[lolinder]

But you can represent 1/3 cleanly in base 12, so inches don't have this problem.

Yeah, you can't represent 1/10, but why does that matter? When 1/10 comes up in practice it's almost always as a side effect of us using base 10, not a natural requirement to partition something 10 ways.

[dudul]

Wait what? Why is 1/3 so critical to represent but not 1/10?

[DemocracyFTW2]

for the reason it was used in the artificial example given above I guess. OTOH it should be expected that the fractions 1/2, 1/3, 1/4, 1/5, 1/6... appear more often than others in practical work, not sure about that

[rhelz]

> more often than others in practical work

Here is a thumbnail sketch of a reason for why they do:

1. Large structures tend to be build from smaller substructures. (E.g., a train is typically built of a number of cars, a 6-pack is built from 6 cans).

2. And large structures tend to be built from integral multiples of smaller substructures, because a fraction of a substructure is typically not as useful as a whole substructure. (e.g. a train car missing its wheels isn't as useful as an intact train car, and a partially drunk-up can of beer isn't nearly as desirable as a whole can of beer.)

3. The fundamental theorem of arithmetic says that every integer can be factored into prime numbers.

4. Small primes are more common factors of integers than large primes are. (e.g. you more often want twice of something than 37 times of something)

Ergo:

5. Most of the numbers involved in designing and building something are going to be divisible by 2 and 3--because the number of subsystems it contains will likely be multiples of 2 and 3. Prime factors of 5 and over are relatively rare.

6. Therefore, when you are measuring the larger system, it is handy to use units which are easily divisible by 2 and 3. (like a foot is 12 inches).

Its why donuts and eggs are sold by the dozen, and beer comes in 6-packs, and cases of 24. You are far more likely to divide up cans of beer or some donuts to a number of people which is divisible by 2 or 3, then by 5 or any higher prime factor.

[rhelz]

> Why is 1/3 so critical to represent but not 1/10?

TLDR reason: Every second number is divisible by 2. Every third number is divisible by 3.

So if you want to divide something (like donuts or cans of beer, or the length of a wood plank) by N, it's far more likely that N will have a factor of 2 or 3 than it will not have a factor of 3, but be divisible by 10. Which is to say, you are far more likely to need tick marks spaced by 1/2 and 1/3 than tick marks spaced by 1/10. Which is to say that a 12-inch ruler is preferable to a 10 cm ruler, Q.E.D.

That's why they sell donuts by the dozen, and beer in 6-packs. And why the US officially (and Canada and the UK unofficially) still use English units for everyday measurements. Its just more practical.

[Jensson]

> Yeah, you can't represent 1/10

You can't represent 1/5 either while base 10 can. You gain 3 but lose 5, it has the same number of primes.

[NikkiA]

Vernier guages are horseshit in anything but metric.

[rhelz]

Here is a vernier gauge for degrees--a non-metric unit, expressed in base 360 :-)

https://www.amazon.com/Universal-Stainless-Protractor-Precis...

[NikkiA]

Thanks, I hate it.