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Re: [Phys-l] Significant figures -- again



On 04/12/2012 09:11 AM, Robert Cohen wrote:

.... it seems to me that the sig fig examples serve to illustrate the
problems with rounding intermediate steps, not the use of sig figs at
the end.

That argument doesn't work in the real world.

It is as easy as π to come up with examples where one
person's "final" output is another person's input, so
from the overall point of view virtually everything is
an intermediate result.

We have recently (03/29/2012 12:05 PM) seen a specific
example of this, where Bob spent all day calculating
the matrix elements and then Carol spent all night
calculating the eigenvalues. Bob rounded off "at the
end" of /his/ calculation, in accordance with the sig-
figs rules, with disastrous results.

Seriously, what's the point of calculating a number if
nobody is going to use it? Then ... if somebody is
going to use your number, it's not really a "final"
result, is it?

AFAICT only case where my counterargument doesn't apply
is in connection with ivory-tower busywork assignments,
where the answer will not be used for any practical
purpose, but instead will simply be checked for compliance
with artificial, nonsensical rules.

Just to pound on this a little more: The suggestion to
use sig figs only "at the end" is IMHO a last-ditch straw-
grasping argument anyway. At this point you have already
conceded that for a 25-step calculation, sig figs are no
good for (at least!) 24 of the 25 steps, and conceded that
sig figs cannot be used for "propagation of error" ... so
why is it even worth mentioning sig figs? Other techniques
must be learned. Other techniques must be used most of
the time ... so why are we bothering to put lipstick on
this pig? Who cares if you can find isolated cases where
sig figs are not a /complete/ disaster?
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