Changes between Initial Version and Version 1 of ProcedureDefinedUnits

Timestamp:

02/13/09 14:51:20 (17 years ago)

Author:

gschadow

Comment:

--

ProcedureDefinedUnits

@@ +1 @@
+= Procedure Defined Units =
+
+How come 1 meter is a good unit but 1 tuberculine unit is not?
+
+How come UCUM has both of these units?
+
+How come the equality of 1 Bq and 1 Hz is not a problem, but the 
+equality of 1 tuberculine unit and 1 allergy unit is a problem?
+
+How come glucose measured in 1 gram or 1 mol is not a problem?
+
+How can we have both allergen unit ![AU] and biological equivalent 
+allergy unit ![BAU] in one system?
+
+How come 1 Gray and 1 Sievert both exist in the SI, are they 
+equal? 
+
+This is the biggest challenge that the UCUM project is currently 
+facing.
+
+== Synthetic Analogy ==
+
+I think the problem always occurs when we measure one thing by an
+equivalent of another. 
+
+  Like if I counted an amount of people by the amount of oxygen they consume in the room. 
+
+And it gets worse if the measurand and the equivalent quantity are of 
+the same dimension, 
+
+  Like if I count the number of people by the number of hairs they leave behind. 
+
+And it is all fine if I have a fixed constant conventional coefficient, 
+ 
+  Like: a person loses 10 hairs per hour, so if after 2 hours a room has 10^6 hairs on the floor, there must have been 5*10^4 people in the room.
+
+But it gets worse if an expert comes along and says: 
+
+  Wait, you can't tell how many people are in the room, all you know is how much hair they lost!
+
+At this very point you start measuring amount of people by some procedure defined unit:
+
+  Like: HEU (hair equivalent unit) the amount of people in a room who lose 10 million hairs in 1 hours.
+
+At this point people demand that UCUM has the HEU unit.
+
+But the problem is, this definition of HEU is explicitly not directly related to the straight-forward number of people in the room, but it is a new kind of quantity, locked to this idiosyncratic proxy measure.
+
+And that now has established its very own dimension also, because in a dimension all units are comparable in fixed conversion formulas (usually proportional, linear, but at least a conventional a-priori defined function.)
+But not here, because the whole premise was that people rejected the idea of just relating the unit directly to number of people or just reporting number of people directly.
+
+Thus all procedure defined units are dimensions unto themselves.
+
+And thus our simple 7 component dimension vector stops being a vector of any finite length.
+
+What do we do?
+
+The present approach was to add a new property "arbitrary unit" into the unit definition.
+This measure at least prevents units to be falsely taken as equivalent.
+But this also prevents any kind of conversion, even between 1 HEU and 1 kHEU.
+This is presently the best we can do, and it is a good idea to limit the ability to form complex terms with arbitrary units.
+It might not even make sense in some cases (e.g., if the unit is not on a ratio scale how can one even multiply it?)
+
+But we need a final solution that deals with this challenge.