I am a mathematician.
I have read the comments in this thread, and I am rather disappointed by
the spin Scientific American put on that article.
It's hardly the case that flight is a great mystery. What is difficult
is finding a complete explanation for flight in various detail from a
'high-level' basic physics perspective. While that is a lofty goal and a
worthy intellectual endeavour, that hardly means we "don't understand"
We may not understand flight from a "top-down" perspective, but we
already have extremely good models in terms of Navier-Stokes equations
and variants, derived from first basic physics principles, that describe
air flow. Therefore, starting from the basic premise of designing wings
on an airplane, we can write down equations that describe exactly what
will happen regarding its flight capability.
However, what we write down are equations, not high-level explanations.
It's no different than many other design problems in engineering. The
only difficulty is that the equations typically cannot be solved
analytically and they need simulation to solve them. However, that is no
great difficulty, as we can solve them approximately to any desired
accuracy and simulate them as well as needed.
There is no danger of airplanes coming down because we don't have a
simple high-level explanation of flight. Absolutely none.
When designing a new airplane, we don't need to be frightened because
simulation together with iterative design allows us to accurately
converge onto a solution mathematically, without the need for a
high-level understanding. The low-level understanding of air flow
(derived from physical principles) is sufficient to tell us what will
happen, even if we can't explain it from a conceptual point of view.
AND, even if we had a better explanation of all aspects of flight, the
complexity of air flow makes it virtually impossible that we will ever
be able to explain the nuances of every aspect of flight, such as the
difference in wing shape between say the Musk Duck and the Australian
Countless aspects of our engineering and scientific knowledge proceeds
this way as well such as the design of car engines and musical
instruments. Many of the optimizations that go into a car engine are
based on low-level, simulatory knowledge of air flow, even if we cannot
articulate high-level reasons why the optimizations work.
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