Pat, (01)
There are many, many examples in *every* branch of science and
engineering: (02)
AT>> The problem is: two contradicting conceptualization can both
>> be right ... (03)
PC> Can you provide one or more examples of that phenomenon? I've
> been looking for "contradictory" models that both conform to
> reality for some time. (04)
First of all, no models ever conform to reality *exactly*, since
every theory of science is at best an approximation that conforms
within the limits of experimental error and within the range of
reality on which it has been tested. (05)
Therefore, we are frequently faced with different approximations
derived for different purposes under different circumstances. (06)
The likelihood that any two such approximations will be consistent
with one another is high under certain conditions: (07)
1. They refer to separable domains and have no common terms
or predicates that could create a contradiction. (08)
2. Or if they do have common terms or predicates, the definitions
of those terms are so vague and underspecified that they
don't impose constraints that could cause contradictions. (09)
But if those approximations have a large overlap that is described
in any detail, then the likelihood of contradiction is extremely high. (010)
One of my favorite examples was the proof that nothing could travel
through the air faster than the speed of sound. It turned out that
the scientist who "proved" this theorem had started with a commonly
used approximation, which was widely assumed in the early days of
aeronautics: that all velocities are very small compared to the
speed of sound. (011)
Of course, that incompatibility has since been ironed out, but similar
problems arise constantly. All the detailed equations of physics are
so difficult to solve in general (even by a supercomputer) that
simplifying assumptions are always necessary. (012)
For example, Newton's equations are always used for the motion
of an automobile and its major mechanical parts. However, quantum
mechanical effects are used in designing new kinds of fuel for
the engine, the computer circuitry in the chips that control the
engine, etc. (013)
Since those systems are separable, in most cases, they can be
treated as case #1 above when the detailed problems are being
analyzed. When the fuel is pumped into the car, case #2 comes
into play, and the details of the fuel are ignored when computing
how its mass would affect the acceleration. (014)
Summary: Physics, the hardest of the "hard" sciences, has some
very general equations that are known to be false in detail, no
general equations that are known to be absolutely true, and an
enormous collection of inconsistent approximations for every
type of practical problem that anyone really needs to deal with. (015)
Compared to physics, every other field of science is a nightmare
of special cases. And the social sciences haven't even reached
the stage where any degree of precision is conceivable. As they
say, economists are great in explaining why something occurred
but hopeless in predicting it. (016)
John (017)
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