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| subject: | A DECLARATION OF MEANING |
I have composed the following form as
a required declaration of meaning for an
sbe meaningful discussion of a model or
theory applied to fictitious or real data.
I have filled the form in with my own answers.
In this case the form outlines Hamiltonian
questions. However its generality is not
confined to this model. I request all
participants to fill it in with their
own answers and return it for public
display ASAP. The form comprises two
parts. The first part deals with three
basic principles. The rest of the form is
comprised of seven questions. The answers
anybody provides remains their own business.
This form or something like it has become
a necessity because of major misunderstandings
and misreading by participants within sbe debate.
Unless we all lay our cards on the table we
are just wasting each others time. I am happy
to make any reasonable adjustments to the form
that may be requested. Please note: The
answers given in this form can be criticised
OUTSIDE of the form but not WITHIN THE FORM.
This last point is critical because the form
is just a declaration of meaning and not a thesis.
I have attached two notes to clarify my
answers. Please make sure that added notes
are easily understood to be such within the
form.
______________________start of Form ______________________
I declare the following as a true statement
of meaning for all ongoing discussion.
If I change any declared meaning that appears
within this declaration I will explicitly acknowledge
that this point of meaning I have provided may have been
refuted where refutation can be proven via either,
logical invalidity or a confirmed point of refutation.
Name: John W. Edser
Address: PO Box 266
Church Pt
NSW 2105
Australia
DECLARATION OF PRINCIPLES:
A) What is the purpose
of processing only fictitious data?
To test the validity of any set
of definitions used to process
data.
B) What is the purpose
of processing non fictitious
data?
To test the validity and discover
an experimental result that only real
data can provide for any set of
definitions used to process
that data.
C) What do you state is the difference
in principle between any relative and
any absolute measure?
All relative measures are minimally,
a bilateral comparison but all absolute
measures are strictly unilateral.
A absolute measure can comprise
a completed total, maximal/minimal/
constant value.
DECLARED DEFINITIONS:
(i) DEFINE ABSOLUTE FITNESS and
describe how it can be measured.
FOR HAMILTON et al:
No definition was provided by
Hamilton et al for absolute fitness.
No measure is provided
within Hamilton's rule for absolute
fitness.
(ii) DEFINE RELATIVE FITNESS and say
how it can be measured.
Within Hamilton's rule the two fitnesses
being compared are inclusive fitness
(rb) and Darwinian fitness implied as
as just the cost (c).
The full cost, cmax, is equal in value
to Darwinian fitness as I have defined
it below. These fitnesses are compared
within the inequality known as
"Hamilton's Rule":
rb > c
(iii) WHAT IS THE PURPOSE OF
FORMING AND COMPARING FITNESSES?
For Hamilton et al, to measure
when fitness associations
can evolve.
(iv) DEFINE ALL THE TERMS
EMPLOYED.
Within the rule:
r: relatedness IBD
b: all resources transferred from the
donor to the recipient where the
donor is also referred to as "the actor".
c: the cost of b
(v) DEFINE ALL THE CONSTANTS
EMPLOYED.
No constant term exists within
Hamilton's inequality.
(vi) WHAT ARE ALL THE COMBINATIONS
OF VARIABLES THAT THE PROPOSITION
ALLOWS?
The rule allows for ten
different combinations of just three
variables: r,b and c:
(a) +r +b +c
(b) +r +b -c
(c) +r -b -c
(d) +r -b +c
(e) -r +b -c
(f) +r +b +c
(g) -r -b -c
(h) -r -b +c
(i) -r +b +c
(j) -r -b -c
---------------------------------------------
Note 1:
-r: It is biologically meaningless
to allow r to become less than zero
reducing the number of valid combinations
to five.
-b: Can be EITHER the removal of resources
from the recipient to the donor OR just the wanton
destruction of the resources owned by the recipient
via the donor. In the former case the donor makes
a gain but in the latter both sustain a loss.
Note that both acts are mathematically identical
but they are not biologically identical.
----------------------------------------------
----------------------------------------------
Note 2:
-r(-b) > c
is mathematically equivalent to:
rb > c
However, they are not
biologically equivalent.
----------------------------------------------
(vii) WHAT ARE THE
SUPPOSED BIOLOGICAL
STATES THAT THE
PROPOSITION IS
SAID TO BE ABLE TO
MEASURE
Out of the ten possible
logical combinations
Hamilton et al only define
four as biologically
meaningful:
Spite: +r -b +c
Mutualism: +r +b -c
Altruism: +r +b +c
Selfishness: +r -b -c
For the majority of cases
-b and -r are simply ignored.
For this majority of cases:
Mutualism: any case of -c
Altruism: any case of +c
2.EDSERIAN DEFINITIONS:
(i) ABSOLUTE FITNESS: The total
number of fertile forms reproduced into
one population by a parent. I will refer
to this total as "Darwinian fitness".
Fertility is determined in the normal way,
i.e. via a simple inspection of the reproductive
system. The living form is not requited to reproduce
an infertile to prove fertility.
(ii) RELATIVE FITNESS: The two fitnesses
compared within the rule are inclusive fitness
rb and Darwinian fitness measured as
the cost c, where total Darwinian fitness
has the value cmax (the maximal cost to the actor).
They are compared using the inequality commonly
known as "Hamilton's Rule".
(iii) As above
(iv) As above
(v) As above
(vi)
Because no constant term is present
within the rule absolutely no frame of
reference exists for any unambiguous
comparisons between rb and c within the rule.
This being the case no difference between
a reduced positive c and a negative c
exists within it. Not a single case
exists within the rule where this failure
remains insignificant re: biological
interpretation. Not a single case within
the 10 possible cases that exist remain
unambiguous disallowing as invalid all cases
of Hamilton's rule.
However, just intuitively, mutualism
as any case of a negative c where spite is
disallowed, remains valid if and only if,
c gains to the actor are concrete gains
and not just a wanton destructive act
on the recipient/recipients.
The rule fails because the Darwinian fitness
of the actor K was not included. K has
the same value as cmax. For any absolute measure
of fitness for the actor altruism is only proven
when:
rb > K
However, this case only produces sterile like,
forms. The actor donating K does not die, it
works maximally for the recipient/recipients
reproductive benefit so it has to fail
to reproduce itself, entirely. Such an actor may
be fully fertile but will act as if was sterile,
i.e. it becomes the equivalent of a sterile form.
The only possible way the rule may work is
when c is reintroduced:
rb > K-c
rb+c > K
The above revision of the rule remains
speculative. I will argue that
absolute fitness mutualism will replace
it where both K for the actor
and K for the recipient/recipients,
increases. Here no rule needs to be
articulated because the logic is
obvious.
For the revised rule above, at least
the actor is not now forced to
become sterile like. Here the donation
of b and the cost c of donating it must
exceed the absolute fitness of the
actor (Darwinian fitness) for the gene
to spread.
Without K, Hamilton's rule cannot
measure any difference between
a cost c that becomes an investment
because it returned more than the cost
c to the actor and a true donation
that returns less than the cost c.
Thus the rule confuses sham
altruism (an investment) with
proven altruism (an absolute fitness
loss). Thus any conclusions that
people reach re: the evolution of
altruism using the rule are mostly
sustained by hidden mutualism, i.e.
such conclusions constitute invalid
self contradictions. If any proposed
rule cannot discriminate between
the extremes of an absolute loss
and an absolute gain then it is
a proven failure.
_________________end of form __________________
Regards,
John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia
edser{at}tpg.com.au
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