A base twelve number system is in general much nicer than base ten for basically every purpose... except backwards compatibility with existing tradition. It’s essentially impossible to switch our whole civilization over to base twelve at this point.
From what I understand, in places without a highly developed positional number system, fractions for units were generally developed in an ad-hoc way, for convenience, whereas in places with a more entrenched base ten tradition (especially in East Asia where the “abacus” was made of beads on a fixed frame instead of a collection of loose pebbles on a board) fractional units were more often tenths. The metric system takes that tendency to an extreme.
In general, the metric system is an example of building a system less well suited to particular use cases, but overall more cohesive and systematic. Since modern people are universally schooled in base ten positional arithmetic, the metric system becomes reasonably familiar and convenient.
I wonder how counting the segments of your remaining four fingers with your thumb fell out of style in favour of just counting your fingers.
You can do it with one hand, you can easily visualize dividing by two and four, you can count higher (144 if you use two hands), and it clearly looks way cooler.
“A traditional counting system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5.”
Sounds pretty speculative. Has there been historical research about the age of these “traditional counting systems”?
I’m skeptical that this is the origin of the Sumerian number system.
I feel like I missed out on something big, having never heard about this in my life. As big as if I'd never heard of this unused (for us) Fahrenheit system, except in this case base 12 is objectively superior.
I can count binary on my fingers and get much further than with decimal obviously, but it's not very practical or easy to learn. This makes fantastic sense and sounds almost as easy as decimal, the only difference being that it goes a few digits further.
Your argument would make sense if our system were actually base 12, or if we actually worked in halves or thirds of feet. Or if we ever had a reason to convert feet to eggs, or feet to hours. No, the base changes for every unit of measurement. Inches are divided into 16ths, feet into 12ths, yards, into thirds, miles into 1760ths. Inches are the worst as the base changes depending on how accurate you want to be, or if the fraction can be simplified, 3/8ths 7/16ths, 15/32nds. And of course all of the numbers used to count them are base 10.
The metric system uses base 10 all around. Not because we have 10 fingers, but because that's the system most widely used.
Edit: This made me think about the scale of things you're measuring. Roads are generally best measured in miles, not yards, feet, or inches. Some things are better measured in yards (like football fields or concrete (cubic yards)). Some things are best measured in feet, and some things in inches.
The avoirdupois system is human sized. The metric system is based on some inaccurate 18th century French calculation of the circumference of the earth, IIRC. Why would you care what your height is in relationship to the circumference of the earth? That never made sense to me.
Rarely does it matter if you can convert from one unit to the other. The only exception I can think of is when doubling or halving a recipe - going from teaspoons to tablespoons or liquid ounces can be a pain.
Maybe I have to cover a road with 11 inch long bricks and I need to know how many to buy?
The problem is that although perhaps certain units may be good for measuring certain things, the things you use those measurements for will frequently involve things that use different units.
To take your road example again, what if I want to find out how many revolutions it takes a wheel with a 4 foot circumference to travel a mile? What if I want to find out how many yard long strides it takes to go down a road?
The metric units are interoperable. That's their big advantage.
I used to think the US would go metric, but more recently I'm not sure. The biggest question is what is the advantage for every day purposes? For example, a foot is a more useful measurement than the meter. Fahrenheit is more useful than Celsius (I know Celisus is not technically metric). Pounds are more useful than kilos (a best it's a wash). I don't see why grams beat ounces.
I just don't see the value of metric for everyday purposes. For science, yes, but not for everyday measurement.
You're saying that foot is more useful than meter and so on but you don't explain why.
As an European who has always used the metric system and never encountered the customary system, I am perfectly fine with the metric system.
For instance, I am puzzled by the affirmation about Fahrenheit. Cooking very often uses water and Celsius having a scale based on that. I'm not sure that having a scale with the highest temperature based on the temperature of horse blood is much more relevant in every day life...
And so on for the other measurements...
Usefulness is not a relevant question for measurements, because we can always find real life objects to make these more visible (for instance, one long step is for me about 1 meter).
It makes absolutely no sense and is a large economic detriment. It leads to dramatic inefficiencies in communication and attempts to form common markets. Yet nobody dares to seriously confront ending the wildly inefficient system of using dozens of languages across Europe. Every excuse in the book is made as to why dozens of languages should be taught and maintained, it still rationally makes no sense. The point is, people do things out of custom, out of comfort, out of laziness, for all sorts of reasons that are not logical.
These languages have evolved during centuries and continue to evolve, whereas the metric system was built purposefully for simplicity.
The equivalent of the metric system would be something like Esperanto. English is as archaic and complicated as the customary system for measurement.
Mori Arinori, the first Japanese ambassador to the United States (and later, Minister of Education), proposed abolishing the Japanese language in favor of English.
> You're saying that foot is more useful than meter and so on but you don't explain why.
To divide a foot, you can divide by 12, 6, 3, 4, or 2 and get round numbers in inches. Round numbers can be easier to deal with than fractions or decimals.
Again this is a 'I'm personally used to this, so it must make sense to everyone' category of claim.
Here in AU we use metric widely. There are some older generation types that drop to imperial measurements for some things, particularly when talking about human height.
A foot is about 30cm (or 300mm) - so if you're talking about working in 1/12, 1/6, 1/3, 1/4, or 1/2 of something around that size, it's not something that blocks us for very long: the calculating of fractions of 30 (or 300) units.
Typically I work with metres (and subsets of) - 1000mm - which your 1/4 and 1/2 are, obviously, easy to apply and still get this enviable 'round number' that you speak of. 1/3 of a metre is 333mm (or close enough to) and it's rare that my pencil is sharp enough (or my care high enough) to denote a third of a millimetre. Similarly 1/6th (I don't recall ever needing to divide a length of anything into 1/6ths - perhaps I'm atypical).
I think the most compelling evidence against any claim that 'it's easier to work in base 12' (or similar) is that our machines, our houses, our infrastructure ... don't all fail to fit together, or fall apart, because their components were measured in metric.
When I say 'our' I mean the 95% of the world's population that isn't the USA.
Another non-american here. That doesn't help much.
How often do you try to describe something a sixth of the length of your foot? I'm trying to think of an example where it matters either way, but the only thing I can come up with is that there is only one measurement in metric distance: the meter. A centimeter is a hundredth of that, a milli- is a thousandth. In the American system I have to know the relation between inches, feet, miles and probably more (isn't yard also part of it? I don't even know).
2 inches is a very useful measure for a lot of things. I know that the middle digit on my little finger is an inch, and my foot is actually a foot long. I have no idea what 5mm looks like unless I convert it.
Also, don't forget that wonderful measure of area, the acre. I have no idea how big a hectare is, only that it's less than an acre. And there are 640 acres to a square mile, which is convenient if you grew up in farm country where there is a road pretty much every mile.
I won't bore you with gallons, chains, rods, furlongs, or hundredweights (American or Imperial).
2 inches is 5 cm, very practical too. My thumb is 1 cm wide, the span of my thumb and index is 15 cm. I can add all this up and end upbwith 137 cm, which is a meter and 37 centimeters. Never had to convert anything.
> a "2x4" board historically started out as a green, rough board actually 2 by 4 inches (51 mm × 102 mm). After drying and planing, it would be smaller, by a nonstandard amount. Today, a "2x4" board starts out as something smaller than 2 inches by 4 inches and not specified by standards, and after drying and planing is reliably 1½ by 3½ inches (38 mm × 89 mm).
And yet there are 3 feet to a yard, 16 ounces to a pound, 32 fluid ounces to a quart, and so on. Yes it would be lovely if our number system were base 12 but it isn't that's not going to change any time soon. Realistically we need to work with the number system we've got, and at the very least be consistent.e
And three teaspoons in a tablespoon. No wait, dammit, it's four teaspoons, or is it ½ a fluid ounce? But is that a US fluid ounce, an imperial fluid ounce, or whatever they use for US food labelling that's different again? What part of the world was this recipe written in?
Meanwhile one litre equals one litre (regional spelling variations notwithstanding).
As someone raised metric I never understood how one unit was more "useful" than the other. The fact of the matter is that you can calculate and reason with metric which is tricky in imperial units. Celsius also makes more sense to me as someone living in the alps ;)
I recently moved from a Fahrenheit-using country to one where the weather is typically given in Celsius.
The Fahrenheit temperatures map onto reasonably discrete "comfort ranges" for me. If it's going to be in the 50s, I might want a light jacket. I don't need one if it's in the 60s, and probably want short sleeves in the 70s (definitely in the 80s).
In contrast, if it's going to be in the "teens" in Celcius, the weather might require anything from a jacket to short sleeves.
Might have something to do with your moving from one to the other. Living in the Netherlands I know perfectly well what to wear when it's 11 or 18 degrees. To me it sounds like you're saying dollars are hard to use since you were used to yen. With dollars everything is 100 times closer together.
Yes... and so when it's going to be in the "teens" in centigrade, they tell you how many damn degrees they think it's going to be, rather than dicking you about by giving you a needlessly large range.
I bet the weather forecasters in America never tell you the temperature is going to be "positive, and in 2 digits".
Whatever next? Difficulty knowing how far away things are because miles are so large compared to km?
On the other hand, in Canada, they do say "temperatures will be in the teens this morning" all the time on the radio without elaborating further.
But...since you brought it up, I also find it's much easier to get in the appropriate lane when the exits (etc) are indicated one mile in advance (~1 minute driving time) than 1 km (~30 seconds). 2km warning would be fine too, but since it's not a round number, they tend not to be signed that way....
While I agree that it probably matters most whatever you were brought up with, Fahrenheit is a smaller unit of measure, and, as a result, more precise. Metric is more logical in every other case I can think of, but most people in the US can think in 'standard' measurements. It's really cultural, for the most part.
Fahrenheit does have smaller units, but nobody uses them. When was the last time you heard somebody distinguish between 72 and 73 degrees Fahrenheit? People use "low 70s", "mid 70s", "high 70s". With that in mind, I would say that the size of a single degree in Fahrenheit is too small of a unit.
> While I agree that it probably matters most whatever you
> were brought up with, Fahrenheit is a smaller unit of measure,
> and, as a result, more precise.
Personally I've never needed or cared to know the outside temperature finer than a Celsius degree.
If you ever did have a need for something 'more precise', please remember:
> Fahrenheit is a smaller unit of measure, and, as a result, more precise
This one always comes up and it's the worst argument to me. Just going from the shade, or out from cover of wind and you'll get more than a degrees temperature difference. What use is that extra precision in daily use? And in any field that actually needs the extra precision (science, engineering), you're not going to shy away from using decimals.
I guess it mostly depends on how you grew up. Coming from the metric system I prefer it a lot because it's much more consistent and easier to convert between units (e.g. mg->g->kg). Even after moving to California I'm still confused by the variety of different units. For example if you look at recipes there are cups, ounces, pounds, teaspoons and none of them is easy to convert.
In Switzerland I used to fly glider planes. Unlike motored airplanes glider planes use the metric system. So heights are measured in meters and speed in km/h. It helps a lot to calculate how far or fast the plane will go compared to feet and miles.
The huge advantage of the metric system is not in its different choice of 1 unit of length, 1 unit of mass, etc. but in the relationships between all units. This is very useful to everyone, even to non-scientists. Illustration: https://i.imgur.com/iDOzAa5.jpg
Actually, unit conversion being complicated, makes a lot of problems complicated to calculate and so makes science appear difficult which only makes people not want to do science.
Using the American customary system of measurements is like using Roman numerals - everything is possible, but harder, so science and engineering progress slower.
That depends entirely on your use case. If your use is easy division that may include denominators of multiples of 3, or 4, then the imperial measurements might be more useful. If your use case is being able to easily scale numbers and keep a handle in your mind of how they relate, then metric is more useful.
How many miles is 154,631 feet? How many kilometers is 724,642 meters?
How many inches in one sixth of a foot? How many centimeters in one sixth of a meter? (in case you don't think there's much gain in the imperial unit, try using 16 and 2/3 centimeters in your calculations,and it quickly becomes more cumbersome)
As someone that has used both systems, I have to say metric is much easier to use and more precise.
Typical daily usage includes cooking, ex "if I need 60g of sugar for 2l of water, how much sugar for half a liter?" Is really easy (60/4=15g), versus "if I need 2oz for 1 quart of water, how much sugar for 8floz?" Is annoying and frankly rather ridiculous: first you have to know that 1qrt=32floz (metric is of course always multiples of 10), then you get a result ½ ounce, that you can't convert to anything else and you're now dealing with fractions...
>I just don't see the value of metric for everyday purposes.
There is a value in saving lives by adopting a universal standard. I remember watching an air crash investigation episode about this confusion causing a fatal crash
I'm guessing it's because you didn't back up your arguments. Why is a foot more useful than a meter? Why is Fahrenheit is more useful than Celsius? Why are pounds more useful than kilos?
So let me kick it back to you: What's your argument?
Metric and imperial are both pretty arbitrary; one strong argument for metric is just to get an international standard.
> one strong argument for metric is just to get an international standard.
And that they are easy to convert among each other (simply powers of 10). And that there is a complete system of units (SI) that is based on it (what is the imperial unit of force, power, voltage, current,...? etc.).
When it comes to grocery shopping the US system is bad.
Take for example ground beef: There's a few brands, both with the same labels: grass fed, no hormones .etc etc.
What's the most important then? The price tag. But each unit of ground beef isn't always the same size: 1.08 lbs, or 1.23 lbs ,etc.
Fortunately vendors are required to put a price PER unit of weight.
In metric system countries it would be : Brand A is 7€/kg, Brand B is 5€/kg , (and for the sake of the argument, Brand C is 0.65c per gram, but usually it's always per kg.)
Which one is the cheapest? Easy answer. Brand B < Brand C < Brand A
In the US? One is $5/lbs , the other is 35c per Oz. Which one is the cheapest? In this base 10 world, It's a bit tricky to make base 16 conversion by head
Same with liquids: fl oz, gal, etc.
with the Metric system? €/cl , €/l , they could even write €/ml, multiplying/dividing by 10, 100, or 1000 doesn't' requires a calculator.
Even if you only have the price per unit, for the same brand: 1 bottle of 2L is $3, 6 bottle of 500ml is $3, here buying the 6 pack is better. (Usually the bigger the bottle, the cheaper per unit of volume, but not always, especially in the US)
In the US? 1 gallon is $3, but a 6 pack of 16 fl oz is $3, which one is the cheapest?
6*16 = 96. but 1 gallon is 128 floz, so the 6 pack is 75% of a gallon, so the gallon is cheaper here
> For example, a foot is a more useful measurement than the meter.
Why? 1m is about the length of one step (heel to heel)
> Fahrenheit is more useful than Celsius
Why? Freezing water has 0°C, boiling water 100°C.
> Pounds are more useful than kilos
By a numeric coincidence (gravity of earth is nearly 10 m/s^2) 1 kg has a weight of about 10 N. This makes it really easy when going climbing to compute what mass you can put on some part of the safety chain.
Generally: It is a pain in the ass to convert these non-metric units among one another. For one example 1 P̸ = 12p, 1 in = 6 P̸, 1 ft=12 in, 1 yd = 3ft, 1 mi = 1760 yd. Sounds very simple and logical to me. :-(
Alone this fact is for me argument enough for metric units.
Do you actually need to convert units a lot in your daily life? Or compare things to the freezing/boiling point of water?
For me, the major advantage of the imperial units is that they're all approximately human-scale. My foot is about a foot, my stride is about a yard, and it's surprising if I encounter weather outside 0-100F. A pint is a big drink; a cup is small one.
I'm a scientist, and all this goes out the window in the lab, of course. Even there though, a lot of the useful conversions do need some arbitrary constant (e.g. density, molarity) and the SI prefixes are not incredibly useful. I've literally never heard anyone measure something in deci/decameters. In practice, we tend to pick a unit that's approximately the right size and and stick with it--tiny things might be between 0.05µm and 2,500 µm, for example.
I wholeheartedly agree. I'm an expat, and it bothers me to no end when I encounter thermostats which can only be adjusted in whole degrees Celsius - I end up being either too cold or too hot.
Given its origins in Revolutionary France, the metric system is quite literally a communist plot.
To ease calculations scientists tend to work around 10^(3*n) kind of numbers. This is why you seldom see hecto- or deca- units, rather than kilo, mega, milli, micro, nano, etc.
"I just don't see the value of metric for everyday purposes. For science, yes, but not for everyday measurement."
Two systems of measurement for essentially the exact same things just complicates matters. Suggesting that your system is better (I'm (perhaps wrongly) assuming that it's because you learned one first) and more 'instinctive' or 'natural' is pretty poor argument.
Are there any truly objective reasons you can argue one system (in your case, imperial/customary) is actually better?
Yes, some units have slightly nicer divisible quantities, but that's easily outweighed by the crazy inconsistencies between different units of a type (stones, pounds and ounces, for example).
Or inches, feet, yards & miles. There's no obvious relation whatsoever, and while there maybe be historical justifications for their values, they're not exactly arithmetically convenient.
Or the horrible mess that happens when you get into fractional quantities. How much is 17/32" + 1/4"? Sure, I can work it out, but just adding some decimals together is a darn sight easier[1]. That can be done in either system, but imperial/customary definitely seems to favour it IME.
Ultimately, I think people are going to have a preference for whichever they learn first, and intuitively approximate.
For that reason, making a distinction between 'those fancy-pants science units' and 'good ol' everyday patriotic inches' strikes me as a foolish compromise that benefits neither.
I could probably object to other things in your original post as well, but maybe I'm just projecting my childhood biases the other way.
[1] for me, anyway. I've grown up with a bastard hybrid knowledge of mostly metric/SI, but enough exposure to imperial that I can intuit some, but not all of the conversions. Temperature is probably my weakest. I know from memory that 37oC ~98F, and that conversion is 5/8x + 32 or something along those lines. But to see '250F' and set my oven correctly, I have to think a bit. Or to guess if a temperature is below freezing or not.
Having a hobbyist/armchair interest in machining & woodworking, the mental mode-switching when reading/watching videos by Americans vs everyone else is jarring.
"There are two types of countries in the world; those who have some sort of national paid law for new parent(s), and those that have been to the Moon (1)"
(1) and Lesotho. I don't think any country starting with an "L" has gotten to the moon.
"There are two types of countries in the world: those that use the metric system and those that have not ratified the Convention on the Rights of the Child (2)"
(2) And Somalia.
For some more cherry-picking: "Only Communist countries have managed to put rovers on the Moon or land probes on Venus."
Did you read the article? It specifically cited a costly NASA error due to mixing measurement systems:
The use of two different systems was the root cause
in the loss of the $125 million Mars Climate Orbiter.
NASA specified metric units in the contract. NASA and
other organizations worked in metric units, but one
subcontractor, Lockheed Martin, provided thruster
performance data to the team in pound force seconds
instead of newton seconds. The spacecraft was intended
to orbit Mars at about 150 kilometers altitude, but
the incorrect data meant that it probably descended
instead to about 57 kilometers, burning up in the thin
Martian atmosphere.
One fascinating thing I discovered a few years ago: Lego Technic is a combination of both metric and imperial units. Hole centers are 8mm apart from each other. But hole diameters are 4.85mm, perfectly sized for a 10-32 (size based on inches) screw.
Ask anyone form the UK their height, weight, or for a glass of beer. Feet/inches, stone (America never really adopted that) and some scale of pint would be the reply.
Yet ask them to do a calculation in these measurements would result in looks of scorn, "THAT'S INSANE' in the words of Moss from IT Crowd.
Because we calculate in metric, and that's because all textbooks post late 70s were in metric and 'new pence' [1].
Fahrenheit is largely dead as a common measurement in day-to-day conversation, pint the least likely to disappear, as it's treated as a countable unit, nor an interval scale; on that matter, probably stone too.
The EU takes pride in multilingualism. Bilingualism is said to be a core part of Canadian identity. Children are encouraged to learn multiple languages. Yet for some reason diversity in measurement systems is bad?
The US uses two measurement systems. As a practical matter, those who need to use metric do so. Many sporting events are metric. Much commerce is metric. Food labels are metric.
I have never seen why this is a problem. Most other folks don't either, which is why we haven't chosen to do stupid stuff like run around and change road signs or insist that people use particular measurements.
Oh, and the story about how the spacecraft crashed does not make a convincing case. Any aerospace contractor worth its salt would check all its units of measure. Being entirely metric does nothing to alleviate this burden. Reporting a measure in centimeters rather than meters will get you the same problem. Units of measure must be labeled, period.
In terms of first order importance, efficiency in language is even more important than efficiency in measurement systems, it's fascinating how that's ignored (as you noted, it's artificially excused away using culture or nationalism). The EU absorbs a massive cost by maintaining dozens of unnecessary languages. In fact it's so bad that a full 1/2 of all the people in the EU are unable to communicate with each other properly: they speak no common language. It's one of the more obvious weaknesses in their economic competitiveness.
What is your point? Consider two color models. One can be "more expressive", that is, have a large gamut, than the second, but be unable to reproduce all of the colors in the second.
Or, certainly Lisp is "more expressive" than APL, and both are Turning computable and thus equivalent, but some trivial constructs in APL require much more Lisp to express.
How do you express Japanese honorific speech in English?
Rather than reiterating a lot of what I've said previously, I'm reposting my greatest hits from previous discussions on this topic: hope that is okay.
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The US rarely uses metric in it's popular culture. Weather reports are in Fahrenheit, movies almost always use miles and pounds. By any measure of cultural output that you export that I've seen (and Australia is a huge consumer of your popular culture) you do not use metric.
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In Australia we started metrication in 1971[1] with 1974 being the effective tipping point when all road signs were changed.
Being born in the early 70's, I have a rough understanding of imperial measurement units. I can roughly understand if something is a few inches or a few feet, but can never remember how many inches in a foot, and have no concept of relation between feet and miles. Miles I understand as a bit over 1.5kms. The only length measurements we tend to still give in imperial is a person's height in feet and inches. The concept that over six foot is tall, and under five is getting to be short (for men at least) has such utility that it's stuck. Official documents will use metric though, usually centimetres.
Weight is similar. Kilograms rule, except when talking about the weight of newborns which will still often be given in pounds and ounces informally. But give me anything else in pounds and I have no idea (very frustrating when that happens in movies.)
Similarly Celsius rules. I know 100°F is a hot day, but wont boil an egg, and 0°F is colder than a mother-in-law's kiss, but those are rough approximations, and anything between those two I have to convert.
Gallons is a foreign language.
However all the colloquialisms such as giving an inch and taking a mile are still common.
And yet somehow despite all this, the world continued to spin.
Just an interesting aside, measurements in construction are almost always given in either metres or millimetres, never centimetres (at least in Australia.)
So that would be 914.4mm and 1219.2mm respectively (or 1.2192m I guess).
The wisdom of this was explained to me by my builder father that metres and millimetres are orders of magnitude far enough apart that you can usually figure out which is which without too much difficulty in a specification even if they are not annotated properly. Centimetres fall close enough to in between that it can be confusing. Plus only using two standard units of measure (one for small stuff, another for large) is less potential confusion then using three.
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Now if we could only stop anybody using m/d/y date formats...
12 inches, dozen eggs, 24 hours, 360 degree circle is 30 sets of 12...
If it weren't for the human justification of having 10 fingers on our hands, the base 10 metric system may not have gained traction at all.