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.
The fun one is a nautical mile. Which is 6076.12 feet. How’d we get there? A nautical mile is equal to a minute of latitude, which happens to be just a bit bigger but on the order of magnitude of most “miles” to include the US statute mile.
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.
The Babylonian number system was base 12, that’s why there are 24 hours in a day and 60 minutes in an hour. Afaik they had the normal number of fingers, they were just smarter about making their numbering system divisible.
There’s really nothing special about base 10 numbering, it just feels natural to us. They probably would use base 12 and just have 2 extra symbols for the digits after 9. Example 10 x 10 = 100 in both base 10 and base 12 math. It’s just the translation of that in base 12 to base 10 looks like 12 × 12 = 144 to us.
You can use your hands to count in base 12 if you want to, and some cultures have done so. Just use the segments on your fingers on one hand, using your thumb to count each segment.
Base 12 is easily divisible by 2, 3, 4, 6 and 12
5,280 ft in a mile is fucking nonsense though
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.
The fun one is a nautical mile. Which is 6076.12 feet. How’d we get there? A nautical mile is equal to a minute of latitude, which happens to be just a bit bigger but on the order of magnitude of most “miles” to include the US statute mile.
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.
The Babylonian number system was base 12, that’s why there are 24 hours in a day and 60 minutes in an hour. Afaik they had the normal number of fingers, they were just smarter about making their numbering system divisible.
The just started counting with zero (fist)
There’s really nothing special about base 10 numbering, it just feels natural to us. They probably would use base 12 and just have 2 extra symbols for the digits after 9. Example 10 x 10 = 100 in both base 10 and base 12 math. It’s just the translation of that in base 12 to base 10 looks like 12 × 12 = 144 to us.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 20, 21, …, A0, A1, A3, …
You can use your hands to count in base 12 if you want to, and some cultures have done so. Just use the segments on your fingers on one hand, using your thumb to count each segment.
https://youtube.com/shorts/ThOuUa_iLnM
Base 60 can do 2, 3, 4, 5, 6, 10, and 12.