# 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 mis-characterization 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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