timbrisc
commented
14 years ago 2010-08-19 21:49:34: gschadow@pragmaticdata.com commented
Dimension: T^-1^ x T, meaning "pack year" is a dimensionless unit.
A "pack" is an object, not a unit. Of course, one may estimate a pack as about 20 cigarettes, but that is not always true, so there is no good fixed conversion between pack and cigarettes. Also, pack-year seems to be the only conventional quantification of smoking behavior, not cigarette-day. So conversion between pack and cigarette seems not required. In that case, pack is not a quantitative concept and can be disregarded (dimensionless count number, unit = 1).
Consequently, the smoking frequency is a normal frequency, dimension T^-1^. Unit for "packs smoked per day" would be "/d". One can of course write "{pack}/d" but that curly brace is not adding any semantics.
The multiplication with the smoking duration (dimension T) means that the resulting number is proportional to the estimated total number of packets smoked. Specifically a "pack-year" is 1/365.25^th^ of the total number of packs smoked. Because of this, the dimension of what is called "pack year" is truly 1, i.e., this quantity is dimensionless, it is simply a count noun.
Note that "pack year" appears to be a misnomer. Compare with the pre-existing analogous term "light year" and "man hour". "Light year" is the distance that light travels in one year. "Man hour" is the amount of effort a person would do in an hour. In that sense, "pack year" should be the amount of smoking-effects that a pack induces in a year. This, of course, is not what is meant. Perhaps a more systematically adequate name would be the "pack-a-day year", i.e., the amount of smoking-effects that a pack-a-day of smoking induces in a year.
This is not a unit and should not be added. Instead the meaning should be entirely in the definition of the quantity concept, i.e., if the quantity is defined as "estimated total amount smoked" and the measurement method defined as "estimated number of packs smoked per day multiplied with the estimated number of years smoked", then the quantity value can be specified as the simple dimensionless number.
Adding units into this term would confuse more than it would help. Because if a person has smoking frequency of 2 packs per day (f # 2 /d) and smokes for 10 years (t10 a) then the product of f t would be 20 a/d # 20 365.25720.50 instead of just 20, as the users would expect. On the other hand, from this, one might define the unit "pack year" as 1 a/d, which then would allow the result of 2 /d * 10 a to be written as 20 a/d or 20 [pack'year].
So, have I now talked myself into accepting such a unit? Comments from others would be needed. I do not like this unit, but it could be defined as
1 [pack'year] = 1 a/d.
But before this is done, need to check if there isn't also a "cigarette year", which would then need to be defined commensurable but different from pack'year.
Issue migrated from trac ticket # 52
component: help | priority: major
2010-08-19 21:22:36: gschadow@pragmaticdata.com created the issue