If an alien species has 12 fingers to our 10, would they work in base 12 as normally as we use 10s? Like would their whole system end (or start) with a 0 or equivalent and not end all different?

My maths coherence is too high-school for this thinking, but now its in there.

Because there's a extra system of measurement change hiding in the middle. The Inches, Feet and Yards system (with the familiar 12:1 and 3:1 ratios we know and love), and Rods, Chains, Furlongs and Miles system. Their conversation rates are generally "nice", with ratios of 4 rods : 1 chain, 10 chains : 1 furlong, and 8 furlongs : 1 mile.

So where do we get 5,280 with prime factors of 2^5, 3, 5 and 11? Because a chain is 22 yards long. Why? Because somewhere along the line, inches, feet and yards went to a smaller standard, and the nice round 5 yards per rods became 5 and 1/2 yards per rod. Instead of a mile containing 4,800 feet (with quarters, twelfths and hundredths of miles all being nice round numbers of feet), it contained an extra 480 feet that were 1/11th smaller than the old feet.

It's not nonsense, just old and focused on priorities that don't matter anymore. A mile was initially a thousand paces. So you send a group of people out, one counts each time their right foot takes a step and after a thousand times they build a mile marker. Bam, roman road system. 1000 strides per mile, 5 feet per stride.

Later the English used the unit as part of their system of measurement, and built the furlong around it, which is the distance a man with an ox team and plow can plow before the ox need to rest. A mile is eight furlong. This got tied into surveying units, since plots of land were broken up into acres, or the amount of land an ox team can plow a day.
When some unit reconciliation needed to be done, they couldn't change the vitality of oxen, and changing the survey unit would cause tax havock, so they changed the size of a foot.

All the units and their relationships were defined deliberately and intentionally. They just factored in priorities that we don't care about anymore.

I think a mile is specified in terms of 'chains' not really feet or yards. Feet and yards are meant for measuring smaller stuff, like the size of a foot, or a courtyard.

The 'chain' was a specific surveyors tool for measuring larger land areas. I imagine defined to be a length of physical chain practically manageable by the surveyor - probably pre-dating optical / triangulation methods before lenses got cheap.

I think an acre was then defined as 10 square chains or something.

But go back in time far enough and different jurisdictions have different lengths of standard chain, so different miles and acres derived from it. But it doesn't really matter because if you were buying land in Scotland, then you'd probably want to use a Scottish surveyor and his big long chain.

The nautical mile is then a whole other kettle of fish.

Base 60 can do 2, 3, 4, 5, 6, 10, and 12.

I do woodworking a bit too, but I normally just do the slanty ruler/tape trick to divide any straight parallel face into n equal lengths. I hate all forms of mental arithmetic; I also avoid measuring as much as possible too. Maybe that's why everything i make is so shit.

I guess if you're mass producing things you can't just manually mark off each and every part though - but even then I'd probably want to work to a template rather than to measure.