Re: Muscle work +- qualitative reasoning

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:24 AM 7/23/01 -0700, Tucker Hiatt hypothesized:
> And therefore the (magnitude of the)
> work done is the same?

I'm still mystified by this hypothesis.

*) I can imagine hypothesizing that the perceived effort depends on the
force dot displacement, with due regard to signs (work is related to energy).

*) I can imagine hypothesizing that the perceived effort depends on the
force times time (isometric exercises).

*) I can imagine hypothesizing additional terms depending on velocity,
representing the effect of "friction" and "damping".

*) I can certainly imagine sums of the above.

... I just can't imagine hypothesizing a perception that depends on the
MAGNITUDE of the work.  I don't see how such a hypothesis has any
precedent, or even any analogy in the known laws of physics.  It's like
asking me to explain why a cow has feathers, or explain why a cow doesn't
have feathers -- either way, it's not a very interesting hypothesis.  It's
making a prediction about the fine points when the coarse points don't fit
together.

====

Pedagogical / psychological analysis:

I'm trying to guess where this hypothesis is coming from.  My best guess is
that the pseudo-derivation goes something like this:  we have a force and a
distance, so we have something with dimensions of work.  So (according to
this pseudo-argument) let's assume that the answer (the perception) depends
on work.  We know we don't benefit from doing negative work on the
downstroke, so it must be the absolute value of the work that matters.

The problem here is that dimensional analysis is not a law of logic, nor a
law of physics, nor even a valid way of deriving valid laws of physics.  In
the hands of a wizard, dimensional analysis is a way of getting the right
answer quickly.  In the hands of ordinary mortals, it is often a way of
getting the wrong answer quickly.

 ++ Dimensional analysis can always be used to check a standard
calculation.  Sometimes it succeeds in detecting and locating errors.

 ++ Dimensional analysis can sometimes be used to rule out an
otherwise-plausible hypothesis, before you even start the formal calculation.

 -- Dimensional analysis cannot be used to construct hypotheses out of
thin air, in the absence of a good feel for the underlying physics.

 -- Dimensional analysis can never be used to prove the correctness of a
hypothesis, nor even to argue for the plausibility of an
otherwise-implausible hypothesis.

 ++ There is a large and important discipline called "qualitative
reasoning".    Dimensional analysis is only a small part of qualitative
reasoning.  Other parts include such things as symmetry arguments.  For example
  http://www.nobel.se/chemistry/laureates/1981/press.html


Returning to the original topic:
> And therefore the (magnitude of the)
> work done is the same?

The "sameness" hypothesis is qualitatively implausible on grounds of
symmetry.  I can't think of any physical process that has the symmetry of
"magnitude of work" -- certainly not one that makes sense in this context.

If anybody can think of such a process, please explain.  Otherwise let's
give up on "magnitude of work" as implausible and uninteresting.