\subsection{Science and Global Climate Modelling}
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\subsubsection{Science and the Problem of Demarcation}
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Science refers to any system of objective knowledge,
in particular knowledge based on the scientific method
as well as an organized body of knowledge gained through 
research\TschSpace%
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\cite{WikipediaScience2007,REP2007}.
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There are essentially three categories of sciences, namely
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\begin{itemize}
\item formal sciences (mathematics),
\item natural sciences (physics, chemistry, biology)
\item social sciences
\end{itemize}
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In natural sciences one has to distinguish 
between 
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\begin{itemize}
\item \textit{a theory:}
      a logically self-consistent framework
      for describing the behavior of certain 
      natural phenomena based on fundamental 
      principles; 
\item \textit{a model:}
      a similar but weaker concept than a theory, 
      describing only certain aspects of natural 
      phenomena typically based on some simplified
      working hypothesis;
\item \textit{a law of nature:}
      a scientific generalization based on 
      a sufficiently large number of empirical
      observations that it is taken as fully
      verified;
\item \textit{a hypothesis:}
      a contention that has been neither proved 
      nor yet ruled out by experiment or falsified
      by contradiction to established laws of nature.
\end{itemize}
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A \textit{consensus}, exactly speaking 
\textit{a consensus about a hypothesis} 
is a notion which lies outside natural science,
since it is completely irrelevant for 
objective truth of a physical law:
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\begin{quote}
\textit{Scientific consens(us) is scientific nonsense}.
\end{quote}
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The \textit{problem of demarcation} is how and where to draw
lines around science, i.e.\ to distinguish science
from religion, from pseudoscience, i.e.\ fraudulent
systems that are dressed up as science, and non-science
in general\TschSpace%
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\cite{WikipediaDemarcationProblem2007,REP2007}.
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In the philosophy of science several approaches 
to the definition of science are discussed\TschSpace%
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\cite{WikipediaScience2007,REP2007}:
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\begin{itemize}
\item 
\textit{empirism%
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\footnote{%
also \textit{logical positivism} or \textit{verificationism}
}
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(Vienna Circle):}
only statements of empirical observations are meaningful,
i.e.\ if a theory is verifiable, then it will be scientific;
\item 
\textit{falsificationism (Popper):}
if a theory is falsifiable, then it will be scientific;  
\item 
\textit{paradigm shift (Kuhn):}
within the process of normal science anomalies 
are created which lead eventually to a crisis 
finally creating a new paradigm; the acceptance of 
a new paradigm by the scientific community 
indicates a new demarcation between science
and pseudoscience;
\item 
\textit{democratic and anarchist 
approach to science (Feyerabend):}
science is not an autonomous form of reasoning
but inseparable from the larger body of human 
thought and inquiry: \lq\lq Anything goes\rq\rq.
\end{itemize}
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Superficially, the last point provides a nice argument 
\textit{for} computer modelers in the framework
of global climatology. 
However, it is highly questionable whether 
this fits into the frame of physics.
Svozil remarked that Feyerabend's understanding of physics 
was superficial\TschSpace% 
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\cite{Svozil2004}.
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Svozil emphasizes: 
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\begin{quote}
\lq\lq Quite generally, partly due to the complexity 
       of the formalism and the new challenges of 
       their findings, which left philosophy proper 
       at a loss, physicists have attempted to develope 
       their own meaning of their subject.\rq\rq
\end{quote}       
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Physics provides a fundament for engineering and, hence, for production and modern economics.
Thus the citizen is left with the alternative (in the sense of a choice between two options)
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\begin{itemize}
\item[(a)] 
either to accept the derivation of political and economical 
decisions from an anarchic standpoint 
that eventually claims that there is 
a connection to experiment and observation,
and, hence, the real world, when there is 
no such connection;
\item[(b)] 
or to call in the derivation of political and economical
decisions from verifiable research results  within the frame of physics,
where there is a connection to experiment and
observation, and hence, the real world.
\end{itemize}
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Evidently, the option (b) defines
a pragmatic approach to science,
defining a minimum of common features, 
such that engineers, managers and 
policymakers have something to rely on: Within the frame of exact sciences
a theory should
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\begin{itemize}
\item[(a)] be logically consistent;
\item[(b)] be consistent with observations;
\item[(c)] have a grounding in empirical evidence;
\item[(d)] be economical in the number of assumptions;
\item[(e)] explain the phenomena;
\item[(f)] be able to make predictions;
\item[(g)] be falsifiable and testable;
\item[(h)] be reproducible, at least for the colleagues;
\item[(i)] be correctable;
\item[(j)] be refinable;
\item[(k)] be tentative;
\item[(l)] be understandable by other scientists.
\end{itemize}
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Can these criteria ever be met by a computer model approach of global climatology?
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\subsubsection{Evaluation of Climatology and Climate Modelling}
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In contrast to meteorology climatology studies the averaged 
  behavior of the local weather. There are several branches,
such as paleoclimatology, historical climatology, and climatology
involving statistical methods which more or less fit into
the realm of sciences. The problem is, what climate modelling
is about, especially if it does refer to chaotic dynamics on the
one hand, and the greenhouse hypothesis on the other.

The equations discussed in 
Section~\ref{Sec:TheEquations} 
may give an idea what the final defining 
equations of the atmospheric and/or oceanic system may look 
like. It has been emphasized that in a more realistic albeit 
phenomenological description of nature the system of the 
relevant equations may be huge. But even by simplifying 
the structure of equations one cannot determine solutions 
numerically, and this will not change, if one does not 
restrict oneself on small space-time domains.

There are serious solvability questions 
in the theory of non-linear partial 
differential equations and the shortage of numerical recipes 
leading to sufficient accurate results will remain 
in the nearer or farer future - for fundamental mathematical 
reasons. The Navier-Stokes equations are something like 
the holy grail of theoretical physics, and a brute force 
discretization with the aid of lattices with very wide meshes 
leads to models, which have nothing to do with the original puzzle 
and thus have no predictability value.

In problems involving partial differential equations the boundary 
condition determine the solutions much more than the differential 
equations themselves. The introduction of a discretization is 
equivalent to an introduction of artificial boundary conditions, 
a procedure, that is characterized in von\,Storch's statement 
\lq\lq The discretization \textit{is} the model\rq\rq\TschSpace%
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\cite{Storch2005}. 
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In this context a correct statement of a mathematical 
or theoretical physicist would be: 
\lq\lq A discretization is a model with unphysical 
boundary conditions.\rq\rq\ 
Discretizations of continua problems will be allowed 
if there is a strategy to compute stepwise refinements. 
Without such a renormalization group analysis 
a finite approximation does not lead to 
a physical conclusion. 
However, in
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           {Ref.~\refcite{Storch2005}}
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\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{Storch2005}}
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\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{Storch2005}}
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von\,Storch emphasized that 
this is by no means the strategy he follows, 
rather he takes the finite 
difference equations are as they are. 
Evidently, this would be a grotesque standpoint, 
if one considered the heat conduction equation, 
being of utmost relevance to the problem and 
being a second order partial differential 
equation, that cannot be replaced by a finite difference model 
with a lattice constant in the range of kilometers.

Generally, it is \textit{impossible} to derive differential equations for averaged functions
and, hence, an averaged non-linear dynamics. 

Thus there is simply no physical foundation of 
global climate computer models, for which still 
the chaos paradigma holds: Even in the case of 
a well-known deterministic dynamics nothing is 
predictable\TschSpace%
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\cite{Lorenz1963}.
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That discretization has neither 
a physical nor a mathematical basis in non-linear 
systems is a lesson that has been taught in the 
discussion of the logistic differential equation, 
whose continuum solutions differ fundamentally 
from the discrete ones
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\cite{Draper1998,Sprott2003}.
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Modern global climatology has confused and continues 
to confuse fact with fantasy by introducing the concept 
of a scenario replacing the concept of a model.
In
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           {Ref.~\refcite{IPCC2000}}
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\ifthenelse{\equal{arXiv}{\TschStyle}}
           {Ref.~\cite{IPCC2000}}
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\ifthenelse{\equal{TeX4ht}{\TschStyle}}
           {Ref.~\cite{IPCC2000}}
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a clear definition of what scenarios are
is given:
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\begin{quote}
Future greenhouse gas (GHG) emissions are the product of
very complex dynamics systems, determined by driving forces
such as demographic development, socio-economic
development, and technological change. Their future evolution
is highly uncertain, Scenarios are alternative images of how the
future might unfold and are an appropriate tool with which to
analyze how driving forces may influence future emission
outcomes and to access the associated uncertainties. They assist
in climate change analysis, including climate modeling and the
assessment of impacts, adaptation and mitigation. The 
possibility that any single emissions path will occur as
described in scenarios is highly uncertain. 
\end{quote}
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Evidently, this is a description 
of a pseudo-scientific (i.e.\ non-scientific) method
by the experts at the IPCC. 
The next meta-plane 
beyond physics would be a questionnaire among 
scientists already performed by von\,Storch\TschSpace%
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\cite{Storch2007}
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or, finally, a democratic vote about 
the validity of a physical law.
Exact science is going to be replaced by 
a sociological methodology involving 
a statistical field analysis and 
by \lq\lq democratic\rq\rq\ rules 
of order. This is in harmony with 
the definition of science advocated 
by the \lq\lq scientific\rq\rq\ website
\textit{RealClimate.org}
that has integrated 
inflammatory statements,
personal attacks and offenses 
against authors as a part 
of their \lq\lq scientific\rq\rq\
workflow.  
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\subsubsection{Conclusion}
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A statistical analysis, no matter how sophisticated it is, 
heavily relies on underlying models and if the latter are 
plainly wrong then the analysis leads to nothing. 
One cannot detect and attribute something that 
does not exist for reason of principle like the
${\rm CO}_2$ greenhouse effect. 
There are so many unsolved and unsolvable problems 
in non-linearity and the climatologists believe to 
beat them all by working with crude approximations
leading to unphysical results that have been corrected 
afterwards by mystic methods, flux control in the past,
obscure ensemble averages 
over different climate institutes today, 
by excluding accidental global cooling results by hand\TschSpace%
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\cite{Stainforth2005},
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continuing the greenhouse 
inspired global climatologic tradition of
\textit{physically meaningless} averages
and 
\textit{physically meaningless} 
applications of mathematical statistics.

In conclusion, the derivation of statements on the 
${\rm CO}_2$ induced anthropogenic global warming 
out of the computer simulations lies 
\textbf{outside any science}.
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