
The Scientific Problem That Must Be Experienced - jcr
http://nautil.us/issue/15/turbulence/the-scientific-problem-that-must-be-experienced/#
======
QuantumChaos
The articles main thesis is that an intuitive, artistic understanding of
turbulence can help inform mathematicians.

And yet none of the historical evidence that was presented supported this
claim. The pure mathematicians made progress and discovered interesting
patterns. Those who focused on art and philosophy (Schauberger and Schwenk)
contributed nothing to the understanding of turbulence.

~~~
jcr
I read the article differently, namely, how the approaches of both art and
science can be similar and often complimentary to understanding and
appreciation. At times, looking at another perspective can really help improve
understanding and appreciation, but at other times, an alternate perspective
is merely entertaining. I wasn't expecting the author to provide strong and
specific evidence of "artistic understanding helping to inform
mathematicians." But saying "none" was presented seems a bit unfair; the
evidence presented was by inference and was anecdotal. For example, both
artists and experimental scientists arriving at remarkably similar ways of
"recording data" and/or "making art" from turbulence in fluids. Even if the
artist doesn't fully understand the math, and the mathematician doesn't fully
understand the art, both can often gain a more enlightened appreciation of
each others' work than someone unversed in both art and math.

A lot of educators agree that studying both art and math are important to
development and are complimentary to both appreciation and understanding.

------
madaxe_again
I did my GCSE physics project on Reynolds' number, many moons ago. The actual
experiment itself was simple, but the hard bit was creating several-meter long
hollow glass syringes in order to inject die into the flow tube well into its
flow, in order to avoid turbulence where the header emptied into it... ended
up dangling borax glass tubes off the roof with a 1kg weight lashed onto the
end, and then blasting the centre with a blowtorch - serious fun.

Anyway, long story short, it's a really interesting experiment to run,
Reynolds number (for water, at least) can be deduced by a teenager with about
£100 of equipment, and the boundary between laminar and turbulent flow is a
mysterious beast indeed.

One interesting artefact was inducing turbulent flow in speeds "too slow" for
turbulence, by increasing flow to the point where turbulence triggered, then
decreasing flow to the laminar realm again, yet retaining the turbulence
indefinitely. Interestingly, this low-speed turbulent domain required a
smaller throttle on the header tank to maintain the same flow rate - i.e. the
turbulence decreases resistance to flow in the tube. Something that pipeline
engineers could/should/maybe do employ.

Had to pay for a new floor at the end of it all, as there's no tidy way of
running this one.

------
Xcelerate
The author mentions that having an equation that describes a system
accomplishes little if the solutions to that equation are unavailable. He kind
of downplays quantum mechanics, but I would argue the situation is just as
severe as that with turbulence. The Schrödinger equation

iħ(∂Ψ/∂t) = HΨ

is a very simple equation. Yet the solution to this equation is nearly
impossible to solve for all but the simplest systems. A lot of approximations
to it have been developed, but to numerically converge on the exact solution
is an NP-hard problem in most cases (using QMC). And we all know what that
means.

There's a famous quote attributed to Max Born: "It would indeed be remarkable
if Nature fortified herself against further advances in knowledge behind the
analytical difficulties of the many-body problem."

In other words, what if we discover all the equations that govern nature, but
they are simply infeasible to solve (and worse, we even mathematically prove
that they're intractable)? It's an interesting, yet somewhat depressing idea.

~~~
drkevorkian
Two counterpoints:

1) What you've written, where H is independent of t is reducible to just the
Eigenvalue problem for H. Certainly better understood than fluid dynamics.
Even with time-dependent hamiltonians we have decent tools for talking about
the solutions (Dyson series).

2) Of course for certain values of H, (esp. in continuous space) you can
contrive ways of making the eigenvalue problem hard, but you don't have to go
as far as quantum mechanics to find difficulty. Just take three bodies under
newton's gravitation.

Yes, the quantum n-body problem is exponentially harder in n, but that's a
fundamentally different type of "hardness" than the hardness of Navier-Stokes.

~~~
Xcelerate
1) is reducible to just the Eigenvalue problem for H. Certainly better
understood than fluid dynamics.

I feel like that's akin to stating that Fermat's theorem _just_ shows there is
no n > 2 such that x^n + y^n = z^n

2) you can contrive ways of making the eigenvalue problem hard

You've got this backward. You can contrive ways of making it easy. Almost all
physical problems for any system larger than but the simplest of atoms is
incredibly hard.

------
ISL
The scientists who study turbulence are quite aware of its beauty. Indeed, the
Division of Fluid Dynamics of the American Society of Physics has an image
contest at their annual meeting -- it's quite competitive.

Their online gallery format could use some modern-design love, but the images
are still beautiful:

[http://www.aps.org/units/dfd/pressroom/gallery/](http://www.aps.org/units/dfd/pressroom/gallery/)

More here:
[http://www.aps.org/units/dfd/gallery/index.cfm](http://www.aps.org/units/dfd/gallery/index.cfm)

------
snowwrestler
To art and math, I would add sport: whitewater kayaking and surfing are two
sports in which participants directly engage and experience transitions
between smooth and turbulent flows in water.

I doubt they will lead anyone to mathematical breakthroughs. But they are both
a lot of fun, and can go beyond physical exertion to inspire deep emotion and
thought, even spiritual experiences.

Edit to add: A fun book along these lines is "The Wave", which is a pop-
science book that contrasts big wave surfers with oceanographers studying
rogue waves.

