One should realize that there are different kinds of significance, too.
If an instrument gives a single figure, its significance can be questioned in two regards. How many digits are of interest to us? And how many digits are the result of false precision in the readout device versus the true resolution fo the measuring device? If the instrument is well built, then a sixteen-decimal figure can be considered significant to the second-to-last digit in this second sense of significance. It depends on the circumstances whether all the fifteen decimals really have a practical significance, though.
However, that's as regards single standalone measurements. The real significance of significance is when measurements are used in calculations. There's no point in giving the result of X/Y=Z at six significant digits if X and Y were each given at three significant digits only; the seeming accuracy of Z is not "real" there. At very best, one should give Z at three significant digits in such a case.
The significance of this sort of significance of significance in Trek is that Spock usually gives the end results of measurements or calculations, not figures that are intermediate steps in calculations. We could and should have full confidence that he has already taken into account the significance of the numbers in the arithmetic and instrument-accuracy senses, but we can still question whether the digits he gives are significant in the application sense.
Timo Saloniemi
If an instrument gives a single figure, its significance can be questioned in two regards. How many digits are of interest to us? And how many digits are the result of false precision in the readout device versus the true resolution fo the measuring device? If the instrument is well built, then a sixteen-decimal figure can be considered significant to the second-to-last digit in this second sense of significance. It depends on the circumstances whether all the fifteen decimals really have a practical significance, though.
However, that's as regards single standalone measurements. The real significance of significance is when measurements are used in calculations. There's no point in giving the result of X/Y=Z at six significant digits if X and Y were each given at three significant digits only; the seeming accuracy of Z is not "real" there. At very best, one should give Z at three significant digits in such a case.
The significance of this sort of significance of significance in Trek is that Spock usually gives the end results of measurements or calculations, not figures that are intermediate steps in calculations. We could and should have full confidence that he has already taken into account the significance of the numbers in the arithmetic and instrument-accuracy senses, but we can still question whether the digits he gives are significant in the application sense.
Timo Saloniemi
