The Rocket Alignment Problem

The fol­low­ing is a fic­tional di­alogue build­ing off of AI Align­ment: Why It’s Hard, and Where to Start.

(Some­where in a not-very-near neigh­bor­ing world, where sci­ence took a very differ­ent course…)

ALFONSO: Hello, Beth. I’ve no­ticed a lot of spec­u­la­tions lately about “space­planes” be­ing used to at­tack cities, or pos­si­bly be­com­ing in­fused with malev­olent spirits that in­habit the ce­les­tial realms so that they turn on their own en­g­ineers.

I’m rather skep­ti­cal of these spec­u­la­tions. In­deed, I’m a bit skep­ti­cal that air­planes will be able to even rise as high as strato­spheric weather bal­loons any­time in the next cen­tury. But I un­der­stand that your in­sti­tute wants to ad­dress the po­ten­tial prob­lem of malev­olent or dan­ger­ous space­planes, and that you think this is an im­por­tant pre­sent-day cause.

BETH: That’s… re­ally not how we at the Math­e­mat­ics of In­ten­tional Rock­etry In­sti­tute would phrase things.

The prob­lem of malev­olent ce­les­tial spirits is what all the news ar­ti­cles are fo­cus­ing on, but we think the real prob­lem is some­thing en­tirely differ­ent. We’re wor­ried that there’s a difficult, the­o­ret­i­cally challeng­ing prob­lem which mod­ern-day rocket pun­ditry is mostly over­look­ing. We’re wor­ried that if you aim a rocket at where the Moon is in the sky, and press the launch but­ton, the rocket may not ac­tu­ally end up at the Moon.

ALFONSO: I un­der­stand that it’s very im­por­tant to de­sign fins that can sta­bi­lize a space­plane’s flight in heavy winds. That’s im­por­tant space­plane safety re­search and some­one needs to do it.

But if you were work­ing on that sort of safety re­search, I’d ex­pect you to be col­lab­o­rat­ing tightly with mod­ern air­plane en­g­ineers to test out your fin de­signs, to demon­strate that they are ac­tu­ally use­ful.

BETH: Aero­dy­namic de­signs are im­por­tant fea­tures of any safe rocket, and we’re quite glad that rocket sci­en­tists are work­ing on these prob­lems and tak­ing safety se­ri­ously. That’s not the sort of prob­lem that we at MIRI fo­cus on, though.

ALFONSO: What’s the con­cern, then? Do you fear that space­planes may be de­vel­oped by ill-in­ten­tioned peo­ple?

BETH: That’s not the failure mode we’re wor­ried about right now. We’re more wor­ried that right now, no­body can tell you how to point your rocket’s nose such that it goes to the moon, nor in­deed any pre­speci­fied ce­les­tial des­ti­na­tion. Whether Google or the US Govern­ment or North Korea is the one to launch the rocket won’t make a prag­matic differ­ence to the prob­a­bil­ity of a suc­cess­ful Moon land­ing from our per­spec­tive, be­cause right now no­body knows how to aim any kind of rocket any­where.

ALFONSO: I’m not sure I un­der­stand.

BETH: We’re wor­ried that even if you aim a rocket at the Moon, such that the nose of the rocket is clearly lined up with the Moon in the sky, the rocket won’t go to the Moon. We’re not sure what a re­al­is­tic path from the Earth to the moon looks like, but we sus­pect it might not be a very straight path, and it may not in­volve point­ing the nose of the rocket at the moon at all. We think the most im­por­tant thing to do next is to ad­vance our un­der­stand­ing of rocket tra­jec­to­ries un­til we have a bet­ter, deeper un­der­stand­ing of what we’ve started call­ing the “rocket al­ign­ment prob­lem”. There are other safety prob­lems, but this rocket al­ign­ment prob­lem will prob­a­bly take the most to­tal time to work on, so it’s the most ur­gent.

ALFONSO: Hmm, that sounds like a bold claim to me. Do you have a rea­son to think that there are in­visi­ble bar­ri­ers be­tween here and the moon that the space­plane might hit? Are you say­ing that it might get very very windy be­tween here and the moon, more so than on Earth? Both even­tu­al­ities could be worth prepar­ing for, I sup­pose, but nei­ther seem likely.

BETH: We don’t think it’s par­tic­u­larly likely that there are in­visi­ble bar­ri­ers, no. And we don’t think it’s go­ing to be es­pe­cially windy in the ce­les­tial reaches — quite the op­po­site, in fact. The prob­lem is just that we don’t yet know how to plot any tra­jec­tory that a ve­hi­cle could re­al­is­ti­cally take to get from Earth to the moon.

ALFONSO: Of course we can’t plot an ac­tual tra­jec­tory; wind and weather are too un­pre­dictable. But your claim still seems too strong to me. Just aim the space­plane at the moon, go up, and have the pi­lot ad­just as nec­es­sary. Why wouldn’t that work? Can you prove that a space­plane aimed at the moon won’t go there?

BETH: We don’t think we can prove any­thing of that sort, no. Part of the prob­lem is that re­al­is­tic calcu­la­tions are ex­tremely hard to do in this area, af­ter you take into ac­count all the at­mo­spheric fric­tion and the move­ments of other ce­les­tial bod­ies and such. We’ve been try­ing to solve some dras­ti­cally sim­plified prob­lems in this area, on the or­der of as­sum­ing that there is no at­mo­sphere and that all rock­ets move in perfectly straight lines. Even those un­re­al­is­tic calcu­la­tions strongly sug­gest that, in the much more com­pli­cated real world, just point­ing your rocket’s nose at the Moon also won’t make your rocket end up at the Moon. I mean, the fact that the real world is more com­pli­cated doesn’t ex­actly make it any eas­ier to get to the Moon.

ALFONSO: Okay, let me take a look at this “un­der­stand­ing” work you say you’re do­ing…

Huh. Based on what I’ve read about the math you’re try­ing to do, I can’t say I un­der­stand what it has to do with the Moon. Shouldn’t helping space­plane pi­lots ex­actly tar­get the Moon in­volve look­ing through lu­nar telescopes and study­ing ex­actly what the Moon looks like, so that the space­plane pi­lots can iden­tify par­tic­u­lar fea­tures of the land­scape to land on?

BETH: We think our pre­sent stage of un­der­stand­ing is much too crude for a de­tailed Moon map to be our next re­search tar­get. We haven’t yet ad­vanced to the point of tar­get­ing one crater or an­other for our land­ing. We can’t tar­get any­thing at this point. It’s more along the lines of “figure out how to talk math­e­mat­i­cally about curved rocket tra­jec­to­ries, in­stead of rock­ets that move in straight lines”. Not even re­al­is­ti­cally curved tra­jec­to­ries, right now, we’re just try­ing to get past straight lines at all –

ALFONSO: But planes on Earth move in curved lines all the time, be­cause the Earth it­self is curved. It seems rea­son­able to ex­pect that fu­ture space­planes will also have the ca­pa­bil­ity to move in curved lines. If your worry is that space­planes will only move in straight lines and miss the Moon, and you want to ad­vise rocket en­g­ineers to build rock­ets that move in curved lines, well, that doesn’t seem to me like a great use of any­one’s time.

BETH: You’re try­ing to draw much too di­rect of a line be­tween the math we’re work­ing on right now, and ac­tual rocket de­signs that might ex­ist in the fu­ture. It’s not that cur­rent rocket ideas are al­most right, and we just need to solve one or two more prob­lems to make them work. The con­cep­tual dis­tance that sep­a­rates any­one from solv­ing the rocket al­ign­ment prob­lem is much greater than that.

Right now ev­ery­one is con­fused about rocket tra­jec­to­ries, and we’re try­ing to be­come less con­fused. That’s what we need to do next, not run out and ad­vise rocket en­g­ineers to build their rock­ets the way that our cur­rent math pa­pers are talk­ing about. Not un­til we stop be­ing con­fused about ex­tremely ba­sic ques­tions like why the Earth doesn’t fall into the Sun.

ALFONSO: I don’t think the Earth is go­ing to col­lide with the Sun any­time soon. The Sun has been steadily cir­cling the Earth for a long time now.

BETH: I’m not say­ing that our goal is to ad­dress the risk of the Earth fal­ling into the Sun. What I’m try­ing to say is that if hu­man­ity’s pre­sent knowl­edge can’t an­swer ques­tions like “Why doesn’t the Earth fall into the Sun?” then we don’t know very much about ce­les­tial me­chan­ics and we won’t be able to aim a rocket through the ce­les­tial reaches in a way that lands softly on the Moon.

As an ex­am­ple of work we’re presently do­ing that’s aimed at im­prov­ing our un­der­stand­ing, there’s what we call the “tiling po­si­tions” prob­lem. The tiling po­si­tions prob­lem is how to fire a can­non­ball from a can­non in such a way that the can­non­ball cir­cum­nav­i­gates the earth over and over again, “tiling” its ini­tial co­or­di­nates like re­peat­ing tiles on a tes­sel­lated floor –

ALFONSO: I read a lit­tle bit about your work on that topic. I have to say, it’s hard for me to see what firing things from can­nons has to do with get­ting to the Moon. Frankly, it sounds an awful lot like Good Old-Fash­ioned Space Travel, which ev­ery­one knows doesn’t work. Maybe Jules Verne thought it was pos­si­ble to travel around the earth by firing cap­sules out of can­nons, but the mod­ern study of high-al­ti­tude planes has com­pletely aban­doned the no­tion of firing things out of can­nons. The fact that you go around talk­ing about firing things out of can­nons sug­gests to me that you haven’t kept up with all the in­no­va­tions in air­plane de­sign over the last cen­tury, and that your space­plane de­signs will be com­pletely un­re­al­is­tic.

BETH: We know that rock­ets will not ac­tu­ally be fired out of can­nons. We re­ally, re­ally know that. We’re in­ti­mately fa­mil­iar with the rea­sons why noth­ing fired out of a mod­ern can­non is ever go­ing to reach es­cape ve­loc­ity. I’ve pre­vi­ously writ­ten sev­eral se­quences of ar­ti­cles in which I de­scribe why can­non-based space travel doesn’t work.

ALFONSO: But your cur­rent work is all about firing some­thing out a can­non in such a way that it cir­cles the earth over and over. What could that have to do with any re­al­is­tic ad­vice that you could give to a space­plane pi­lot about how to travel to the Moon?

BETH: Again, you’re try­ing to draw much too straight a line be­tween the math we’re do­ing right now, and di­rect ad­vice to fu­ture rocket en­g­ineers.

We think that if we could find an an­gle and firing speed such that an ideal can­non, firing an ideal can­non­ball at that speed, on a perfectly spher­i­cal Earth with no at­mo­sphere, would lead to that can­non­ball en­ter­ing what we would call a “sta­ble or­bit” with­out hit­ting the ground, then… we might have un­der­stood some­thing re­ally fun­da­men­tal and im­por­tant about ce­les­tial me­chan­ics.

Or maybe not! It’s hard to know in ad­vance which ques­tions are im­por­tant and which re­search av­enues will pan out. All you can do is figure out the next tractable-look­ing prob­lem that con­fuses you, and try to come up with a solu­tion, and hope that you’ll be less con­fused af­ter that.

ALFONSO: You’re talk­ing about the can­non­ball hit­ting the ground as a prob­lem, and how you want to avoid that and just have the can­non­ball keep go­ing for­ever, right? But real space­planes aren’t go­ing to be aimed at the ground in the first place, and lots of reg­u­lar air­planes man­age to not hit the ground. It seems to me that this “be­ing fired out of a can­non and hit­ting the ground” sce­nario that you’re try­ing to avoid in this “tiling po­si­tions prob­lem” of yours just isn’t a failure mode that real space­plane de­sign­ers would need to worry about.

BETH: We are not wor­ried about real rock­ets be­ing fired out of can­nons and hit­ting the ground. That is not why we’re work­ing on the tiling po­si­tions prob­lem. In a way, you’re be­ing far too op­ti­mistic about how much of rocket al­ign­ment the­ory is already solved! We’re not so close to un­der­stand­ing how to aim rock­ets that the kind of de­signs peo­ple are talk­ing about now would work if only we solved a par­tic­u­lar set of re­main­ing difficul­ties like not firing the rocket into the ground. You need to go more meta on un­der­stand­ing the kind of progress we’re try­ing to make.

We’re work­ing on the tiling po­si­tions prob­lem be­cause we think that be­ing able to fire a can­non­ball at a cer­tain in­stan­ta­neous ve­loc­ity such that it en­ters a sta­ble or­bit… is the sort of prob­lem that some­body who could re­ally ac­tu­ally launch a rocket through space and have it move in a par­tic­u­lar curve that re­ally ac­tu­ally ended with softly land­ing on the Moon would be able to solve eas­ily. So the fact that we can’t solve it is alarm­ing. If we can figure out how to solve this much sim­pler, much more crisply stated “tiling po­si­tions prob­lem” with imag­i­nary can­non­balls on a perfectly spher­i­cal earth with no at­mo­sphere, which is a lot eas­ier to an­a­lyze than a Moon launch, we might thereby take one more in­cre­men­tal step to­wards even­tu­ally be­com­ing the sort of peo­ple who could plot out a Moon launch.

ALFONSO: If you don’t think that Jules-Verne-style space can­nons are the wave of the fu­ture, I don’t un­der­stand why you keep talk­ing about can­nons in par­tic­u­lar.

BETH: Be­cause there’s a lot of so­phis­ti­cated math­e­mat­i­cal ma­chin­ery already de­vel­oped for aiming can­nons. Peo­ple have been aiming can­nons and plot­ting can­non­ball tra­jec­to­ries since the six­teenth cen­tury. We can take ad­van­tage of that ex­ist­ing math­e­mat­ics to say ex­actly how, if we fired an ideal can­non­ball in a cer­tain di­rec­tion, it would plow into the ground. If we tried talk­ing about rock­ets with re­al­is­ti­cally vary­ing ac­cel­er­a­tion, we can’t even man­age to prove that a rocket like that won’t travel around the Earth in a perfect square, be­cause with all that re­al­is­ti­cally vary­ing ac­cel­er­a­tion and re­al­is­tic air fric­tion it’s im­pos­si­ble to make any sort of definite state­ment one way or an­other. Our pre­sent un­der­stand­ing isn’t up to it.

ALFONSO: Okay, an­other ques­tion in the same vein. Why is MIRI spon­sor­ing work on adding up lots of tiny vec­tors? I don’t even see what that has to do with rock­ets in the first place; it seems like this weird side prob­lem in ab­stract math.

BETH: It’s more like… at sev­eral points in our in­ves­ti­ga­tion so far, we’ve run into the prob­lem of go­ing from a func­tion about time-vary­ing ac­cel­er­a­tions to a func­tion about time-vary­ing po­si­tions. We kept run­ning into this prob­lem as a block­ing point in our math, in sev­eral places, so we branched off and started try­ing to an­a­lyze it ex­plic­itly. Since it’s about the pure math­e­mat­ics of points that don’t move in dis­crete in­ter­vals, we call it the “log­i­cal undis­crete­ness” prob­lem. Some of the ways of in­ves­ti­gat­ing this prob­lem in­volve try­ing to add up lots of tiny, vary­ing vec­tors to get a big vec­tor. Then we talk about how that sum seems to change more and more slowly, ap­proach­ing a limit, as the vec­tors get tinier and tinier and we add up more and more of them… or at least that’s one av­enue of ap­proach.

ALFONSO: I just find it hard to imag­ine peo­ple in fu­ture space­plane rock­ets star­ing out their view­ports and go­ing, “Oh, no, we don’t have tiny enough vec­tors with which to cor­rect our course! If only there was some way of adding up even more vec­tors that are even smaller!” I’d ex­pect fu­ture calcu­lat­ing ma­chines to do a pretty good job of that already.

BETH: Again, you’re try­ing to draw much too straight a line be­tween the work we’re do­ing now, and the im­pli­ca­tions for fu­ture rocket de­signs. It’s not like we think a rocket de­sign will al­most work, but the pi­lot won’t be able to add up lots of tiny vec­tors fast enough, so we just need a faster al­gorithm and then the rocket will get to the Moon. This is foun­da­tional math­e­mat­i­cal work that we think might play a role in mul­ti­ple ba­sic con­cepts for un­der­stand­ing ce­les­tial tra­jec­to­ries. When we try to plot out a tra­jec­tory that goes all the way to a soft land­ing on a mov­ing Moon, we feel con­fused and blocked. We think part of the con­fu­sion comes from not be­ing able to go from ac­cel­er­a­tion func­tions to po­si­tion func­tions, so we’re try­ing to re­solve our con­fu­sion.

ALFONSO: This sounds sus­pi­ciously like a philos­o­phy-of-math­e­mat­ics prob­lem, and I don’t think that it’s pos­si­ble to progress on space­plane de­sign by do­ing philo­soph­i­cal re­search. The field of philos­o­phy is a stag­nant quag­mire. Some philoso­phers still be­lieve that go­ing to the moon is im­pos­si­ble; they say that the ce­les­tial plane is fun­da­men­tally sep­a­rate from the earthly plane and there­fore in­ac­cessible, which is clearly silly. Space­plane de­sign is an en­g­ineer­ing prob­lem, and progress will be made by en­g­ineers.

BETH: I agree that rocket de­sign will be car­ried out by en­g­ineers rather than philoso­phers. I also share some of your frus­tra­tion with philos­o­phy in gen­eral. For that rea­son, we stick to well-defined math­e­mat­i­cal ques­tions that are likely to have ac­tual an­swers, such as ques­tions about how to fire a can­non­ball on a perfectly spher­i­cal planet with no at­mo­sphere such that it winds up in a sta­ble or­bit.

This of­ten re­quires de­vel­op­ing new math­e­mat­i­cal frame­works. For ex­am­ple, in the case of the log­i­cal undis­crete­ness prob­lem, we’re de­vel­op­ing meth­ods for trans­lat­ing be­tween time-vary­ing ac­cel­er­a­tions and time-vary­ing po­si­tions. You can call the de­vel­op­ment of new math­e­mat­i­cal frame­works “philo­soph­i­cal” if you’d like — but if you do, re­mem­ber that it’s a very differ­ent kind of philos­o­phy than the “spec­u­late about the heav­enly and earthly planes” sort, and that we’re always push­ing to de­velop new math­e­mat­i­cal frame­works or tools.

ALFONSO: So from the per­spec­tive of the pub­lic good, what’s a good thing that might hap­pen if you solved this log­i­cal undis­crete­ness prob­lem?

BETH: Mainly, we’d be less con­fused and our re­search wouldn’t be blocked and hu­man­ity could ac­tu­ally land on the Moon some­day. To try and make it more con­crete – though it’s hard to do that with­out ac­tu­ally know­ing the con­crete solu­tion – we might be able to talk about in­cre­men­tally more re­al­is­tic rocket tra­jec­to­ries, be­cause our math­e­mat­ics would no longer break down as soon as we stopped as­sum­ing that rock­ets moved in straight lines. Our math would be able to talk about ex­act curves, in­stead of a se­ries of straight lines that ap­prox­i­mate the curve.

ALFONSO: An ex­act curve that a rocket fol­lows? This gets me into the main prob­lem I have with your pro­ject in gen­eral. I just don’t be­lieve that any fu­ture rocket de­sign will be the sort of thing that can be an­a­lyzed with ab­solute, perfect pre­ci­sion so that you can get the rocket to the Moon based on an ab­solutely plot­ted tra­jec­tory with no need to steer. That seems to me like a bunch of math­e­mat­i­ci­ans who have no clue how things work in the real world, want­ing ev­ery­thing to be perfectly calcu­lated. Look at the way Venus moves in the sky; usu­ally it trav­els in one di­rec­tion, but some­times it goes ret­ro­grade in the other di­rec­tion. We’ll just have to steer as we go.

BETH: That’s not what I meant by talk­ing about ex­act curves… Look, even if we can in­vent log­i­cal undis­crete­ness, I agree that it’s fu­tile to try to pre­dict, in ad­vance, the pre­cise tra­jec­to­ries of all of the winds that will strike a rocket on its way off the ground. Though I’ll men­tion par­en­thet­i­cally that things might ac­tu­ally be­come calmer and eas­ier to pre­dict, once a rocket gets suffi­ciently high up –


BETH: Let’s just leave that aside for now, since we both agree that rocket po­si­tions are hard to pre­dict ex­actly dur­ing the at­mo­spheric part of the tra­jec­tory, due to winds and such. And yes, if you can’t ex­actly pre­dict the ini­tial tra­jec­tory, you can’t ex­actly pre­dict the later tra­jec­tory. So, in­deed, the pro­posal is definitely not to have a rocket de­sign so perfect that you can fire it at ex­actly the right an­gle and then walk away with­out the pi­lot do­ing any fur­ther steer­ing. The point of do­ing rocket math isn’t that you want to pre­dict the rocket’s ex­act po­si­tion at ev­ery microsec­ond, in ad­vance.

ALFONSO: Then why ob­sess over pure math that’s too sim­ple to de­scribe the rich, com­pli­cated real uni­verse where some­times it rains?

BETH: It’s true that a real rocket isn’t a sim­ple equa­tion on a board. It’s true that there are all sorts of as­pects of a real rocket’s shape and in­ter­nal plumb­ing that aren’t go­ing to have a math­e­mat­i­cally com­pact char­ac­ter­i­za­tion. What MIRI is do­ing isn’t the right de­gree of math­ema­ti­za­tion for all rocket en­g­ineers for all time; it’s the math­e­mat­ics for us to be us­ing right now (or so we hope).

To build up the field’s un­der­stand­ing in­cre­men­tally, we need to talk about ideas whose con­se­quences can be pin­pointed pre­cisely enough that peo­ple can an­a­lyze sce­nar­ios in a shared frame­work. We need enough pre­ci­sion that some­one can say, “I think in sce­nario X, de­sign Y does Z”, and some­one else can say, “No, in sce­nario X, Y ac­tu­ally does W”, and the first per­son re­sponds, “Darn, you’re right. Well, is there some way to change Y so that it would do Z?”

If you try to make things re­al­is­ti­cally com­pli­cated at this stage of re­search, all you’re left with is ver­bal fan­tasies. When we try to talk to some­one with an enor­mous flowchart of all the gears and steer­ing rud­ders they think should go into a rocket de­sign, and we try to ex­plain why a rocket pointed at the Moon doesn’t nec­es­sar­ily end up at the Moon, they just re­ply, “Oh, my rocket won’t do that.” Their ideas have enough vague­ness and flex and un­der­speci­fi­ca­tion that they’ve achieved the safety of no­body be­ing able to prove to them that they’re wrong. It’s im­pos­si­ble to in­cre­men­tally build up a body of col­lec­tive knowl­edge that way.

The goal is to start build­ing up a library of tools and ideas we can use to dis­cuss tra­jec­to­ries for­mally. Some of the key tools for for­mal­iz­ing and an­a­lyz­ing in­tu­itively plau­si­ble-seem­ing tra­jec­to­ries haven’t yet been ex­pressed us­ing math, and we can live with that for now. We still try to find ways to rep­re­sent the key ideas in math­e­mat­i­cally crisp ways when­ever we can. That’s not be­cause math is so neat or so pres­ti­gious; it’s part of an on­go­ing pro­ject to have ar­gu­ments about rock­etry that go be­yond “Does not!” vs. “Does so!”

ALFONSO: I still get the im­pres­sion that you’re reach­ing for the warm, com­fort­ing blan­ket of math­e­mat­i­cal re­as­surance in a realm where math­e­mat­i­cal re­as­surance doesn’t ap­ply. We can’t ob­tain a math­e­mat­i­cal cer­tainty of our space­planes be­ing ab­solutely sure to reach the Moon with noth­ing go­ing wrong. That be­ing the case, there’s no point in try­ing to pre­tend that we can use math­e­mat­ics to get ab­solute guaran­tees about space­planes.

BETH: Trust me, I am not go­ing to feel “re­as­sured” about rock­etry no mat­ter what math MIRI comes up with. But, yes, of course you can’t ob­tain a math­e­mat­i­cal as­surance of any phys­i­cal propo­si­tion, nor as­sign prob­a­bil­ity 1 to any em­piri­cal state­ment.

ALFONSO: Yet you talk about prov­ing the­o­rems – prov­ing that a can­non­ball will go in cir­cles around the earth in­definitely, for ex­am­ple.

BETH: Prov­ing a the­o­rem about a rocket’s tra­jec­tory won’t ever let us feel com­fort­ingly cer­tain about where the rocket is ac­tu­ally go­ing to end up. But if you can prove a the­o­rem which says that your rocket would go to the Moon if it launched in a perfect vac­uum, maybe you can at­tach some steer­ing jets to the rocket and then have it ac­tu­ally go to the Moon in real life. Not with 100% prob­a­bil­ity, but with prob­a­bil­ity greater than zero.

The point of our work isn’t to take cur­rent ideas about rocket aiming from a 99% prob­a­bil­ity of suc­cess to a 100% chance of suc­cess. It’s to get past an ap­prox­i­mately 0% chance of suc­cess, which is where we are now.

ALFONSO: Zero per­cent?!

BETH: Mo­dulo Cromwell’s Rule, yes, zero per­cent. If you point a rocket’s nose at the Moon and launch it, it does not go to the Moon.

ALFONSO: I don’t think fu­ture space­plane en­g­ineers will ac­tu­ally be that silly, if di­rect Moon-aiming isn’t a method that works. They’ll lead the Moon’s cur­rent mo­tion in the sky, and aim at the part of the sky where Moon will ap­pear on the day the space­plane is a Moon’s dis­tance away. I’m a bit wor­ried that you’ve been talk­ing about this prob­lem so long with­out con­sid­er­ing such an ob­vi­ous idea.

BETH: We con­sid­ered that idea very early on, and we’re pretty sure that it still doesn’t get us to the Moon.

ALFONSO: What if I add steer­ing fins so that the rocket moves in a more curved tra­jec­tory? Can you prove that no ver­sion of that class of rocket de­signs will go to the Moon, no mat­ter what I try?

BETH: Can you sketch out the tra­jec­tory that you think your rocket will fol­low?

ALFONSO: It goes from the Earth to the Moon.

BETH: In a bit more de­tail, maybe?

ALFONSO: No, be­cause in the real world there are always vari­able wind speeds, we don’t have in­finite fuel, and our space­planes don’t move in perfectly straight lines.

BETH: Can you sketch out a tra­jec­tory that you think a sim­plified ver­sion of your rocket will fol­low, so we can ex­am­ine the as­sump­tions your idea re­quires?

ALFONSO: I just don’t be­lieve in the gen­eral method­ol­ogy you’re propos­ing for space­plane de­signs. We’ll put on some steer­ing fins, turn the wheel as we go, and keep the Moon in our view­ports. If we’re off course, we’ll steer back.

BETH: … We’re ac­tu­ally a bit con­cerned that stan­dard steer­ing fins may stop work­ing once the rocket gets high enough, so you won’t ac­tu­ally find your­self able to cor­rect course by much once you’re in the ce­les­tial reaches – like, if you’re already on a good course, you can cor­rect it, but if you screwed up, you won’t just be able to turn around like you could turn around an air­plane –

ALFONSO: Why not?

BETH: We can go into that topic too; but even given a sim­plified model of a rocket that you could steer, a walk­through of the steps along the path that sim­plified rocket would take to the Moon would be an im­por­tant step in mov­ing this dis­cus­sion for­ward. Ce­les­tial rock­etry is a do­main that we ex­pect to be un­usu­ally difficult – even com­pared to build­ing rock­ets on Earth, which is already a fa­mously hard prob­lem be­cause they usu­ally just ex­plode. It’s not that ev­ery­thing has to be neat and math­e­mat­i­cal. But the over­all difficulty is such that, in a pro­posal like “lead the moon in the sky,” if the core ideas don’t have a cer­tain amount of solidity about them, it would be equiv­a­lent to firing your rocket ran­domly into the void.

If it feels like you don’t know for sure whether your idea works, but that it might work; if your idea has many plau­si­ble-sound­ing el­e­ments, and to you it feels like no­body has been able to con­vinc­ingly ex­plain to you how it would fail; then, in real life, that pro­posal has a roughly 0% chance of steer­ing a rocket to the Moon.

If it seems like an idea is ex­tremely solid and clearly well-un­der­stood, if it feels like this pro­posal should definitely take a rocket to the Moon with­out fail in good con­di­tions, then maybe un­der the best-case con­di­tions we should as­sign an 85% sub­jec­tive cre­dence in suc­cess, or some­thing in that vicinity.

ALFONSO: So un­cer­tainty au­to­mat­i­cally means failure? This is start­ing to sound a bit para­noid, hon­estly.

BETH: The idea I’m try­ing to com­mu­ni­cate is some­thing along the lines of, “If you can rea­son rigor­ously about why a rocket should definitely work in prin­ci­ple, it might work in real life, but if you have any­thing less than that, then it definitely won’t work in real life.”

I’m not ask­ing you to give me an ab­solute math­e­mat­i­cal proof of em­piri­cal suc­cess. I’m ask­ing you to give me some­thing more like a sketch for how a sim­plified ver­sion of your rocket could move, that’s suffi­ciently de­ter­mined in its mean­ing that you can’t just come back and say “Oh, I didn’t mean that” ev­ery time some­one tries to figure out what it ac­tu­ally does or pin­point a failure mode.

This isn’t an un­rea­son­able de­mand that I’m im­pos­ing to make it im­pos­si­ble for any ideas to pass my filters. It’s the pri­mary bar all of us have to pass to con­tribute to col­lec­tive progress in this field. And a rocket de­sign which can’t even pass that con­cep­tual bar has roughly a 0% chance of land­ing softly on the Moon.