[Phys-L] Re: fall cleanup: sig figs

[clement at HAL-PC.ORG (John Clement)]

And what you did with expensive technology the ear or rather ear & brain do
with ease.  You can distinguish sound buried under noise when you listen to
it.  Digital recordings artificially put in a small amount of noise by
dithering the lowest bit.  As a result you can actually hear the music when
it is lower than that lowest bit.  As I recall you can distinguish music
about 7 dB below the threshold.  Early digital recordings sometimes lacked
this dither and as a result they did not sound as good as later ones.

John M. Clement
Houston, TX

> > > > And it is silly to penalize students for reporting results with one
> > > > or
> > > > two insignificant digits.
> > >
> > > Indeed ... call them "guard digits" and encourage them.
> > >
> > > Guard digits are your friends.
> >
> > I appreciate your thoughts and have fought against the way sig figs
> > have
> > been taught for years but I am confused by your previous statement.
> > How can
> > digits that carry no significance (meaning I have no idea what the real
> > value in that place should be) guard anything?
>
> Let me try to guess what john had in mind.
> Two year ago I was participated in an experiment in which the signal
> was totally covered by the background noise. The noise, is random and
> nearly ten times larger than the signal. The signal would be barely
> visible (in the single pulses mode of our digital scope) if it were ten
> times larger. But we managed to measure the signal because it was not
> random. It was a repetitive pulse (once every second). This was
> possible because our scope also had the cumulative mode. In that mode
> one hundred single pulses were superimposed (added to produce the sum).
> In that sum the pulse became 100 times stronger and was sticking
> clearly above the cumulative noise. Why did noise not increase by the
> same factor as the signal? Because it was random (positive and negative
> often cancel, partially.
>
> Accumulating ten times longer we had even more impressive signal to
> noise ratio (in the sum). I was very impressed. But I would not say
> that this was a conversion of nonsignificant digits into significant
> digits. It was nothing else but gaining precision by getting an average
> value from many measurements.
>
> Ludwik Kowalski
> Let the perfect not be the enemy of the good.