Precision

[fkleedorfer]

Precision is not handled very well in QUDT, which can lead to numeric issues, among other things.

We are looking to improve the situation. The question is: what is the correct precision for each unit's multiplier?

I hope but doubt that there is a general rule by which to decide. I suppose it may include prefixes, it may include quantity kinds, it may include the power of 10 of the first nonzero digit in the number. I remember @steveraysteveray saying that it is a deep issue (and he had a 70 page technical paper to show for it), so maybe we should not aim for total correctness. So a good question may be: What does the 80% solution look like?

[steveraysteveray]

@fkleedorfer, maybe I was overthinking the problem. Assuming we have uncertainty values for the base units, then I think most cases will be covered by either multiplication or exponentiation. So, normal techniques apply:

It's another matter whether we can easily perform these calculations in SPARQL!

[fkleedorfer]

as long as we have integer exponents < N (N being, say, 10), we can write it as repeated multiplication, so none of this should be a problem.

[fkleedorfer]

But: are we even talking about uncertainty in the case of a conversionmultiplier?

[steveraysteveray]

I believe so since we are multiplying the uncertainty of each of the underlying base units

[steveraysteveray]

If there is only one underlying base unit, then no

[fkleedorfer]

Ok let's stay with non-derived units for the time being. How do we know anything about their inherent precision? And: is precision a property of the unit or the measurement or maybe the quantitykind or all of them?

[steveraysteveray]

OK, having dug a bit deeper, in 2019 the SI redefined all 7 base units such that, by definition, they have zero uncertainty, because they are defined in terms of fundamental constants (such as the Planck constant, the hyperfine transition frequency of Cs-133, and the speed of light) that are specified with zero uncertainty. Physical constants that are not defining SI constants, however, do have uncertainties. They include the Gravitational constant, 6.67430×10*-11 with a standard uncertainty of 0.00015×10*−11, and others. Regarding conversion multipliers, things like the BTU has an uncertainty for conversion to Joule for the ones we list such as unit:BTU_39DEG_F, because it is based on experimental measurement, but unit:BTU_IT is definitional, and thus has zero uncertainty.

[fkleedorfer]

So we can say, a unit has 0 uncertainty by default but we may specify uncertainty for a unit.

What does that mean for a putative non derived unit u with uncertainty 0.0001 that currently (in qudt) converts to a Si base unit with multiplier 0.123456789123456789123456789?

[steveraysteveray]

The multiplier should not state a higher precision than the uncertainty. So your example shows an uncertainty down to the 5th decimal place, so the multiplier should be 0.12345, but not 0.123456.

I believe, but may be wrong, that if the uncertainty was 0.000013 (i.e. the 6th decimal place), then it would be appropriate to state the multiplier as 0.123456.

For the units with zero uncertainty, we can go wild provided the digits are real and not an artifact of rounding or truncation.

1 pound of mass = 0.45359237 kg exactly, which is what we list in QUDT. No more digits, i.e. they are all zero after that.

[fkleedorfer]

I think I can work with that. How would we identify units with uncertainty and how many do you estimate are there?

[steveraysteveray]

I don't think it will be very many, but I'll need to think if there is some query-based or other systematic way of finding them...