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"Why do they use the much more complicated system?" "Nobody actually knows."
I'm not defending it, but it's because 12 has more factors than 10
10 has 2 and 5
But 12 has 2,3,4,6
So 1/2 ft, 1/3 ft, 1/4ft and 1/6 ft all have a whole number of inches
Using a base12 system would only make sense if we all started counting in base12 too.
If enough people want that, i'd be down to start counting in base12, but i don't think many people will lol.
if we all started counting in base12 too
You could start by calling it twelve instead of 12.
To keep things as simple/intuitive as they are today, we'd need two new symbols to represent the additional numbers. 0,1,2,3,4,5,6,7,8,9,§,∆,10
Of course it would be confusing as all hell for anyone alive today.
With hexadecimal we typically use a-f for the remaining numbers. We probably would use something like this for base 12:
012345679ab
Of course everyone knows the correct base to use is 2. Or as we call it, base 10.
Actually, come to think of it, it would always be 10 in the base that it is.
Yes, 10 can be any number if you change the base. Non-integer bases are weird, but a few (like base φ) see some use.
But it doesn't use base 12. Take distance. Values smaller than 1/64" are measured using "thou", "tenths", and "millionths", which are decimal multiples of 1/1000', 1/10000", and 1/1000000" respectively.
Values between 1/64" and 1" are measured using dyadic rationals, i.e. base-2 fractions.
Above 1" it's mostly base 12,except for the yard.
So 1/2 ft, 1/3 ft, 1/4ft and 1/6 ft all have a whole number of inches
The same is true if you start with 300 mm instead of 1 foot.
Though dozenal numbers with a corresponding dozenal metric system would be very convenient, if you ignore the enormous cost of switching.
So all imperial measurements are factors of 12 apart?
Wait now, why would this matter? Decimal doesn't need full factors?
It makes it easier to divvy up into groups: halves, thirds, quarters, sixths (vs. just halves and fifths). Makes doing math easier in the head (fewer digits, checking for divisibility are the big ones).
Some info (warning: they are trying to convince you it is better than decimal, so you are not going to get a balanced argument there): https://dozenal.org/drupal/sites_bck/default/files/DSA-DozenalFAQs_0.pdf
Also, on the practical level, I have a specific mark to go to for 1/4". 1/4cm involves me guestimating the middle between two mm marks and just deciding that that's middle enough. Small errors like this can actually add up really fast in something like woodworking
Okay, so why inches divided into 8ths?
And why are there 16 cups in a gallon, 15-and-some tablespoons in a cup and 3 teaspoons in a tablespoon?
Better make it 12 tablespoons in a cup and 12 cups in a gallon, then!And why are there 14 pounds in a stone and 16 ounce in a pound?
The imperial system does not use dozenal.
It uses a clusterfuck of bases because it's actually a clusterfuck of measuring systems in a really big trenchcoat