View Full Version : The final word RE: tethered swimmer

Craig Nevin
09-26-1995, 11:01 PM
Dear subscribers

I must thank Peter Davidson for an excellent summary, regarding the
technical aspects of the debate. I would also also like to add some
thoughts about the why there is so much disagreement in the first
place, and conclude my input with a final word.

I think the some confusion arises from the introduction of the
thermodynamic equation

dE = dW + dQ

which does not fall within the true definition (boundaries) of the
biomechanic list.

This equation is, however, the foundation of the industrial
revolution, which permitted the energy trapped in inanimate
fuel to be converted into "work" that could replace the
manual labour of workmen. [This is the classical domain of the
mechanical engineer]. In essence this is similar to the
goal of biomechanists, who are often mechanical engineers looking
for modern day applications of their trade. The goal of biomechanists
is to try understand how men do things, so that we can do them

However, (getting back to specifics) the thermo equation is merely a
rather simple statement of transfer of energy.

One of the key starting points in classical mechanics (the mechanics
of the known (certain) universe, is that we can draw a "perfect
boundary" around any system (including the know universe). In this
case, there are two options available to us (and hence the two sides
to the debate). First of all the boundary can be drawn either
BEWTEEN the source and destination of the energy transfer, or
alternatively it can always be drawn around both the source AND the
destination of the energy transfer. [Another third option exists,
which is to literally draw the line on considering the issue

But in the case where the boundary includes both source and
destination, the equation is rendered trivial (0=0). Therefore the
statement that the work done during swimming is zero is often
perceived as unhelpful. However, it does serve as an absolute check
that your assumptions about the situations are correct. This is the
real power of a zero balance. It is used with great effect by
accountants when trying to balance a set of books. Accountants don't
"make" money when they report a credit balance, they just ensure that
the transfer is in their favour (a POSITIVE credit). However, the
separate credit and debit balances must be equal. If they aren't, it
is simply an indication that an error has occurred in the accounting
procedure, and nothing else.

What intrugues me was the equivalence or the terms on the right
hand side of the equation (since the dW and dQ terms can be added).
The fact is that dW is the "transfer of mechanical work", which can
either be stored in an elevated weight, or immediately recovered by
another adjacent system such as the water surrounding the swimmer. On
the other hand, once dQ has been transferred to the lowest thermal
reserviour it is "trapped". This is because at a molecular level the
interactions are frictionless. Frictionless interactions cannot
"grip" anything and hence cannot tranfer "mechanical" energy out of
the system. Friction is in itself a boundary phenomenon -- which
relates directly back choice of boundaries.

We also need to know the ultimate destination of this heat flow
(since we need to draw a boundary somewhere to moniter it).
Also the isolation of the lowest thermal energy source i.e. the
destination of all heat flow, eventually involves containment within
a physical isothermal boundary. Any thermal momentum of the
particles within this boundary must, on homgeneous average, be less
than the surroundings. Therefore the internal energy within the
boundary cannot 'pressure' our perfect boundary into displacing
POSITIVELY in the direction of the force.

[ work = force x displacement
or work = pressure x area x displacement ]

The interesting thing about the "perfect boundary" is that it is in
essence an elimentary particle. (Here is where I get accused by
just about everyone of digressing into theoretical physics - but why
not?) Rhetorical answer (if there is such a thing): because it falls
outside the "boundaries" of biomechanics and hence threatens our very

Returning to theoretical physics, loosely intepreted by me,
Heisenbergs uncertainty principle states that the product of the
uncertainty in the position and velocity of an elimentary particle is
a small, but IS a finite number, i.e. neither the velocity or the
position of its boundary can be simultaneously determined (with
perfect accuracy) at any given instant. As "proof" of this, I offer
the interminable "tethered swimmer" debate!

On one side the zero lobby argue that work is zero; but THIS answer
cannot answer the question the non-zero lobby asks, i.e. what is the
power of the swimmer? (Remember that power = work/time. If the
work can be determined, then we can answer the ORIGINAL question
by an exercise scientist about how exercise can affect performance.
To those uninitiated by classical mechanics this might seem a
reasonable question; by simply measuring the work at two discrete
times before and after training, and subtracting them we can
determine how effective the training was).

To help out, the ever willing POSITIVE lobby contend that work IS
being done, but are hard pressed to quantify this -- for example, it
is one thing to say that the work is done at the skin of the swimmer,
but it is completely another to try measure it! At this point,
needing clarification, the subscriber referred the problem to BIOMCH-

In reply, the POSITIVE lobby are in a sense correct, in that they are
seeking to determine the credit balance (the non-zero work). BUT the
zero-work lobby are trying to balance the books. It is important to
realise that these objectives are complimentary AND simultaneous, or
alternatively they they be held to be contradictory, and hence
uncertain. It is a bit like trying to balance the Federal budget.

It is at this stage helpful to try understand what are the intentions
underlying these conflicting points of view? First of all, it can
be held (rightly) that the quantity of the credit balance
representing the positive work as measured by whatever means, is
unreliable unless the energy books balance. But on the other hand,
balancing the books without first determining the credit balance is a
trivial task. I would contend that there are two equations and two
variables, but that these equations are not independant. Therefore
there is no currently known solution to the tethered swimmer problem.

I would suggest (at the risk of persecution) that the bona fides of
both lobbies in this debate need to be accepted. This would in fact
reduce the "uncertainty" surrounding the debate to zero, and the
debate will cease.

(Never mind the fact that this "transfers" the "uncertainty" back to
the person who asked the question in the first place :).

Some others might say, leave thermodynamics out of it, as there would
then not be a problem...(or an answer).

In conclusion, I would suggest that it is all about the choice of
self-imposed boundaries -- not only the boundaries that define the
swimmer, pool, weights and logically ultimately even the known
universe; but also about the self-imposed boundaries of the engineer,
scientist, accountant, physicist, biomechanist....

One of the hallmarks of a genius is that it is suspected that he/she
can live with contradiction. Also historically genii tend not to
distinguish overduely between astronomy, art and science. Perhaps
there is a morale in this for all of us non-genii in earthly
(mechanical?) matters, but that is just my 2 cents worth.

However for my reference for the day, I would like to mention a
certain nameless parable. Authoritive ancient legend has it that
everone was once working (no pun intended) to build a tower so
high that they must eventually discover the ultimate TRUTH.

The scribes say that it all broke down when everyone started to speak
different languages, the "work"men, the slave drivers (the exercise
scientists? ;) the engineers, and accounts. Soon no one could
understand anything anymore and the work had to stop due to the
incessent quibbling. There seems to me to be a modern parallel here.

If the truth be known, my final word in this debate is that the
answer is (at least in principle) remains demonstrably "uncertain".


Craig Nevin
Biomedical Engineer
Department of Physiology/Sports Science
University of Cape Town, South Africa