn’t mak­ing sense. Con­cepts like “phlo­gis­ton”, “lu­minifer­ous aether”, and even New­to­nian grav­ity are also pretty ridicu­lous in light of our cur­rent sci­en­tific un­der­stand­ing, but they’re all still perfectly valid the­o­ries to thought-ex­per­i­ment with.

Zoom­ing Out From Specifics

So far, we’ve seen a lot about the power of zoom­ing into speci­fics. Let’s see the power of start­ing with a fo­cus on col­lect­ing speci­fics and then zoom­ing out to a gen­eral the­ory.

In the 1830s, many in­tel­lec­tu­als were pas­sion­ately de­bat­ing the ques­tion: Do species of life evolve grad­u­ally from other species, or does God put them on Earth in one or more dis­crete “cre­ation events”?

Charles Dar­win had a pas­sion for mak­ing ob­ser­va­tions of the nat­u­ral world. In his fa­mous 5-year voy­age on the H.M.S. Bea­gle (whose main pur­pose was sup­posed to be map­ping the coast of South Amer­ica for the Bri­tish gov­ern­ment), he ob­served a wide va­ri­ety of an­i­mal species in South Amer­ica and the Gala­pa­gos is­lands and noted their similar­i­ties in de­tail.

For ex­am­ple, he saw a bunch of Gala­pa­gos tor­toise species which seemed al­most iden­ti­cal to one an­other, only differ­ing in lit­tle traits that made them adapted to their re­spec­tive en­vi­ron­ments:

Galá­pa­gos tor­toises are adapted for differ­ent feed­ing habits. The “sad­dle-backed” tor­toises have shells that rise in the front like a sad­dle. This adap­ta­tion makes it eas­ier for them to lift their necks and feed on taller cac­tus. “Dome-shaped” tor­toises live on is­lands where most of the veg­e­ta­tion is close to the ground, mak­ing it un­nec­es­sary for them to raise their heads to feed. Source

Plus, since Dar­win also had a pas­sion for ge­ol­ogy, he was also dig­ging up fos­sils and com­par­ing them to the area’s liv­ing species. By the time he got back to Bri­tain, he was ready to gen­er­al­ize what he saw:

Species are grad­u­ally evolv­ing all the time. There seem to be no dis­crete cre­ation events.

Next, he wanted to an­swer an­other ques­tion: What kind of nat­u­ral pro­cess drives species to evolve?

Once again, he set out to col­lect a bunch of spe­cific ob­ser­va­tions. He spent a lot of time with Bri­tish pi­geon breed­ers to un­der­stand the speci­fics of how the breed­ing pro­cess cre­ates new types of of pi­geons.

The car­rier pi­geon (bot­tom left) and the Brun­ner pouter (bot­tom right) were de­rived from the wild rock pi­geon (top). Source

Zoom­ing out from his ob­ser­va­tions of pi­geon breed­ing, Dar­win put forth this gen­er­al­iza­tion:

Some kind of nat­u­ral force that acts on species the way breed­ers do would be able to cause the ob­served evolu­tion of species.

As far as I know, those were Dar­win’s break­throughs lead­ing to the The­ory of Evolu­tion by Nat­u­ral Selec­tion, and they both con­sist of ob­serv­ing a bunch of spe­cific ex­am­ples be­fore ven­tur­ing to zoom out and make a gen­eral claim.

(Also, he and Alfred Rus­sel Wal­lace si­mul­ta­neously figured out that this “nat­u­ral breed­ing force” is a con­se­quence of Thomas Malthus’s ob­ser­va­tion that all pop­u­la­tions are even­tu­ally forced to com­pete for re­sources.)

So now you have two ways you can ac­ti­vate your speci­fic­ity pow­ers to help make sci­en­tific break­throughs:

  1. Zoom into ex­ist­ing the­o­ries: Take the cur­rent the­o­ries of your time and think about how they ap­ply to spe­cific hy­po­thet­i­cal sce­nar­ios in or­der to un­der­stand the con­tra­dic­tions you’ll need to fix with new the­o­ries.

  2. Zoom out from spe­cific ob­ser­va­tions: Make spe­cific ob­ser­va­tions of a kind of thing in the world un­til you can gen­er­al­ize a the­o­ret­i­cal in­sight that neatly or­ga­nizes all the spe­cific stuff you’ve been ob­serv­ing.

Try these out and let us know what you dis­cover.

Next post: The Power to Solve Cli­mate Change

Com­pan­ion post: Ex­am­ples of Examples