Yeah, 1/3 of a foot is 4 inches. You chose very conveniently. What about 1/5 of a foot (or a yard)? That's a proportion that happens to work beautifully in metric. We can pick and choose, and find both winners and losers in both systems.
except i didn't just randomly choose numbers that will work.. the most likely division we (humans) will do when measuring something is a half.. dividing by two works great in Imperial and pretty good in Metric.. the next most likely division we need is 1/3.. then 1/4.. then 1/5 etc..
i didn't just choose randomly... i chose numbers which are of significant importance.. the odds of someone needing to divide by 5 are far smaller than dividing by 2, 3, or 4.
for example-- if you're building a cabinet, the carcass will most likely be divided in half... (or one shelf)... next highest chance is that the designer puts 2 shelves (thirds).. then 3 shelves.. then fifths come after that..
yes, 5ths work well in Metric (decimal) but the amount of times you need to actually divide by 5 is very small... especially when compared to how often you would divide by 2 or 3 or 4
Let's make this closer to equivalent... inches vs. centimeters (although at 2.54 cm to the inch, still not square on).
Divide an inch into 3rds. Whether inch or centimeter, you'll need to do some rounding on a typical ruler. 5/16-inch is under (.3125). If that stick is more finely ruled, 11/32-inch is over (0.3475), 21/64-inch (0.328125) is about as close as you'll get. Proportionally, 3 mm is not quite as close to .333 cm as any of those others. But to be fair, 1/3-inch = 8.4666... mm - close enough to interpolate 8.5 mm and be very near the mark.
this is because the inch is in base-16.. the foot is base-12... base16 has some neat features (in fact, it's by far the most simple scale to make and use.. logically).
..but i think if i explained myself fully, you'd see i'm not necessarily championing Imperial.. or meaning to argue USA vs World.. i'm arguing for base-12..
a system that works almost exactly how Metric does except our counting system is base-12.. that's what should be the standard.. that's my argument.
The thing is, 1/3 is problematic in either system, outside 1/3 of a yard and 1/3 of a foot. I don't ever recall seeing a ruler marked with 1/3, 1/9, and 1/27 of a foot or inch. We see 1/3 on kitchen measuring cups, and just about nowhere else.
1/3 works great in anything that's base-12..
a third of a foot is 4"... third of a yard is one foot.. in fact, since the root unit (1 foot) is base 12, any amount of feet is divisible by 3... 57 feet ÷ 3 = 19'.... 58' ÷ 3 = 19'4"..... 59' ÷ 3 = 19'8"... etc
the same can be said for 1/4 in base12 systems.
a similar example using something a lot more people are familiar with is the calendar... a third of a year is 4 months... a fourth of a year is 3 months..
any amount of years is divisible.. 57years ÷ 3 = 19 years... 58years÷3= 19yrs 4mth... 59yrs÷3 = 19yrs 8mth... etc..
another example is the clock.. it's base-60 but since 60 is divisible by 12, it works well..
1 hour ÷ 3 = 20minutes.. 2hours ÷ 3 = 40 minutes.. etc..
clocks/calenders are weird because we write them with decimal even though they aren't base10...
1 ÷ 2 = .6? what.. that can't be right?? but it is right if your scale is base12 such as a calendar.
1 ÷ 2 = .30? what? that's crazy looking.. but it's not. not if you're using a clock.
this happens a lot in Imperial... we say 1/2 inch instead of .8 inch... because everyone knows .5 is a half.. not .8...
even though .8 is actually 1/2 in base16 (inch)..
the math, the actual logic behind using the systems is better/cleaner in imperial/calender/clocks.. but using base10 to describe the logic is far from optimal.. we should be using base12
[snip]
this could go on for a long time.. i have some stuff to do today.. i'll pick up later.