Re: [Phys-l] "Looking up" results on a graph

[John Denker <jsd@av8n.com>]

On 01/13/2012 08:19 AM, LaMontagne, Bob wrote:
> There are many cases where the choice of which variable to put on
> which axis has to do with ease of interpretation of the data. In
> meteorology, when plotting the state of the atmosphere at a
> particular time, it makes most sense to plot altitude (or pressure)
> on the vertical axis and temperature and dew point on the horizontal.
> This gives one a mental "snapshot" of the air above. Sticking with
> the dependent-independent rule would give the same information but
> would be less intuitive and harder to interpret.

Amen, brother.  An excellent example.  Here's an instance of 
just such a plot:
  http://mintaka.sdsu.edu/GF/explain/thermal/std_atm.html


As another example where the horizontal axis-variable is (more 
nearly) a function of the vertical axis-variable, consider a 
density-of-states diagram.  This can go either way, but plotting 
energy vertically is certainly not uncommon or unreasonable.
I suspect the logic here is that people like to see energy
increasing vertically.  For example:
  http://www.bristol.ac.uk/aerospace/contact/academicstaff/drsrahatekar/sameerwebsite/research/fig5.jpg


As yet another example, consider the two-slit diffraction pattern:
  http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/dslit.html
It is very common, even in high-school physics texts, to see
this plotted as a function of the vertical axis-variable.

The interesting thing about this is that there are two related
plots, namely 
 a) propagation: x versus t; and
 b) diffraction: intensity versus x.

This is no problem for those of us who think the orientation of
the axes can go either way, but it is a lose/lose proposition 
for those who want to make "rules" about the orientation.  Either
the propagation diagram violates the "rule", or the diffraction
diagram violates the "rule", or the x-direction is inconsistent
between the two plots.


See also next message (independent variables, or not).