(Somewhere in physical reality or the Internet, in a not-very-near neighboring world...)
Beta: Hello, Alpha. We've noticed that talk has become a great deal more common of late, about various speculations of "space-planes" 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. We're rather skeptical of these speculations, and indeed, we're a bit skeptical that airplanes will be able to rise as high as geosynchronous orbit anytime in the next century. But we understand that your institute wants to address the potential problem of malevolent or dangerous space-planes, and that you think this is an important present-day cause.
Alpha: That's... really not how we at the Mathematics of Intentional Rocketry Institute would phrase things. Yes, 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 hard, theoretically confusing problem which modern-day rocket punditry is mostly overlooking. Roughly, we're worried that even if you aim a rocket at the Moon, so that the nose of the rocket is clearly lined up with the Moon in the sky, the rocket won't go to the Moon.
Beta: Why?
Alpha: Well... that's not easy to explain. It doesn't have anything to do with malevolent celestial spirits, the rocket is still obeying the laws of causality and being driven by the operation of its own design. And it's not that no rocket can ever go to the Moon. We just don't know yet how to aim the nose.
Beta: Can you prove that a spaceplane aimed at the Moon won't go there?
Alpha: 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 gravitational pulls of the other celestial bodies and such. But we've been trying to figure out some admittedly unrealistic example problems in this area, on the order of assuming that all rockets move in straight lines. Even those unrealistic calculations strongly suggest on an intuitive level 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.
Beta: I'm not sure I understand. Is the problem that you're worried spaceplanes will be developed by bad, evil people like the Islamic Republic of North Korea, and they'll be sloppy with where they aim the spaceplane due to lack of concerned governmental oversight?
Alpha: In popular discussion, you see worries like "What if North Korea develops rocket technology first?" but that's not the failure mode we're worried about right now. Right now, nobody can tell you where you should point your rocket's nose to make it go to the Moon, or 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. What we think is the most important thing to do next is try 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 problems, but that one will probably take the most total time to work on, so it's the most urgent.
Beta: Okay, let me take a look at this "understanding" work you say you're doing... huh. Based on the explanations I've read about this 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?
Alpha: 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 -
Beta: 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.
Alpha: 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 right 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.
Beta: 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.
Alpha: We're not saying that our goal is to address the risk of the Earth falling into the Sun. What I'm trying to convey 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 returns to its exact initial position an infinite number of times, "tiling" the sequence of coordinates like repeating tiles on a tesselated floor -
Beta: I read a little bit about your work there, and I have to say, it's very hard for me to see what firing things from cannons has to do with getting to the Moon. Frankly, it sounds extremely like Good Old-Fashioned Space Travel, which everyone knows doesn't work. Maybe Jules Verne thought it was possible to get to geosynchronous orbit 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.
Alpha: We know that rockets will not actually be fired out of cannons. We really, really know that. We are 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 how why cannon-based space travel doesn't work.
Beta: But your current work is all about firing something out a cannon in such a way that it returns to its exact initial position. What could that possibly have to do with any realistic advice that you could give to a spaceplane pilot about how to travel to the Moon and back?
Alpha: 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 returning to the starting point, 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.
Beta: You talk 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 into 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.
Alpha: We are not worried about real rockets being fired out of cannons into 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 theoery 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 returns to its starting point... 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" that's a lot easier to analyze mathematically than a Moon launch, we might thereby take one more incremental step towards someday being the sort of people who could plot out a Moon launch.
Beta: 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.
Alpha: 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.
Beta: 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 rocket alignments at all. It seems like this weird side problem in abstract math.
Alpha: 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.
Beta: I just find it hard to imagine that future spaceplane rockets will be staring out their viewports going, "Oh, no, we don't have enough tiny vectors to add up! 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.
Alpha: 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.
Beta: So from a philanthropic perspective, what's a good thing that might happen if you solved the logical undiscreteness problem?
Alpha: Mainly, we'd be less confused and our research wouldn't be blocked and we 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.
Beta: 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 absolutely calculated and perfect. Look at the way Venus moves in the sky; usually it travels in one direction, and sometimes it goes retrograde in the other direction. We'll just have to steer as we go.
Alpha: 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 -
Beta: Why?
Alpha: 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.
Beta: Then why obsess over pure math that's too simple to describe the rich, complicated real universe where sometimes it rains?
Alpha: I know that a real rocket isn't a simple equation on a board. I know 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 right degree of 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, Y actually does not Z", and the first person is like "Darn, you're right. Well, is there some way to change Y so that it would 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 one of the people who have this enormous flowchart of all the machinery 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. Maybe those people are having fun as individuals, but it's impossible to incrementally build up a body of collective knowledge that way. The goal is to start building up a mental library of ideas whose consequences we understand. Some of the key ideas that seem to have understandable consequences haven't yet been expressed using math that really gets to their core point. But we do 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!"
Beta: I feel like 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. Since we can't obtain the absolute certainty you long for, there's no point in trying to pretend that we can do math that claims to provide absolute guarantees about spaceplanes.
Alpha: Trust us. We are not going to feel "reassured" about rocketry no matter what math we come up with. And we are well aware that you can't obtain a mathematical assurance of any physical proposition, nor assign probability 1 to any empirical statement.
Beta: But you talk about proving theorems, like proving that a cannonball will return to its starting point.
Alpha: That's not because proving a theorem about a rocket's trajectory will make comfortingly absolutely certain that the rocket actually ends up where it ought to go. 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.
Beta: Zero percent?!
Alpha: Modulo Cromwell's Rule, yes, zero percent. If you point a rocket's nose at the Moon, it does not go to the Moon.
Beta: I don't think future spaceplane engineers will actually be that silly, if you're right about direct Moon-aiming being a method that doesn't work. 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 people have been talking about this problem so long without considering such an obvious idea.
Alpha: We considered that idea very early on and we're pretty sure that it still doesn't get us to the Moon.
Beta: How about if I add some steering fins so that the rocket moves in a more curved trajectory? Can you prove that every possible version of that class of rocket designs won't go to the Moon, no matter what I try?
Alpha: Can you sketch out the trajectory that you think your rocket will follow?
Beta: It goes from the Earth to the Moon.
Alpha: In a bit more detail, maybe?
Beta: No, because in the real world there are always variable wind speeds and we don't have infinite fuel and our spaceplanes don't move in perfectly straight lines.
Alpha: Can you sketch out a trajectory that you think a simplified version of your rocket will follow, so I can look at the assumptions or derivations involved in that trajectory?
Beta: 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.
Alpha: Um... 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 -
Beta: Why not?
Alpha: 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 yours, 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, then maybe under the best-case conditions we should assign an 85% subjective credence in success, or something in that vicinity.
Beta: This is starting to sound a bit weird and paranoid, honestly. It sounds like you just said that if success seems 50-50 then the spaceplane has a 0% chance of working and if success seems certain then it has at most an 85% chance of working? I'm not much of Bayesian, but even I can tell when a probability assignment is that incoherent.
Alpha: 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, 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 is not 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.
Beta: I'm concerned that you seem to be dismissing my promising-sounding solution out of hand. Probably your organization suffers from Not-Invented-Here syndrome when it comes to considering ideas from outsiders. This is a known bias that causes people to consider very promising ideas, such as mine, and underestimate how promising they are. That is the most obvious explanation for what could be going on here.
Alpha: Well, since you've taken the initiative to raise the topic of cognitive biases and methodological flaws, I'll be equally frank: I think you're making a number of mistakes that are common in people considering the rocket alignment problem for the first time. Perhaps the most basic of these is that people encountering this problem for the first time try to seize on some single idea or strategy, and call that a solution. In the worst cases, they immediately pass on to talking about how to get the DeepSpace corporation to adopt their rocket safety proposals. Here at MIRI, we have several full-time researchers whose job it is to come up with clever ideas. None of them would dream of calling any of those ideas "a solution to the rocket alignment problem", because at best the next idea will only be one more piece of the puzzle. Our people don't get their hopes up that fast. The first cognitive question we train them to ask is not "Can I argue that this idea ought to solve the whole rocket alignment problem?" but rather "What would this idea actually do if I built a rocket like that?" When we bring a new researcher on board, our hazing ritual involves asking them to solve much simpler problems like "How would you design an ideal rocket to plunge into the Sun using infinite fuel?" and then we stand around the whiteboard arguing whether their rocket design really heads off into interstellar space or just explodes on the launchpad. You have an idea about trying to lead the Moon's predicted trajectory in the sky with the rocket's nose alignment. When I get back to the office, I might go to the whiteboard and see if that proposal is well-specified enough that I can say in any rigorous way what would happen, although I'm pretty sure that it does not, in fact, produce a soft, survivable Moon landing.
Beta: But you can't explain to me why it won't work.
Alpha: After I add enough detail that your proposal is well-specified enough to be analyzed, I'll be able to explain to other people at the office why my specification of it won't work. You, of course, will just reply "But that's not what I meant." Among the ways in which you're not approaching this problem using the methodology that we think is appropriate, is that you're having all these brilliant ideas and then waiting for someone else to show you why you're wrong. You need to take responsibility for looking for ways that your own ideas might fail, not wait around for MIRI to argue you out of them. You need to do your own work toward making those ideas rigorous, not wait for MIRI to make them rigorous and then complain that well of course that's not what I really had in mind. And above all, you need to SLOW DOWN. Right now, you're shooting from the hip -
Beta: What do you mean, shooting from the hip?
Alpha: I mean that you're forming opinions in a way that strikes me as, well... spontaneous.
Beta: I spent a lot of time looking at the consequences of spaceplanes! I talked to a lot of people and asked them for their opinions before forming mine!
Alpha: I didn't mean to imply that you'd put in a small amount of total labor or that you hadn't put enough raw effort into the problem. I understand that your own view on methodology says that, to be virtuous, you should talk with lots of people and ask them for their opinions, and then after this, it's okay to form your own. I wasn't trying to say that you'd put in too little effort to be virtuous under your own methodology. However, I think there are still some thought subprocesses inside your cognitive labors which are, by my standards, running from start to finish much too quickly.
Beta: Are you saying I need to talk to more experienced airplane pilots first?
Alpha: No, that is not what I'm saying.
(some time later)
Gamma: Hey, Alpha. I've got a new solution to the rocket alignment problem!
Alpha: That was your first mistake.
Gamma: Huh?
Alpha: Don't try to solve the rocket alignment problem. That's biting off way more than anyone could chew at this point. First, try to grasp the collective library of ideas whose consequences we allegedly understand. Stare at the equations until you feel like you have an intuition for what these simplified rockets actually do when they head off into the void; then vary the ideas, and see if you can understand what the variations would do. Then come up with a new idea; then, try to understand what your new idea would actually do. Very few things actually work, so if you ask "How does this fail?" instead of "How does this succeed?", you have the advantage of trying to rationalize a true proposition instead of a false proposition. If the results of your investigation are non-obvious, then you bring it to MIRI so we can add your idea to the current cognitive library. If it's an idea that, under unrealistic conditions, seems to do one more potentially useful thing we didn't understand how to do at all before, then that's really exciting and we'll hire you in the hope that you do it again someday.
Gamma: Look, let me just explain my proposed solution and then you can tell me what you think of it.
Alpha (sighing): Go ahead.
(30 minutes later)
Gamma: ...and then this box here represents the backup tailfin adjustment system! But of course, the real key is that we use three rockets tied together with heavy ropes, each rocket with an independent pilot given rations bought at a different supermarket, so that even if one of the rockets starts to go off course after the pilot eats a rotten grape, the pilots of the other two rockets can steer in the other direction and keep the rocket collectively on track.
Alpha: We have a saying around here: if you can't say how to steer towards the Moon using one rocket, you can't say how to steer towards the Moon using multiple rockets. If you knew how to get there, you'd just point the rocket that way, not have a whole system of rockets firing in different directions.
Gamma: But there are all sorts of cities that we can travel to by changing airplanes. There's no direct flight from Oakland to Mumbai. Doesn't that suggest that we might be able to reach the Moon with three rockets, even if we can't reach it with one rocket?
Alpha: I don't think that particular analogy carries over to the celestial reaches. I don't want to rule out all possible gains from using more than one rocket, but it seems unlikely to contribute to rocket safety or the rocket alignment problem in particular. If you can aim three rockets, you can aim one. If you can make three rockets not explode, you can make one rocket not explode.
Gamma: Because the failure probabilities are extremely likely to correlate highly between rockets? I don't see why that would be true. It seems to me that I can imagine lots of problems that would pull one rocket design off course, but not affect a different rocket design. So if we use three different rocket designs and rope them together, we should have a much higher chance of reaching the Moon.
Alpha: If I thought we currently knew enough to reach the Moon by default and we were now just trying to be robust against unusual non-default events, I might agree. Though even there, a system of three rockets might just be three times more likely to explode, if the two other rockets can't stop the first one from exploding. But we are not currently in a state of knowing how to reach the Moon barring weird anomalies. "Not having any goddamned idea where to point your rocket" is a failure mode that seems extremely likely to correlate between three different rocket designs. The root cause why I tend to be skeptical of multi-rocket designs is that, to an even greater degree than not helping with "not pointing your rocket in the right direction", multiple rockets seem unlikely to help with "not understanding rocket science well enough". But anyway, we'd better pass on so you can finish your whole presentation.
Gamma: Right! So, this box here, with a line to that box, represents the rocket explosion prevention system, which reports the current fuel temperature to the pilot and enables them to make a U-turn back toward Earth in the event that fuel temperatures are rising too quickly...
(30 more minutes later)
Gamma (standing next to a large whiteboard now entirely covered with boxes with lines to other boxes): ...and that's how this rocket design also helps to prevent thieves from stealing lunar metals from the return flights, once systematic trade is set up between the Moon and Earth. So, what do you think?
Alpha: I think your proposal has too many lines and boxes, and you should simplify it down to one idea that you think is new and interesting and whose local consequences you try to make solid, defensible statements about. Less "And then we have to make sure that lunar mining doesn't disrupt countries that presently produce metals", and more "I believe that relatively smoother surfaces will stay relatively cooler during movement through the atmosphere, and I believe that otherwise the rocket's skin might catch fire, and here's why I believe that, and what assumed similarity of atmospheric friction to solid friction would need to hold." Take one idea, explicitly state your other assumptions especially the ones that other people might dispute, and try to lay out a solid path from your premises to your conclusions, marking new required assumptions whenever necessary.
Gamma: So you don't think my proposal would be able to land on the Moon?
Alpha: Once the diagram has more than three boxes in it, my usual reaction is less "You might miss the Moon" and more "You will not go to space today". This proposal is not well-specified, and if somebody did well-specify it then it couldn't be built, and if Omega materialized a copy for us then it would explode as soon as it was fueled, and if it didn't explode it would dive straight into the Earth, and if it didn't dive straight into the Earth it wouldn't rise more than ten meters off the ground. And, don't get me wrong, if something can't realistically get ten meters off the ground but might still move in an interesting way given unphysically powerful fuel, I'm happy to assume that the rocket has whatever unrealistic fuel is required, and try to understand what trajectory it would follow in that case. And in that case, not even God knows where this monstrosity would end up. That might sound a bit harsh, but it shouldn't dismay you because with all the boxes and lines you drew, it's not surprising that I think at least one of the boxes contains a design element that doesn't work period.
Gamma: But I am dismayed! I think your organization has not-invented-here syndrome about my proposal, and I'm going to take it to the DeepSpace corporation instead.
Alpha (sighing again): I do wish you wouldn't.
Alpha: We're worried that most of the current proposals we've read for steering the rockets basically just say "We'll point it at the Moon and fire the engines", and our own preliminary analysis suggests that this kind of rocket doesn't go anywhere near the Moon, even if the only forces acting on the rocket are its own engines. Actually, it's a bit worse than this, the proposals that call for aiming the rocket in the general direction of the Moon are the good ones, there seem to be an awful lot of rocketeers out there who are solely concerned with rising higher than geosynchronous orbit.
Alpha: As we believe for reasons that it would torture this metaphor to try to describe in rocketry language, if a rocket lands on the Moon, that's extremely good. But if any rocket is successfully launched at faster than escape velocity and it doesn't land on the Moon, that's extremely bad -
Beta: Yes, it's clear that you have a number of weird assumptions at work, such as this concept of "escape velocity". Why wouldn't spaceplanes eventually slow down and halt in the celestial atmosphere, which could easily be even more resistant than the atmosphere on Earth? Special Relativity says that no rocket can go infinitely fast, and that seems to argue against them moving at dangerous speeds.
Alpha: The concept of "escape velocity" isn't as non-mainstream as you seem to think; it's been a pretty well-known hypothesis since the days the field of rocketry got started.