[FOM] Frank Quinn article in January Notices
irving.anellis at gmail.com
Wed Dec 28 19:40:34 EST 2011
I think that David Roberts has hit on a crucial facor, which he does
not. however, make quite as explicit as one might perhaps like when he
reminds us that "... whenever statistical reasoning is involved in
exact sciences (and some inexact ones), one inherently cannot assume
excluded middle. Hypothesis testing - in its simplest form asking
whether a measurement yields a null result - is full of phrases like
'fail to reject the null hypothesis at x level of uncertainty', which
is definitely *not* the same as accepting the null hypothesis. This is
one area where beginning students of statistics trip up all the time,
mostly because the are expecting, implicitly, EM to hold."
Specifically, the scientist (and if one accepts that the "applied"
mathematician may be distinguished from the "pure"), the applied
mathematician, comes to problems of expressing physical reality in
mathematical terms from a much different perspective than the pure
mathematician whos interest is in deriving logically what theorems
s'he can from a given set of axioms. In other words, scientists are
not thinking in terms of the validity or applicability of LEM -- or,
for that matter, any aspect of the underlying foundations of their
mathematics; rather, the concern is to atune as accurately as
possible, their formulas to fit their data.
I had, in my days as a college student, the privilege of seeing close
up how an experimental scientist approaches the statistical analysis
of laboratory data. My father, a food microbiologist, did his
experiments, of course, in the laboratory, but wrote his publications
at home, on the dining room table, so I was able to have an
illustration of how observational data was dealt with mathematically.
When he was a university student, the statistical method he was taught
by his advisor was devised by his advisor, the noted bacteriologist H.
O. Halvorson. The formula that was used was employed for the next two
decades to represent the death kinetics of bacteria subject to thermal
treatment at different specified temperatures. In the mid-1950s, one
of my father's cross-country colleagues, Clarence Schmidt and one of
his colleagues, devised a formiula, since known as the Nank-Schmidt
formula, which was used into the mid-1970s. More accurate than
Halvorson's, there was a problem.
Namely, the formula predicted a specific curve which increased with
accelerating morbidity of bacterial as temperature and/or
gamma-radiation dosage increased, up to
a certain given combination of temperature and radition, after which
the effectiveness of the treatments declined, and the curve began its
decrease, and a modified Nank-Schmidt formula was introduced. The
problem was reproduced, with slightly less anamolous effect, in the
modified formula. The problem was that for both the original and the
modified formula, the experimental data failed to match the predicted
pattern of the curve postulated by the Nank-Schmidt formula. Instead,
there was an unexpected and unexplained "tail" to the curve before it
continued increasing and then decreasing. In the early 1970s, my
father and Stanley Werkowski, one of the statisticians from their
institute collaborated to devise a new formula, to replace the
Nank-Schmidt formula, that would more accurately reflect the
experimental data. The statistician continued to further refine the
formula after my father retired.
I suggest that this account may more accurately illustrate the
attitudes which scientists and applied mathematicians have towards the
mathematical representation of physical reality than anything
logicists or formalists have described.
Irving H. Anellis
8905 Evergreen Avenue, Apt. 171
Indianapolis, IN 46240-2073
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