TWENTY YEARS and three lifetimes ago I was in a puzzle shop in Camden Lock Market, Camden Town, London where I bought a curious item. It was an aluminium cylinder, about four inches tall and two inches across; passing across and all the way through the middle of it were two thinner brass cylinders, each maybe three inches long and three quarters of an inch thick, and each at right angles to each other and to the bigger aluminium cylinder. The arrangement was a sort of a cross, in three dimensions. And the two brass cylinders overlapped each other: it was clear that they must have some kind of thin sections or cutouts in their middles, inside the device where it couldn’t be seen.

The puzzle didn’t come with any instructions but if you picked it up you would find the two brass cylinders would turn, and slide through. But they would only twist so far, and slide so far, and then they’d be blocked: they’d not slide out completely. It was obvious the goal was to free the two brass cylinders so you’d end up with the device disassembled. If you played with it a bit longer you’d discover there was also some kind of internal mechanism: each brass cylinder was free to slide further or rotate less or more depending on the rotation or position of the other. And every now and then there would be a satisfying click as some sort of latch or pin sprung free or locked as you moved the parts.

I bought the puzzle as a birthday gift for a friend, but naturally I couldn’t give it away until I’d solved it myself. So when I got it home I had a couple of absorbed hours twisting and sliding and pulling, and thinking, and listening, and puzzling, and twisting, and sliding until – without ever having seen the insides I had intuited knowledge of the internal mechanism, and it became very easy to free the two brass cylinders and slide each of them free from their constraint.

I gave the puzzle to my friend. A couple of weeks later when I visited him, he mentioned that he’d enjoyed working out the solution very much. I knew that he’d followed exactly the same process as I had. He’d invented in his own mind exactly the same mental image of the mechanism inside as me, also sight unseen.

Now, what does this have to do with flying airplanes? Let the airplane be the puzzle: let the twisting and sliding of the cylinders be the moving of the yoke to move the ailerons and elevator, the throttle to adjust the power, the rudder pedals, and, if you wish, the trim and the flap controls. Let mastery over the puzzle be the ability to make the airplane take-off, fly to a destination, and land. Perhaps with some manoeuvring in the middle of the flight. Just like the puzzle, the airplane response to moving the controls is not at first instance, obvious. In some ways it’s opaque or even perverse. But just like the puzzle solver, the pilot needs to own a mental model of how the airplane responds to the controls and how they interact in different circumstances order to move them correctly, in the right sequence, and by just the right amounts, to solve the puzzle and make the airplane complete the flight.

Of course there are some differences too: the puzzle can be solved in a couple of hours, while people are going to take somewhat longer to learn to fly an airplane. Also if you fail to solve the puzzle you can just put it down and come back to it later without mortal danger. And, significantly, when you learn to fly you have an instructor beside you to teach you.

But the biggest parallel has to be this: while you could, in theory solve the puzzle by following a set of rote instructions: slide cylinder A to the left by 0.75 inches, then rotate cylinder be 90 degrees clockwise and slide it forward 0.5 inches, then rotate cylinder A 135 degrees anti-clockwise, and so on – until the parts slide apart – that doesn’t count as having solved it. The really satisfying part of doing the puzzle comes at the moment just before you release the pieces. It’s that moment when your imagination about the geometry of the mechanism inside gets tested and found to be true. You think to yourself, if I understand this right, then if I slide cylinder A just so, and rotate cylinder B just so, then I must hear a click as that pin drops. And then you try it – and lo and behold – that’s exactly what happens. At that moment you know for sure that you understand what’s going on inside in the parts you can’t see and you you know for sure that you can get the parts released at will. That they finally slide out into your hand merely reinforces a fact you already knew.

And so it is with being able to fly an airplane: if you want to land, or take-off, or carry out a particular manoeuvre one can of course follow a rote list of instructions. In fact everyone learns this way. Keep the nose-wheel on the centreline with the rudder. Deflect the ailerons into the wind. Pull back on the yoke when the airspeed reaches 55 knots.

Eventually, however, if you want to be a competent pilot, you’re going to have to build yourself a mental model of an airplane. Not like an Airfix kit that you glue together and paint. But a model in which you can, if you want, move some imaginary flight controls, and see the imaginary flight instruments behave just as they would in real life, and appreciate the mental airplane behave in exactly the same way as a real airplane would.

Once you have such a mental model it’s easy to invert it: you can imagine the airplane behaving the way you want – climbing, or making a nice landing, or in a steep climbing turn, or a chandelle, or a wingover – and you know – you already made them – what control inputs were needed to make the airplane behave this way. At that point you have become a pilot rather than a follower of instructions.

Where does the flight instructor fit in this process? In the first instance, the instructor has to feed you that list of rote instructions that describe how to fly some basic manoeuvres. But that’s not enough. Let’s say you follow that recipe. And you learn how to fly a steep turn. And then you learn the recipe for taking off. And for demonstrating a stall. And so on. But what if you never progress beyond being an instruction-follower? What if you can only ever solve the airplane “puzzle” using the recipes the instructor gave you? What if your mental picture of an airplane never advances beyond what an airplane is – what it looks like – how many seats it has – where you put in the fuel and the oil – to what an airplane does, how it behaves when you force it to side slip, or fly at maximum angle of attack? What if you never get that imaginary system into your head? Has the instructor done their job?

I’m pretty sure that, like the puzzle, an airplane will reveal its behaviour to anyone who wants to really know, with enough practice. If you move the levers enough times, in enough different combinations, eventually you’re going to teach yourself to fly. But in that circumstance instructor has been demoted to a baby-sitter there to stop you from hurting yourself. Or maybe you worked your way through your flight test and the instructor absented themselves a hundred hours ago, leaving the job half done. The Wright Brothers were able to work out the details of aircraft control for themselves. It did however take them several years. It seems to me that a really good instructor must take up the challenge of helping you to build an accurate imaginary airplane in your head in a way that’s enjoyable and effective and also gets you there a lot faster than leaving you to work it out for yourself.

To do that an instructor does have to have a set of recipes to teach you. To begin with. In the early stages it’s fine to be told the sequence of control inputs to demonstrate a power-on stall and recovery. But being able to follow those instructions correctly and without assistance should be the beginning of the process and not the end. Using the stall as an example, I think the instructor then has to encourage and cajole and describe and plead and insist and connect and diagram and evoke and query so that you know you’re gaining experience in the breakaway of pitch and roll stability as the angle of attack exceeds the critical value, and how the recovery involves reattaching laminar flow over the top surface of the wing. It’s not the recipe for a stall demonstration that you have to internalize: it’s how to control the angle of attack and how the airplane behaves as that angle increases that you have to take home with you and build on. You have to connect the stall to the behaviour of the wing on the back of the power curve; and that in turn is something you have to connect to the reduction of drag as you approach best lift-to-drag ratio and the subsequent increase in drag as you slow down and move away from it.

The point here is not to focus on phrases like “lift-to-drag ratio” and “laminar flow” which describe actually simple ideas. But you do need to internalize those ideas, even if you don’t know what they’re called. If you’re merely a follower of recipes those concepts won’t resonate with you. But if you’re a pilot with a good mental airplane to fly, and if I mention flight at high and increasing angle of attack, you’re already imagining the yoke back-pressure and the decay of airspeed, you’re wondering whether the stall warning horn will sound, and you’re unable not to flick your eyes to the ball, because you understand the importance of maintaining coordinated flight. If you’re a low time student pilot and you did that, congratulations. Your instructor is doing a great job.

A quote widely and probably wrongly attributed to Michelangelo on the subject of how to create beautiful sculpture goes something like this: “Just remove all the bits of stone that don’t look like David.” That’s funny and sassy and it’s not wrong – but it only works for someone who already has a perfect mental image of what David looks like. As instruction to someone who wants to learn stone carving, it’s no help. Neither is a list of places where to put the chisel and how hard to strike it. The first method of instruction assumes you know what the statue is going to look like when it’s finished; the second just leads you to someone else’s sculpture. The challenge for a good instructor is to fill and shorten the gap between the two: the gap between the recipes and the time when a student can land the plane by “just landing the plane”. It’s a fascinating, challenging and fulfilling task to do well.