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[Phys-l] data ± model ± trust



Here's a little chestnut that a 4th-grader recently brought me.

The kids have a couple of tables, namely a dark blue table and
a red table, as shown in this perspective diagram:
http://www.av8n.com/physics/img48/tables-perspective.png

Please disregard the legs of the tables; I want to talk about
the tabletops.

Kid #1 says that the red tabletop is more-or-less square (like
a card table), whereas the blue tabletop is longer and narrower
(like a banquet table).

Kid #2 says, no, the two tabletops have the same size and shape.

Kid #3 says I can tell just by looking at the diagram that they
are not the same.

Kid #4 says that if you look at the diagram closely enough, you
will see that the red parallelogram is the same size and shape
as the blue parallelogram.

So ... what is the actual physical situation with the tables,
and how does that explain what we see in the diagram? Obviously
not all four of the kids' statements are correct, so you might
start by deciding which of the four numbered statements are
correct and which are not. You might also want to consider
the possibility that a statement might be a red herring, i.e.
irrelevant and grossly misleading, even if it is technically
true.

Note: The answer to my question does *not* consist of saying
that the diagram is wrong. I give you a money-back guarantee
that the diagram is a faithful representation of the physical
situation. For present purposes, the diagram *is* the data;
infer from it what you will. This situation is not unlike
astronomy, where you might wish for hands-on data, but you're
not going to get it. All you have to go on are the pictures.

Also I don't want to engage in nitpicky word games about the
meaning of "same". Here "same" means same to a good approximation.
The kids know what "same" means. Of course no two tables are
ever /exactly/ the same, but I assure you this non-exactness
has nothing to do with the topic we are discussing.

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

And in case you're wondering, there is a point to all this.
There is a connection to physics ... and to pedagogy. We
can discuss this later.