In space, no-one can reason by analogy

Part of my series on common misconceptions in space journalism.

Humans evolved a rare symbolic reasoning ability during our emergence over the last million or so years. As running apes, we lacked the usual evolutionary features such as sharp teeth, claws, spines, poison, and armor. Instead, we deployed social structures and intelligence to bootstrap science and technology from stone tools to synthetic elements.

Symbolic reasoning, and indeed much of scientific progress, is the process of understanding things in terms of other things. By creating abstractions, humans are able to quickly solve new problems, predict the future, and ultimately pass on brainy genes to the next generation.

We’re so good at it, in fact, that we often barely notice these abstractions even with concerted effort. There’s nothing natural about driving or browsing Twitter, but almost all humans can learn to do it very quickly. This is not automatic – other skills are much harder to learn, such as playing violin or performing surgery.

When it comes to modelling the natural world, analogies are powerful mechanisms for reasoning, education, and communication, because they rely on little more than universally common experience and are quick to articulate. As an example, water flow is commonly used as an analogy for electricity, while the rubber sheet is used as an analogy for gravity.

What analogies gain in convenience they lose in precision, so all analogies are, to some extent, wrong. The water electricity analogy is useless for designing radios or transformers, while the rubber sheet doesn’t actually help people understand why gravity mixes space and time.

The alternative to employing analogies is to break down the problem into fundamental concepts and reason by first principles. This process, while relatively formulaic, is tougher to learn and generally much slower, and almost impossible to communicate between people unless they are both already experts in the same thing.

As a halfway measure, it is useful to measure the wrongness of an analogy by trying to break it, either by relaxing an assumption or taking it to some limit. At the least, practicing this skill can help to avoid the more obvious errors and sharpen argumentative abilities! Deep insight is unlikely to result, however, except by thorough first principles derivation.

Image result for lunar gas station

To the topic at hand. Space travel is an unusual combination of exciting and esoteric, so an entire ecosystem of handy analogies has developed to help journalists explain incredibly technical information to interested lay people. This, like other aspects of science communication is a worthwhile goal.

Where it falls down is when the pros resort to analogies instead of first principles reasoning, and get things wrong as a result.

Space travel is esoteric and so different from every day experience that it’s simply not possible to use analogies in a technically useful way. Of course designers employ symbolic abstractions but these are (hopefully) built on a rigorous foundation.

As an example, the process of designing and building a Mars rover employs over 400 engineering subspecialities. There will never be a human with more than an indicial understanding of even a subset of these. Spacecraft are complicated because the problems their designs solve are really tough. Because no-one can specialize in every area, it falls to systems people to define the interfaces and tie it together, and here it can be almost irresistible to use analogies.

What are some examples of popular but uselessly inaccurate analogies in space?

  • Rockets as generic transport. The idea that because rockets transport cargo they’re like trucks or planes, but somehow cost 1000x as much. What rockets do is so ridiculously difficult it is hard for non-specialists to grasp. A really good rocket, broken into two stages, can launch about 4% of its launch mass into orbit. Something like 85% of that mass is fuel. That fuel is burned so violently that the engines would melt except that they’re literally made of coolant channels. Most terrestrial vehicles are built with a safety margin of at least 50%. A few bad welds on a car is okay because it’s designed to be stronger than it needs to be. On a rocket, there’s no room for safety margin. Every single part needs to be exactly as strong and heavy as it needs to be, which means every weld might need X-ray inspection. Every panel might need painstaking pockets milled away. Every piece of metal must be tested to ensure it meets material property specifications. Rockets are in a class of their own, and each type should be modeled as an independent vehicle.
  • The moon is a stepping stone, a way station, or gas station in space. This is partly covered in my blog on Lunar water. For conventional travel, stepping stones are useful ways to nimbly cross a stream without getting feet wet. Gas stations are essential for internal combustion vehicles traveling long distances. But neither of these analogies makes any sense in the context of space. The moon is made of rocks, but it’s not in the middle of a stream. Traveling long distances in space requires time but no constant consumption of fuel. The most fuel intensive step is getting from Earth to Low Earth Orbit (LEO). The next most is escaping LEO, whether to the Moon or Mars or anywhere else. Landing on the Moon takes just as much effort as launching from the Moon, since it has no atmosphere to slow down in. As a result, the Moon is on the way to nowhere except itself. Indeed, just getting to the Lunar surface to refuel would consume more fuel than going directly to almost anywhere else in the inner solar system.
  • The Lunar gateway as a gas station or stepping stone. Similar to the Moon, there’s no value in stopping somewhere along the way to somewhere else in space. For more detail, see my blogs on Lunar exploration architectures, or the Lunar Gateway specifically. Typically, the injection burn is performed in LEO to exploit the Oberth effect, and the vehicle coasts the rest of the way. The Lunar gateway also doesn’t have its own fuel supply, so any refueling would require dedicated tankers. But since all rockets are hyperfocused specialty machines, the tankers would be well placed to perform the actual mission, without stopping anywhere to refuel. In other words, it makes no sense to build gas station analogs in deep space.
  • Do you know of any others? Let me know and I’ll add them to this list.

Reasoning by first principles is a nice idea, but how do we do it? This blog would be incomplete without a recipe for people to follow.

When I did the Physics Olympiad I was taught a powerful problem solving algorithm that is designed for rapid, accurate first principles reasoning, calculation, and importantly, communication. It can be readily adapted for any quantitative problem. As counter-intuitive as it may seem, its steps help the user to overcome our innate software flaws and cognitive biases.

The method was called “the seven Ds and the little s”, comprising (in descending order of importance) Diagram, Directions, Definitions, Diagnosis, Derivation, Determination, Dimensions, and substitution.

In more detail:

A good diagram captures necessary information and consumes about half a page. The process of drawing a diagram activates the brain’s spatial reasoning capacities and prevents hasty or panicked assumptions.

Directions establish the local coordinate system, so that all quantities are defined in a consistent frame of reference.

Definitions unambiguously assign symbols to concepts or quantities such as length or mass, and help expedite algebraic manipulation later.

At the end of the first three steps, the problem has been summarized and read into memory. This may seem pointless or obvious, but asking the right question is often the hardest part of solving open or poorly defined problems. What is the relevant figure of merit? How is optimal defined?

Diagnosis is the fourth step, and consists of a single phrase summary of the physical principle used to solve the problem, such as application of a conserved quantity or a vector algebra bash. Usually, the more fundamental the principle, the better.

Derivation takes fundamental physical equations, of which there are about ten, and transforms them into the necessary form for the problem at hand. For example, rather than memorize the moment of inertia for hundreds of different shapes, one would memorize the general formula and, in the Derivation step, solve an integral to give the desired version.

Determination combines derived equations to produce a formula for the solution of the problem. By convention, this formula is boxed to make it easier to find on the page.

Dimension check ensures the dimensions on each side of the equation match and is a good “check sum” to detect algebraic mistakes. A successful dimension check is notated with a smiley face.

Finally, if necessary, numerical values can be substituted in to get a numerical answer.

By combining this method with intuition and other problem solving tools it’s possible to reliably get the right answer first time, every time. It’s like a super power!

The next time you encounter a questionable analogy anywhere, but particularly in space mission design literature, you’ll have the tools to not only recognize its limitations but to get the right answer yourself.

6 thoughts on “In space, no-one can reason by analogy

  1. “Derivation takes fundamental physical equations, of which there are about ten…”

    It would be interesting to hear a top-of-your-head listing of those ten.

    Liked by 1 person

    1. F = ma
      F = -kx
      Fourier and series expansion
      dI = r^2 dm
      Navier Stokes
      Maxwell equations
      F = – G m M/r^2
      V = IR
      P = sigma epsilon T^4
      Q = k delta T
      Schrodinger’s equation
      Snell’s law
      Viscosity definition

      That’s a good start. A bit of overlap in that list, as there should be.

      Liked by 1 person

    2. I had a college physics professor who repeatedly told us to not memorize equations, but to remember the definitions (like f=ma) and use math (such as geometry) to make our own equations for the problem at hand.

      It took me quite a while to figure out what he really meant by that (the Derivation step listed here), but it was a very good lesson. He wasn’t a very popular professor, most people just wanted to be given a list of equations that were needed for the final, preferably on a cheat sheet.

      Liked by 1 person

  2. I agree that your basic point is correct. But I would quibble with you you describe it.

    What you’re talking about isn’t reasoning by analogy. It’s using analogy to try to cover up a lack of reasoning.

    Reasoning by analogy is useful for overcoming the human mind’s tendency to get bogged down when confronted with lots of unfamiliar details. If you know the logic of a situation, you can concoct a situation that follows the same logic but without the burden of all those worrisome details. The key is that you do know (or at least plausibly hypothesize) the logic of the situation that you’re trying to reason about.

    In the case of spaceflight, the usual example is the old story problem where you have to cross a desert wide enough that you’ll need more water than your camel can carry. So you set up a cache of water partway across. Water corresponds to propellant, travel time by camel corresponds to delta-v, and the amount of water a camel can carry corresponds to specific impulse. There’s a world of difference between two stages of caching water and ten, because exponential increase soon reaches the point where it makes a qualitative difference. Importantly, nothing in the story corresponds to travel time in space, or distance in space, because those normally don’t matter.

    I don’t know how to make a rocket engine with better specific impulse. There are many details involved. I don’t know how to solve any useful reduced four-body problem (i.e. how to solve for trajectories of a negligible-mass fourth body in solvable sub-cases of the three-body problem). If I tried to think about all of that at once, without the camel story to help remind me that delta-v matters and time doesn’t, I would be even worse than I am at imagining how spaceflight might proceed.


  3. Space is so complex that if we get to a solution by analogy one day then it happens that we stuck to something else even with the same analogy.
    But we dont have other choices to move ahead or solve the complex mystery of the Space.
    Also, in order to travel long distances in space, we need stepping stones or some intermediate fuelling stations, so that refueling can be done in order to move the astronauts to large distances but these cannot be made on the surface of moons of planets as as increase the fuel consumption during goin into or coming out from the planet gravitational pull. So, it would be better to to make the Space Station like structures instead on celestial bodies.
    But suppling them with the fuel is a matter of concern, it is also a herculean task.


  4. “Most terrestrial vehicles are built with a safety margin of at least 50%. A few bad welds on a car is okay because it’s designed to be stronger than it needs to be. On a rocket, there’s no room for safety margin. ”

    Not quite accurate, the safety margin is more like 10-25%.

    Liked by 1 person

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