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Thanks for this! I loved this explanation and I had never heard that divisibility is the reason we have 24 hours in a day and 60 minutes in an hour. After reading your comment, I found this article in Scientific American that gave additional detail: https://www.scientificamerican.com/article/experts-time-divi...

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I believe divisibility is also the reason we have 360-degrees in a circle.

And 12 inches in a foot, etc. Perhaps in centuries to come, the US will be vindicated for its metric system resistance :)

It would have been nice if numbers had developed into a base-12 instead of a base-10 system. But it's even nicer that the number system (now 10-based) and the measurement system (now metric) are in sync.

They in fact did, many years ago. This is discussed elsewhere on this very page.

Yeah, I was aware of that. I could have been more precise; it developed multiple times, but didn't stick around to the present.

How's that working out for inches->feet->yards->miles. Seriously, there are some good things about the imperial system but divisibility isn't exactly one. It's more relatable and human, probably yes.

Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense. However, for most day-to-day, hands-on tasks (with the major exception of driving), those shorter distances are sufficient.

I find this same principle is perhaps better exemplified by weights/volumes commonly used in cooking. Since many sizes (1 cup = 8 fl.oz, 1 pound = 16 oz, 1 gallon = 128 fl.oz, 1 fl.oz = 2 tablespoons, etc) are powers of 2, scaling recipes up or down on the fly is extremely easy.

On the other hand, given an accurate metric scale, all recipes can be converted to weights, allowing scalar conversions. However, I suspect the proliferation of accurate scales in home kitchens is a relatively recent (nascent?) phenomena.

>Up to about a yard, divisibility for imperial distances is pretty good, but you're absolutely right that past yards, it doesn't make much sense.

Seems to work well with miles

miles ft 1/10 528 1/11 480 1/12 440 1/15 352 1/16 330 1/20 264 1/22 240 1/24 220 1/30 176 1/32 165 1/40 132

miles yds 1/2 880 1/4 440 1/5 352 1/8 220 1/10 176 1/11 160 1/16 110 1/20 88

One of the problems here is that given that our "home" numeric base is 2 times 5, we just aren't going to get both convenient unit conversion via moving the decimal point (or appropriate term in base of choice) and convenient divisibility.

So I suppose if metric just isn't signal-y enough for you (in the general sense of "you", not JackFr), you can join the call for the world to convert to duodecimal: http://www.dozenal.org/

That's tremendous -- never knew such an organization existed.

It's surprisingly easy once you get the hang of it. I started counting in dozenal for fun, and now when I think "7, 8, 9" my brain finishes the series with "X, E, 19".

It's not common enough to use with other people, but I use dozenal in my personal projects and journal whenever possible.

This problem will solve itself when we apply appropriate sexual selective pressure to evolve 6-digit hands and feet.

"Hey honey, this is going to sound weird, but hear me out..."

In a way, there are parallels with a type system. Yards, a measure taken from a human limb, are for fabric, furlongs are for arable land, and miles (a thousand paces) for roads. Prior to the need for exercises in teaching arithmetic to the masses, it might have seemed rather pointless (if not exactly a type error) to express the measurement of one thing in the units for another.

In fact, land wasn't really measured in units of area as much as it was measured in units of productivity (ie bushels), which was much more useful to know

And distances (on land and maybe sea too) were long ago measured in interesting units like maybe an arrow shot (distance an arrow can travel) and such like (from my memory of reading legends as a kid, both Indian and probably Western or other ones) :)

E.g.:

https://en.wikipedia.org/wiki/Yojana

An acre (which is still used in the US for land measurement) is roughly the amount of land a team of oxen can plough in a day.

And a league is the distance a person can walk in an hour. The actual distance doesn't actually matter; two places can be 5 leagues away and be at different distances. However, it'll take you 5 hours to get to any of them, be it because different quality roads or elevation changes

Really? an acre is quite small. i find it hard to believe that a team of oxen can't do much more.

Metric recipes are quite easy to scale too. 8 desiliters / 3=2.6 desiliters, not 7.2 arbitrary units.

People often point to that decimal portion and say it makes metric impossibly hard, but to anyone used to the system, it reads “‘bout half”. Most home measurement problems are not super exact science.

Well, if you don't skip all the intermediate units there is actually a nice, highly composite chain all the way up. Admittedly, the numbers are variable... but

22 yards in a chain 10 chains in a furlong 8 furlongs in a mile.

But base 10 is an archaic, arbitrary or divisibility based number system itself

Every base is base 10!

Decimal is natural hands-based system. It's perhaps archaic, but neither arbitrary nor particularly divisible compared to its neighbors. (It's better than undecimal (9+2), but same as novemal (9), and worse than octal (8) or duodecimal (9+3))

In metric land we just tend to standardise measurements of things to fit into easily divisible numbers and keep our internally consistent system of units.

E.g. IKEA cabinets are 60cm wide, and so are most appliances like fridges. Double-wide things are 120cm etc. Pre-cut lumber is sold by 120cm lengths, sheetrock is 120x240cm etc.

All the easy division, plus the fancy units.

So, you’re saying that europe is about to switch away from meters to “ikeas” as the canonical unit?

With brexit, it should be easy for the brits to lead the charge.

I for one welcome the day when all the dimensions of all manmade objects are either products of numbers in the set {5, 3, 2, 1} or the set {1/2, 1/3, 1/5}. It will drastically simplify real world long division and factoring, and also lead to tighter packing of shipping containers.

Knowing apple, they’ll screw it all up when they drop some port and shrink some device from 1/6000 to 1/6001 thick.

Metric system is beautiful. Here’s a little poem

1 litre of water weights 1 kilogram and fills a 10cm cube to its brims. At 0 centigrade, it freezes, and at 100 it steams.

Let’s try imperial units.

1 gallon of water weighs 8.34 pounds and fills 6.8in cube to its brims. At 32 farenheit it freezes and 212 it steams.

Yuck!

1 fluid ounce of water was supposed to weigh 1 ounce. But municipal differences have foiled that equivalency over time. The goal with Metric is that this won't happen - we'll see how long it takes for one group to claim their meter is 1.1 official meters.

This has to do with Preferred numbers and ISO 2848: https://en.wikipedia.org/wiki/ISO_2848

Ahhh, thank you. I knew there had to be some standard behind their preferred number use - just didn't know what it might be.

The number of Ikea things that you can mash together and have work is awesome.

it's "curious" that there isn't a standard metric time. We are all happy with our Imperial clocks, i guess.

Some science fiction authors like Charles Stross I think (or was it Vernor Vinge) have used kiloseconds, megaseconds, etc. as units of time for space faring civilizations.

There were attempts, the latest was https://en.wikipedia.org/wiki/Swatch_Internet_Time

Nice thought, but not in my book!

Once you need to work with real precision, the US system is even more awful.

From an exactly 12" wide board, you cannot get three 4" pieces, since the saw kerf width is nonzero. It gets worse when you work with "standard" dimensions. A common 2x4 is actually only about 1.5" x 3.5" (and I don't think even the big sawmill blades take that big a kerf), and similar discrepancies all over.

And converting drill bit sizes? Don't even start; it's either tables or a calculator.

Whenever I get metric projects it's always such a pleasure. I wish we'd get our act together and switch...

But... none of those issues have to do with imperial units. If you have a 30cm wide board, you can't get 3 10cm wide pieces either. And 2"x4" in lumber sizes refers to the size of the lumber prior to drying, treating and planing, all of which shrink the wood a bit.

What is it about metric projects that makes those issues go away?

Good point - it's not so much that the issues of accounting for the kerf go away, they're just easier to deal with in decimal.

I usually am using materials like structural foam, carbon fiber, or metals, just used wood as an easy example.

And I'm using higher precision than most carpenters, so typically measuring with a micrometer which reads out in 0.001in (or 0.01mm) units. You can't just go from 1x12in to 3x4in pieces, you have to knock off maybe 5/64in for a kerf, which is 0.078125in so to get 3x 4in wide pieces, I'll need a board which is 12+5/32...

Lots easier to work with 1.984mm so for my 3x 10cm pieces I'll need a 304 mm wide board.

The bottom line is that once you get precise, the fractional regime which is indeed often easier to divide out by 1/2, 1/3, 1/4, 1/5, 1/6... etc. turns out to be no use at all because you can never actually use those nice fractions, and you're in a decimal regime with lots of fractional conversions (some micrometers even have a fractional inch readout mode, but it turns out to be not all that useful.)

Once you're in decimal, it's WAAAAY easier to be in metric all the way.

I know you're joking, but I hope not, actually. Although it's fun to divide by different numbers like 2, 3, 4, 6, 12, etc., on the whole, I prefer the decimal system, because it is much easier (and hence faster) to calculate things mentally, using uniform powers of 10.

As a simple example, when I need to mentally convert between millions and billions (used in the West) and lakhs and crores (used in India), it is so easy, because I convert everything to powers of 10 (e.g. million = 10^6, lakh = 10^5) and then multiply or divide as necessary, which really just amounts (pun not intended) to addition or subtraction of powers, using simple algebra.

40 million / 2 lakh = 4 * 10 * 10^6 / 2 lakh = 4 * 10^7 / 2 lakh = (4 * 10^7) / (2 * 10^5) = 2 * 10^7 / 10^5 = 2 * 10^2 = 200.

https://en.wikipedia.org/wiki/Lakh

https://en.wikipedia.org/wiki/Crore

https://en.wikipedia.org/wiki/Indian_numbering_system

I also prefer the Western numbering system (groups of 3 powers of 10) over the Indian system linked above, due to its uniformity (for the same reason as metric over Imperial).

USA isn't some sort of "metric-system hold-out". We sell soda in liters and wrenches in millimeters, among other things. And in the UK, cars are still rated in miles per gallon, as well as using Stones for human weight.

FWIW, according to WP, "the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year." https://en.wikipedia.org/wiki/Degree_(angle)

From many other sources, it's suggested that the length of the year is rounded to 360 for divisibility reasons, possibly because of the Babylonians' sexagesimal number system.

Where do you think the sexagesimal number system came from?

I think it came from 60 being highly divisible. Why do you ask?

There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year.

> There are other highly divisible numbers. 60 was probably chosen because of its approximate relationship to the length of the solar year.

I had heard & read the reason was more one of counting convenience, more directly related to divisibility. What sources do you have suggesting that the length of the year is the "probable" reason?

Poking around, I see several suggestions that it might be related to the number of months, which has nothing to do with the number of days. I also found this opinion, which seems to contradict the idea that the number system is related to days in the year:

"Several theories have been based on astronomical events. The suggestion that 60 is the product of the number of months in the year (moons per year) with the number of planets (Mercury, Venus, Mars, Jupiter, Saturn) again seems far fetched as a reason for base 60. That the year was thought to have 360 days was suggested as a reason for the number base of 60 by the historian of mathematics Moritz Cantor. Again the idea is not that convincing since the Sumerians certainly knew that the year was longer than 360 days. Another hypothesis concerns the fact that the sun moves through its diameter 720 times during a day and, with 12 Sumerian hours in a day, one can come up with 60. [...] I [EFR] feel that all of these reasons are really not worth considering seriously."

http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_nu...

That completely ignores the fact that ancient communities used the lunar calendar with periodic corrections every few years. 360 is equal to 12 lunar months, to the precision required of the ancients who practiced the insertion of entire leap months to compensate for drift (because the phase of the moon served as a more reliable clock than anything else that was available).

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