John Edser wrote:
>>>>>JE:-
>>>>>...[zero] only represents a zero state of some biological
>>>>>_unknown_.
>>>>
> 
>>>>BOH:-
>>>>Would you care to demostrate why my statement is wrong,
rather than just
>>>>ignoring the content of what I wrote?  I can't accept your statements
>>>>without you persuading me that my ideas are wrong.  And I
can't do that
>>>>if you don't try and say what are wrng with my ideas.
>>>
> 
>>>>JE:-
>>>>When rb-c=0 what is left?
>>>
> 
>>>BOH:-
>>>What is left from what?
>>
> 
>>>JE:-
>>>Hamilton's rule is supposed
>>>to be a fitness road map. Suddenly
>>>no road map exists, i.e. we have gone
>>>off the map because zero fitness is
>>>represented. However a real fitness
>>>still remains. What biological fitness
>>>actually remains when rb-c=0?
>>
> 
>>BOH:-
>>The fitnesses of the two behaviours.
>>But now they're equal.
> 
> 
> 
>>JE:-
>>You failed to mention the two equal
>>fitnesses are logically _opposed_.
>>If both fitnesses are equal but
>>logically opposed, as Hamilton's rule
>>insists that they are, then _relatively_
>>no fitness, i.e. just a zero fitness exists
>>within Hamilton's rule when rb-c.
> 
> 
> BOH:-
> "no fitness" and "zero fitness" are not the same things.
> A temperature  of zero degrees Celcius does not mean no
> temperature.
> 
> JE:-
> Exactly, but this is my argument _against_
> Hamilton. You cannot have relative temperature
> without an assumption of asolute temperature.
> Nought temperature is 0 degrees Kelvin. This
> point has never been reached but provides an
> absolute measure of temperature. Without it,
> just a relative celcius measure in is
> meaningless.
> 
> Hamilton's rules attemptes to invalidly
> subsitute a relative measure for an
> absolute measure. 

No it dosn't.  It ONLY provides the relative measure - it only compares 
the fitnesses of the two behaviours.


>>BOH:-
>>If I want to find out if I'm taller than you, I do it by measuring my
>>height and your height, and taking the difference.  IF we're both 188cm
>>tall, then the difference is zero.  But that doesn't mean that neither
>>of us has no height at all.
> 
> 
>>JE:-
>>Exactly, but the above is my argument _against_
>>Hamilton. Two and not just one, height concepts
>>exist in your argument: relative and absolute
>>height. In biology two concepts of fitness
>>exist, relative and absolute fitness. When you just
>>compare heights you are only using a relative concept of
>>height so that when they are equal but opposed, the
>>absolute concept of height must remain otherwise
>>no such comparison was possible. Likewise, when rb-c=0,
>>absolute fitness remains within the science of biology
>>but remains absent from Hamilton's rule.
> 
> 
> BOH:-
> Because it doesn't need to be there.  If the question is "Am I taller
> than you?", then if I'm 1cm taller, it doesn't matter if I'm 54cm tall
> or 724km tall - the answer is still "yes".
> Recently there has been quite a bit of work on the dynamics of
> populations, but none of it (as far as I'm aware) invalidates Hamilton's
> rule.
> 
> JE:-
> An absolute reduction is parental fitness
> has nothing to do with "population dynamics",
> it remains solely the concern of fitness _definitions_.
> The relative measure only answers the one question.
> It can only do so because the absolute measure exists,
> _implicitly_.  Do you agree or disagree?
> 
I agree.  And as Hamilton was only trying to answer the question about 
relative fitness, that's all he needed.

> Why did you just snip the hypothetical argument provided
> which demonstrated in very simple terms the absurdity of
> just measuring a relative gain in height increase if it
> costs an absolute height reduction for both? 

Because it wasn't relevant.  Hamilton was only interested in answering 
questions about relative fitness.

Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
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