John Edser wrote:

>>>>>>JE:-
>>>>>>A constant/maximum is always required because 
>>>>>>it alone provides an absolute _supposition_,
>>>>>>i.e. a fixed point of logical reference.
> 
>  
> 
>>>>>BOH:-
>>>>>Good.  Will you allow us to use zero as a constant?
> 
>  
> 
>>>>>JE:-
>>>>>Do you mean zero or nothing?
>>>>>These two views are _not_ the same.
> 
> 
>>>>BOH:-
>>>>Zero.  That's why I wrote "zero".
> 
> 
>>>>JE:-
>>>>Zero is not a constant it is just
>>>>another number that may or may not
>>>>be used to represent a constant
>>>>term within a mathematical expression.
> 
> 
>>>BOH:- 
>>>What?  Do you mean zero can vary?
> 
> 
>>>JE:-
>>>OK, zero _is_ a constant as a number 
>>>but what a number is used to represent 
>>>can _vary_ since other numbers may be 
>>>added/subtracted from it, if and only if, 
>>>it represents a variable. A variable
>>>is just a relative concept so you are
>>>required to ask: relative to what and
>>>then, supply an answer! The only possible
>>>answer is: a constant. 
>>
>>
>>BOH:-
>>Good.  So, I'll re-write Hamilton's Rule as rb-c>0, and there you have 
>>it.  rb-c is a variable, and 0 is your missing constant.
> 
> 
>>JE:-
>>This zero state has to represent
>>something within a testable theory
>>of nature. 
> 
> 
> BOH:-
> Yes.  In this case, no difference between the costs and benefits of an 
> altruistic behaviour.
> 
> JE:-
> Please replace the number "0" with a new 
> defined term, within Hamilton's rule.
> 
Why?  Zero is zero in Hamilton's rule.  It's a constant.  If the 
benefits are greater than the costs (i.e. if rb>c), then the altruistic 
trait can evolve.  Zero is the critical value here - it's this that rb-c 
is compared to.

> I repeat:
> Zero, as used above, is not a
> valid TERM it is just a valid NUMBER.
> I did state a constant/maximal term
> must be included. Nobody knows what
> just the number zero is supposed to 
> represent within Hamilton's rule.
> 
This is not the first time I've been described as Nobody this week - but 
the last time it was by a printer.

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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