[Phys-l] step-by-step reductionism versus single-leap reductionism

[John Denker <jsd@av8n.com>]

First, a parable:  

To a decent approximation:
 -- We can understand atoms in terms of protons, neutrons, and electrons.
 -- We can understand semiconductor materials in terms of atoms etc.
 -- We can understand transistors in terms of semiconductor materials.
 -- We can understand logic gates and amplifiers in terms of transistors.
 -- We can understand memory, PLAs, registers, etc. in terms of gates,
  amplifiers, transistors, etc.
 -- We can understand computers in terms of memory, PLAs, registers, etc.
 -- And so on.

This means we have a series of black boxes within black boxes, like
the layers of an onion, or like a Russian doll.  It is possible and 
very useful to be able to explain each layer in terms of what's inside.

However (!) it is strongly recommended to take one step at a time.  
Behold the contrast:
 -- Yes, we can explain computers in terms of protons, neutrons, and
  electrons.
 -- No, we should not do it in a single step.

Or more generally:
 -- Step-by-step reductionism is helpful.
 -- Single-leap reductionism is a disaster.

This is a very old idea.  The idea of hierarchy is older than hieroglyphics.

==================

Possibly this may be contributing to some of the metaphysical questions
about fluid dynamics in general and Bernoulli in particular that have
been swirling around for the last week or more.  I doubt this is the
only issue, but it is a hypothesis that should be considered.

There is a process of selection that attracts _reductionists_ to the
study of physics.  It is nice to be able to understand things in the
most fundamental terms.  It is not, however, a good idea to do it in
a single leap.

Yes, we can and should understand fluids in terms of particles ... 
indirectly, step by step!  The first step is to derive the first-order 
fluid properties such as the momentum, energy, entropy, mass, pressure, 
and volume of a parcel of fluid.  The next step is to derive the second-
order properties, i.e. the transport properties, such as viscosity and 
thermal conductivity.  Then we can understand practical applications -- 
such as how wings work -- in terms of the properties of the /fluid/.  
It is arguably possible to do it all in one giant leap, in terms of 
molecules hitting the wing, but this is vehemently not recommended, 
for the same reason that we do not explain computers directly in 
terms of elementary particles.

Specifically, students predictably have very wrong intuitions about
the particles in a fluid.  They tend to grossly overestimate the
size of the particles and grossly underestimate the importance of
particle/particle collisions.  For more on this, see
  http://www.av8n.com/how/htm/airfoils.html#sec-fluid




On 11/24/2010 04:33 PM, LaMontagne, Bob wrote:

> That is what I meant by my comment in a previous posting that an
> individual molecule does not know that it is moving from a wide pipe
> into a narrower one. It only knows that the symmetry of its
> collisions with the molecules around it is changing - it only
> experiences the results of the laws of physics by banging into other
> molecules in a purely local way.

OK.

> I once wrote a simulation for this in FORTRAN. I started with a large
> number of molecules in a box all with the same speed but traveling in
> random directions in 3D. I then let them collide with each other
> randomly and soon a Boltzmann distribution of speeds developed. Once
> this part of the simulation was secure, I put the molecules in a pipe
> with a restriction followed by a widening of the pipe. The molecules
> were all  given the same initial KE but with a slightly higher value
> to the right for the component parallel to the pipe. I had the
> molecules leaving one end of the pipe reappear back on the other end.
> After a long run to establish an equilibrium flow, the molecules
> moved faster through the constriction as expected. What disappointed
> me was that I didn't learn anything I didn't already know about the
> microscopic details of the process in the simulation versus a real
> flow, The mechanism (on a molecular level) for the increased speed
> and reduced pressure was not revealed r egardless of how I reduced
> and presented the data about individual molecules. 

This illustrates the point I was making about the perils of
single-leap reductionism.

> It was the old
> thing that the better a simulation gets the less sense it makes to
> run it versus looking at the real process.

I've never heard that one before ... and I don't believe it.

There are lots of things you can do with a realistic simulation
that you can't do with the actual system.  As an example, consider
the fact that Boeing performs exceedingly detailed and realistic 
simulations of each new aircraft design.  Advantages include:
 -- The simulation is just plain cheaper than building the real
  thing.
 -- The simulation is incomparably easier to change than the 
  real thing.
 -- The simulation can be instrumented in ways that would not
  be possible with the real thing.
 -- Etc. etc. etc.  I could go on, but you get the point.