Re: Hamilton's Rule In The Mirror

From: John Edser (edser_at_tpg.com.au)
Date: 03/26/05 

Date: Sat, 26 Mar 2005 01:46:33 -0500 (EST)

"Anon." bob.ohara@NOSPAM.helsinki.fi

> >>NAS:-
> >>So, I actually think we are agreeing with eachother, pretty much.
And
> >>where you are disagreeing with me it is actually because you have
> >>misunderstood my point.

> > JE:-
> > No, we remain in disagreement. Hamilton's sub total rb when
multiplied
> > by -1 becomes -rb even while r and b remain positive within
Hamilton's
> > critical multiple. The point of total disagreement is what -(+r*+b)
=
> > -rb actually means. It is possible to disregard r for the moment and
> > just discuss b. In Hamilton's Rule b represents resources
transferred
> > from the actor to recipients,

> BOH:-
> No, John. It's the change in fitness of the recipient, due to the
> action of the actor.

JE:-
Hi Bob,
Absolutely not. The variable +b is strictly the movement of resources
from the actor to recipients such as food, protection taking or risks
etc. These resources can only become a fitness when multiplied by +r,
i.e. only the entire multiple rb (which is just a probability) can ever
represent a valid fitness. When you multiply +b by -1 you get -b which
represents exactly the same resources actually moving in the opposite
direction: from the recipients to the actor. This must result in a loss
of fitness for the recipients unless these recipients have infinite
resources. In this case any donation to them is of no consequence,
anyway.

> > JE:-
> > i.e. b represents Hamilton's resource
> > vector.

> BOH:-
> No, it's a scalar.

JE:-
Only the rb multiple can be a (sub) total fitness which is indeed a
scaler but b remains the critical resource vector allowing this fitness
scaler to change in size.

> > JE:-
> > When you multiply any vector by -1 it must reverse direction.
> > Thus in this case b*-1 =-b. This represents resources transferred
FROM
> > the original recipients to the original actor if the actor and
> > recipients do not change places.

> BOH:-
> No, it means that you have multiplied b by -1.

JE:-
Was the above supposed to explain anything?!? Is it supposed to mean
that
multiplying by -1 produces _absolutely_ no difference simply because -c
> -rb remains mathematically identical to rb > c? I don't think so! Have
you ever heard of stereo chemistry which is unique to living things?
Anything can be mapped to its mirror image by multiplying it by -1 yet
within living forms these isomers have entirely different properties.
Using your logic which is only based on a misuse of mathematics, my
right hand must be _identical_ to my left hand. Only an idiot
mathematician would ever think so...

> BOH:-
> If you are using this as
> a notation to say that b is negative, then it means that the change in
> fitness of the recipient is negative - i.e. the recipient looses
fitness.

JE:-
Do you agree or disagree that -b within Hamilton's Rule must result in
the recipient losing and not now gaining fitness?

> > JE:-
> > This has to result in the cost to the
> > original actor becoming negative because it now provides a gain for
that
> > actor and not a loss.

> BOH:-
> No, the change in fitness of the actor is c.

JE:-
The variable cost c becomes negative when you multiply it by -1. You
have to define exactly what this fitness change actually represents.
Hamilton et al have always failed to do so. The variable c represents
EXACTLY a cost in fitness units for the actor as measured by the number
of normal reproductions _foregone_. If c = 0 no normal reproductions
were forgone. If c = -3 then the actor actually _increases_ and does not
decrease by 3 the number of normal reproductions it reproduced. Of
course, this is only possible if the resource vector b reversed
direction unless you are arguing that Hamilton's Rule was just a Neo
Darwinian perpetual motion machine, i.e. has assumed infinite resources.

> BOH:-
> You have failed to say
> anything about the relationship between b and c.

JE:-
No at all. As +b increases then +c has to increase otherwise recipients
are getting b resources for just nothing at all. The relative opposite
applies: as the resource vector b increases but in the opposing
direction: from recipients to actor then the cost c for the actor must
decrease, i.e. actually constitute a gain otherwise the actor is
suggested to have done nothing at all with the -b (resources it has
received from the recipients).

> BOH:-
> I must say that I'm impressed at your ability to become confused over
> even the simplest mathematics. This is not helped by the way that you
> confuse mathematical operations with reality.

JE:-
Thank you for the compliment.

Regards,

John Edser
Independent Researcher
PO Box 266
Church Pt
NSW 2105
Australia

edser@tpg.com.au

Relevant Pages

  • AN EMPIRICAL EXPRIMENT TO VERIFY THE BIOLOGICAL EVENTS THAT OCCUR WITHIN HAMILTONS RULE
    ... different clone to the recipient clone so that the actor is related r ... One actor and a set of recipients are set up using as identical ... the experimenter would move x of a ... via the transfer of x resources from the actor to the recipients via the ...
    (sci.bio.evolution)
  • Re: Hamiltons rule
    ... independent in FITNESS. ... both cases an independent proactive actor must reprocess x resources in just ... This act decreases the recipients as a whole fitness ...
    (sci.bio.evolution)
  • Re: Hamiltons Rule In The Mirror
    ... In Hamilton's Rule b represents resources ... The fitness benefit derived from the movement of b ... fitness sub total rb unless the recipients get something for nothing. ... the recipients of b resources are not related enough to the actor then ...
    (sci.bio.evolution)
  • Re: Applying TDF (was understanding y)
    ... I will assume that it is the average TDF of those members ... > TDF of the actor if he acts altruistically, or the TDF that he would have ... >>> are unlucky enough to never act as recipients. ... >> resources to the recipients as a whole only leaving just R-x resources ...
    (sci.bio.evolution)
  • RE: Issues: A Question Of Integrity (was: Issues)
    ... exactly the same FITNESS events do NOT happen using both rules. ... From the actor to the recipient. ... The same logic applied to the recipients ... via the transfer of x resources from the actor to the recipients via the ...
    (sci.bio.evolution)