## Weighty Matters

26 September 2010

The metric system has some points of genuine superiority to those of the English (aka American) system, but that superiority tends to be exaggerated. For example, the every-day English measures for volume tend to be implicitly binary, allowing easy halving or doubling. (If base 10 were everywhere superior to base 2, then our computers would be designed differently.)

One of the things that I was told as a child was that the metric system were superior because it measured in terms of mass, rather than weight, with the former being invariant while the latter would change in the face of a gravitational field. Well, actually, the English system has a unit of mass; it's the slug, 1 lb·sec2/ft, which is about 14.6 kg.

Meanwhile, I observe that, in countries where the metric system ostensibly prevails, people typically use its names of units of mass (gram and kilogram) for units of weight; they even refer to what is measured as a weight. Now, the real metric system does have a unit for weight, because weight is a force; weight can be measured by the newton (or by the dyne, which is a hundred-thousandth of a newton). But people aren't doing that; they're using kilogram as if it means about 9.807 N.

Much as it may be claimed that America is the only industrialized nation not on the metric system, really nobody's on it.

I notice that the Beeb most often wants to speak and write of weight, rather than of mass, but in the most ghastly unit of all, the stone (pronounced /stɛun/, with at least one pinkie extended). The stone is 14 pounds (divisible by 2 and, uh, 7). When weights don't divide into integer multiples of 14 pounds, tradition is to represent weight in terms of a combination of stone and pounds, as in Me mum weighs 19 stone and 12. Of course, if the Beeb were using pounds at all, there'd be the two obvious questions of

Why aren't you just using pounds for the whole lot?
and
Wait, now that I think of it, what happened to that metric stuff?
So the Beeb feels compelled just to round everything up or down to an integral number of stone, and somebody's mum either gains two pounds or loses twelve.

### 8 Responses to Weighty Matters

• Gaal says:

I've never heard the argument that the metric system is superior to the English because it indicates mass instead of weight. I don't understand why anyone would make it.

In informal use the two are invariably conflated and the unit conventionally used for one takes over the to mean the other in certain pure conditions and some parameters assumed. (Perhaps this is an example of people doing functional-programming currying without thinking about it.) My point is that this behavior is very common: the slug, for example, only got its name sometime in the last 100 years.

Units, of course, are entirely a conventional matter. Arguments to one system's superiority appeal to usefulness and usability. Doubling is indeed useful for day-to-day weighings. But if you go down this road, you must also consider distances. The meter is not innately better than the yard, but I find it hard to imagine a practical application where someone would prefer 1/16ths of an inch to 1.5mm. As for literary language, of course, kilometers are more clunky than miles.

• Daniel says:

I would say that the argument for using the metric system because of its giving priority to mass rather than to weight were made because the people making it thought of mass as a more fundamental concept than force. Certainly it is most common in physics to take mass as undefined and force as a derived concept, though at least one of the two standard physics textbooks in America, that by Sears and Zemansky, not only explicitly made the point that one could do it the other way around, but through a number of its editions did exactly that. (I don't recall what the other text, that by Halliday and Resnick, may have said on that issue, but they used mass as the fundamental concept.)

From an epistemological perspective, the notion of mass is ultimately derived from a sense of exertion, which is analogous and more closely related to the notion of force, and I think that this is why people incline to think and to speak in terms of weight rather than of mass.

Again, I agree that the metric system has some points of genuine superiority; I simply claim that its relative superiority has been overstated, and that nations that have ostensibly converted to it haven't really done so, regardless of whether they should.

As to practical applications of a sixteenth of an inch versus 1.5 mm, woodworkers come immediately to mind, exactly because a sixteenth is a power of two, and I know of woodworkers who don't like overt mathematics. However, there is no intrinsic reason that one cannot work in, say, eighths of centimeters, and my drafting scale breaks inches into fractions n/(m·10in, where m and n are integers. I do find myself doing vector graphics in eighths and sixteenths of something fairly often.

• Gaal Yahas says:

I would say that the argument for using the metric system because of its giving priority to mass rather than to weight were made because the people making it thought of mass as a more fundamental concept than force.

But note the existence of the pound-mass. Historically it was likely created because of the aforementioned conflation in common use, but that doesn't make it a less worthy unit than the slug.

• Daniel says:

I confess to having forgot the pound-mass to the point that I could recognize it but might never have recalled it.

I agree that the pound-mass wouldn't be rendered an unworthy unit for having arisen from treating masses and forces as perfectly correspondent, and I don't see that the slug has some other claim to superiority unless it is one of being the more widely adopted unit. (And I don't even know that the slug is that.)

• Oshi says:

According to the freshmen this semester, the metric system is better (or worse, depending on who you ask) because the units are smaller so it's easier to measure small things and harder to measure big things. I should have them read this and really blow their minds...

• Daniel says:

Of course, the English system has a various units for tiny measurements (mils for distance; drams and grains for weight; fluid drams and minims for volume), the metric system has its system of prefices for rescaling to larger units (or to smaller units), and in either system one can just throw-in a ×10m.

I'd say that, actually, the metric system normalized badly, such that for scientific purposes one ordinarily uses a kilogram-meter-second system or a gram-centimeter-second system, rather than one with no scaling prefices (a gms system, as it were). And, for everyday use, the gram is plainly too small and the meter is rather large.

• "(If base 10 were everywhere superior to base 2, then our computers would be designed differently.)"

I enjoyed the piece except for this part. Base 2 was a necessity when computers were born. Electricity either had current or it didn't. That was, after all, how machines had to calculate back then, they didn't have fingers and toes 😉

• Daniel says:

The section that you quote doesn't purport to show that binary is everywhere superior to decimal; it illustrates the principle that 10 isn't always the best radix.

Nor was base 2 necessary when digital electronic computers were born. For example, it was quite possible to build systems that had three states — off, low voltage, and high voltage; or negative voltage, zero voltage, and positive voltage.

In fact, because voltages and currents have a virtually continuous range of possible values (far more than twenty fingers and toes), there used to be a fair amount of interest in analog computers. It was a weaker practicality than necessity that brought the triumph of binary computers.

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