But "the" metric system, so called, functions entirely on the happy coincidence of macroscopic distance being divisible at human discretion, while the similar and simultaneous effort at decimalizing time foundered on the rocks of how long it actually takes Earth to revolve upon its axis and to circle the sun. Both efforts originate in the same silly hamartiac human desire to prescribe a shape to which reality must conform, and thus may come in for about equal gentle contumely on that score. Especially since, in another example of its designers' foolishly misplaced priorities, metric offers no units at the human scale. They may have prefigured the brutalists in this way.
Oh, and my "inch" is almost exactly 3 centimeters.
30cm is a "metric foot" (it's actually even closer to 1 light nanosecond which is kinda cool for thinking about distances at computer speeds)
250ml is a "metric cup"
It turns out that UK/US sizes are based on the length of a barley corn.
Quite why it isn’t just in centimetres is baffling. https://en.wikipedia.org/wiki/Shoe_size
Inches vs. centimeters? Baby stuff. Get on my level. :D
Another "close enough" value is the binary inch of 25.6 mm. Makes dealing with /32s and /64s oh so much easier.
with all the handy halvings in between + higher granularity of ml.. 'course I'm usually approximating on a gramme scale anyway.
But for larger stuff I round up to 250.
In everyday life, the metric system offers no big benefit, except for consistency for international standards and trade. But if you're doing anything engineering-related, your life is simpler if you don't need conversion factors to move between liters, meters, joules, watts, amperes, volts, ohms, and so on.
And FWIW, even to the extent that US engineers sometimes use inches and Fahrenheit, almost everything else they do is anchored to SI.
Inches are defined relative to the SI as well.
I do think it's funny all these folks insisting metric is so humanist seem never to have noticed which of their finger joints is an inch long. For me that's the second of the little finger, but I have large squarish peasant hands. As for the rest, treating a centimeter as 10/25 of an inch and vice versa seems to work well enough for measurements not requiring particular precision, or in other words anything I'd be comfortable doing without a caliper. Where's the trouble, really?
Should we go back to fathoms, furlongs, chains, drams and bushels?
This was settled a long time ago for the vast majority of the word.
Someone hasn't been to an apple orchard recently.
https://en.m.wikipedia.org/wiki/Yojana
https://en.m.wikipedia.org/wiki/History_of_measurement_syste...
And give me also the precise rational tenths-and-tens units, too, of course, for when we need accuracy more than soul. I work in thou all the time! All I've really been saying is, there's a place in the world for both ways of doing things. Why's everyone else so hellbent on having exactly one or the other?
People who grow up with metric instead notice which of their fingers is ~1 cm thick.
That's not entirely true. An American driving across the Canadian border on an interstate can automatically go from 55 to 100. That's almost twice as much.
What do you mean exactly? Any distance is divisible arbitrarily, it’s a continuous scale regardless of the unit system. We could define the metre as a foot (or rather, as the distance of some physical phenomenon close enough to a foot) and build a decimal system out of it, and it would have the same advantages as the metric system.
> while the similar and simultaneous effort at decimalizing time foundered on the rocks of how long it actually takes Earth to revolve upon its axis and to circle the sun
The fact that there are 60 seconds in an hour and 24 hours per day has absolutely nothing to do with how quickly the earth revolves. Your argument works (kinda) for the number of days in a year, that’s all.
> Both efforts originate in the same silly hamartiac human desire to prescribe a shape to which reality must conform
No, this is completely backwards. This effort originates from the idea that we should observe and understand nature, and build a rational society based on this understanding. The original metre was a fraction of the length of a meridian for a reason. They did not change the size of the Earth to conform to an arbitrary unit. Instead they came up with a unit that made sense to them, for both philosophical and practical reasons. They did the opposite of what you say.
> Especially since, in another example of its designers' foolishly misplaced priorities, metric offers no units at the human scale
The metre is about 2 thirds of an average human height (give or take, the average also changed with time). How is that not a human scale? If you want to go lower, to the scale of something you can hold, you have centimetres. If you want to go larger, to the scale of a distance you can walk, you have kilometres. And all conversions and comparisons spanning the 5 orders of magnitude relevant to our daily lives are seamless and make sense. What is your problem with this system?
> They may have prefigured the brutalists in this way
That is actually hilarious. The enlightenment philosophers and humanists who came up with the metric system are polar opposites of the brutalists. They rationalised our understanding of the world around us. They did not rebuild it square.
This is a distinction without a difference. Read James C. Scott, for pity's sake.
The long version is Seeing Like a State.
It just explains that many of these things got traction despite the resistance against them only because the state needed them.
In the case of measurement units, one was that the natural units varied in size and could be gamed, which is a big problem for fair tax collection.
How do you apply this to the imperial system?
I’ve heard this criticism before, but limited to temperature, with people saying they want more increments. I’m not sure why half a degree centigrade is so hateful.
It is all subjective. You like what you grew up with because it is familiar, not because it is better. You know by rote memorisation how much 100 feet is and what 75F feels like, the same way I know by rote memorisation how much 50 meters is and what 25C feels like.
In the meantime your grasp of nuance or lack thereof is no pressing concern of mine. And my entire thesis has been flagrantly subjective throughout, save where the minor matter of relevant history is involved. To attempt to answer this with the charge of subjectivity, as though to do so accomplished other than to recapitulate what has been obvious all day, seems not only pointless but risible.
A very common morning coffee table discussion (translated from Finnish):
"What's the weather like?" "Plus all day" "Kids, wear your Gore-Tex shoes to school"
For other measueres you may have a point but Celsius is defined around very useful points. Water is very important to us humans.
For 12 years of the revolutionary era, France did use decimal time. And the calendar and clocks were organized around a 10 day week and a 10 hour day. But those changes, coupled with the loss of Sunday worship, had other effects on the population.
Here’s an assessment of what was really meant and then lost by the elimination of Sunday:
“‘The elderly ladies took advantage of the long journey (to church) to exchange old stories with other old gossips … they met friends and relatives on the way, or when they reached the county town, whom they enjoyed seeing … there then followed a meal or perhaps a reciprocal invitation, which led to one relative or another….’ But if that was the way it was for the old ladies, what did Sunday mean to ‘young girls, whose blood throbbed with the sweetest desire of nature!’ We can well understand their impatience, ‘they waited for each other at the start of the road they shared,’ they danced.
“Now, however, when the Tenth Day came around, ‘the men were left to the devices they always had:’ the old men went to the tavern, and they bargained. The young men drank and, deprived of their ‘lovely village girls’, they quarrelled. As for the women, they had nothing left to do in village. The mothers were miserable in their little hamlets, the daughters too, and out of this came their need to gather together in crowds. If the need for recreation is necessary because of moral forces… there is absolutely no doubt that village girls find it very hard to bear privations which are likely to prolong their unmarried state: ‘in all regions the pleasure of love is the greatest pleasure.'”
– from The Revolution Against the Church, From Reason to the Supreme Being, by Michel Vovelle, pp 158-159.
However, all I ever read about this part of the revolution seems to indicate that people just didn't comply and went to church anyway on Sundays, and also didn't work that day. On that account, I feel likr your quote is kind of partisan. People wouldn't have been left lost and aimlessly drinking on their tenth day because of a lack of God, because they never quit going to church!
For example, the new state transformed Notre Dame and other Catholic churches into Temples of Reason, from which the new state religion, the Cult of Reason, would be celebrated. It didn't last long. Hard to create a new religion quickly. Maybe some echoes of recent history there.
https://en.wikipedia.org/wiki/Dechristianization_of_France_d...
Also, the months were given names by a Poet, and the days had minerals, vertues or plants instead of Saints. The calendar itself was pretty cool.
Honestly, if they had 5 weeks of 6 days each instead of the 3 weeks of 10 days, I'd even call it the perfect calendar.
60 can be split into 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 evenly for example
The other number that accomplishes this is 12: 2, 3, 4, 6 are all factors.
That's why 12 and 60 are so common for real life systems.
There's an argument for 12 for sure, but I still think having a power of 2 would be more beneficial than having the extra factors. 8 would give you the same number of integer factors as 10, plus all the benefits of being a power of 2.
It's 100,000 s/day as opposed to our current 86,400 s/day which is not far off.
Hours, however, were twice as long.
They had time pieces that displayed both together.
Or more to the point: since they had no use for milliseconds at that time, their milliseconds would have been 86.4% of standard milliseconds.
Consequently, the seconds-pendulum/metre relationship gets in the way as one might want to go to sub-millimetre length precision for parts made in different locations or at different times of the day or year. Precision copies of a prototype was more reliable in practice.
(In practice we mostly still generate precise and accurate physical artifacts and make copies from those, it's just that there one can in principle generate such an artifact just about anywhere and anywhen, calibrating with (for example) interferometry <https://iopscience.iop.org/book/edit/978-0-7503-1578-4/chapt...>)
Finally, the Trinity Clock <https://clock.trin.cam.ac.uk/main.php?menu_option=theory> is a neat examination of a well known pendulum clock that's surprisingly accurate (if not really precise; it's been reliably accurate to within two seconds over the course of a month for a very long time, but it's not going to give you a 10MHz sine-wave, and it's not a good for disciplining an oscillator which does so). Do check out the various plots.
Probably not by 15% which was the difference between the traditional second and the decimal second.
Many difficulties of using pendulum clocks (and in transporting any sort of chronometer) in real circumstances were also known before the revolution, with French clockmakers competing for the prize money in Britain's Longitude Act 1714 (13 Ann. c. 14) and the ancien regime's various prize offers in the 1740-1770s.
Prior to Harrison's marine chronometers, minimum longitude errors introduced in multi-degree changes of latitudes were indeed on the order of 10% across an oceanic part of a great circle or other more favourable route under cloudy conditions, and sufficient that in the early 18th century it was common for ships to navigate by dead reckoning along a single line of latitude -- a boon to pirates and other enemies, and also often adding many days to the travel time, in an effort to avoid the common problem (eg. HMS Centurion, 1741) of not knowing whether one was west or east of a landmark at a known latitude.
Prominent pre-revolutionary figures also disliked the idea of relying on chronometry for position/length/angle measurements generally -- most notably the excellent geometer and astronomer Pierre Bouguer (after whom the relevant <https://en.wikipedia.org/wiki/Bouguer_anomaly> is named) -- so it's not as if messing up a seconds-pendulum-based definition of a metre (and its consequences for the neat pole-to-equator 1/4 great circle length or mass of a cm^3 of water at STP, both of which now are just approximately round numbers) would have been universally outrageous.
And anyway surely one could consider a solution in which the half-period of the metre pendulum might not be exactly one decimal second. After all, at the time in practice one had to measure across many swings to obtain the effective length with reasonable precision. And Earth's rotation was known to be unstable (Richer, Newton, Maupertuis).
It made sense to keep some things like angle measurement and time as disruption was too great for very little practical benefit.
It's still used in some industries, where convenient.
Anyway, my non-metric preference is the radian unless I'm doing something manual like woodworking.
Honestly a brilliant marketing move by the French revolutionaries, just a few hundred years too early.
So imagine we get to Mars, establish a colony.
Mars has a day which is 24h 36m.
We could have all of our Martian colonists adhere to an Earth day of 24 hours, with sunrise and sunset drifting around the clock, or we could have them observe an extra 25th hour of the day that lasts 36 minutes.
Or, we could define the Martian day as 24 Martian hours of 60 Martian minutes of 61.5 seconds, with seconds the invariant interchange time between planets.
In turn, seconds stop being a unit of human timekeeping, and everyone just uses decimal minutes as the final subdivision.
[edit: corrected spelling of Quartidi]
It goes well with the metre because 1 km is 1/100 grad of latitude on earth. It mirrors the nautical mile in that 1 nautical mile is 1/60 degree (1 arcminute) of latitude on earth.
The grad is almost never used on a day to day basis, even in France. It is still used in specialized fields, like surveying.
Accidentally staying in "grad" mode when cycling through them (DEG -> RAD -> GRAD) was always a concern, especially since the difference between RAD and GRAD was easy to miss on the small LCD display (the indicator was via partial selection of the letters within a mask spelling "DEGRAD").
I still must have one of these digital wristwatches in some box in a closet, with a big button that starts a glorious monochrome LCD animation of "going online" (while of course the watch stayed as offline as any other Quartz watch).
The thought of a watch that could actually go online seemed ridiculously utopian back then, even when everybody was otherwise dreaming of cyberspace. But only a few weeks ago, in a moment of closure spanning a quarter of a century, I finally downloaded a "Swatch Internet Time" complication – from the Internet, directly onto my wristwatch.
That last one is what I have the biggest problem with. When you are doing anything with derived units, 'kilo' suddenly disappears.
Having decimal numbers, it’s the best solution. Otherwise you’re bound to make mistakes scaling things up or down.
> a liter is not a cubic meter
Well, it’s a dm^3, close enough ;) Conversion is trivial, 1 m^3 is 1000 l. A cubic metre is a bit large for everyday use, but it makes sense e.g. when measuring water consumption or larger volumes. The litre also had the advantage of being close to 2 pints, so it already made sense as a unit when it was introduced. Contrary to hours with 100s.
> 'kilogram' is the base unit, not 'gram'
Yeah, this one is perplexing. It’s an annoying inconsistency on an otherwise beautifully regular system.
Anyway, the point is the inconsistency in the system due to the kilogram being the base unit. So derived units are defined in terms of kilogram rather than gram. Say, the unit of force, Newton (N), is defined as kgm/s^2 and not gm/s^2). Or pressure, Pascal (Pa) which is N/m^2 which inherits N being defined in terms of the kilogram). And so on. Anyway, an annoying inconsistency maybe but doesn't really affect usage of the system once you get used to it.
Considering today we set the kilogram by fixing the Planck constant and deriving it from there, we can just divide each side of the definition by 1000 and use that as a base unit. Using kg as the base unit is completely arbitrary, as we can derive each unit of weight directly from the meter and the second, not from the base unit.
Changing it to ~1,000 times what it used to be, or giving it a new name, would force people to realign.
There's reason many people still prefer customary and imperial units, and it's not just bigotry and nationalism (even if they play a part in that preference).
As the name kilogram implies, gram is actually the unit here. But it was derived from the mass of a standard 1 kg chunk of metal that lives in a museum somewhere near Paris. This is the literal base unit of mass (at least historically, the definition has since been redefined using the Planck constant). A 1 gram chunk would have been tiny and be tedious to work with doing e.g. experiments with gravity.
They also have the original prototype meter in the form of a length of platinum-iridium alloy bar. And because the specific reference object for mass weighs 1kg instead of 1g, it means 1kg is the base unit in SI.
But quite obvious in the system of measurements, the gram is the logical unit here that you augment with prefixes and people commonly handle a lot of mass quantities that are in the order of grams rather than kg.
Derivations are simple. Simply apply powers of ten and their commonly used prefixes (kilo, milli, mega, micro etc.). The base unit is something physical that you can point at as the base unit. Or at least historically that was the intention.
There's also convenience. A 1l of water is about 1kg and a volume of 10x10x10cm. or 1 dm3. That's not accidental but intentional. It makes it easy to work with volumes and masses for people. Never mind that a liter of water isn't exactly a kg (because water purity, temperature, and a few other things).
Every formula using SI will expect mass in kg and you will be off a factor of 1000 if you use gram as the base unit. Same with derivative units like the newton which all use mass in kg for conversion.
This one isn't metric's fault to be fair. That's just what you get for inventing numbers before inventing math.
Makes me wonder what would have happened if 'French numbers' in base 12, 36 or 60 were introduced at the same time.
People got used to working in octal.or hexadecimal in the past for computers, doesn't seem like it would have been as big of a change as you think.
Irrelevant with a decimal system.
You're making an argument from familiarity. Yes, a 12-base system using fractions works very neatly in a small human-sized domain, but it disintegrates into complete uselessness outside that domain. That's why you get ridiculousness as things being 13/64th of an inch, or that there's 63360 inches in a mile. It's unworkable for very large distances and very small distances. With a metre and standard prefixes, you don't need any conversion factors, and you can represent any distance at any scale with a single unit.
Quick, what's 11/64" + 3/8"?
Quick, which weight is bigger: 0.6lbs or 10oz?
You can use hexadecimal numbers if you wish. "He's B6 cm tall."
I have found this, which seems neat: https://en.wikipedia.org/wiki/Bibi-binary
So he's ki-ba cm tall.
Such fractions are very rarely used, you're more likely to use mils (1/1000 of an inch) at that scale.
> or that there's 63360 inches in a mile.
Likewise, something that will probably never come up in your life. Inches/feet/yards and miles just remain separate things, never mixed.
> With a metre and standard prefixes, you don't need any conversion factors, and you can represent any distance at any scale with a single unit.
There's no intuition for them. Knowing what a meter is does not help with getting a feel for a kilometer. They might as well be as separate as feet and miles at that scale.
> Quick, what's 11/64" + 3/8"?
That one's not even hard, it's just a fraction. 35/64"
> Quick, which weight is bigger: 0.6lbs or 10oz?
Another arbitrary problem that will probably never come up, but to entertain you: since 0.5 lbs is 8oz, adding 1.6oz to that (another tenth of a lbs) results in 9.6oz. 10oz is bigger than 0.6 lbs. Not hard, but at least mildly harder than the first question.
None of this really had to do with the convenience highlighted initially: 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors. You can trivially divide things by 2, 3, 4, and 6 and keep with whole integer values. The same definitely cannot be said of metric.
How tall are you, maybe 70 inches? Or 5⅚ft?
178cm or 1.78m are so obviously equivalent it doesn't matter which is used.
> 12 inches in a foot and 3 feet in a yard make extremely convenient divisible factors.
This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful.
If you can choose, then you can just as easily start with 36cm. For example, European kitchens are designed around a 300mm base size.
Are you purposely doing this? That is obviously not what I meant. Nobody says "3 miles, 500 feet", they say "3.1 miles". Effectively two systems of distance measurement: inches/feet/yards (near scale), and miles (distant scale).
"5 feet 10 inches" is completely normal and fine.
> This requires you to start with 12 inches. If you're making a cupboard to fit in an 18¾" (476mm) space, it's no use, or is only randomly useful.
So you cut the cupboard to fit a 18¾" space, no big deal. Same as anything else, and just as random as 476mm.
Typically they come in (integer!) 12-inch, 24-inch, 36-inch, or 48-inch variants.
Fucking bushels, man.
Nobody cares how many inches are in a mile. It doesn’t matter.
> Quick, what's 11/64" + 3/8"?
35/64. Was that supposed to be hard? Common denominators are elementary school level arithmetic.
> Quick, which weight is bigger: 0.6lbs or 10oz?
10oz. 10/16 is 5/8 which is .625.
I agree that metric is easier for people who don’t have a grasp of fifth grade arithmetic.
Highly relevant if you are using T-squares, compasses, and dividing calipers.
So instead of buying 100cm planks, buy 120cm planks?
Which is why the imperial lovers all cry out about their fractions not "working" in metric. Yes, exactly, that is the point. They don't understand that they're reaching for a tool they shouldn't be reaching for, and then they blame the unit system for it.
Base 6 would've been the real deal.
The _other_ reason to use a measurement system is for doing _science_, and for that, having everything in base ten makes things _immensely_ easier, especially if you're working the math out by hand
Again, this is just familiarity. You think it's super neat that you can divide a cup of whatever by 2 or 3 or 4, but if I tell you to divide it by 5, you're gonna deflect and ask me "who does that?!?"
Imperial works neatly for a small domain of problems, and is useless outside that domain.
Metric is less neat in that small domain, but works equally well everywhere.
Firstly, we can divide a cup by 2, 3, and 4 in the kitchen because those are common measuring-cup sizes. Nobody is prevented from using a fractional size: if I divide a cup by 5 then I have 1/5th of a cup, nothing more and nothing less.
While 1/4th of a cup is 2 oz, and 1/3rd of a cup is 16 teaspoons, 1/5th of a cup doesn't divide evenly into a smaller unit and that's why "we don't do it", but there is nothing to stop the chef from using 9 teaspoons. [Or he can instinctively go up to 45mL on his graduated measuring cup, which almost always has both systems on it!] Teaspoons, tablespoons, ounces, cups, quarts and gallons are all inter-related multiples, and once you internalize it, you can convert like a boss.
While I'm sure it's lovely that metric measures divide by 2 and 5, that's all they divide by, so in terms of divisors, you've lost 3, 4, 6, 8...
So if it really is about dividing things usefully without resorting to fractions, then using a system that is nothing but multiples of 10 is a handicap, when we've had systems with lovely 12s and 16s with many different options for dividing them up.
But the metric people can simply chop up the measures even more finely and claim victory. For example, currency: it was in multiples of 16 or 8 which allowed for limited permutations. Decimalization chopped it into pennies, and we find 100 gradations in every pound sterling. All that did is make base-10 math easier for bean counters, and confuse people on the streets with a mystifying array of coinage. [Mental math indicates that it must increase the volume of coins per average transaction, as well.]
If a basic customary unit of length is an inch, many people can put two fingers together and estimate that on the human scale. But who can estimate or eyeball a millimeter?
Oh, and, have you ever found a nice British recipe in metric, shopped at your American grocery store, and prepared that in your American kitchen with your Fahrenheit range? You will eventually want to tip it all in the rubbish bin. Adam Ragusea suggests as much: https://youtu.be/TE8xg3d8dBg?si=SD8wLxD6ib6InLX4
"It's super easy if you're familiar with it!"
Yes, that is exactly the problem that you are unable to see.
If you'd grown with a metric system you could eyeball a centimeter with ease. Also comparing orders of magnitude different measures for estimation isn't fair, how precise would be your guess of a barleycorn?
And the division issue is almost trivial in my view; you can just take 120 cm or 12 gram quantity. You don't magically lose the ability to divide things by other than 10 or 5 or 2 when using metric. Its not like decimal fractions disappear in imperial systems either. The metric system is there for making it easy to scale things between orders of magnitude and have sane conversions between units.
Probably most people in the world. I can for sure do it. It's trivial if you grew up with the system.
EDIT: Yes, yes, SI defines the kg and then the g by reference to kg, but so what, notionally it's still the gram that's the base unit.
[0] https://en.wikipedia.org/wiki/Special:BookSources/978-0-349-...
I am angry that IKEA's localization does not allow Americans to view dimensions in metric site-wide. You can still see dimensions in metric but those only appear on the pictures of some items. The webpage still converts all textual measurements to Imperial. You can't sort and search using metric values. IKEA designs everything in metric, using nice, even, whole numbers. Please let me see those. Seeing them converted to the nearest 32nd of an inch feels like vandalism.
I’m not American and laughed at this.
Welcome to the other side. Also, here in New Zealand people seem to do everything in metric, except their height and the weight of their baby. Why?
People stop asking me to convert to Imperial pretty quick.
It took me an embarrassingly long amount of time to realize that there are four quarts in a gallon...
I have no such trouble with any SI unit. So with that, I will leave you with this!
"For of all sad words of tongue or pen, the saddest are these: 'The French were right again!'"
They were drilled into my brain when I was in primary school: 10, 100 and 1000.
5 us gallons is about 4 imperial gallons.
In practice the volume units are a much bigger problem. I have not hit anyone with the "cubic hand" yet...
[0] well, really, it uses metric with a redefined version of the old US customary system layered over it to prevent people from noticing, but...
Now, choosing wine gallons as our standard gallon, that might deserve a little blame.
In Sweden, 1 foot was around 28.96cm (in modern dimensions), whilst 1 foot in Amsterdam was 28.31cm.
On such differences (OK, and a few other contributing factors) a ship was sunk.
Imperial height is because 6 feet is the generic height of a "tall person" - we get so much of our sporting news from overseas and no one bothers to convert it.
Also, the US doesn't use imperial, dammit. It uses US customary units. They're related but different systems with radically different definitions on many units.
Change to the IKEA site of a different country (via what comes immediately after `ikea.com/`).
I guess they thought the mere sight of metric would offend the Americans. :)
Maybe the product ranges between the countries is close enough that the Canadian site is an alternative?
You've made an artificially hard example (Ikea doesn't separate units, it is just inches).
What's harder, a 24" object on a 160" wall, or a 59cm object on a 4m 3cm wall?
Or to compare like for like (rounding & unified units), a 24" object on a 160" wall vs a 60cm object on a 400cm wall? Seems the same.
Malicious compliance.
As a non-American: I love it. ;)
He died when I was 4 so it's not a first hand account, I'm not sure how much of it is true or what he really thought, but somehow it feels right.
The metric system is incredibly useful and practical (of course) but there's something rigid and unpleasant about it.
*Yes, it should be craftspeople, but that doesn't exactly sound like the same thing, and anyway all of them happen to be men.
For example, 1/4 being 0.3 in base 12 can make certain computations easier (just as a 1/3 being 0.4_12 would), but again, what's wrong with 1/4 and 1/3 respectively.
Of course, things like duodecimal and base-6 are interesting to use, but at this point the convention is base-10 and it probably won't change for a while. It's kinda like the \pi Vs \tau debate, where even with all the elegance and easier pedagogy brought by the use of \tau as the fundamental circle constant, the existing convention does matter, and probably matters a lot more in general than the better alternative.
Of course, this also applied to the SI units. It literally took a major historical revolution for these units to be a) defined and b) getting used over the old units.
You could do it that way if you didn't care at all for how people actually use the system or what they would prefer; however, it's just your decision that's arbitrary, not the actual choice of "best base for worldwide everyday use."
> 1/4 being 0.3 in base 12
And 5/6ths is 0.A in hexadecimal base 12. The choice of a base should imply a choice of alphabet. For something like base 12 you may actually want to rediscover or invent new numeral characters.
> but at this point the convention is base-10
Except for time. Which appears constantly in physical units.
> b) getting used over the old units.
Even then. No one will tell you the sun is "93 Gm" from Earth. It's always 93 million km. They haven't exactly gotten into the new system just yet. They've just swapped base units.
They are not: base 2 is minimal, but not practical for humans. You would not force base 2310 to anyone even though it has a nice set of divisors. So there is a sweet spot somewhere between 6 and 16.
Traditional body measurements (thumb, palm, span, foot, cubit) follow a Fibonacci-like progression where each unit ≈ φ times the previous one. If we consider the Egyptian cubit as π/6 meters (which matches historical measurements), here's a possible insight:
Draw a circle with diameter 1 meter. Remove 1/6 of the perimeter (π/6), subtract the diameter (1), and you get ≈1.618 – essentially φ. This geometric construction lets you build an entire measurement system using just a stick and basic geometry. Once you have any two consecutive units, you can generate the entire sequence by addition (palm + span = foot) or subtraction (span – palm = thumb's breadth).
In the pre-metric French system, a span was exactly 20cm. When you scale 0.2 × φ² you get π/6 with 4-digit precision. But here's what's interesting: using our geometric approximation φ ≈ 5π/6 – 1, the equation 0.2 × φ² = π/6 works out *exactly*. The "approximation error" in φ perfectly cancels out due to φ² = φ + 1, making 0.2 × (5π/6 - 1 + 1) = π/6.
Here's another "coincidence": Multiple 17th-century scientists (Mersenne, Huygens, Wilkins) proposed defining a universal unit as the length of a pendulum with a half-period of 1 second. Tito Livio Burattini, inspired by his travels in Egypt, formalized this in his "Misura Universale" (1675), measuring this pendulum length at 0.9939 meters - essentially our modern meter.
The "revolutionary" meter system was really just formalizing measurement relationships that builders had been using for millennia. The French didn't invent it - they just gave ancient φ-based measurements a decimal makeover.
First, the "conspiracy theory" that the meter is linked to Earth's dimensions and harmonizes with ancient measurement units through a shared reference actually predates the meter's definition. This idea was a thread of interest among the scientists who developed a universal measurement system – one that could be derived anywhere on the planet.
>One can well sense that it can only be through comparisons of measurements made in ancient times & in our days on monuments still existing, that I can determine to how many of our toises the Geometers of antiquity would have evaluated a degree of Meridian. Now I find, 1st. that the side of the base of the great pyramid of Egypt taken five hundred times; 2nd. that the cubit of the Nilometer taken two hundred thousand times; 3rd. that a stadium existing & measured at Laodicea in Asia Minor, by Mr. Smith, & taken five hundred times; I find, I say, that these three products are each of the same value, & that each in particular is precisely the same measure of a degree [of a Meridian], which has been determined by our modern Geometers.
Alexis-Jean-Pierre Paucton, Metrology, or Treatise on measures, weights and currencies, of the ancients and the moderns, 1780
more context: https://anonpaste.pw/v/71abb0f8-5a03-4cb5-879a-d4f44ad6d57c#...
original: https://gallica.bnf.fr/ark:/12148/bpt6k55491755/f126.item
>Newton was trying to uncover the unit of measurement used by those constructing the pyramids. He thought it was likely that the ancient Egyptians had been able to measure the Earth and that, by unlocking the cubit of the Great Pyramid, he too would be able to measure the circumference of the Earth.
https://www.theguardian.com/science/2020/dec/06/revealed-isa...
Having said that(-1 downvotes!), let's recap:
This is how we can construct a royal cubit from a circle of diameter = 1m:
φ = 2cos(π/5) lead us to this construction around a pentagon from which we can derive the "pige" or "quine" of cathedral builders (for now consider this is historically true) https://fr.wikipedia.org/wiki/Pige_(mesure)
What I mentioned earlier was that using a circle-based construction(diameter = 1m), one can derive a non-constructible approximation of φ, namely φ̃ = 5π/6 – 1, with the remarkable property that 0.2 × φ̃² = π/6, thanks to φ² = φ + 1.
But what’s truly elegant is that this process has a symmetric counterpart, where we approximate π using φ. This time, we begin with a constructible triangle, sometimes called the triangle of the builders (1, 2, √5), whose perimeter is:
t = (1 + 2 + √5)/10
φ = 5t – 1
φ = (5 × (3 + √5)/10) – 1 = (1 + √5)/2
0.2 × φ² = t again
- the constructible (t from the triangle),
- the transcendental (π/6 from the circle), and
- the algebraic (φ² = φ + 1)
For the historically conservative, arguments can be made that these considerations are pseudo-historical, that the "quine of cathedral builders" is an unsubstantiated myth. See the wikipedia link above for the "pige"
or this recent article: https://classiques-garnier.com/aedificare-2021-2-revue-inter...
this one too: http://compagnonsdudevoir.fr/?p=790
>This greatly saddens those who have built an entire "operative" narrative around this kind of knowledge supposedly passed down in secret among the compagnons of the Tour de France for centuries… and have made it their pedestal. The question of how "tradition" is constructed among the compagnons (and incidentally among the Freemasons) remains a taboo that absolutely needs to be broken — and not just for the sake of advancing historical knowledge.
Also this blog post traces the confabulation of the quine to Le Corbusier's Modulor system based on the golden ratio: https://blogruz.blogspot.com/2007/12/en-qui-quine.html
>Le Corbusier considered various sets of proportions, notably using a human height of 1.75 meters, before settling in 1947 on a single set based on a height of 1.83 meters. He chose this because the associated Modulor measurement of 226 cm corresponds to within less than a millimeter of 89 inches — 89 being a number in the Fibonacci sequence that provides some of the best approximations of the golden ratio.
>This system was intended to unite all nations around a universal standard, effectively casting aside the metric system, if not the decimal system entirely. We know how that turned out: the Modulor was essentially used for only one major creation — albeit a significant one — the Cité Radieuse in Marseille, completed in 1952, where all dimensions, down to the built-in furniture, are derived from the Modulor.
Makes you think... The fact we don't have documents isn't surprising given that the campagnons (or later freemasons) communicated practical (then mystical) knowledge esoterically for political reasons (See https://fr.wikipedia.org/wiki/Compagnonnage).
Nonetheless, the same motivations and the same quest for harmony (in the obsessive, symbolic sense) can be observed in Le Corbusier. As if the situation follows a geometric progression: in this sense, the "ancients" were as puzzled as we are by unexpected harmonies and actively sought them, and if you look at the historical sequence that lead to the definition of the meter, this is what you find.
Compare the length of a greek foot with a roman foot: 30.87cm vs 29.62cm. The ratio matches 24/25 with 3 nines of precision. 24•25•7 forms a pythagorean triangle. As if the definition of some measurement units were retrofitted to facilitate conversion. If this kind of behavior leads to the formation of a strange graph of quasi-conversions or numerical coincidences, then maybe we could explain the emergence of patterns such as the 5π/6 - 1 approximation of φ without needing to argue for (or against) someone's intention behind what appears as a design choice.
Alternatively the measures of the tools or geometric constructs that drive these conversions are idealized/approximated with a ratio, hence the delusion of the conspiracy theorists. But as I said, "ancients" had the same attitude, in particular with irrational numbers they wished to express as a ratio. Imagine the kind of problem the pseudo-phi <-> pseudo-π/6 complex I desribed above posed to people who where attempting to construct a straight line of length pi using only a compass and a straight-edge and establishing mathematics more rigorously. That's quite a nasty trap. Surely they found themselves in a mindstate that must not be that different from ours. Put in other words, the situation is hyperstionnal, and if we want to understand what is happening (whether this is an illusion or not) I think we should try to tackle this from a cognitive angle and model surprise explicitly.
Some more links:
https://www.messagedelanuitdestemps.org/les-principales-unit...
https://martouf.ch/2021/03/le-metre-une-matrice-universelle-...
So the speed of light was calculated using a previous definition of metre, and that magic number was used to upgrade its own definition? That's a tautology, sounds wrong to me.
What unit did they use to measure the length of the platinum bar?
They measured the distance between the Mediterranean Sea and the North Sea through Paris with platinum rulers measuring 2 Toise de Paris.
The toise was different in different parts of France, so it was specifically the Paris one they used, and the goal was to get rid of local variants of the same units with vague definitions like toise, point, line, inch, feet, mil(e) etc.
Once they had the distance in Toise de Paris and did some math they could define the circumference of the earth and define the meter at 1/40 000 000 of that.
That length was 443.44 Lignes de Paris where a ligne is 1/864 toise.
> The arc measurement of Delambre and Méchain was a geodetic survey carried out by Jean-Baptiste Delambre and Pierre Méchain in 1792–1798 to measure an arc section of the Paris meridian between Dunkirk and Barcelona. This arc measurement served as the basis for the original definition of the metre.
[1] https://en.wikipedia.org/wiki/Arc_measurement_of_Delambre_an...
skrebbel•8mo ago
That's actually impressively good accuracy for the time! Hats off to the astronomers.
hilbert42•8mo ago
I'd go further, I think their work was a remarkable feat for the late 1790s. That they achieved that accuracy given the primitive equipment of the day says much for their abilities and understanding.
Also at the time France was in turmoil, numbers of its scientists were victims of the French Revolution—Antoine Lavoisier, probably the greatest chemist of his time—was beheaded by guillotine in 1794, so the political environment was anything but stable.
Look back 225+ years ago: there was no electricity, no material science to speak of to make precision instrumentation—journal bearings on lathes, etc. couldn't be made with the accuracy of today, backlash would have been a constant worry. All instrumentation would have been crafted by hand.
And the old French pre-metric system of units was an imperial system similar to the British (France even had an inch that was similar in length to British Imperial unit). All instrumentation up to that point would have relied on the less precise standards of that old system.
Traveling was by horse and sailing ship, and so on. Surveying would have been difficult. There wasn't even the electric telegraph, only the crude optical Chappe telegraph, and even then it was only invented in the 1790s and wasn't fully implemented during the survey.
They did a truly excellent job without any of today's high tech infrastructure but they made up for all these limitations by being brilliant.
In today's modern world we often underestimate how inventive our forefathers were.
selkin•8mo ago
[0] about a modern pound, depending where you were. Toulouse’s livre was almost 1.3 modern pounds, for example.
[1] about 13853/27000 meter.
hilbert42•8mo ago
The issue came up in a round about way on HN several weeks ago and I should have been more careful here because I wasn't precise enough in my comment then. As I inferred in that post 'imperial' nomenclature is used rather loosely to refer to measurement and coinage/currency as they're often closely linked (in the sense that the 'Crown' once regulated both).
Pre-revolution French coinage used the same 1/12/20 number divisions as did the old English LSD and currencies in other parts of Europe, and that system is often referred to as 'imperial' coinage which likely goes back to Roman Imperial Coinage — but to confuse matters it was decimal.
One can't cover the long historical lineage here except to mention the sign for the Roman [decimal] denarius is 'd' which is also used for the LSD penny, 12 of which make the shilling (£=240d).
So for various reasons both 'old' physical measurement and 'old' coinage are often referred to as (I)imperial. To add to the confusion, modern currencies when converting from LSD/1/12/20 to metric and '1/12… measurement' are often done around the same time. Nomenclature overlaps.
For example, I'm in Australia and the 1966 conversion from LSD to metrified coinage occurred shortly before the metrication of measurement. It was all lumped together as Imperial (note u/c) to Metric (that's how the public perceived it). The Government staged both changeovers close enough so that the reeducation of the citizenry wasn't forgotten by the time the measurement program started.
For the record here's part of length in the old French measurement system:
"Pied du Roi (foot) ≈ 32.48 cm (Slightly longer than an English foot, which is about 30.48 cm.)
Pouce (inch) = 1/12 of a pied ≈ 2.707 cm
Ligne = 1/12 of a pouce ≈ 2.256 mm
Toise ≈ 1.949 metres (A toise is 6 pieds.) <...>"
The other units can be found on the same site: https://interessia.com/medieval-french-measurements/
selkin•8mo ago
Pre-metrification there wasn't a French unit system, like we think about those today, where a meter in Paris is the same meter used in Limoges. The actual length of a ligne changed from one region to the next. There was no country wide standard of exactly how much a certain unit is. Such standards were regional, at best, sometimes the regions being as small as a single village.
This is one of the most important results of the French resolution: a consistent system of measurements, regardless of the units chosen for it.
hilbert42•8mo ago
That's not to say local standards—let's call them weights and measures—weren't strictly adhered to and enforced. They were. There are many recorded instances from history to illustrate the point from, say, Archimedes' eureka moment to that of the obsessive and overzealous Issac Newton† when Warden of the Royal Mint was roaming around London checking for clipped coins and bringing the perpetrators to justice.
I'm fiercely pro-metric, and I've had much to say on the matter on HN over the years. So I'm used to the guns coming out from those in the US defending the Imperial system. I've good reason, at school I learned the Imperial system, CGS and MKS (it was before SI). In say physics learning to do things fluently in three different systems was a recipe for mistakes and confusion.
At the risk of repeating myself (link below), learning foot poundals, dynes and Newtons was bad enough but to have to convert between them in exams really was pretty rotten. The other reasons I've also menrioned, I've sat on standards committees and have writtern standards (nothing as illustrious as the ISO but it was for an intergovernmental organization nonetheless). Writing standards is often a tedious thankless task (I don't have to tell you people don't read them for the fun of it).
The link below is me getting worked up on HN over the metric system over a number of rolling posts, and it's not the first. I've referred to it here more for the sake of completeness than anything else. (I don't like rereading my old posts so I don't expect others to do so.)
https://news.ycombinator.com/context?id=43880977
† Newton. Not exactly weights and measures but a well documented case: https://coinsandhistoryfoundation.org/2021/04/30/sir-isaac-n...
saalweachter•8mo ago
They're similar but very different.
An Imperial pint is 568 ml; a US pint is 473.
An Imperial hundredweight is 112 lbs. A US hundredweight is 100.
hilbert42•8mo ago
Right. …And that's even worse—the US wasn't even satisfied with the well-established Imperial system and had to mess it up.
Everyone who takes an interest in measurement matters knows the story of the various aircraft that have run out of fuel because the US 'shortchanged' the gallon.
It'd be funny if it wasn't so serious, the last major incident was an Air Canada flight in the 80s.
The rest of the world shakes its head in disbelief.
maxerickson•8mo ago
Wrong size gallons is a terrible analysis of that incident.
The fueler reported that the density of jet fuel at the time was 1.77, which was in lb/L, since other Air Canada aircraft used lb. Pearson and Quintal both used the density of jet fuel in lb/L without converting to kg/L
In fact, Air Canada was in the process of standardizing their fleet on metric, but failed to carefully train their personnel and failed to establish procedures for accurately transmitting measurements.
saalweachter•8mo ago
The US did screw up a bit by standardizing on the wine gallon (231 cubic inches) instead of 222 cubic inches. This leads to a fluid ounce that is about 4% larger than an Imperial fluid ounce, and breaks the "a pint's a pound the whole world round" relationship (an Imperial fluid ounce of water weighs an ounce, and a pint of water being 16 fluid ounces is also a pound, which is 16 ounces of weight); in the US, a gallon of water now weighs "a little more" than 8 pounds.
Of course, in the UK, an Imperial gallon of water now weighs exactly 10 pounds. This is because in the 1820s -- which you will note is half a century after the US and UK parted ways -- the UK decided to add more factors of 10 and 7 into their units, and redefined the pint to be 20 fluid ounces instead of 16, and a gallon became 160 instead of 128.
The US and UK systems of measure diverged after 1776, and I'd argue the UK system changed more during standardization and re-standardization from the semi-formal system they shared before.
saalweachter•8mo ago
So they played around with various definitions like the 2-second pendulum, until they found one which worked and produced a single indisputable length.
(As opposed to picking something fundamental which was unrelated to previous units. Eg (not that they could have derived it at the time), the hydrogen line, the wavelength of the 1420MHz watering hole frequency, is human scale at about 21cm/8.3 inches, fundamental throughout the universe, and unrelated to previous units.)
ahazred8ta•8mo ago
batisteo•8mo ago