3 Mar
2013
3 Mar
'13
12:59 p.m.
One aspect that seems absolutely critical, at least in
my opinion,
is that when a slide rule is being used, it forces the ability to at
least estimate the answer since the slide rule only provides the
first 3 digits in the answer, NOT where the decimal point is
located.
I should have read your reply before making essentially the same point
myself.
Using a calculator robs the individual of the ability
to estimate an
answer since the decimal point is provided along with the mandatory
digits. Using a calculator also seems to encourage an individual to
fail to understand that the input data usually has far too little accuracy
to justify more than about two digits of accuracy in the final answer.
This is a classic case of GIGO, of course. One problem with
calculators (and HP RPL machines are worse than most in this becuase they
will produce complex numbers, not errors, if you take the sqrt of a
negative number or arcsin(2) or..) is that in general no matter what you
put in you get _an_ answer. It may be incorrect, but there are digits on
the display.
Doing an order-of-magnitude estimate first will at least let you see if
the anser is reasonable.
When values accurate to 8 digits always appear as the
result, it
becomes very easy to forget that the initial data was often accurate
to less than 1%. Further, even when the initial data is very accurate,
the equations used to provide a solution can often be VERY non-linear.
It is possible to produce variations in the result of more than 50%
due to variations in the input of much less than 1%, especially when
non-linear differential equations are being used. Of course, doing
Indeed.
Als, some equations may be mathematically correct but be totally
unsuitable for machine calculation. The well-know formula for findign the
roots of a quadratic equation can have problems if 4*a*c is small
compared to b^2. You end up subtracing 2 nearly equal numbers. The
work-around is well-known and quite obvious if you think about it, but an
awful lot of people don't think about it.
-tony