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



Absolutely. This is essentially one of my points. The P-V diagram is a
case in point. When you put V on the horizontal axis it is an analogy with
an F-x graph. Essentially you are talking about working. And the P-V
implies that P is the dependent variable, or the variable you wish to look
at. It is the same grammar as "Plot P vs. V". If you put V on the vertical
axis it should be called a V-P graph. Yes, grammar is merely a set of
guidelines and it is often violated. Math uses strict grammatical rules,
unlike science and common speech. So in math the horizontal axis always is
the independent variable. Are students ever told that math rules are often
really grammar? And they do change with the fashion. As I have pointed out
AB/CD used to be (AB)/(CD) and now it is (AB/C)D, and there is a math
journal that insists on this.

We do have normal grammatical rules in math and science. The left hand side
of the equation is often treated as the dependent variable, and it can be
helpful for students to think that way. Trying to introduce pure
abstraction early on in variables is the kiss of death. At first students
have to understand that most variables are things you can measure and that
equations establish relationships. Of course this is taught in math, but
only in the context of X and Y. Graphs of Y vs. X are really maps, and not
graphs. As a result when many seniors in HS are asked to find the area
under a scaled graph they resort to counting the blocks as if it is a map.

Then the use of calculus to figure things like the area under a graph, or
slopes has only been presented to students where the horizontal variable is
the independent variable. Doing it with the vertical variable as the
independent variable poses huge problems to students. There are also other
issues such as multiple representations. Students have to learn to create
and interpret motion maps, graphs, descriptions, and equations. So making
t-X graphs would make this harder. You do X-t graphs and maps of motion on
the X axis, and X=... equations. When they can translate between the
various representations, they understand the physics. There are a number of
articles in JRST about this going back probably 40 years.

So from a purely abstract point of view it really makes no difference which
is on which axis, but from a practical, and human conceptual point of view
it can make a huge difference. And the usual math terminology obfuscates
things. Students do not think of the axes as being abscissa and ordinate,
they think of them as X and Y which is very unfortunate. They don't have
the connection between variables and physical quantities. It is just a math
game. Indeed even the term horizontal is not in their active vocabulary.
If it were they would not use straight as a synonym for horizontal.

So I think the rule of independent variable on the horizontal axis should be
presented as the conventional rule to use when you don't have a reason for
doing it the other way. The important thing students have to learn is how
variables work, and which ones are independent. They also have to learn how
to handle multiple representations.

John M. Clement
Houston, TX


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.