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

"better".

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

altogether...].

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

existence.

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-

L...

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".

Regards

Craig Nevin

Biomedical Engineer

Department of Physiology/Sports Science

University of Cape Town, South Africa

CNEVIN@anat.uct.ac.za

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

"better".

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

altogether...].

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

existence.

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-

L...

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".

Regards

Craig Nevin

Biomedical Engineer

Department of Physiology/Sports Science

University of Cape Town, South Africa

CNEVIN@anat.uct.ac.za