At first sight, this may seem like a non-issue. It seems self-evident that everybody and everything experiences the same time, and it was taken for granted until a little over a century ago. But since then, an abundance of counterevidence has been discovered, though it is only observable with the technology that was developed over this time.

GPS and Relativity - a consequence of general relativity is that Global Positioning System satellites are observed from the ground have faster time relative to the ground by 38 microseconds per day. To keep them in sync with their users, they are run slow by that amount. From being high above the Earth's surface, at much greater gravitational potential, they run 45 mcsec/day fast, and from traveling around the Earth in their orbits, 7 mcsec/day slow, thus the 38 mcsec/day fast.

These "time dilation" effects cause a problem for defining time standards. Here is a history of them.

The first time standard, if it can be called that, was true solar time, time relative to some landmark event like sunrise, noon, sunset, or midnight. Solar time - Wikipedia

But that had some problems. The Sun's apparent orbit plane is tilted to the Earth's equator, and the Sun's apparent orbit has a measurable eccentricity. These effects produce a discrepancy between physical time and true solar time, the Equation of time - Wikipedia For doing comparisons, physical time is represented by a "mean Sun" that moves at a constant rate on the celestial equator, distinct from the true Sun. Claudius Ptolemy wrote about this discrepancy some 1900 years ago in his classic book on astronomy, the Almagest.

By the middle of the 19th cy., trains were carrying people fast enough and far enough to make changing one's clocks very annoying. Railroad companies first used their own time standards, then agreed to various time zones of Standard time - Wikipedia Late in the 19th cy., this was made worldwide as Universal Time - Wikipedia (UT) with all other times referred to it.

By the mid 20th cy., astronomers discovered that other celestial bodies go tiny bits fast and slow, and do so in synchrony, and they decided that it was from the Earth spinning tiny bits slow and fast. So in 1952, they decided to instead use the Earth's orbit as a time reference: Ephemeris time - Wikipedia (ET)

When cesium atomic clocks became good enough, astronomers used these clocks to implement International Atomic Time - Wikipedia (TAI, from its French initials) TAI is a realization of Terrestrial Time - Wikipedia originally "Terrestrial Dynamical Time". UT is kept in sync with TAI by inserting leap seconds every now and then.

But these clocks turned out to have a problem. Clocks at higher altitudes ticked a tiny bit faster than those at lower altitudes, in agreement with gravitational-potential time dilation. So in 1977, TAI was officially referred to the geoid, the surface of mean sea level.

In 1991, Geocentric Coordinate Time - Wikipedia (TCG) was defined. It is essentially the time at infinity relative to the Earth. That makes it fast by 22 milliseconds per year.

Coordinate time? In relativity (special and general), every object has its own internal "proper time", but relating different objects' proper times to each other can be a nontrivial task. One defines slices of space-time and gives each one its own value of some coordinate time. One can then relate each object's proper time to this coordinate time, and then different objects' proper times to each other.

• Pre-relativity: a single universal coordinate time with all proper times equal to it.
• Special relativity (flat space-time): coordinate times are for sets of parallel hypersurfaces.
• General relativity (curved space-time): coordinate times are for sets of arbitrary stacked hypersurfaces.

Considering the rest of the Solar System, in 1976, Barycentric Dynamical Time - Wikipedia (TDB) was defined as the successor of Ephemeris Time, and improved in 1991 as Barycentric Coordinate Time - Wikipedia (TCB) Barycentric? That refers to the Solar System's barycenter, though this time standard is the time at infinity relative to the Solar System. That makes it fast by 490 milliseconds per year relative to the Earth's surface.

The Earth's time dilation varies because of its orbit eccentricity. It alternately orbits a little bit closer and faster, and a little bit farther and slower, and pulsars are precise enough clocks to make the resulting variations observable: Does the observed period of a pulsar change with the time of year? - Astronomy Stack Exchange This is also observed in pulsars in close binary systems with eccentric orbits.

One can go further, across our Galaxy, and from gravitational time dilation, time would be fast by some 15 seconds per year near the rim and slow by some 30 seconds per year near the bulge (very rough estimates).

Threepences, bobs, half-crowns, etc.

I can’t believe it wasn’t even that long ago that much of the world was using this system all because of the Brits. It could have very well continued into today if USD didn’t take over.

​

Hello, I am an American, however, ethnically I am not so this isn’t a matter of nationality or anything like that. I just wanted to say that I personally do not like the metric system. I don’t disagree with it, nor argue against it. I believe that it is indeed an accurate and more superior form of measurement. But there’s nothing that boils my blood more than seeing a grown man being measured at like 15 kilograms (this is not an accurate measurement I know that). Point is, I don’t like it. I like science, I like to compare the weight of things and height of things. But for some reason, the metric system seems so unsatisfying to me. Is there anything that can make the metric system more enjoyable? I would love any suggestion. I’m not saying the American system is objectively better, but it’s just easier to compare the weight of things in my head. So is there like a fun way of doing this for the metric system. I know this is very specific, but any suggestions would help.

Thank you in advance for any suggestions.

I read some articles about the current scientific studies on chronometry which have been exploring the use of strontium for atomic clocks. How does it compare though to the current definition of the SI second based on the caesium-133 atom? Is there a prospect for the SI second be redefined in terms of strontium? The 2019 redefinition would've been the perfect time to have done along with the other base units.

Any good suggestions?

“The measure of all things” is a good story of the difficulty measuring the earth in the middle of a civil war to determine the length of the metre.

Any other recommendations?

The story goes back some 5,000 years to Sumer, in what's now southeastern Iraq.

• [2207.12102] Sexagesimal Calculations in Ancient Sumer
• Sexagesimal - Wikipedia
• Three thousand years of sexagesimal numbers in Mesopotamian mathematical texts | Archive for History of Exact Sciences
• Sumerian and Akkadian Numerals

Sumerian number words:

• 1: as, dis, 2: min, 3: es, 4: limmu, 5: ta, 6: aas (< ia+as), 7: imin (<ia+min), 8: ussu, 9: ilimmu (<ia+limmu)
• 10: u, 20: nis, 30: usu, 40: nimin (<nis+min), 50: ninnu (<nimin+u)
• 60: ges, 60^2: sar, 60^3: sargal ("big sar") or sarges ("60 sar"), 60^4: sargal sunutagga ("big sar that is not touched").

They wrote numbers from 1 to 59 by repeats of a ones symbol and a tens symbol. Beyond that, they used a sexagesimal place system, though with zero not often indicated. I note in passing that Egyptians used a similar system, but with repeats of symbols for powers of ten.

Sumer was conquered by Akkadian empire builders in the 24th century BCE. Akkadian number words:

• 1: isten, 2: sina, 3: salas, 4: erbe, 5: hamis, 6: sedis, 7: sebe, 8: samane, 9: tise
• 10: eser, 100: me'at, 1000: limum

The Akkadians used Sumerian as a liturgical and highbrow language, much like Latin in Europe and Sanskrit in India, and they also used sexagesimal numerals, even though their language had decimal numerals (base 10). They used sexagesimal numerals in Babylonian mathematics - Wikipedia and Babylonian astronomy - Wikipedia and indirectly in Babylonian astrology - Wikipedia all the way to the time of the last cuneiform writings, around 100 CE.

But in 331 BCE, Babylon was conquered by Alexander the Great, opening up to his fellow Greeks the world of Mesopotamian mathematics, astronomy, and astrology. Along with them came sexagesimal numerals, even though the Greek language, like the Akkadian one, uses decimal numerals.

Among the legacies of Greek mathematics and astronomy was the division of the day into 24 hours, originally 12 hours of daytime and 12 hours of nighttime, and the division of the circle into 360 degrees.

Claudius Ptolemy (~100 CE to ~170 CE) wrote a compendium of astronomy, his Almagest - Wikipedia That book sexagesimal numerals a lot: The Almagest – Book I: Sexagesimal & Ptolemy’s Math – Following Kepler He also wrote a book about astrology, Tetrabiblos - Wikipedia Both books were classic works for centuries.

Medieval astronomers in the Islamic world also used sexagesimal numerals, despite the Arabic language, which they wrote in, having decimal numerals. Late-medieval and some early-modern European astronomers also did that, despite Latin having decimal numerals.

Minutes and seconds of time and angle are survivals of this heavy use of sexagesimal numerals in astronomy:

1. pars minûta prîma - Latin: first very small part - minute
2. pars minûta secunda - Latin: second very small part - second

Why did sexagesimal last so long? I think that it was because of the abundance of previous work in sexagesimal, including mathematical tables. Before recent centuries, all calculations had to be done by hand, and using precalculated tables saved a *lot* of work. It did take a lot of work to calculate those tables, but once one has done so, one can refer to those tables instead of repeating that work. Even at the present day, it can be helpful to precalculate tables of computationally-expensive quantities.

• Mathematical table - Wikipedia
• Ephemeris - Wikipedia - table of calculated positions of celestial bodies over time
• Timeline of computing hardware before 1950 - Wikipedia - that work also has 1950-1989, then each decade

​

4 tablespoons of butter is 50 grams

A while back I converted a family recipe from imperial to metric. I was surprised at how challenging it was to convert ingredient amounts from cups and tablespoons into grams. The problem is ingredient density. 1 cup of honey weighs significantly more than 1 cup of marshmallows. Even 1 cup of compact (pressed) brown sugar weighs a lot more than 1 cup of loose brown sugar.

This variation in ingredient density is why recipes in grams are more consistent and reliable than typical imperial recipes. Imperial recipes suffer additional inconsistencies due to a cup having different volumes in different locations around the world. And that doesn’t even touch on the hassle of the extra clean up required when measuring ingredients by volume.

Metric recipes are the way to go.

Sadly, the existing online conversion calculators are ridiculously cumbersome to use. I’m building a conversion calculator that will be easy to use, but I can’t find the recipe ingredient density data to feed into the calculator.

Anyone know where I can obtain a list of densities for common recipe ingredients?

Many people's (natural) languages have words for numbers built on words for powers of ten, like English one, ten, hundred, thousand. Did different people separately invent those words? Did they copy those words off of each other? ("borrowing") Did they inherit those words from some common ancestor? Using the methods of historical linguistics, we find abundant evidence of all three processes.

Borrowing is very common, especially for words for relatively large numbers. English "million" is borrowed from Old French, in turn from late medieval Italian milione from mille "thousand" -one (augmentative: big version of something): "big thousand". Looking in eastern Asia, Korean, Japanese, and Vietnamese have Chinese borrowings alongside their native words, and in Thai, the Chinese borrowings displaced most of the native words.

Inheritance is also common, though one has to be careful in cases of multiple descendant forms. Did the ancestor lack a word with the descendants having some invented words? Did the ancestor have a word, with that word getting replaced in many of the descendants? For instance, in the Indo-European language family, 2 to 10, and 100, are very well-preserved, but 1, 11, 20, and 1000 are less stable.

For several families, 1, 10, 100, 1000:

• Indo-European: *oynos, *dekm ("two hands"?), *kmtom ("big ten"), *gheslom ("heap")
• Turkic: *bîr, *ôn, *yûr', *bïng
• Sino-Tibetan: */it ~ *kat ~ *tjak ~ *gt(jik, *gip ~ ts(j)i(j) ~ *tsjaj , *brgja, *stawng
• Dravidian: *ontu, *paHtu, *nûttu
• Semitic: *\asst- ~ */ahhad-, *\asar-, *mi/at-, */alp- ("herd")
• Egyptian: *wi\jVv, *mûcaw, *shit, *khar
• Austronesian: *asa ~ *esa ~ *isa, *puluq, *RaCus
  • Malayo-Polynesian: *asa ~ *esa ~ *isa, *puluq, *Ratus, *Ribu

But there are some high counters who have used other bases, like Central Americans, with base 20, and Sumerians, with base 60. Nevertheless, most high counters have used base 10.

Why base 10? It does not have as many divisors as 12 or 20 or 60: 10 = 2*5, 12 = 2*2*3, 20 = 2*2*5, 60 = 2*2*3*5.

We get a clue by considering that many languages do not have many words for numbers, some of them going up only to 2 or 3 or 4 or 5. That is common in languages of warm-climate hunter-gatherers, people who do not have much that they have to count. But when they want to go further, they count on their fingers and toes and other body parts.

Counting on fingers easily explains base 10, because we have 10 fingers. Counting on fingers and toes explains base 20, because we have 20 of those appendages.

But when one starts farming or herding or storing food, one has a lot that one has to count, so one ends up inventing words for high numbers. That is what people in different places did, doing so independently, but carrying over counting on their fingers.

Sources:

• Wiktionary, the free dictionary - has many translations and etymologies; was my main source
• Austronesian Comparative Dictionary - PAN Index
• Numeral Systems of the World
• The Numbers List
• Typology of Numeral Systems
• Numeral (linguistics) - Wikipedia
  • Base 10: Decimal - Wikipedia
  • Base 20: Vigesimal - Wikipedia
  • Other bases with some use: 4, 5, 6, 8, 12, 24, 32, 60, 80
• Mesoamerican Long Count calendar - Wikipedia
• [2207.12102] Sexagesimal Calculations in Ancient Sumer
• Finger-counting - Wikipedia - counting on one's fingers

I have some speculation on why that happened.

Traditional units of length, area, volume, and mass were total chaos. Not only numerous units, but also numerous values of units with the same name, like the foot. Nicolas Pike's "New Complete System of Arithmetic" has some examples of this chaos.

But traditional units of time, despite their awkwardness, were much more uniform.

Why the difference?

Some traditional units of length were based on natural phenomena, like the sizes of human body parts like arms and hands and feet. But those sizes are very variable, and local attempts to standardize yielded numerous different sizes of the same unit.

But the more basic time units are based on universally-accessible natural phenomena. Everybody sees the same length of day and (lunar) month and year.

That made it easier to standardize calendars and divisions of the day.

The inventors of the metric system also wanted to have this universal accessibility, by making the meter 1/10,000,000 of the equator-pole distance and the gram the mass of a cubic centimeter of water. Their choices turned out to be less precise than one might want, but the spirit lives on in more recent definitions, including the present ones.

In parallel with some posts here about units of length and mass, I'll discuss units of time.

The first units of time measurement were

• Sun-relative "solar" day
• Sun-relative "synodic" month
• Season-relative "tropical" year

Start times:

• Day: morning, evening, midnight (what we use), noon (what astronomers used for a while)
• Months: new Moon
• Years: a solstice, an equinox, various days in between

Year counting was originally year-reign, like this year being Biden 4, Charles III 2, ... a variety of epochs or reference dates have been used, like the first recorded ancient Olympics, a certain Greek general's return to Babylon (Seleucid era), the creation of the Universe (Jewish calendar), and when Jesus Christ was born (our calendar).

These time units' ratios are very irregular: 1 month = 29.53059 days, 1 year = 365.24217 days = 12.368265 months

Using both months and years led to lunisolar calendars, where one adds a month every two or three years. That is rather kludgy, and someone in Egypt decided to fix the length of all the months to 30 days and add 5 extra days to the year, even if it meant being out of sync with the Moon. Julius Caesar decreed a modification of that calendar, and Pope Gregory XIII some further fixes, giving the calendar that we now use.

Astronomers like using only days, because it make their arithmetic a LOT easier: the Julian day - Wikipedia Likewise, computers use only days internally, with various epochs.

Turning to shorter durations, I've been unable to find out the origin of a day having 24 hours. Some early timekeeping adjusted the lengths of daytime hours to make daytime exactly 12 hours, but with mechanical clocks, it was easier to let daytime vary in hours and make the overall day 24 hours.

Shorter durations are the result of sexagesimal, base-60 counting, using by the people of Sumer, 5,000 years ago in southeastern Iraq. This was carried over by people with decimal number words, all the way to the present. I've seen proposals of decimal hours, minutes, and seconds:

• 1 day = 24 / 10 hours = 1,440 / 1,000 minutes = 86,400 / 100,000 seconds
• 1 hour = 60 / 100 minutes = 3,600 / 10,000 seconds
• 1 minute = 60 / 100 seconds

Using the day as a time reference has a further problem. It starts at different places on our planet. That was a big problem for railroad scheduling, and railroad companies solved that problem by using the time in one city in their systems. Standardized time zones were introduced in the late 19th century: Time zone - Wikipedia An overall time standard was introduced in the International Meridian Conference - Wikipedia of 1884, using the solar time of the Royal Observatory of Greenwich, UK as a time reference: Universal Time - Wikipedia

Are we done? Not yet. The Earth's rotation is a tiny bit irregular, and that was apparent in observations of the rest of the Solar System -- they had the same irregular variations. So in 1952, Ephemeris time - Wikipedia was introduced, defining the second in terms of the year.

By the 1960's, our timekeeping devices finally surpassed astronomical timekeeping in precision, in the form of atomic clocks that use as a time-unit reference the frequency of radio waves emitted by spin flips in cesium atoms. So in 1967, the second was redefined in terms of this frequency.

This led to International Atomic Time - Wikipedia (TAI, from its French initials). TAI is defined on the geoid, the shape of the Earth's sea level, as determined by the Earth's gravity and rotation.

Why on the geoid? To oversimplify, time flows at different rates at different places. For instance, GPS satellites are made to run very slightly slow, because otherwise they would look very slightly fast, but fast enough to make them too out of sync to be usable.

The time reference for anything orbiting the Earth is Geocentric Coordinate Time - Wikipedia which we observe on our planet's surface as running faster by 7.0*10^(-10) or 22 milliseconds per year.

The corresponding time reference for the Solar System is Barycentric Coordinate Time - Wikipedia which we observe as running faster by 1.55*10^(-8) or 490 milliseconds per year.

April 2024

An article in online magazine europastar.com gives us some of the history behind adopting the Greenwich meridian as the prime reference for navigation, map-making and timekeeping.

An American of English origin posted the following comment to metric views:

Celsius only works above 0. When you drop below 0; it starts going back up. I was telling my Dad it was -30°f and I asked him if that was -90°c, but it starts going up. When I grew up in England we used Fahrenheit. I’ve been in America for 22 years and we have extreme temperatures ranging from -30°f to 120°f. So Celsius wouldn’t work.

https://metricviews.uk/2012/10/15/50-years-of-celsius-weather-forecasts-time-to-kill-off-fahrenheit-for-good/comment-page-2/#comment-54865

It almost looks like it was written by a child, but the author claims to have lived in the US for 22 years and grew up in England when foreignheat was still in use, which was over 50 years ago. Seeing that the entire post is incoherent it had to be written by someone with dementia.

I can't help but feel that there are countless other Americans who would agree with this sentiment and cheer her on and not even notice the incoherency of what is written. Those Americans who feel embarrassed by this comment need to go to Metric Views and post a counter view to this highly idiotic comment.

The obvious meaning the freezing temp being zero.

A while ago, I read about the additional labour costs of using, or allowing for, dual units in computer programs – US and metric. (Sorry, I can't remember where I read this.)

The writer said that in addition to the programming, conversion factors need to be checked, and the whole program may need to be tested twice, once in metric units then again in US units. It's not just the conversion factor that is important, but the rounding of decimal fractions to something sensible and checking the input values so that absurdly large or small values are rejected. Also, it has to be made obvious to the user which units they are using.

Do you know of other areas in industry, or life in general, where dual units are necessary and visible?

One obvious area is labelling of goods in US and metric measures, and getting the right kind of ounce, fluid or avoirdupois. Again this should need extra checking to ensure it is done correctly. (Has anyone found gross errors in dual labelling of mass or volume?)

The tyre pressure pump at my local service station is another example. It can be switched between kPa and psi, so I set it to kPa every time I use it.

Other examples might be as simple as my digital clock with a built in thermometer which can show ºC or ºF.

5 1/3 cm??? Really???

​

https://preview.redd.it/s0swrwmzgwvc1.jpg?width=640&format=pjpg&auto=webp&s=3eb2ee0c24e466a4f22bf1704b2c266cc460d074

2024-04-19

A writer for the online magazine of a cooking school, the Institute of Culinary Education teaches us how to calculate the volume of a cake from the size of the baking pans (in inches and cubic inches,) and how to use this figure to calculate the amount of ingredients needed for a different-sized version of the same product.

The writer emphasises the importance of measuring ingredients by weight to ensure a consistent result, and using the metric system to measure ingredients. There is also a link to an article on why a kitchen scale is a necessity for baking.

Measure by Weight and Go Metric

For greater accuracy, Chef Ravi highly recommends measuring ingredients by weight instead of volume. If you don’t have a kitchen scale, here’s more on why it’s necessary according to ICE Pastry & Baking chefs.

And, while you’re ditching the measuring cups and spoons, Chef Ravi underscored the benefits of using the metric system instead of the imperial system. He gives an example: imagine trying to divide a third of a cup of oil by four or five, versus dividing 1,000 grams by the same number. If your recipe uses imperial measurements, consider converting it to metric. Weighing ingredients and using the metric system leave less room for error and will make conversions easier.  

2024-04-17

An article about French climate change advocate Jean-Marc Jancovici in connexionfrance.com ends by telling us about the difference between producing versions of his book for the European market, (which includes the UK, notwithstanding Brexit,) and the US market.

Le Monde sans Fin* will be released in the US in May and then in the UK. Is global warming explained to Americans and Britons in the same way as it is to French people?

While Great Britain has had Brexit, British people remain close enough to Europe to understand what it is. They know what a kilowatt is and they use bicycles much more than Americans.

They also know EDF, the French company that is the main shareholder and electricity producer in Great Britain. So the British version is the European version.

The American version was heavily adjusted for Americans. The metric-system, the comparison size with countries and the examples were all explained with American references. 

The main character, Iron Man, was changed to The Armour to avoid a lawsuit by Marvel.

* The Endless World

2024-04-16

An online science magazine livescience.com ran a story with the headline 2,000-foot-wide 'potentially hazardous' asteroid has just made its closest approach to Earth — and you can see it with a telescope

All the measurements mentioned in the text were in feet and miles followed by the metric equivalent in parentheses.

This caused a user named thunderbolt to comment:

As this is a science site, could you please use the metric system in your articles. This is an article about space. Scientists that study space use the metric system.

The magazine is based in New York, but has several writers based in the UK, including the writer of the article, all of whom should be a little more familiar with the metric system than US writers.

If you want to make a comment you will need to register on their Forum page.

2024-04-16

A writer for a Canadian agricultural magazine looks at the measurement systems in use in Canada, US, Imperial, and metric, and explains some oddities.

I mean by that partial conversion of measurements to the metric system. I say that because perusing Metrication - Wikipedia and Metrication in the United States - Wikipedia and Metrication in other countries – US Metric Association makes it evident that conversion to metric units is often partial, with some measures converted and others not. In cases of complete or nearly complete conversion, some measures may be converted before others. What patterns might partial conversion have?

I was moved to think about that when I noticed here in the US some food containers having both English and metric units on them, even though in the US there isn't much that's publicly visible with metric units on them. Could that be because they are easy to export?

Could food-container sizes be among the first publicly-visible items to become metric-only in the US?

Time units are a horrible hodgepodge, and that's due to various accidents of history.

Part of this hodgepodge is unavoidable, from using astronomical effects: the Earth's rotation and its orbiting the Sun, and the Moon's orbiting the Earth.

• Day - the Earth's rotation relative to the Sun's direction
• Month - 29.530589 days - synodic month: the Moon's orbit relative to the Sun's direction
• Year - 365.242198 days - tropical year: the Sun's direction relative to the equinoxes, for the seasons

But other time units are much more arbitrary. Week - Wikipedia had several different numbers of days before our current number of 7, which was originally astrological.

Hour - Wikipedia was originally 1/12 of daytime, and was later fixed at 1/24 of the complete daytime-nighttime cycle.

But the minute and the second are sexagesimal, base 60. "Minute" is from medieval Latin "pars minuta prima" ("first minute part") and "second" form medieval Latin "pars minuta secunda" ("second minute part"). However, a "pars minuta tertia" ("third minute part") would be too small for our time perception.

Their ultimate origin? [2207.12102] Sexagesimal Calculations in Ancient Sumer some 5,000 years ago in what's now southeastern Iraq. Also Mesopotamian Mathematics

Sumerian speakers had words for 1, 2, 3, 4, 5, 6 (5+1), 7 (5+2), 8, 9 (5+4), 10, 20, 30, 40 (2*20), 50 (40+1), 60, 60^2, 60^3 (big 60^2, 60 * 60^2), and 60^4 (60^3 that is not touched).

But around 2500 BCE, Akkadians moved in. Their language, like other Semitic languages (Hebrew, Arabic, Aramaic, Amharic, ...) uses base 10: 1 to 10, 10^2, 10^3. But they ended up using Sumerian numbering for calculations, doing so for over 2 millennia.

The land was conquered in 331 BCE by Alexander the Great, and Greek astronomers borrowed some mathematics from there, including sexagesimal numbering. Their language, like other Indo-European languages, also uses base 10: 1 to 10, 10^2, 10^3, with 10^4 (murias > "myriad") added on.

Medieval Arabs continued to use sexagesimal numbering, despite Arabic using base 10, and late medieval Europeans followed them, also despite their highbrow language, Latin, using base 10. Europeans gradually came to use vernacular languages for highbrow discourse, and these all use base 10, with some occasional base 20 between 10 and 10^2, but we still have sexagesimal time and angle units.

Cross-linguistically, base 10 was invented several times, even restricting oneself to systems with powers of the base. Aside from the sexagesimal system, the main exception that I know of is base 20 in Central America, where some Mayans counted very high in it: Mesoamerican Long Count calendar - Wikipedia

Various systems of Decimal time - Wikipedia for subdividing the day have been proposed, but they never caught on very much. For days themselves, astronomers use the Julian day - Wikipedia a straight count of days since some epoch or reference date. Computers internally often do something similar, but with seconds, notably Unix time - Wikipedia

A new and complete system of arithmetick : composed for the use of the citizens of the United States : Pike, Nicolas, 1743-1819 : Free Download, Borrow, and Streaming : Internet Archive - Fourth Edition, 1822

A new and complete system of arithmetick : composed for the use of the citizens of the United States : Pike, Nicolas, 1743-1819 : Free Download, Borrow, and Streaming : Internet Archive - Third Edition, 1809

It has not only plain arithmetic, but also compound arithmetic, using as an example pre-decimal British currency: 4 farthings = 1 penny, 12 pence (pennies) = 1 shilling, 20 shillings = 1 pound. One has to do that a lot with English units, and in the metric system, the only surviving bits are time units and angle units.

In the fourth edition, page 404 has "A Comparison of the American Foot with the Feet of other Countries." - listing several cities and countries, each with its own standard foot length. Amsterdam has 0.942 English feet, France 1.066 English feet, etc. In the next pages, it also does that with pounds, and it also has a conversion table for avoirdupois and troy English-system mass units.

Page 48 and following list several units:

Troy weight: 24 grains = 1 pennyweight, 20 pennyweights = 1 ounce, 12 ounces = 1 pound.

Avoirdupois weight: 16 drams = 1 ounce, 16 ounces = 1 pound, 100 pounds = 1 hundredweight, 20 hundredweight = 1 ton.

Apothecaries weight: 20 grains = 1 scruple, 3 scruples = 1 dram, 8 drams = 1 ounce, 12 ounces = 1 pound.

That's why one ounce of gold (troy) does not weigh the same as one ounce of lead (avoirdupois, the usual system). But a gram of gold weighs the same amount as a gram of lead.

Cloth measure: 2 1/4 inches = 1 nail, 6 nails (9 inches) = 1 quarter yard, 4 quarter yards = 1 yard, 3 quarter yards = 1 Flemish ell, 5 quarter yards = English ell, 6 quarter yards = 1 French ell, 4 quarter yards + 1 1/5 inches = 1 Scotch ell, 3 2/3 quarter yards = Spanish var.

Long measure: 3 barleycorns = 1 inch, 12 inches = 1 foot, 3 feet = 1 yard, 5 1/2 yards (16 1/2 feet) = rod, perch, pole, 40 poles (660 feet) = 1 furlong, 8 furlongs (5280 feet) = 1 mile. Also, 7.92 inches = 1 link, 25 links = 1 pole, 100 links = 1 chain, 10 chains = 1 furlong, 8 furlongs = 1 mile.

Wine: 2 pints = 1 quart, 4 quarts = 1 gallon, 10 gallons = 1 anchor of brandy, 18 gallons = 1 runlet, 42 gallons = 1 tierce, 63 gallons = hogshead, 2 hogsheads = pipe or but, 2 pipes = 1 tun.

Ale or Beer: 2 pints = 1 quart, 4 quarts = 1 gallon, 8 gallons = 1 firkin of ale in London, 8 1/2 gallons = 1 firkin of ale or beer, 9 gallons = 1 firkin of beer in London, 2 firkins (beer in London) = 1 kilderkin, 2 kilderkins = 1 barrel, 1 1/2 barrels = 1 hogshead of beer, 2 barrels = 1 puncheon, 3 barrels (2 hogsheads) = 1 butt.

Dry measure: 2 pints = 1 quart, 2 quarts = 1 pottle (not bottle!), 2 pottles = 1 gallon, 2 gallons = 1 peck, 4 pecks = 1 bushel, 2 bushels = 1 strike, 2 strikes = 1 coom, 2 cooms = 1 quarter, 4 quarters = 1 chaldron, 4 1/2 quarters = 1 chaldron in London, 5 quarters = 1 wey, 2 weys = 1 last.

Fortunately, the author also gives volume units in cubic inches.

I first learned of that book from Isaac Asimov's essay "Forget It!", collected in "Asimov on Numbers". He had quite a chortle over those numerous units, though I don't agree with his slamming of Roman numerals. They make a nice alternative display.

• "kilo" for "kilogram"
• "klick" for "kilometer" (US, UK military slang)
• "metric ton" or "tonne" for "megagram"

Any others? I like the system of prefixes, but they can be a mouthful.