Two short conversations recently made me aware that I had
strong ideas on modes of understanding and at the same time a real confusion
about what it means to understand.
My strong opinion is that if there is now not a significant variety
in modes of understanding, such a variety will emerge in the next few centuries.
In attempting to make this claim more precise I discovered a great morass
of ideas. Here are a few anecdotes, centering curiously on hydrodynamics.
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Some famous old 19th century scientist was speaking circa 1930. He said
that he expected a coherent description of quantum mechanics when he went
to heaven but held out no hope regarding turbulence.
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When the first general circulation calculation for earth's atmosphere was
undertaken, many or most thought that it would be necessary to add then
unknown physics before the jet stream would emerge. In fact the jet stream
emerged with only Navier-Stokes, radiation balance, water content, and
Coriolis forces. It would seem that the computer understood the jet stream
whereas the programmers did not.
Non turbulent hydrodynamics requires an amount of calculation in some sense
proportional to the complexity of the question and the degree of accuracy
of the answer. When turbulence arises this limit seems to fail. Many turbulence
models have attempted to gloss over the details much as Navier-Stokes equations
gloss over details below the level of detail of the input and output. These
models have not succeeded.
If we lacked the Navier-Stokes equations for hydrodynamics we could
still in principle compute atom by atom. It is as if we lacked such equations
for turbulent flow.
Many satisfactory turbulence equations are available for very narrow
problem sets, but they amount to little more than empirical curve fitting.
I have a strong feeling that we do not understand turbulence.
I am not impressed with arguments that in principle, given enough time,
attention and expansion of memory capacity we could "understand turbulence".