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Has anyone got the impression I've had for years that teaching the
topic of significant figures is counterproductive?
[we care about] the *uncertainty* in the result,
*not* the "number of significant digits".
The big problem with rules for significant digits is that the number is
necessarily quantized. Uncertainty is not quantized to factors of ten.
I could construct many examples of the application of significant digit
rules where the baby gets thrown out and the bathwater gets retained
because of these rules, but I won't.
.... the
precision-losing practice of writing down intermediate results in a
calculation and then reentering them from the keyboard, often after
rounding and truncating. Surely this is an even worse sin.
the
significant digit rules are not part of the laws of Nature, and they
play no part in reporting results in the scientific literature.