Reg said:
Mathematical programs are of any use only when you already understand
exactly how to do it using pencil and paper. They have no
educational value regarding the subject matter in hand.
The most disastrous, catastrophic mistakes have been made using maths
programs in the dark, without knowing exactly what the computer is
doing with the input data. Only mathematicians should be licensed to
use them.
They are purely grey-matter, time and labour-saving devices at which
they make excellent tools. All due only to the fantastic speed of
modern computers. Otherwise they would be no better than log tables
and slide rules.
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I have to disagree with the overall concept here. I agree, it is true
that one needs to understand in reasonable detail what the maths is.
However, today it is simply not possible to understand *exactly* the
implications of the equations from pen and paper. In general, equations
are too intractable to deal with in the sense that you are alluding to
here. For example, consider nuclear bomb simulations, or black hole
collision simulations. The equations are way too complex to understand
in detail. Its *only* by doing the simulations that one can actually
develop a feel for how the equations operate. Your view is the "nice
idea if in an ideal world", but it isn't. The world simply can't be
analysed using only pen and paper. There isn't even a finite closed form
solution to algebraic equations of degree greater than 4.
Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
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