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.
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.
- 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.
- When the first general circulation calculation for earth’s atmosphere was undertaken, many or most thought that it would be necessary to add additional 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 and physicists did not.
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”.
If this is so in some sense it seems not to bear on our lives.