Re: 2. Nested Verses Intersecting Sets of Fitness
- From: johnhewitt22@xxxxxxxxx
- Date: Fri, 3 Apr 2009 12:35:06 -0500 (EST)
John,
I continue to feel a sense of agreeing with some aspects of what you
are saying, but remain quite unclear on the details and am unable to
convert that feeling into specifics. For example, I am not clear
whether you perceive your nested sets in terms of set theory, which is
the basis for a lot of the terminology you use, or in terms of nested
data processes, which seems to apply to many of the examples you
choose. I don't think set theory would necessarily apply to data
processes.
I am also unclear how you compare or contrast your approach with more
classical or conventional expositions on evolutionary theory. In
particular, how do you make use of these ideas in interpreting real
observations and, finally, does your approach lead to observably
different predictions when it is compared with conventional theory?
I really can only ask you again, have you assembled your ideas into
one place and made them available in a form that people like me can
read or even cite?
I have asked you this question before but you did not reply; I do
assume that the absence of a reply implies that you have not done so,
which seems a shame.
Sincerely
John Hewitt
On Apr 2, 7:01=A0pm, John Edser <ed...@xxxxxxxxxxxxxx> wrote:
[This is an edited resend. The original was sent on 31/3/09 but appearsss.
not to have been posted to the group]
Jim requested that I provide a series of posts as a tutorial
specifically referring to my use of set theory within evolutionary
theory. This is the second post of a series.
The previous post (1) employed simple nested and non nested programming
loops to illustrate the critical difference between nested and non
nested sets of information. In these examples I demonstrated that nested
loops are more complex than non nested loops. When exactly the same
nested loops are placed in a simple programming list allowing set
intersection whenever they are compared, or merged loops when they are
added together, the critical difference between nested and non nested
becomes apparent. The relationship of programming loops in just a list
can be characterized as "additive". OTOH the relationship between the
same loops when nested become non additive. In the same way, nested sets
of fitness remain entirely different to intersecting/merged sets of fitne=
It should be clear from these examples that a set of nested =A0loops have
to be selected in oder to select one nested loop within a nested set. In
exactly the same way, any nested fitness remains minimally linked to at
least one other like links in a chain. For example, if all gene
fitnesses remain nested within one competing organism fitnesses then in
order to be able to select a single gene _one entire organism will have
to be selected and not just one gene_. However, if the fitnesses of each
gene remains additive i.e. their fitnesses are intersected/merged then,
like the simple programming list of loops, each gene can now be selected
_independent of any other within the same genome_. IOW, nested fitnesses
always remain critically multiplicative and therefore entirely DEPENDENT
on the fitness of the entire nested set they remain _a part of_. These
set nested dependent fitnesses I contend are what Neo Darwinism is
referring to when employing the term "epistatic". However, intersecting
i.e. compared fitnesses are additive and therefore NON epistatic so they
remain INDEPENDENT of each other, i.e. they can be selected on an
entirely separate basis. In short, a biological population can be
defined as any additive fitness association between independent units of
selection. These simply add up to form any population where each added
unit is comprised of one nested fitness set within which all parts
remain fitness nested. In this way Darwinism remains strictly
mono-centric, i.e. it only defines a SINGLE UNIT OF SELECTION. IOW,
selection can only operate at just the one level within Darwinism: the
fertile organism level. OTOH Neo Darwinism remains poly-centric but only
because it does not/cannot differentiate between nested and intersecting
sets of fitness using the simplified/oversimplified models it employs as
bona fide theories.
By employing programming examples it is possible to reason that only
additive and therefore intersecting (compared) nested sets of fitness
can validly be defined as independently selectable within nature. Quite
clearly, additive populations cannot be selected as a single unit
because their "parts" remain additive, i.e. their parts are not fitness
independent wholes. The net result of attempted group selection is just
individual selection because selecting one additive in fitness
population is exactly the same as selecting individually, each nested
set within that population. In this way group selection cannot
contradict individual selection as it has been argued that it can.
The TOTAL fitness of each nested set is only presented by the size of
the largest (outside) concentric circle representing the most outer set
element which contains all the others as nested within itself. This
single FITNESS SUPER SET represents the total number of reproduced
nested sets that have _ exactly the same number of nested elements as
their parent/parents_. In biological terms =A0this represents the total
number of fertile forms reproduced per parent per population which is
the definition of TDF. A sub adult infertile organism is represented as
a reproduced nested set with only a SMALLER number of nested elements.
IOW an infertile immature form represents a critically incomplete
reproduction or if you like, just a reproduction in progress. In this
way growth can be objectively separated from reproduction:
Growth: building a single nested i.e. concentric set of fitness by
starting from the smallest and ending with the largest. In biological
terms growth represents a concentric development of non additive
fitness. In simple terms growth is the development of body parts which
display a non reversible and therefore hierarchical, non additive,
single concentric set of fitness.
Reproduction: the minimal replication of one entire, i.e. a complete
single nested set of fitnesses into a population of same.
The most outer circle of each fitness nested set can alone depict a
single TDF SUPERSET OF FITNESS. It can easily be identified as the
largest concentric fitness within each nested fitness set. TDF
represents a critical, single fitness constant per Darwinian unit of
selection per population providing the only falsifiable frame of
reference available to evolutionary theory. TDF insists on a constant
FITNESS INCREASE, i.e. TDF represents a falsifiable maximand fitness per
parent per population. This entirely prohibits any TDF fitness from
being selected to be reduced (fitness altruism).
An evolving population of TDF fitness supersets can be simply
illustrated as a single population of many concentric fitness sets (many
concentric circles) each with the largest concentric super set
representing one TDF. These are compared (intersected) by default in one
population in a naturally competitive way _only allowing the largest TDF
per population to be naturally selected FOR_. Note =A0that this strictly
default comparison is not by intent defining the Darwinian process as
strictly "bottom up" (inductive), i.e. a process in which complexity can
continually increase without the direction of an even more complex
system, i.e. not "top down" (deductive).
Regards,
John Edser
Independent Researcher
ed...@xxxxxxxxxxxxxx
.
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