The so-called toy model is a critical tool for the physicist. It is
what in fact often will separate the physicist from the other
scientist.
For an x-ray signal processing project I have been working on for
about 18 months now, I had no idea whether the approach to solution
was viable. There are still questions but since ultimately the design
and understanding was/is going to be based on a great deal of
numerical computation, it was/is critical (in my mind) to create toy
models to further my understanding and check my results.
Just because it's a "toy" model doesn't mean it's unsophisticated. As
development proceeds, the toys become more sophisticated. But they
are still idealized in just such a way that I have confidence I'm
still going in the right direction.
The toy model has an additional benefit in applied science when
outsiders are involved. Say you have to present results or ideas, to
another scientist, or perhaps a project manager or even CEO - they
will sadly expect, and often get, the sort of presentation that makes
their eyes glaze over and could leave them wondering if their workers
are doing anything they are supposed to. Instead, I build a
presentation around an appropriate toy model, and using it, try to
convince them of the *plausibility* of my approach and my results.
Adjust according to the audience, but never be afraid to dumb it down
a bit - if the CEO for example walks out *believing* what the heck he
was just told, you've started to make yourself invaluable, not to
mention reinforcing that you are on the right track. Some call it
"capturing the imagination," and wrt students, this is where you can
either lose, or hook them, for life.
I'll unfairly beat up on "other scientists" now. If I'm in on a
presentation or discussion that I'm not following, I try to invent a
toy model on the spot and question thusly. If the presenter can
immediately grasp what I'm suggesting, or tell me why my toy model is
in fact inappropriate, even on merely a plausibility level, my
confidence (personally as well as on behalf of the idea presented)
goes way up. Not to mention, I feel I can then contribute a real
comment! If on the other hand I get a blank look or just a "well but
the equations here say...," I don't know for sure that anything is
suspicious but my guard sure is up.
I don't know how to transfer this notion to students in a way that it
will stick, other than to capture their imagination with the power of
the toy. The marching band might capture the imagination, but if it's
of limited plausibility that you know will ultimately do a disservice
or worse, come up with a better toy.
As an undergraduate and even a graduate student, I was oblivious to
this discussion. Had too much to do, physics and otherwise, and was
too immature scientifically to appreciate it. If anything, it must be
worse today. Like the CEO above though, it only takes one powerful
experience to advance a cause.