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

derived.

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

as:

[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