Re: Did prime numbers evolve?
- From: "John W Edser" <edser@xxxxxxxxxxxxxx>
- Date: Tue, 15 Apr 2008 19:46:52 -0400 (EDT)
dk@xxxxxxxxxxxxxxxxxxxxxxxxx (DK) wrote:-
Not true. Mathematics is based
on pure logic, on things that
must be true regardless of
whether or not their are any
sentients to
discover or use them.
Lots of mathematicians disagree.
Alternative point of view is that
math/logic merely reflect the way
our brains work and have nothing
to do with the "objective"
reality.
JE:-
The short answer is that mathematics is *NOT* a science. This is only
because mathematics cannot be falsified so we can never know if prime
numbers evolved or not _until they become predicated by a falsifiable NON
number_. Just numbers alone, like the non predicated number 3 represent an
uncorrected, oversimplification of exactly the same number so predicated
e.g. three APPLES. In mathematics these three apples can be written in two
very different ways _additive_ and _non additive_. Three as a prime number
represents three ENTIRE (additive) apples as just 1 apple + 2 apples or 1
apple + 1 apple + one more apple forming the one, same _population_ of
apples. Non additively this is written as 3*Apple which is shortened in
algebra to 3A such that 3*A =A*3 _critically reversing subject and
predicate in the process because A represents a critical predicate for the
number 3 but not the reverse_. Empirically, addition and non addition are
NOT AT ALL the same because any non addition represents proper subsets
(nested sets) of numbers where the proper set configuration cannot be
reversed and the same meaning maintained. In fact this nested set reversal
always provides a refutation for the original. However, in just mathematics
multiplicative proper so-they-always-remain-non-reversible sets have become
oversimplified to mean additive so-they-always-remain-reversible
intersecting sets allowing the commutative law (without which mathematics
cannot function).
A strictly non additive (in this case multiplicative) association between
the number three and "apples" does not indicate one population but the very
opposite: a single discrete unit such that the number three represents a
_dependent part of the predicate "apple" such that three cannot be
independently selected_. Many times over the last ten years I have argued
that empirically, "multiplicative" indicates parts-to-a-whole while
"additive" indicates a population of independent wholes _which cannot be
selected as a single unit of selection_ as it is within uncorrected,
polycentric mathematical models ranging from dicentric classical group
selection to _minimally_ tricentric Hamilton's Inclusive Fitness. Darwinian
theory remains strictly monocentric but only because this alone can provide
a falsifiable theory of evolution using TDF (total Darwinian fitness). The
polycentric theories of Neo Darwinism were and remain, uncorrected
oversimplifications of monocentric Darwinism which have been misused to
replace/compete against, the one theory all of them were oversimplified
from.
One way of providing a falsifiable theory as to what prime numbers are
empirically is to hypothesise that prime numbers are more likely to
represent NON additive wholes, i.e. not just parts of some (other) whole.
This has interesting ramifications for evolutionary theory because it may
help to provide a mathematical way of modelling the unit of selection
problem which has reduced Neo Darwinism to just irrefutable mathematics. The
view that the prime numbers of 5 or more are empirically important can
verified by the two Goldbach conjectures:
1) Strong Goldbach conjecture: Every even integer greater than 2 can be
written as a SUM of two primes.
2) Weak Goldbach conjecture: Every odd integer greater than 5 can be written
as a SUM of three primes.
IOW prime things which remain greater than 5 are more likely to represent
populations of FITNESS INDEPENDENT (additive) UNITS OF SELECTION. This can
be tested to refutation if the fitness of one population is NOT just the
additive fitness of each unit which comprises that population (no matter how
fitness is defined). How might this work in practice? For gene centric Neo
Darwinism, when gene fitness epistasis is included, it should involve 5 or
more loci. For example within Hamilton's rule (within which all gene fitness
epistasis remains deleted ) becomes: (r^e)b > c where e = 5 minimally when
gene fitness epistasis becomes undeleted while at the same time proposing
independent (selfish) genes.
The ancient greeks recognized
the five
platonic solids and realized
that their could not be a sixth
long before examples of all five
were found in nature--and no sixth
has been found in nature.
Regards,
John Edser
Independent Researcher
edser@xxxxxxxxxxxxxx
.
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