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<head><title>Corroborating_Models.html -- ACL2 Version 3.1</title></head>
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<h2>Corroborating Models</h2>
<p>
After producing a model, it must be <b>corroborated</B> against
reality. The Falling Body Model has been corroborated by a vast
number of experiments in which the time and distance were measured
and compared according to the formula. In general all models must
be corroborated by experiment.<p>
The Falling Body Model can be derived from deeper models, namely
Newton's laws of motion and the assertion that, over the limited
distances concerned, graviation exerts a constant acceleration on
the object. When the model in question can be derived from other
models, it is the other models that are being corroborated by our
experiments.<p>
Because nature is not formal, we cannot <b>prove</B> that our models
of it are correct. All we can do is test our models against
nature's behavior.<p>
Such testing often exposes restrictions on the applicability of
our models. For example, the Falling Body Model is inaccurate
if air resistance is significant. Thus, we learn not to use that
model to predict how long it takes a feather to fall from a 200
foot tower in the earth's atmosphere.<p>
In addition, attempts at corroboration might reveal that the model
is actually incorrect. Careful measurements might expose the fact
that the gravitational force increases as the body falls closer to
earth. Very careful measurements might reveal relativistic effects.
Technically, the familiar Falling Body Model is just wrong, even
under excessive restrictions such as ``in a perfect vacuum'' and
``over small distances.'' But it is an incredibly useful model
nonetheless.<p>
There are several morals here.<p>
<b>Models need not be complete to be useful.</B><p>
<b>Models need not be perfectly accurate to be useful.</B><p>
<b>The user of a model must understand its limitations.</B><p>
<a href="Models_of_Computer_Hardware_and_Software.html"><img src=flying.gif></a>
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