| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
On 01/31/2011 01:01 PM, Dr. Richard Tarara wrote:
So--I would suggest a reasonable mix of derived and given equations is not
too bad.
Indeed.
It is the way we all (well almost all, I suspect some do derive
everything from first principles) operate.
Anybody who thinks we should derive everything from first principles
should be teaching high-school geometry, not any kind of physics.
That approach works OK for Euclidean geometry, but not much else.
It doesn't even work for arithmetic! There will always be parts of
arithmetic that /cannot/ be derived. Kurt Gödel had something to
say about this.
The same goes for physics, only more so. There are a zillion things
in physics that cannot be derived. There are a zillion-squared things
that could maybe be derived, but not in a way even remotely suitable
for an introductory class. (For example: F=ma from Euler-Lagrange
from principle of least action from the stationary-phase approximation
of the Schrödinger equation from ....... never mind.)
Feynman argued that we shouldn't even try to make physics look like high-
school geometry. The important thing is to understand the relationships
between ideas, and "derived from" is not the typical relationship, let
alone the only possible relationship. Trying to coerce the logical
structure into the shape of a tree -- branching from a small root of
"first principles" -- grossly distorts the relationships. Usually there
are little groups of facts, each of which can be inferred from the others,
such that none of them is more fundamental than the others. Feynman
thought of it as a grand tapestry. A forgotten fact is like a hole in
the tapestry. It can be repaired by reweaving up from the bottom, or
down from the top, or in from the sides.
This conforms to what we know about physics ... but there is also a nice
side-effect, in that it dovetails with what we know about human learning,
memory, and thinking. The more ways you have of relating an idea to other
ideas, the more useful that idea becomes, and the more firmly remembered.
Galileo was a masterful experimenter and also a masterful mathematical
analyst. Modern science begins with the realization that you need both
theory and experiment.
There is no requirement that equations be "derived". The only requirement
is that the equations be useful in describing and predicting the data.
Equation-hunting is bad, not because equations are bad, but because
the hunting approach asks people to manipulate the equations without
understanding them. This creates the appearance that something useful
is happening, but it is in fact utterly pointless. It reminds me of
the dark ages, when a bunch monks who didn't speak Latin would stand
around chanting in Latin. It is quite possible to manipulate a language
(mathematical or otherwise) without understanding it ... but it is also
quite pointless.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l