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Comment by quantum_mcts | Hacker News Reader

There is an analogy between this and infeasibility of "Explainable AI".

For the Lift Theory we have Navier-Stokes equations that give you the lift if you solve them numerically or, maybe, figure an analytical solution. But most people won't accept it as an "explanation" - they want a simpler description in more coarse-grained concepts and relationships. And, it seems, that there is no such satisfactory reduction for the Lift Theory - there are just too many interrelated things happening at the same time.

Same thing goes for some decision-making AI. One might like to have an "explanation" for why AlphaZero decided to make a particular move. And sometimes there could be a general high-level pattern rule, that one could extract from the model. But, it seems, that in most cases no simple rule can be expected.

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I upvoted this, because I think the fundamental thesis is right: most of the time, for physical phenomena, there is a wrong-but-close approximate explanation that is within the understanding of someone with high-school science, or at least within intuitive grasp thereof. This is the basis of popular science.

The errors with the approximation reduce as you apply better models, and those models are the domain of practitioners.

The question of why airfoils generate lift seems to be resistant to the popular science technique. The first useful approximations all require calculus and are the result of whole-system effects at a macro-level. So all the explanations you can get to from high-school science are contradicted by real-world experience.

"There is no gravity in outer space. Gravity ends at the top of Earth's atmosphere. That's why astronauts in the ISS are weightless."

Simple and concise. Easily understood by little kids. Textbooks in the 1950s actually taught this "fact." What could be the problem?

It's not "simplified," instead IT'S WRONG...

...and it creates a massive physics-misconception, where if a student actually believed it, later they'd have enormous trouble in physics classes. (Also, if they later became a teacher, then they'd give all their students the same destructive misconception. If later they became a textbook author for K6 grades, millions of students would become infected! Heh, education is a viral effect: a meme-spreading process, and "mental diseases" like the above are common.)

I like this explanation that likens the search for principles to compression:

The natural human urge to look for simple explanations is a compression problem. If you can find a simple mechanism for operating in a complex universe, you can teach it to your children more easily.

Training AIs has a similar motivation — a simpler function is cheaper to store and compute.

Perhaps we can call the simplest explanations we've found so far "Principles". We want to believe they are universally true. For example, conservation of energy, or humans should have equal rights. They seem to fit our current reality, and they are vast simplifications over doing things ad-hoc, but are they more than lucky simplifications of a complex universe?

On the other hand, simple intuitive explanations may not lead to simple mathematical analyses. Things which are obvious and simple to grasp, may involve near-insoluable systems of equations! This seems to be the case with lifting force.

We can easily explain lifting-force if first we get rid of the wingtips. Just explain 2D airfoils in a 2D "flatland world." Infinitely-wide wings are almost trivial to analyze.

There is a simple "explanation" of wing lift, though: the wing pushes air down, it applies downward force on air masses. This is a trivial consequence of Newton's third rule and the facts that a) there's gravity, b) airplanes don't fall from the sky.

If you want to know what exactly is happening to the air around the wing you need fluid dynamics of course.

I don't know if we'll get any such "conservation of X" principle from the AI world, but that would be pretty cool.

I'd argue that that is not really an "explanation", because you cannot meaningfully generalize it. Yes, there is a lift because there is upward force on the wing, because there is a downward force on the air... But, how do you use it in another context? That feels more like a sequence of tautologies, than an explanation.

Generalize to what?

Also, what other context?

But if air is pushed down, then it must continue moving down (much like with a hovering rocket, or a helicopter.)

But this effect does not appear in typical airfoil flow-diagrams. Instead, the air approaches horizontally, and leaves horizontally. It's a symmetrical pattern, as guaranteed by "circulation theory." In these diagrams, the wing doesn't fling any air downwards. (Heh, the same thing happens with helicopters that fly inside a giant vertical pipe, where the blade-tips slide along the inside surface of the pipe.)

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