>> 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,