Hmm, don't see a big deal. Maybe it is a big deal to someone striving for some engineering beauty and consistency, but in every day life, centimeters and decimeters even are popular because they relate to sizes on human scale -- size of a palm, thickness of a finger and so on.
But I grew up with those units and didn't encounter them first in the university or high school. Just have everything be divisible by 10 is easy enough and knowing the prefixes is easy.
I was very confused and still am by inches, yards, stones, pounds, ounces, gallons. I don't know how many in each of each.
You feel a bit of the effect when you go to a country which uses different metric units. For instance in Sweden you commonly have hekto (= hectogram = 100 g) and mil (= 10 km). Or Germany where Pfund is still common (500 g). It will make you need to think a bit at first.
I never encounter decimeter. Centiliter only for shot glasses, every kitchen measure thing I have only shows mLiter. Same with grams. There are no centi/decigram on my kitchen weighing scales.
I remember one of the educational toys my school had, which I played with when I was 5 or 6. We called it "tens, hundreds, units" [1]. There were many 1×1×1cm "units", 10×1×1 "tens", 10×10×1 "hundreds" and a 10×10×10 "thousand". You could fill the hundreds and thousand with water, the thousand obviously being 1L.
The British National Curriculum [2] says children
- In year 1 (age 5-6) should be able to count centimetres
- In year 2, recognise place value, choose appropriate units (cm/m, g/kg, °C etc) and use measuring tools for these
- In year 3, to add milli- to that,
- In year 4, convert between centimetres and metres, and other units (time and £ and pence)
- In year 5, to convert between milli-, centi-, base, and kilo- measures. Calculate square areas in cm² and m²
- In year 6, volumes in m³ etc, and converting everything, to three decimal places.
(This hasn't changed since the 1960s or something, so it's a shame the country won't get rid of road signs with miles and yards on.)
As a first generation Chinese-American, I run into a similar problem converting back and forth between Chinese and English -- where English only has words for thousand and million, the Chinese prefer to speak in units of ten thousand (wan). You get a feel for how unintuitive it is to say things like "twenty-five ten-thousands" to read the number 250000, or "a thousand ten-thousands" for ten million.
With regards to why America doesn't make the change to metric, I recall reading somewhere that the American manufacturing base didn't want to have to convert all their infrastructure, currently set up to manufacture screws, bolts, and other such tools in units of inches, half-inches, five-eighths inches and so forth. It's not just a question of cultural shifts in intuition -- there's a physical cost associated with making the change as well.
Knuth's quote comes to mind -- the root of all evil being premature optimization. I wonder about the full price when you integrate the little costs of these scenarios of suboptimal standards -- not just in the realm of physical measurement, but the QWERTY keyboard, pi vs. tao, English grammar rules, even the base ten number system among others. But at some point you have to declare "good enough", and stop refactoring to instead pay upkeep on the accumulated technical debt. Perhaps it is a shame that America chose not to refactor to metric, but maybe some day down the road we will find a generation generous enough to raise their children with better-optimized standards, and pay the costs of re-learning a new intuition themselves.
You can use units which are very neat and pretty logical for some things - and very inconvenient for others.
That's, I think, the reason we have all that variety of units, which don't quite follow the same system. Centimeters are there just because of utility in less than strict cases; may be brains are simplifying by dropping unnecessary precision digits from consideration. Same for Kelvin - we don't measure temperature in, say, electron-volts, not only because Volt isn't a natural unit.
Two remarks: firstly, the unit for temperature is kelvin. Secondly, and more importantly I don't see how temperature would be special. The second is a larger outlier. Whe have milliseconds, microseconds, etc, but rarely use kiloseconds, megaseconds. Another outlier is angles, where degrees, minutes, and seconds are used more often than radians. More examples at https://en.m.wikipedia.org/wiki/International_System_of_Unit...
As a side note, the French (at least) architectural drawings are in centimeters, that's the only place I have seen centimeters as the default, but it's one of the most important engineering field.
Are you sure? "ISO 129 Technical drawings -- Indication of dimensions and tolerances" specifies that SI units be used, i.e. µm, mm, m, km.
I've only seen British drawings, which almost exclusively use mm for things up to the size of a moderate building (school etc). I've seen metres used on really big things, like 10km of railway.
As an (italian) architect, I can confirm: architects usually use centimetres. Millimetres would imply a level of precision which is not practical in construction.
It’s quite unfortunate that the SI system of units is built on top of the base 10 number system.
If we all switched to base 12 instead (especially if we likewise unified measurement for time, angles, geographic coordinates, money, etc.), the arithmetic would be much friendlier for humans.
"Every third number is a multiple of three; yet no power of ten, no matter how high one multiplies, is ever also a multiple of three. Similarly, every fourth number is a multiple of four; but one must get to 102 before the fourth becomes an even divisor. Every power of ten also misses six as an even factor, and one must wait until 103 (1000) before eight divides in evenly. All told, ten simply skips many of the most important fractions, and those it does catch it generally catches imperfectly. Ten is certainly a poor base from this perspective."
and
"This shows that all bases have irregular wholenumber fractions; for example, the reciprocal of the base less one is always 0.1. However, it also shows that one base stands out in the regularity of the most common and important fractions (1/2, 1/3, 1/4, 1/6, 1/8): that is the base of twelve."
This PDF is just an example, showing some of the simplification you could get with a base 12 metric system. I’m not advocating this particular design.
In general I think the “dozenal society” people need better numeral glyphs and better names for things. When reading their materials, try to look past the choices of names.
As for the advantage of base 12, try writing out multiplication and addition tables for both base 12 and base 10. Here are those multiplication tables using modular arithmetic:
Here's a table showing the fraction i/n in decimal (white columns) and in dozenal (blue columns) for i=1,12 and n=1,12.[1]
There's absolutely no way I can get most people I know to mix the alphabet and numerals. I'll definitely look more into it, but for the moment I doubt it's immense usefulness.
And honestly, I think the naming of units is very important. Numeral prefixes are important and I think the metric prefixes are quite easy to work with (maybe that's because I grew up with them). Gravyard is a bad choice I think!
Outside of scientific and engineering fields, most everyday interactions people have with their units of measure do not involve translating between orders of magnitude, and yet the metric system optimizes for that to the exclusion of all other conveniences, through its focus on base 10 and "it's so easy, just move the decimal point!"
Meanwhile, in most other areas of life, dividing into halves, thirds or quarters is overwhelmingly more common than dividing into tenths, hundredths or other powers of ten. If you wonder why the "unintuitive" imperial units have such staying power, consider that 12 and 16 are more typical bases for them, and 12 is essentially ideal (evenly divisible by 2, 3, 4 and 6) while 16 is better than 10 (evenly divisible by 2, 4 and 8).
Kitchen cupboards, appliances etc are designed in multiples of 300mm, which has factors of 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. The smallest part is still in mm, not awkward fractions of an inch, and the whole wall can be put in mm: 3880mm. That's easy to understand, but 152 inches is less so (who uses inches for something that long?). 12ft 9in is presumably intuitive for those familiar with imperial, but annoying to convert as soon as it needs dividing or multiplying.
Also, imperial units didn't have much staying power in the ex-British Empire, apart from in Britain.
I think the main question is why we feel a need to impose a single one-size-fits-all universal unit set onto disparate domains with different ideas of what properties make a unit desirable. There are domains where base-10 units are a good fit, and other domains where base-12 units are a good fit, and I don't see why we need to try to force one set of units to serve both.
If the nurse had been used to working in kilograms, she would have realised 25kg was a huge sack of coal / much bigger child / whatever. (She would have known that her own weight as a child was 40kg or whatever.) Or, if the country had been properly metric, the scale wouldn't have had the option of pounds.
(Hopefully, you see no reason to divide a child into 3, 4 or 6 equally massed parts.)
So... the metric system magically prevents data-entry errors? Or somehow you can't believe that there actually are common everyday tasks involving splitting something into halves, thirds, quarters, etc. and so feel a need to engage with a hyperbolic child-dissecting strawman instead?
You're really not doing a great job of presenting your case here.
Order of magnitude is defined as power of 10 precisely because we work with base 10 system. The same would stand for base 12, only the order of magnitude would be defined as a power of 12.
Yes, to me, as a SI person, argument for 12-based system looks ridiculous :) . Starting with "we don't have 12 digits" and then just saying there's no problem with division by 3 - you sure can handle the .3333... infinite tail in your head; by 4 - those .25 with properly adjusted comma - by 5, 6, 8, 9... It's all just a matter of habit.
It's almost as if the metric system was designed to be useful to ordinary people rather than to fit a nice-looking model of units.
Most people use a ruler or their hands to measure things, not dial calipers. And most people don't want to have to say "230 millimeters" as opposed to "23 centimeters" (or more realistically, 20 centimeters).
The old 12-base system is actually very useful once you put your calculator aside. Dividing 1 foot by 4 is much easier than dividing 30cm.
Also regarding your comment on mm vs cm, in my line of work (organ building [1]), we always talk in mm, just to prevent confusion, even for lengths of multiple meters).
> Dividing 1 foot by 4 is much easier than dividing 30cm.
That's of course very subjective. One has to remember that 1 foot is 12 inches, where in metrics one only remember once all prefixes and applies them to all units uniformly.
I think part of the point here is that you wouldn't have to say "230 millimeters" at all, because mm could be assumed. Therefore you'd simply be able to say "two thirty" in most contexts, and be clearly understood.
Saving syllables has to be balanced against the cost and difficulty of confusion. More units mean more confusion. So do inconsistent factors like 1/100.
I agree, though – the Google Video URL invalidation is a discrace. One would think that Google, who owns YouTube, should be able to create 301 redirects for all its own videos to their location on YouTube.
In everyday use using only the smaller unit implies a precision that usually isn't there.
Millimeters certainly has its place, but so do centimetres.