Perplexed in Peoria wrote:
> "Bob O'Hara"  wrote in
message news:cels01$175j$1{at}darwin.ediacara.org...
> 
>>someone wrote:
>>
>>>(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
>>>
>>
>>(a) and (f), and (g) and (j) are the same.  It is easy to show that
>>there are only 8 possible states.
> 
> 
> Or, if you distinguish zero values from positive or negative ones,
> then there are 27.
> 
Damn!  Out-pedanted!

> But it would be better to say that there is only one class of states
> to be considered:
> r is a (pure) number
> c is a number (in units of some kind of fitness)
> b is a number (in the same units as c)
> 
> Since the rule does not distinguish between positive and negative
> parameter values, and treats all combinations the same, there is
> no reason to do a case analysis, unless you think that the concept
> of a negative number is somehow philosophically difficult to comprehend.
> 
It can be useful for categorising behaviours.  The case where c is 
negative and b is positive is not interested, because it's obvious from 
the individual's direct fitness that the trait will invade the 
population.  By categorising in this way, we can focus on the different 
parts of the parameter space that are more interesting, even if we use 
the same mathematical tools to analyse them.

Bob

-- 
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf H„llstr”min katu 2b)
FIN-00014 University of Helsinki
Finland

Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax:  +358-9-191 51400
WWW:  http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
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