From Bob Clark (931217.1725 EST)

Bill Powers (931214.1950 MST)

With reference to Bob Clark, and Martin Taylor (9331214), you note:

Both of you questioned my statement that energy can be "reduced to"
force and distance, but not vice versa. Perhaps I used the wrong
term. I meant that energy can be expressed as a function of force
and distance, but neither force nor distance can be expressed as a
function of energy.

In this situation, I do not understand the phrase, "reduced to." Your
elaboration does not help. To me the relation among energy, force,
distance and angle between force and distance is simply an algebraic
expression. Given the values of any three of the four variable, the
fourth can be calculated. This is not "reduction," it is merely
rearrangement. In some situations, one or another of these variables
may be hard to determine so the algebraic re-arrangement may not be
possible. At least three of the four must come from other sources.
As you point out, if only energy is available, the others cannot be

The usual second order linear differential equation is a mathematical
statement of the conservation of energy.

[Kinetic Energy] + [Energy Losses] + [Potential Energy] = 0

[Kinetic Energy] = 1/2 mv^2

"Energy Losses" are usually considered quasi-frictional and expressed
[Energy Losses] = sv, where s is a constant of the system and v is
the rate of change of the variable in question.

[Potential Energy] = 1/2 kx^2, where k is a constant and x is the
variable in question.

I agree, Bill, with your comments about "abstractions." Except, to
me, these are all abstractions -- some closer to directly perceivable
variables than others. In that sense, "energy" is more highly
"abstracted" than "force" and "distance."

Are these remarks consistent with your views, Bill?

Regards, Bob Clark