In article <[EMAIL PROTECTED]>,
Muriel Strand <[EMAIL PROTECTED]> wrote:
>herman, you have the patience of a saint. however, it is not unusual in the
>physical sciences to locally approximate nonlinear phenomena with linear
>equations *within clearly specified ranges* where the linearity is reasonably
>accurate. i don't understand why you say this requires an infinite set of
>subdivisions?
A locally linear relation can be useful, but the range must
be quite small. If you make the relation piecewise linear,
a large number of pieces are needed to get even a fair
approximation over a substantial region. It cannot be
exactly represented without an "infinite" set, just as a
circle can be considered by a polygon with an infinite
number of sides.
If NASA linearized spacecraft trajectories, would we
get anything to work?
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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