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.
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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.
If memory serves me correctly, at the time we were debating going decimal (currency) there was some serious suggestion that base 12 was more convinient than base 10. This is very true, 10 factorises to 2 and 5 only, 12 factorises to 2, 2, and 3. However base 8 and base 16 with which we were familiar from computer programming at that time (we had to programme our own!) are even better, and also has the same argument. Base 10 is very difficult to compute electronically (as is base 12), probably only being used because we just happen to have 10 fingers. If you have a cheap old calculator and try 10 divided by 3 then multyply by 3 you will get the wrong answer. (9.9999..not 10)
Common sense prevailed and base 10 it was, the same as the rest of the world.
Here we come to our basic discussion of the current metric system, based on the current decimal system, based on known and constant physical factors vis a mish-mash of unrelated measuring systems based on what was convinient to the traders of the day in the products they were trading with no regard nor necessity for a unified system.
@BrianAC
12 has more factors than 10 but so what? In what circumstances does the number of factors have a bearing on its application in measurement? Don’t let the critics fool you.
Electronic machines handle information in binary because information processing and storage devices have elements with only two states (+5v/0v voltage level, polarity of electric field, charge or magnetic region, presence or absence of reflected light beam etc). Hex (base 16) is just a convenient way for humans to read binary data (binary digits in groups of 4).
But we are in no position to move away from base 10 for numbers generally. The change would be quite horrendous and most of the population would not be able to cope. We certainly couldn’t work in binary and base 16 would burden us with having to remember too many intermediate results between single digits for doing arithmetic (think of the 16 times tables!)
The importance of the decimal system of measurement is that units are counted in the same way as ordinary numbers. For example a length of 1234 mm is the same as 1 m + 2 dm + 3 cm + 4 mm, in other words the digts 1,2,3,4 have a place value much as they do in the number 1234 itself (1 x 1000, 2 x 100, 3 x 10, 4 x 1). And that’s what really matters! The compatibility is superb which makes doing arithmetic with metric measurements so easy.
@philh
This is in fact becoming topical as I understand the selling of eggs in dozens is to be stopped, they must be sold in units of ten.
12 (the dozen) is much more convenient to package. 10 eggs can be packed in one row of ten, two rows of 5 or 3 x 4 with two spare holes, which makes for awkward packaging. packing 3 x 4 = 12 gives a nice 3:4 ratio package. With base 10 you need to go to 20 (4 x 5) or 25 (5 x 5)to get an elegant and stable package.
The point you make above would apply no matter what the base, so long as it applied to all units ie the whole decimal/metric system would be base 12 so therefore uniform. However this is outside the scope of this site and me, and does not apply so not really relevant. I just made the point base 12 was considered (never seriously) and rejected. This is in context of the original question and certainly does not reflect my opinion. Now, someone start a topic on TV/Monitor screen ratios and being in inches only!
Was not the “ten-egg” thing shown last year to be either a scare tactic or a misunderstanding on the part of the Daily Mail and like newspapers?
The fear: http://www.freerepublic.com/focus/f-news/2542309/posts
The reality:
http://www.independent.co.uk/news/world/europe/scrambled-ndash-the-eu-threat-to-british-eggs-2015264.html
US eggs also have to meet a weight standard depending on whether they are called small, medium, large, etc, although that weight is not printed on the carton. It is only known to the regulators and producers. Some means of disclosing the weight requirement on the package would be more transparent.
It seems to me the topic was discussed last year but I can’t find the thread.
A little more searching found the old egg thread.
http://metricviews.org.uk/2010/06/eggs-by-the-kilo/
@ BrianAC
The “eggs must be sold in 10′s” story was just a typical Daily Mail distortion of the true position.
This article is a bit nearer the truth
http://liberalconspiracy.org/2010/06/28/dozen-eggs-banned-yes-they-did-make-it-up/
Even better, the Daily Mail ran an article a few days later admitting that their original article was absolute nonsense, but then tried to claim that the EU had changed their mind because of a “British Backlash”!
http://www.dailymail.co.uk/news/article-1290768/Eggs-dozen-NOT-banned-say-Brussels-backlash-Britain.html
For a laugh-out-loud reimagination of current affairs, you can always rely on the Mail……..
Thank goodness for that!! I never really believe what I hear and see on TV, but like many people that is where my current edjicashn in world affairs and modern English usage comes from, heaven help me. Sometimes I do rush to the internet to try to find the real story behind the media story, but that has to happen before I forget what it was I wanted to know about in the first place. As a side line on watching the news, one may often get a less biased viewpoint from Euronews (Free to air on Sky Ch. 508), alas though, it is so Anglisised that the miles, feet and ‘football pitches’ still give me a kick I really dont want.
It has often passed though my mind, are there not any laws making it a criminal offence to publish lies in this fashion? Lies are what mis truths and half truths are (We shall have the truth, the whole truth and nothing but the truth..etc)( I am listening, I hear what you say. … for sure does not mean they will take any notice) (up to 80Mbs, just means it could be 300bps) and I personally have on two occasions (to my knowledge) been the subject of such lies read and or published by the media.
Irrespective of whether the story of egg packaging was true or not (would have been odd given the recent moves away from prescribed quantities) it is not a measurement issue and there is no general reason for things being to sold in quantities of ten, metric system or no.
As for the journalists who peddled that nonsense, they’d make good politicians – it is a well known ploy to claim credit for winning a battle that never actually happened.
I have heard arguments about imperial units being divisible by 3, being duodecimal, using powers of 2 (e.g. 2, 4, 8, 16, etc) and using multiples that are divisible by more factors than the number 10. All these arguments are undermined by the fact that the imperial system uses all kinds of multiples, many of which do not fit these criteria (e.g. 5.5 yards to a rod, 22 yards to a chain, etc).