Regarding Allen Roy's remarks:
> ...
>
>But I am talking about the basic assumption of measurement, you
>measure with an appropriate tool to fit the job to be measured. For
>instance you don't use the width of you thumb to measure the
>circumference of the earth. The earth is too big to be measrued
>accurately because of the size of the thumb in comparison to the earth
>and the margin of error in measuring by a thumb. You don't measure
>the size of an atom with a meter stick. The stick is many orders of
>magnatude too big. You don't measure the vast distances of the
>universe according to your height.
It may be quite impractical to measure the circumference of the earth
with your thumb, an atom with a meter stick, or intergalactic distances
with your height. But I know how one can measure the circumference of
the earth with either a meter stick or with your height (and with a stop
watch).
> ...
>
>The same applies to radiometric dating. You must first assume that a
>rock is old enough to be measured by whatever means of measurement you
>expect will get the correct results. Then you do your measurments.
>Then you compute the resulting age. BUT, that age does not and connot
>prove that the rock old, nor that it is even that age, BECAUSE it is
>FIRST ASSUMED that the rock is old enough to be measured as that old!
>One of the first rules of logic is that you cannot prove what you have
>assumed.
I don't think your argument is justified. Of course one tries to make
use of all the data at one's disposal in finding a rock date. Usually
this includes using some nonradiometric clues as to a ball park order of
magnitude estimate for the age of the rock so an appropriate dating
technique can be applied. But this assumption is not logically
necessary. The main reason it is usually made is for mundane and
practical concerns relating to the amount of expense and effort gone to
to get a date. Using nonradiometric clues for a prior order of magnitude
age estimate of a rock allows one to avoid wasting much time, effort and
expense in getting the actual age. Often dating a rock radiometrically
is a tedious, time consuming, and expensive task. Because of this
usually one doesn't want to needlessly waste resources by subjecting the
rock to a whole battery of different dating techniques each with its own
different usable age range of possible datable ages in the hope that
the actual age of the rock will happen to fall in the usuable datable age
range of one of the techniques in the battery of tests.
Usually (as I understand it) in practice, if a dating technique is
inappropriate for the actual age of the rock the technique just doesn't
give an age with a usable error bar.
For instance, suppose some technique uses a radioactive decay whose
half-life is 10 million years, and the technology of the detection
methods of counting the atoms of the relevant isotopes allows a decent
estimate of the age as long as the age falls between 2% of this half-life
and 15 half-lives. This means that the range of reasonably datable ages
for the technique is between 200,000 yrs and 150,000,000 yrs. Now suppose
that a rock to be dated with this method is actually only 120 years old
because it came from a recent lava flow. Then the dating technique will
typically *not* yield a false age in the usable range, but will give the
inconclusive result that the age is just too young to date by that
method. Maybe a naive application of the technique would indicate that
the date is 70,000 yrs +/- 70,000 yrs. Since the error estimate for
the technique includes an age of zero we see that the technique is
just the wrong one to use on the rock. The only thing we can conclude
from our dating method is that the rock's age is probably not any older
than about 140,000 yrs.
OTOH, suppose that the rock is actually 540,000,000 yrs old. Then again,
the technique would typically not be able to arrive at an actual age. In
this case the rock is so old that there is essentially no measurable
amount of the parent isotope left in the sample. All that the technique
would be able to say is that the rock is significantly older than
150,000,000 yrs old which corresponds to the age at the usable detection
limit of the technique. The technique would not be expected to
give a false age (such as an age of 120,000,000 yrs). Rather, it would
not give any usable age at all.
Of course, sometimes the rock's age is in the correct range for the
technique and the technique might still not give a single clean
predicted date. Such would be the case if some *other* assumption that
needs to hold for the technique's validity breaks down. Although it
is possible that the technique could even be completely fooled into
predicting an incorrect date due to some process subsequent to the rock's
formation that messed up the results, geologists typically are
aware of the kinds of things that could go wrong and look for evidence
in the rock's original environmental context that those distracting
processes might have take place. Some techniques, such as the
isochron methods, are hard to fool in this regard. For these techniques
disruptive events subsequent to the rock's formation typically leave a
tell-tale signature in the data analysis that either prevents a clean
low error bar value from being predicted for the age, or even sometimes
allows two separate dates to be extracted--one date for the rock's
original formation and another date for the subsequent disruptive event.
David Bowman
David_Bowman@georgetowncollege.edu
This archive was generated by hypermail 2b29 : Wed Mar 01 2000 - 23:40:46 EST