One can, with a modicum of searching, find many places on the internet where anglophones argue with one another about the relative merits of their customary units and the Système International (SI) units. All sorts of fascinating rationales are advanced on both sides (such as the relative precision of the relationship between various volumes of water and their masses, under certain conditions of temperature and pressure) but there is one simple fact thanks to which I vastly prefer SI: it places fewer demands on my memory.
I should note that one must distinguish between SI
and
the metric system
, since the latter may equally refer to the cgs
system, in which the centimetre and gramme are used in place of the metre and
the kilogramme. Quite why no system uses the metre, gramme, second system I am
at a loss to discern, but adding such a system now wouldn't really help anyone
much: it would merely add to the confusion. The cgs system yields derived units
that are power of ten multiples of SI units; but I seem to remember that the
electrical units used with it are defined sufficiently differently as to yield
rather more complications in converting between the two. But at least it still
only has one unit for each kind of quantity, for the most part.
In SI, there is one unit of length, one unit of time (although we continue using the customary units of time in practice) and one unit of mass. Likewise there's one unit for each of the small number of other independent kinds of quantity. For each kind of quantity dependent on these, there is a natural way to derive a single base unit for that kind of quantity from these base units. For each kind of quantity, one may use some standard quantifiers (milli, kilo, micro, mega and so on) or one can use powers of ten directly. There are indeed some minor quirks (the unit of mass uses one of the quantifiers in its name, for example) but they are few and far between. It's not perfect, but it is at least largely systematic.
The customary units
of the anglophone world, on the other hand,
require me to remember more than the entire SI base system merely to describe
lengths. I still remember being taught these units when I was a child: the
teacher expected me to memorise a vast vocabulary of names for units of lengths
and stated the value of each in terms of some earlier one (not necessarily the
last, nor all in terms of one start-point), expecting me to remember this
bewildering mass or ratios. Let me just list part of that litany:
That's eighteen distinct units for lengths in the range from a third of a millimetre to less than two km. Every number from two to eleven, except for seven, shows up among the eleven factors used, ignoring the uses of twelve in hence clauses. We also had to remember that an acre was a chain by a furlong and, just to confuse us all a bit more, our teacher threw in the hectare (a metric unit, but the teacher neglected to point this out), which is a little under two and a half acres but I can't remember what value our teacher gave us for it. It's probably a good thing she didn't tell us that some engineers take the chain to be 100 foot (instead of the 66 feet you'll get if you work your way through the above).
Six of those units aren't relevant to the sequence from point up to mile;
and we can shed another four by simplifying the sequence to: twelve points make
a pica, twelve pica make an inch, twelve inches make a foot, six feet make a
fathom, eleven fathoms make a chain, ten chains make a furlong and eight
furlongs make a mile, but that's still eight units and five distinct multipliers
to remember; and none of that remembered information does me any good in
learning the kindred mess of complexity involved for weights (seven units, five
distinct ratios) or for volumes (I forget which units we were taught). These
days I have a python module, study.value.archaea in my study package, to remember all this arcane
complexity for me.
Having to remember so many things increases the over-head of learning to use
such a system, quite apart from the complications that arise from different
nations having different versions of some of these units – the US and UK,
hence much of the commonwealth, differ significantly on volumes and on some
weights; and many of these units also existed in other nations, with usually
(but not always) the same ratios among values and similar values. It gets even
more confusing when some of the names show up for different kinds of
unit: the timber foot
is a unit of volume, one cubic foot; the water
ton
is a unit of volume (and, at the right temperature and pressure, this
much water does, indeed, have a weight of one UK ton; only be sure not to
confuse the water ton with the tun, which is a slightly smaller volume) and the
bushel is a unit of volume except when it's a unit of mass – the wheat
bushel
and similar for other grains – doubtless approximately equal to
the mass of a bushel of each grain involved. And then of course there's the use
of pound both as unit of weight (i.e. force) and as unit of mass.
All that diversity of base units complicates matters even further when we come to deal with derived units. I have had occasion to work with software in which volume flow-rates could emerge from calculation in either cubic feet per second or US gallons per minute (and, to the credit of the US gallon, unlike the UK one, there is at least a defined ratio of whole numbers between these); and forces could come out in pound (mass) feet per second per second or in pounds weight (requiring a factor of 32.174 and a bit to convert between them).
So the true virtue of SI is its simplicity. All arguments about how convenient it is (or isn't) that one system's units of volume and mass give handy values to the density of water (or any other physical constant) are essentially irrelevant: no matter how handy such a datum is, it's a physical property of a material and it changes with circumstances (e.g. temperature and pressure), so any practical work with the given material requires you to have the correct value for the conditions you're in, at which point it isn't really very important that the value is close to one, except when one is doing rough calculations – at which point, the systems tend to do roughly as well as one another.
It should be noted that SI could be made better, although the upheaval in doing so would probably be more effort than it's worth. Getting anglophones to abandon an archaic system in favour of one that's simpler by a factor of several dozen has taken us two centuries and we're not done yet: getting the whole world to change over to a marginally simpler system is probably too much to expect. Still, it's interesting to consider what improvements we could consider.
There would be a certain virtue to switching from base ten to base two, if only for the sake of our computations. There are already quantifiers ready to serve if we do: Kibi, Mibi and Gibi have been introduced for the powers of 1024 = twoten, although I'd be inclined to suggest some other factor than (roughly) a thousand would be more suitable; 256 = twoeight fits better with how computers actually manage data; but sixteen = twotwotwo or 65536 = 2562 = twosixteen would fit more elegantly with base two. Still, our units are meant for our use, so it's perhaps better to stick with base ten, as it's embedded in most of our languages and the computers can handle the arithmetic better than we can anyway.
The metre is now defined in terms of the second: there are exactly 299792458
metres in the distance light travels in vacuum in a second. This could sensibly
be construed as an argument for replacing the metre with the light second as
unit of length. Of course, that's rather a large distance for most terrestrial
purposes; but the light nanosecond is quite a practical length – in fact,
it's roughly a foot; slightly more than the archaic Swedish foot and slightly
less than the anglophone foot. It would thus be natural to introduce the light
nanosecond as the SI foot
. The original specification of the metre tried
hard (but failed) to be a definite fraction of the Earth's circumference, so
there's no particularly strong reason to be attached to it; and an SI foot has
a certain charm to it ;^>
Just as the metre can be defined in terms of the second via the speed of light, c, the kilogramme could be defined in terms of the second and metre via Planck's constant, h, if we knew it with suitably great precision (which, at present, we don't). The resulting unit would, however, be spectactularly tiny: even neutrino masses are (probably) huge when measured in it. Worse yet, I can't even find (despite their diversity) an archaic unit of mass that's close to a neat power of ten times it. But, in any case, Planck's constant appears to describe real physics, where the speed of light is merely an artefact of our relationship with space and time, a conversion factor between displacements in different space-time directions; not fundamentally different from a conversion factor between furlongs (a unit of archetypically horizontal length) and fathoms (the archetypical unit of vertical length).
Written by Eddy.