> >To summarise;
[CLIP]
> >Science cannot be applied to social studies.
>
> Regardless of your friend's cogent points, any social scientist would
> disagree with this. As do I.
There's a huge difference between 'cannot' and 'is not usually'.
Keep in mind that the reasonably detailed mathematical models that do
show up are usually intractable computationally.
I will take an example from economics. [Introductory econometrics
is a 700-level course at K-State.] I am certain that as computer power
[both in clock speed and in algorithms] goes up, that economics will
become a much more well-tested science.
For instance, reverse-fitting a fair-wage scale, under assumed
variables X_1, X_2, ... X_n, is intractable; one needs to reverse fit
the following constants: The leading constant for each possible
combination of 0 to n variables ['primitive monomials']: 2^n.
The exponent for each of the 2^(n-1) instances of these variables in
the formula [this can be reduced by 0's in the previous phase]: at most
n*(2^(n-1)).
Even if this exercise were to succeed, the result is usually a
general multi-nonlinear function: practically useless for more than a few
variables currently, and for 'large' numbers of variables permanently.
['Large' is a technology-dependent thing. Evaluating a 26x26 matrix's
determinant BY THE DEFINITION will take 26!-1 additions, and 26!*25
multiplications. (Not to mention sorting everything so that numerical
error doesn't reduce the number of significant digits to 0. If that is
even possible. If overhead is NIL and each operation takes 1 nanosecond
each, let's call the execution time on a sequential computer about
3.22*10^11 years.) However, certain rules about manipulating determinants
are known. We just tell the computer to use Gaussian reduction (invented by
Gauss: somewhen in the 1800's), with certain recently-invented finesses,
and reliably handle a 1000x1000 matrix in minutes(?).]
Apparently, this may have something to do with the recent collapse
of some planned economies.
[I'm referring to a 1995 mathematics paper for this result.]
[CLIP]
> >Martz <m.traynor@ic.ac.uk>
>
> *****************************************************
> Wade T. Smith | 'There ain't nuthin' you
> wade_smith@harvard.edu | shouldn't do to a god.'
> ****** http://www.channel1.com/users/morbius/ *******
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/ Kenneth Boyd
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