# Customary Never Went Away

Dozens Disciple
Treisaran
Dozens Disciple
Joined: Feb 14 2012, 01:00 PM
To hear it from quite a few sources on both sides of the divide, a world that once used customary units of weights and measurement underwent a Massive Paradigm Shiftâ„¢ beginning from the early 19th century in the course of which it abandoned customary units for the totally different decimal system of metrology, now called SI.

As someone who lives in a country where only SI is used, I can tell you that simply ain't so. And I'm not talking about the survival of named units now sporting rounded decimal metric equivalents, such as the French livre of 500 grams. Those are very few, and fading, and in my country I can recall just one single instance of those (the dunam, an Ottoman unit of area now rounded to 1000 mÂ², or a decare).

Customary units as they used to exist are gone, but the customary way of thinking about weights and measurements is still with us. Even in the most staunchly metric countries. It isn't obvious, which is why it took me a reading about Australia's conversion to SI to realise it. The United States Metric Association website has this to say about the metrication of Australia:
Adult education classes on the metric system failed to attract interest, which confirmed the Board's belief that such courses were unnecessary. It also confirmed the Board's belief that people do not perceive metric in systematic form but learn each unit and its application as an independent and unrelated piece of information. As a consequence the highly logical nature of the metric system or the unsystematic nature of the imperial system had very little meaning for the ordinary citizen.
It's not just an insight on a country converting to SI at the time of writing, it's about all of them, including those that converted long ago, like mine. The observation above is one I know to be true from my everyday life.

Of all the SI length units, with or without prefixes, I and most of my fellow countrymen use these: the metre, the kilometre, the centimetre and the millimetre. That's it. Nothing else. No bigger prefixes, and no smaller ones. Gaps too (hecto-, deca-, deci-) are left.

And there's more to be said on that:

SI advocates will tell you you have only to multiply or divide by some power of ten to get an idea of the units. That is, if you just manage to make the metre meaningful to you, all the others are nothing but a decimal multiplication or division away from being so too.

Wrong! I don't divide the metre by a thousand to picture the millimetre, or the opposite to visualise the kilometre. Everyone in the SI-using world takes the units separately, visualising them by the uses they put them to:
• The metre is the height of the shelf in my kitchen.
• The kilometre is the distance of a city-wide walk where I live.
• The centimetre is the length of a single square of chocolate.
• The millimetre is the difference between hair cropped short and a buzz cut.
That goes for me; others have different markers for the units, but the principle is the same. The units are perceived separately - just like the mile, yard, foot and inch are for those still using Imperial or USC units! We do not wonder at that, because those have separate names, but the advocates of SI would have you believe things are totally different for their name-sharing units. It isn't.

And it's not just in everyday life. Stating out the distance from Rome to New York isn't an everyday activity, yet the lifelong users of SI stick to the customary unit of long distances: the kilometre. That's despite the fact that such distances span thousands of kilometres, inviting the use of the prefix 'mega-'. But nobody uses megametres (Mm), except for the very few who wish to make a point; it's thousands of kilometres for everyone, including passenger plane pilots. The kilometre is the metric mile.

Or take astronomy. The entire size of the universe could be measured in yottametres ('yotta-' meaning ten to the two-dozenth power), and therefore yottametres, zettametres and exametres could be substituted for all those light-years. Fat chance: light-years are used all the time, as are Astronomic Units, multiples of the distance between our planet and our star. Apparently astronomers think light-years convey the information better than units taken from a system meant 'for all people, for all time'.

But, you protest, scientists working on the microscopic level do use femtometres and the like. That's true. However, this underscores another point in contrast to SI advocacy:

By using SI, say its advocates, one can benefit from having the same units in everyday life as in the science lab. Indeed that would be a great benefit, if it were so. Unfortunately, this theoretical advantage comes up against the fact I mentioned above, that merely having prefixed units does not a bevy of easily visualised units make. Taking a scientist's paper and just reading the measures, I can understand whatever is given in metres or millimetres, but micrometres are already a problem. I have a vague idea of what a micrometre is from discussion of font sizes in printing. Nanometres, well, another hazy idea from the term 'nanotechnology'. Go down to picometres and further and I'm stumped. I have no idea what a femtometre is. You could tell me, but it would still be meaningless for lack of use. It's meaningful to scientists because they use femtometres, just as the demibushel is probably meaningful for American farmers.

That's the point. When SI advocates taunt users of USC about the 'myriad of conversion factors' between units like the firkin, kilderkin, hogshead and demibushel, they fail to realise their system is equally opaque to most people. Yes, there's a nice decimal power relationship between the metre and the femtometre, but it's of no help. Nobody can visualise a quantity by thinking about it as a millionth of another quantity. A tenfold relationship is good; a hundredfold, already vague; a thousandfold gives a very faint idea; and beyond that, those are just numbers, with a train of meaningless zeroes.

The world has mostly given up on its various miles, yards, feet, inches and lines, having non-decimal factors, to replace them with the decimal customary units of kilometres, metres, centimetres and millimetres. The changes are as follows: prefixes instead of unrelated names, consistently decimal relationships, and worldwide coverage. The first change might be easier on the memory. The second change is actually a disadvantage (because, as we all know, dividing by three is a dicey proposition in base ten) and in many places not even a change (Chinese weights and measures have always had decimal relationships).

The third change is the only substantial advantage of the worldwide conversion to SI. Truly it was easier for late 19th-century Italy and Germany to pick up the deci-metric system instead of deciding on one of so many local pre-unification standards, and it was a blessing to be rid of the plethora of weights and measures extant in the Ottoman Empire. And it is easier today when weights and measures mean the same to all people everywhere. But this is a benefit of standardisation, not an intrinsic one; the virtue being pushed here is that of conformism, and it would be valid no matter the system used. The debate on the intrinsic merits of SI and other system is something else entirely.

In conclusion, the old customary units themselves could be abolished, but the customary way of using weights and measures, any weights and measures, endures because it is the way humans do it. Seen in this light, the conversion to SI is not such a great change as it is portrayed; and it is all the more lamentable that old customary units often having useful factors between them have been replaced by new customary units related by factors of ten alone. The scientist and the non-scientist have not been brought closer, and the needs of practical life have been set back by the adoption of a system that confines all numeric representation of weights and measures to base ten, providing next to no escape routes for more useful divisions.

TGM beckons.

wendy.krieger
wendy.krieger
Reading a book on scientific weights and measures is also an insight into the process. There are many units that are not coherent with any of the various pre-SI systems or SI itself, which suggests that a good deal of these were invented for human scale, rather than any sort of numerical completeness.

Much of the metric system was in place well before the SI, so the actual design of SI is at best sub-optimal mix of pre-SI units. For example, the designation 'practical' was applied to units that made use through a natural constant, such as lb-f or Btu. Metric has its own good share of these.

Practical units are of course, disdained. So the various 'practical' units that are allowed in SI (eg electron volt, mole, etc), are variously admitted as 'alternate allowed units', or 'new dimensions' (mole). electron volt is allowed as an energy unit, but nearly every application i have seen of it is a MASS unit. Oh dear. charge * voltage does not give mass. Of course, the measured value is indeed volts, but like everyone else who uses practical units, there is a practical reason.

Kilograms are of course, a good source of amusement for the non-metricist. Here it it, the neat set of prefixes, which when applied to the unit, gives a neat multiple of unit and base. Except the kilogram. This is a tragic that dates back to the 1800s, when most of the world divided weight into avoirdupoise (or Handelmass or market weights), and troy (or fine weights, or balance-weight). The gram was supposed to cover the troy, and the grave the marketweights. Like all scales, units run from kilo to milli, cover this. The tragedy was the system usuelle displaced the grave, and by the time they got around to reimplementing it, it becomes an extended troy weight. But because there was nothing higher than myria, one had to invent names for the hectograve (quintal), and kilograve (millier, later tonne). So in deference to tradition, a 'milligram' is actually 1e-6 of the base unit.

One uses powers of 6 with electricity and magnetism, since the usual units were ÂµF and ÂµÂµF, pico is a very late addition, but has its own entry as 'puff'.

Studying metrics is a good thing in what NOT to do with a system.

Dozens Disciple
Treisaran
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Joined: Feb 14 2012, 01:00 PM
wendy.krieger wrote:For example, the designation 'practical' was applied to units that made use through a natural constant, such as lb-f or Btu. Metric has its own good share of these.
I lament the loss of the old calorie (distinct from the food calorie still used) most of all, since it tied energy to the specific heat of water. As it was disconnected from the joule, it was jettisoned from SI, so now the measurement of energy is disjoint from the specific heat of water.

TGM, of course, solves this problem by purposefully tying the energy measure (Werg) and the specific heat of water together in the Calg. This is the shining example of TGM's scientific superiority over SI, a vivid demonstration of how a modern system is supposed to work, and how SI, for all its modernisation, still carries the baggage of over two centuries past.
wendy.krieger wrote:The gram was supposed to cover the troy, and the grave the marketweights. Like all scales, units run from kilo to milli, cover this. The tragedy was the system usuelle displaced the grave, and by the time they got around to reimplementing it, it becomes an extended troy weight.
It's even worse when you recall why the grave was abandoned: for political reasons. The word 'grave' in French also served for one rank of the nobility (cf German Graf), and that became gauche in the days of Revolutionary fervour. It's for this impertinent reason that we have the kilogram, a prefixed unit, as the fundamental SI unit of mass, rather than the grave, which has no prefix. The unprefixed 'gram' is really a 'milli-' unit.

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Ruthe
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Treisaran @ Jan 6 2013, 01:53 PM wrote:It's even worse when you recall why the grave was abandoned: for political reasons. The word 'grave' in French also served for one rank of the nobility (cf German Graf), and that became gauche in the days of Revolutionary fervour. It's for this impertinent reason that we have the kilogram, a prefixed unit, as the fundamental SI unit of mass, rather than the grave, which has no prefix. The unprefixed 'gram' is really a 'milli-' unit.
Although not in the same catagory as the grave, but one major reason for the choice of new metric measures to replace the measures "usuelle", was the French third of a toise, the French foot or "peid du Roi, the King's foot". It would not have been safe at that time to retain any measure that had ANY link to royalty or aristocracy.

However, any change did not mandate a system based and a decimal numeral system. I have read but cannot find now, references to a statement that the French Acadamy did at one point consider using a numeric basis of twelve for the metric system, but did not adopt it as they believed it would be too difficult to re-educate the masses (largely innumerate anyway) in a dozenal number system.

In fact it would probably have been easier at that time than any time since as the use of dozens was well entrenched in both daily commerce and length (12 pouce in a pied) and in Bavaria as late as 1842, Bavarians used both decimal and dozenal measures, but preferred the dozenal measures of 12 points = 1 line, 12 lines = 1 inch, 12 inches = 1 foot and 12 feet = 1 Rod (Ruthe, now in modern German, Rute). Of course, due to national and even local differences, these measures were often never exactly the same from place to place.

PS Unfortunately, the reference for the Bavarian measures is longer available on the web, but I have a text file which I created from that website that replicates those measures. With any luck, Shaun may have copied some of the original website pages as I gave him the URl of that website before it disappeared.
Why a Roman pocket abacus? They used dozenal fractions as their main form of fractions, 12 inches per foot & originally 12 oz per pound (inch=ounce=uncia=1/12). Columns 1 & 2 of the abacus are for dozenal fractions, column two for twelfths and column one, dozenal fractions of a twelfth. Columns 3 through 8 provided a decimal place value system with values from 1s to millions where each lower bead counts as 1 & the upper beads count 5 of a column's base 10 power, Is, Vs, Xs, Ls, Cs ,Ds, Ms etc.

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Treisaran
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Joined: Feb 14 2012, 01:00 PM
Ruthe wrote:However, any change did not mandate a system based and a decimal numeral system. I have read but cannot find now, references to a statement that the French Acadamy did at one point consider using a numeric basis of twelve for the metric system
Icarus mentioned this in his tour for base E, as a background to his account of an even more incredible proposal made, to have the Metric System built on base eleven.
Ruthe wrote:PS Unfortunately, the reference for the Bavarian measures is longer available on the web
Have you tried finding an archived copy on the Wayback Machine?

Dozens Demigod
dgoodmaniii
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Joined: May 21 2009, 01:45 PM
Treisaran @ Jan 6 2013, 07:43 PM wrote: Icarus mentioned this in his tour for base E, as a background to his account of an even more incredible proposal made, to have the Metric System built on base eleven.
Indeed, I think LaPlace made the suggestion. And contrary to popular belief, it's been shown that the pre-Revolutionary French were much more literate and numerate than has typically been held by Anglo-Saxon historians; as many as three in four French could read at that time. It was precisely this widespread literacy and numeracy that convinced LaPlace against going with dozenal; the French were already numerate in decimal. If they were not numerate, training them in dozenal would be no more difficult than decimal.

The Wayback Machine surely has some version of it; perhaps not the very latest, but it's bound to be there.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use or X; for elv, I use or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!

Dozens Disciple
Shaun
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Joined: Aug 2 2005, 04:09 PM
I have just a couple of screenshots - but here's the page on the Wayback machine:
GermanMeasures

Note also it may be possible to get his book:

"Das Buch "Alte Meß- und Währungssysteme aus dem deutschen Sprachgebiet" von Fritz Verdenhalven, Verlag Degener 1993, ISBN 3-7686-1036-5

Das Buch ist meiner Recherchen nach über den Onlinehandel nicht zu bekommen. Deshalb hier die Verlagsanschrift:
Degener Verlag; Postfach 1360; 91403 Neustadt (Aisch)

Aldefeld's Maaß und Gewichte der deutschen Zoll-Vereinsstaaten etc. Stuttgart bei Cotta 1838

Nelkenbrechers Taschenbuch der Münz-, Maaß- und Gewichtskunde, 16te Aufl. Berlin 1842

Dank-Mails nehme ich gerne entgegen."
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.

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Ruthe
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Shaun @ Jan 7 2013, 12:09 PM wrote:I have just a couple of screenshots - but here's the page on the Wayback machine:
GermanMeasures
Great news, I found his new site. I looked at the Wayback machine, took a copy of one of his titles, did a google search and LO!, found his current site. It seems to be all there!!! Here is his home page http://www.spasslernen.de/index.html and here is the direct link to the page I referred to
Amtliche MaÃŸeinheiten in Europa 1842.

Such a large work as this should be archived to avoid it ever being lost.

Â¼ Â½ Â¾ Â² Â³ Â¹
Why a Roman pocket abacus? They used dozenal fractions as their main form of fractions, 12 inches per foot & originally 12 oz per pound (inch=ounce=uncia=1/12). Columns 1 & 2 of the abacus are for dozenal fractions, column two for twelfths and column one, dozenal fractions of a twelfth. Columns 3 through 8 provided a decimal place value system with values from 1s to millions where each lower bead counts as 1 & the upper beads count 5 of a column's base 10 power, Is, Vs, Xs, Ls, Cs ,Ds, Ms etc.

wendy.krieger
wendy.krieger
There's also Patrick Kelly's "Universal Cambalist" of 1835. This gives by country, the various money, weights and Measures as might be needed for commercial activities. You could go for a later tome by Norback on Gewicht und Masseinheit.

A good number of these are available on google books.

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Nigellus
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wendy.krieger @ Jan 6 2013, 10:29 AM wrote: Practical units are of course, disdained.
It seems like metric might be deliberately designed to measure the unknown, which would make sense since that's what scientists like to look for. When you don't know what you will use your system for, or don't have a specific use in mind, it's easy to make it uniform.

Customary is vilified for having seemingly haphazard collections of units. However, it's not really haphazard. It's, as you put it, practical. The reason the collections of units don't necessarily mesh well is because they were adopted with specific uses in mind. They didn't worry about how they fit into a larger "system."

For example, manufacturing needed very precise, very small measurements, so they liked to use thousandths of an inch, of the mil. This is in spite of the fact that the inch is traditionally divided into halves, quarters, eighths, sixteenths, etc.

The metric system would not tolerate such deviation, but customary does.

wendy.krieger
wendy.krieger
One should not suppose that the SI is the paragon of correct metrological thinking. It's a hodgepodge done to keep with past traditions and international desires in exactly the same way that the imperial system is.

If ye look at the customary system, every prime factor over 5 indicates that the units come from different systems, and these, like the stitches on Frankenstein's monster, show where the parts have been stitched together. Even the seven-day week.

The human mind accomidates for division and multiplication in different parts of the mind, so the division-bases are typically different to the multiple bases. The dozenal society suggests that we ought count in a division base, in much the same way that Stevins suggest that we should do sub-multiples.

The modern electrical units date from 1864. That's something like 80 years before 'SI', and forty years before Giorgi made his system. In the intervening time, we have had things like the CGS (1873), proposals to rationalise (1880 - Heaviside), 'corrected units' (heaviside's and lorentz's systems. But the established tradition was laid in 1861, and that is how the world ought be.

SI supposes a series of powers of 1000. But the number 10^7 does not fit here. It beggars belief.

The base unit of weight is a 'kilogram'. I mean, for god's sake. You have a base unit that is '1000 grams'. Not a chog. If you used chogs mentally as ye might use metres, you will see there is a whole scale of weights (avoirdupoise), that nicely runs from millichogs to kilochogs, and a different set (troy), that run from milligrams to kilograms. That was the intent of the system.

Decimal time. Don't make me laugh. People talk of dividing the day into 10 hours of 100 minutes of 100 seconds. The 'correct' time to preserve right ascession, is to divide the day into 40 demurs of 1000 hesits, so 1 m/h = 1 km/kh.

And then there's moles. Oh dear, here we go right off the track. The way moles work is like this. You weigh the chemical in weight units, say w, and you look up the published weight of the chemical in daltons. That's what the unit for the atomic masses are. So you have w/d = number of molecules, expressed as a weight. It's simply a weight-scale for big numbers. Thus a lb-mole is a gazillion molecules, and the weight of a lb-mole = lb/Da * weight of molecule in daltons.

So the formula is weight-mole = weight / daltons. Ah do you think SI can keep to such a simple formulation? Nah! weight-mole = 1000 * weight / daltons. Super simple stuff, really. And hey presto, a new constant, and a new base unit!

wendy.krieger
wendy.krieger
Nigellus's comment is of course, totally missing the point.

A measurement is not more precise because it is wrought in decimal.

The IWMA states the inch can be divided in binary, into decimal, or into twelve-mal. So it's perfectly legal to divide the inch to 12 lines of 12 points of 12 seconds of 12 thirds. It's perfectly legal to divide the inch to decimals, or binary.

With binary division, every previous division appears on the next division, so the sixteenths are parts of the thirtyseconds, which are parts of the sixtyfourths, &c. You can't do that with 10 or 12, since at any given point, the choice is between 2 or 5, or 2, 2Â½, 2, or twelve-wise, 2,2,3 or 2,3,2. This is why binary was preferred in industry. It's worth noting that metric paper sizes are of course, binary divisions, A5 = Â½A4, and where there is a non-standard division, well.

Practical in the sense that Maxwell used it means something like 'the weight of 27 cubic inches of water', or 'the resistance of 1 mile of 6-guage copper wire'. There is of course, nothing stopping you using such measures, but they don't conform to Gauss's LMT formulation.

The definitions of both TGM and SI are both 'practical'. Essig and Pajul both replicated metric definitions in their dozenal system. All of these systems (as well as Cassini's geographic mile of 6000 feet), merge nautical measure at the surface of the earth, and one can with little supposition, take water as the second link.

TGM is abidingly more practical, since on the simple scale, it converges weight and heft (the force of weight), and as nearly every one else does, the density of water is '1'.

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Nigellus
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wendy.krieger @ Jun 22 2015, 07:41 AM wrote:A measurement is not more precise because it is wrought in decimal.&nbsp;
That wasn't my point at all, and also not even remotely what I said. The mil is not precise because it it decimal; it is precise because it is very small. A 1/1024th inch unit would be even more precise and be binary.

The question of why machinists wanted a 1/1000th inch unit instead of a 1/1024th inch unit is a separate discussion, and is not what I was getting at.

My point was that customary units are purpose-driven. They exist largely because of how they are used, and what they are used for.
wendy.krieger @ Jun 22 2015, 07:41 AM wrote: The IWMA states the inch can be divided in binary, into decimal, or into twelve-mal.&nbsp; So it's perfectly legal to divide the inch to 12 lines of 12 points of 12 seconds of 12 thirds.&nbsp; It's perfectly legal to divide the inch to decimals, or binary.&nbsp;
Exactly. You simply don't see this kind of diversity of usage with metric units.