> > > > >>JE:-
> > > > >>Here we go 'round  the mulberry bush....
> > > > >>
> > > > >>--------------quote----------------------
> > > > >>
> > > > >>1) 22/01/2004:
> > > > >>
> > > > >>JE:-
> > > > >>What is the difference between
> > > > >>a reduced positive c and a negative c?
> > > > >>If c was an abolute measure of fitness
> > > > >>then yes, a real difference exists. However
> > > > >>c is only a relative fitness cost and not
> > > > >>an absolute fitness cost, so what is the
> > > > >>difference?
> > > > >>
> > > > >>BOH:-
> > > > >>
> > > > >>As far as the rule is concerned, none.
> > > > >>
> > > > >>----------- end quote --------------------
> > > > >>For the 6th (?) time and counting:
> > > > >>Do you agree or disagree with the
> > > > >>answer Dr O'Hara provided? A simple
> > > > >>YES or NO will suffice.

> > > > > NAS:-
> > > > > No, a simple yes or no will not suffice to your
question as it has
> > > > > been put
> > > > > My answer is: I disagree with Dr O'Hara.

> > > > BOH:-
> > > > Oh!  The point behind the statement I made there was that the
> > > > rule still
> > > > holds whether c is positive or negative, i.e. it can still
> > > > be used to
> > > > decide whether a behaviour will invade a population.  Obviously
> > > > changing
> > > > the value of c may change the prediction, but the rule
> > > > would still be
> > > > used.  Therfore as far as the rule is concerned, there is no
> > > > difference,
> > > > even if there would be a diffeence in a particular application
> > > > of the rule.

> > > NAS:-
> > > Right, I agree with this. I would say that the sign of c makes no
> > > difference to the validity of Hamilton's rule (which is always valid,
> > > as it is a mathematical truism) but it does make a difference for the
> > > interpretation.

> > JE:-
> > The Mad Hatter "mathematical truism" is
> > now giving away (absolutely) free gifts
> > to almost everybody he likes at
> > his famous Dept Of Biology Tea Party.
> > His gift: everybody remains correct
> > except (of course) JE who remains
> > a Neo Darwinistic tribal outcast
> > (with thanks).

> NAS:-
> Pure mathematics - not ad hoc, simplified models, but pure mathematics
> - shows that you are wrong. Hamilton's rule is a correct mathematical
> statement. Only lunatics chase after disproofs of mathematical
> theorems.

JE:-
Only lunatics substitute irrefutable "mathematical
theorems" for refutable propositions of biology
within the biological sciences. This is exactly
what Hamilton et al have been doing and getting
away with, for over 50 years.


> > JE:-:-
> > NAS and BOH _seriously_ maintain that
> > as long as the mathematics remains valid,
> > the biology (the "application") doesn't
> > matter.

> JE:-
> So long as that application of the rule is correct.

JE:-
Is the validity re: the "application of the
rule" within any science equally
important to mathematical validlity, i.e.
do you agree two and not just the one level
of mathematical validity must be met for any
model within the sciences?

> NAS:-
> Of course, if your
> application of the rule involves redefining its components - for
> instance, r as a convenient probability measure - then, yes, you will
> run into difficulties.

JE:-
I have compeleted the form:
"A DECLARATION OF MEANING"
providing proof that I have
nothing to hide. You have
failed to complete this
form proving you may have
something to hide. In
order to remove this doubt
and save everybody time and
effort please complete the
form.

In the form I provided
my understanding of Hamilton
et al's definitions and provided
just ONE extra addition: a
definition of Darwinian fitness
as the missing maximand of the
rule. You have falied to provide
any maximand for the rule. You
have not made it clear to
sbe readers if a maximand
is even required.

> > JE:-
> > ERGO: No matter if the critical
> > case of the rule that allows organism
> > fitness altruism is proven biologically
> > meaningless, it remains valid mathematics
> > and that is ALL that matters. Their
> > argument demeans the science of biology.

> NAS:-
> I haven't seen any demonstration of biological meaninglessness in
> Hamilton's rule.

> > > NAS:-
> > > For example, if we have a positive b then positive c
> > > is associated with altruism, and negative c with mutualism.

> > JE:-
> > Yes, it does not matter at all to
> > the science of biology that the
> > rule cannot measure any difference
> > between just a reduced donation
> > and an investment cost by the actor.

> NAS:-
> Be explicit. Do you mean
> reduced donation: c < 0
> investment cost: c > 0

JE:-
I have defined donation and
investment. They are self
explanatory.

DEFINITIONS:

The cost c: is the cost of b.

An investment cost c: is a
paid cost that returns more
than c for an investment b.

A donation cost c: is a paid
cost that returns less than
c for the donation of b.

>snip "or what" <

Please complete:

 "A DECLARATION OF MEANING"

so that sbe readers can more
easily understand what you are
talking about.


> > JE:-
> > Did anybody here have shares in
> > Enron?
> > Dear oh dear..

> NAS:-
> I'd concentrate on the logic of your argument before drawing such
> parallels, John. This only serves to betray a fundamental ignorance in
> relation to your grasp of Hamilton's rule.

JE:-
Yes, it "may serve to betray a fundamental
ignorance" in relation to my grasp of Hamilton's
rule. However, because I have provided a refutable
position based on biology but you have only provided
a position based on "irrefutable" mathematics you
are not even in the race.  Until
you provide a refutable position within the
biological sciences for Hamilton et al assumption
that organism fitness altruism can evolve you
are proven to have misused a mathematical model.
To be able to do so you must supply a REAL
testable maximand for the rule. Prices theorem
is just that, "a theorem". You must supply
a biological THEORY not just a mathematical
THEOREM.

Regards,

John Edser
Independent Researcher

PO Box 266
Church Pt
NSW 2105
Australia

edser{at}tpg.com.au
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