There's a recent article in NewScientist that illustrates
how scientists build models by working with theories that
are known to be mutually inconsistent. (Excerpts below.) (01)
Following is a brief summary of the procedure: (02)
1. The equations of quantum mechanics require so much
computation that even the world's fastest supercomputer
can only compute the interactions among a very small
number of atoms at a time. (03)
2. The equations for Newtonian mechanics are much easier
to compute, but they are known to be false on an atomic
scale. (04)
3. However, for large atoms, such as molybdenum, the nucleus
is sufficiently heavy that its behavior can be calculated
by Newtonian mechanics, while the behavior of the electrons
is computed by the equations of quantum mechanics. (05)
4. Using a hybrid model with classical mechanics for approximating
the behavior of molybdenum nuclei and quantum mechanics for
the electrons, the physicists are able to simulate the behavior
of 1000 interacting molybdenum atoms, but only on the world's
fastest supercomputer. (06)
Notice how they can use inconsistent theories without creating
contradictions: The classical equations are used only to compute
the behavior of the nuclei and the QM equations are used only
to compute the behavior of the electrons. This illustrates a
fundamental principle: (07)
It is possible to combine the results from different methods
of reasoning or computation, even when the methods themselves
are mutually inconsistent. (08)
Such models, which combine two or more theories that are known
to be inconsistent, are typical in every branch of science and
engineering. As the professor of engineering George Box said, (09)
"All models are wrong. Some models are useful." (010)
Even in physics, where very precise equations are known, it is
common to use such patchwork-quilt models because computations
with the more precise equations are impractical. In engineering,
complex systems may require different theories for each subsystem
or even each part of a subsystem. Interoperability does *not*
require all subsystems to use exactly the same axioms. (011)
This is the state of the art in the "hardest" branches of science
and engineering. In the softer areas of economics, business, and
government, nothing remotely resembling such precision is available,
and it is ludicrous to standardize a unified theory of everything. (012)
However, there are very useful things that can be done: large
terminologies and taxonomies with very few axioms are practical,
and they have been in use for years in all fields. A great deal
of confusion has been created by using the word "ontology" for
what should more properly be called a terminology or taxonomy. (013)
Summary: We must make a clear distinction between formal ontology
and informal terminologies and taxonomies. There is no hope of
having a unified theory of everything with detailed axioms that
can be used and reused at every level. It is very practical to
have large informal terminologies and taxonomies of everything,
but the detailed axioms for precise reasoning can only be used
on the much smaller, more specialized subsystems. Even for such
subsystems, ad hoc models are often needed, which may be assembled
from a patchwork of two or more mutually inconsistent theories. (014)
John Sowa
_____________________________________________________________________ (015)
http://www.newscientisttech.com/article/dn9394-atomic-simulation-most-intensive-computer-program-ever.html
Atomic simulation most intensive computer program ever (016)
Excerpts: (017)
Other software can be used to simulate interactions between billions of
atoms, but only using classical molecular dynamics. Performing
simulations involving quantum-mechanical behaviour is far more complex
and, until now, such quantum simulations have only involved about 50
atoms at a time.... (018)
The enhanced version of Qbox, however, reaches a sustained performance
of 207.3 teraflops, a record for any software. It simulates interactions
between 1000 molybdenum atoms under high pressure using equations that
take the quantum behaviour of electrons into account.... (019)
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