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It is useful to consider the foundation of a physical analysis for it
offers a measure of the limits of credibility of the analysis. Micro
physical systems are a selection of a small number of physical
properties for which an isomorphism can be realized. One then studies
this isomorphism to discover the properties that can be attributed to
the micro physical system that was visualized. The point of using the
micro physical system is that the isomorphism can be made to be a
logical system with a metric and an arithmetic. Newton's equations have
that structure with calculus being the arithmetic and the equations that
describe the possible transformations of the system by the arithmetic
serving as the metric. A logical structure has the property of closure.
This mean that no matter where or by whom a prediction about the system
is made for a logical system the result will be the same. Of course,
that property is valid only for the micro physical system. The
limitation on these benign properties is that the isomorphism is valid
only within the range of variables for which it was crafted. For
example, Newton's isomorphism is not valid for velocities of magnitude
larger than the those available to him.
Comment on Climate Studies: Where's the Ensemble?
Malcom W. P. Strandberg
Cambridge Massachusetts 02138 USA
First Edition started 11 March 2010
This Edition Updated, March 17, 2010
Date of this copy for review, March 18, 2010
Then there are macro physical systems with so many interacting
parameters that it is impossible to make an isomorphism with a
manageable set of parameters. Macro economics or the financial markets
are certainly good examples of systems with a large number of
parameters, most of which are not even recognized.
But these macro systems do elicit rational opinions which are true, for
all opinions are true, but they probably do not agree with the true
opinions of any other person. And they vary in rationality from
religious faith to something near a true logical conclusion.
When these considerations are applied to rational opinions about Climate
Change one can not expect unanimity of opinion, and the true prediction
can not be decided by a vote. Most of Einstein's work never won a vote
initially. Furthermore the system that is studied is the one within the
range of present study both in time and space, and an attempt to extend
a model or an isomorphism into the future reduces the validity of the
model. One simply cannot predict what the future parameters of the model
We live in a rational world. Its pro and con legal system produces
opinions with a judge or jury that does not try to decide truth but
tries to make decisions that find for justice. Its a world in which
economic decisions can not foresee the unforeseeable future and hence it
minimizes risk with social and political equity. Its science has models
which are not the truth but descriptions of the real world that are
sufficient until they are amended or extended by future increase in
knowledge. The IPCC Climate Change reports produce a rational opinion of
what the future climate will be based on an analytic continuation of the
parameters determined as those which describe the climate in the present
epoch. This prediction is only one of many of an ensemble of rational
opinions depicting future global effects of global temperature change.
The IPCC 2007 report seems to acknowledge this fact by characterizing
their model of the future as "very likely" or 90 percent and "likely" or
60 percent. However to use probability one needs an ensemble of a
complete set of models. A single model can have only probability 0 or 1,
that is, it does not match the future physical state of the planet, or
it does match the future physical state.
In our commercial world a rational opinion, on one hand, could be the
opinion on buying Microsoft stock in 1986, and then have the stock,
according to the advice script, increase in value 5300 percent. On the
other hand, logical opinion also prompted people to invest in Bernie
Madoff's funds with an end point of a total loss. The unexpected happens
and there is no reason to think that the logical opinion on Climate
Change can provide for the unexpected.
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