It is often claimed that imperial is based on 12s (duodecimal) and that this has advantages over decimal. But is this truth or myth?
Of course it makes more sense to use the same number system for measurement, money and other practical uses. But let’s look at whether imperial is duodecimal.
Consider length:
One foot = 12 inches
One yard = 3 feet
One rod = 5.5 yards
One chain = 4 rods
One furlong = 10 chains
One mile = 8 furlongs
Only the foot uses a base of 12.
Consider volume
One pint = 20 fluid ounces
One gallon = 8 pints
No duodecimal units
Consider avoirdupois weight
One pound = 16 ounces
One stone = 14 pounds
One hundredweight = 8 stones
One imperial ton = 20 hundredweight
Again no duodecimal units
A disadvantage of imperial is that it does not have any consistent number system but uses a hodgepodge of bases.
One pint = 20 fluid ounces?????
Everyone (i.e. we over here) knows that one pint = 16 fluid ounces!
(Not just a hodgepodge of bases — there isn’t even a single unified hodgepodge!)
From the other side of The Pond,
Ezra
Never mind 12s; why use a system where some units don’t even relate to each other using whole numbers?
MASS
1 avoirdupois ounce = 437.5 grains
LENGTH
1 US survey foot = 12.000024000048 inches
AREA
1 square pole = 30.25 square yards
VOLUME
1 imperial pint = 34.677429099 cubic inches
1 US wet pint = 28.875 cubic inches
1 US dry pint = 33.6003125 cubic inches
Those of us who are “above a certain age� will remember being taught £sd at school. (For the benefit of younger readers and readers from abroad, there were 12 pennies in a shilling and 20 shillings in a pound). Pounds, shillings and pence were added up separately and conversions done between the columns. It would have made no difference if £sd was a pure duo-decimal system (ie 12 shillings to the pound) – arithmetic manipulation would still be awkward. It would be no different using feet, inches and lines or any other “pure� duo-decimal system.
Of course, it we counted using a duo-decimal system rather than a decimal system (such as Tolkien’s Elves), then a duo-decimal system of measurement would work very well, but the cost and effort required to convert the world from a decimal culture to a duo-decimal culture does not bear thinking about.
Even if we generously ignore the non-integer rod as 5.5 yards, the list of imperial units given in the article does not contain a single prime factor spanning the whole set of units.
The one that almost does it is 2 but then it’s absent from the relationship between yards and feet. In the metric case we have 2 and 5 which are used throughout.
I have seen attempts to extoll the virtues of imperial on the basis that it has evolved over time and thus (somehow) represents a mature and sensible conclusion to history.
The reality is that imperial is the result of belated attempts to rationalise or correlate units that came into existence for different unrelated purposes and were never designed to be compatible with one another.
It is quite a crass argument to suggest that this has lead to a mathematically superior system.
The fact that the imperial system evolved over time suggests to me that various incompatible systems were shoehorned into some kind of single system.
The worst of these shoehorning tactics was the Imperial gallon in 1826 by which one gallon of water weighed 10 lbs, but nothing was done to ensure any other easy relationships. Of course, at the same time the Dutch had been rationalising their system of weights and measures and they decided to reintroduce the metric system which has been imposed on them a few years ealier.