Re: The Misuse Of Mathematics Within The Evolutionary Sciences (
 From: John Edser <edser@xxxxxxxxxxxxxx>
 Date: Tue, 29 Jul 2008 02:00:14 0400 (EDT)
Andresqp wrote:
JE:
IMHO it is mostly the reverse: mathematics was and remains misused
within the sciences _by mathematicians working in the sciences_.
Scientists and sadly, the world in general are easily intimidated by
mathematics and the simplified/oversimplified models of empirical
science that mathematicians produce because mathematics is so
appallingly taught. Note that even if you are right, i.e. mostly
scientists are misusing mathematics and not the reverse, your attitude
"I do not much care how they may be misusing it" is in my opinion,
typical of mathematical based arrogance. It seems to me that
mathematicians, somehow, view themselves above the empirically based
world we actually inhabit..
What is required is a no holds barred discussion by MATHEMATICIANS and
SCIENTISTS as to what exactly _does and does not constitute a misuse of
mathematics within the sciences_. I have been attempting to initiate
this here, for over 10 years without success. The attitude is always,
"this has nothing to do with me". One of the best examples of misuse
that I know of is within evolutionary theory. It was Galileo in the mid
1600's who first taught us how to use mathematics within the sciences:
you absolutely require at least one defined constant in order to provide
a necessary frame of reference otherwise cause and effect proposed
within the science remains reversible and therefore just tautological.
As a mathematician you may appreciate that this has always been
illustrated within Zeno's Paradox which has been around, unsolved, for
over a 1000 years. The only way to solve Zeno's is to import from
OUTSIDE of mathematics (as Godel predicted) into what is just an
empirically oversimplified mathematical model of a bona fide proposition
of science, two simple constants: the start and the end of the proposed
race. Only if you measure the distance of both the rabbit and the
tortoise to these proposed constants and not just relative to each other
as variables, can it be calculated when the rabbit overtakes the
tortoise and then goes on to win. It should have been obvious, even to
mathematicians(!), that this proposed oversimplified, uncorrected model
of a theory of a race cannot even start unless these constants are
provided _as propositions from outside of mathematics_ because it is not
possible to give the tortoise a head start unless the start is actually
defined. A head start from where exactly?!? Zeno's amply sums up the
stupidity of mathematics misused as an empirical based science. Yet,
this stupidity continues unabated within the evolutionary sciences via
the misuse of random patterns as somehow, a proposed valid process of
evolution (the so called Neutral Theory). There is not and can never be
any valid Neutral Theory of evolution just a misused Neutral model which
was and remains oversimplified from Darwinian theory.
My other detailed example was and remains Hamilton's Rule :rb>c. This is
supposed to provide the conditions as to when an organism fitness
altruistic gene can spread within one population. Just a glance at
Hamilton's inequality demonstrates that not one single constant term has
been defined within it. IOW the rule has no Galilean frame of reference
so it has about as much chance of making any scientific sense as Zeno's
Paradox did without the defined start and end of the race acting as a
falsifiable frame of reference. Yet, evolutionary theorists of the
stature of Professor J. Felsenstein have argued here that Hamilton's
inclusive fitness proposition, which allows more than just the one
fitness maximand per falsifiable unit of selection, constitutes one of
the most important advances in evolutionary theory. IOW, the misuse of
mathematically based oversimplified models of empirically falsifiable
Darwinism continues unabated within evolutionary theory by people who
were and remain, predominately mathematicians.
I am a biologist very much interested in the use of mathematical
models in biology, specially in evolution. I was wondering if you
could help me to get more information about the subjets discussed
before. Particulary about hoe to recognize valide mathematical models
in science.
thanks for the attention,
Hi Andres,
I have provided here, two detailed examples within the biological
sciences of the misuse of mathematics:
1) The constant misuse of just the random process of genetic drift
(sampling error within proposed "Neutral Theory") as somehow, a valid
theory of evolutionary change IN ITS OWN RIGHT when all it can ever
provide is heritable, random variation for the non random process of
natural selection. The ONE SINGLE falsifiable theory of evolution that
we have, as it was proposed by Charles Darwin, argued that ubiquitous
random heritable change, which can only constitute variation and not
evolution, must be acted on using the non random process of natural
selection WITHIN THE ONE, SAME THEORY to produce EVOLUTION. However,
mathematicians working within the evolutionary sciences artificially
separate just the random process of drift from the non random process of
natural selection and then proceed to propose that one can somehow,
validly contest the other e.g. please refer to the posts to sbe of Dr L.
Morand.
Note that the misuse of genetic drift as evolution and not as just
variation always working with selection within the one same falsifiable
theory of science represents a repeat of the early mutationist argument.
All this succeeded in doing was to hold up a better understanding of
evolutionary theory for many years. The mutationists argued that random
mutation constituted an evolutionary change in its own right and not
just a change in random variation. Neutral Theory repeats the same
invalid separation but only because they can be separated within
mathematics. _They cannot be separated within the sciences_.
2) The misuse of W.D. Hamilton's oversimplified and uncorrected model of
falsifiable Darwinism known as "Inclusive Fitness". It was this misused
model that Dawkins deployed to promote his "selfish gene" concept which
only provided a mischaracterization of evolutionary theory. Hamilton's
model was based on a mathematical idea by JBS Haldane (one of the
founding fathers of population genetics) in which he allowed the fitness
indivisible fertile organism of Darwinism to be broken down into
heuristic, contesting, additive units of selection when NO EMPIRICAL
OBSERVATION OF NATURE will allow it. In Hamilton's model individual
genes contest the fertile organism they exist entirely within as
somehow, independent units of selection in their own right. This
required the deletion of all epistatic (non additive) gene fitness
associations within the Darwinian fertile form as a drastic, uncorrected
oversimplification of Darwinism. This surgery performed on Darwinian
theory by mathematicians was required in order to explain what was only
misconceived to be fertile organism fitness altruism (FOFA). Darwinism
100% prohibits FOFA as a refutation of of Darwinian theory! What the
proponents of Hamilton's Inclusive Fitness ended up arguing is that more
than just the one fitness maximand can be validly allocated to the one,
same falsifiable unit of selection. Such a silly proposition was and
remains contradictory within the sciences BUT REMAINS VALID WITHIN
MATHEMATICS. The problem here is that mathematics, unlike the sciences,
has no Galilean (constant) frame of reference. Please refer to the many
posts I have posted to sbe on this critical topic. It was Galileo who
firstly showed us how to validly employ mathematics within the sciences.
Regards,
John Edser
Independent Researcher
edser@xxxxxxxxxxxxxx
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