3 ms·

For miles, pounds, and ounces, I have no defense, but I will say that having a base 12 length measuring system (in/ft/yd) is much nicer for carpentry than base

For miles, pounds, and ounces, I have no defense, but I will say that having a base 12 length measuring system (in/ft/yd) is much nicer for carpentry than base 10 (m/cm), since it can be divided evenly by 2 and 3. It's the same reason why having 12 notes in a scale works for music.

mdorazio 4y ago
I genuinely don't understand what you mean here, and I say that as an American who has done a fair amount of carpentry. I can't think of a single time I've thought to myself that using fractions was superior to measuring straight units in mm/cm/m.
- throwway120385 4y ago
  Because the ratios are pleasing to the eye.
- 22c 4y ago
  I think GP means if you have a 12ft piece of lumber, you can cut in half to have 2 x 6ft, or cut it in thirds to have 3 x 4ft pieces. It doesn't really follow though, I think what's more important is the length of wood you start with. It's easier to divide 3m into 2 x 1.5m or 3 x 1m than it is to divide 9'10" into 2 x 4'11" or 3 x 3'3.333333333"
  - uoaei 4y ago
    That would be true, except saw blades are not infinitely thin, so you still get these small unwieldy fractions pretty early on in your cut list. If your blade was e.g. 2mm thick instead of 1/16", I think it would be easier to manage.
billpg 4y ago
I would have a lot more respect for those units if it were consistent around 12. You mentioned the yard but that's equal to 3ft. What's the name of the 12 ft unit? Why isn't the mile equal to 12×12×12×12 ft? Why isn't an lb equal to 12 oz?
- thaumasiotes 4y ago
  > Why isn't an lb equal to 12 oz? It is; that's called Troy weight.
  - billpg 4y ago
    Fair enough. Nonetheless, the 16 oz = 1 lb system is prevalent. I had never heard of "Troy" units until I read your response.
    - thaumasiotes 4y ago
      Troy weight is used for precious metals. It's important to the standard trick question "which weighs more, a pound of feathers or a pound of gold?"
thaumasiotes 4y ago
> I will say that having a base 12 length measuring system (in/ft/yd) is much nicer for carpentry than base 10 (m/cm), since it can be divided evenly by 2 and 3. It's the same reason why having 12 notes in a scale works for music. When would you want to divide an octave into two or three intervals like that? The normal way to divide an octave in "half" is at the fifth, which is a ratio of 3:2. If you instead go six half-steps up from the tonic, you'll be a half-step short of a fifth, at fi instead of so, with an irrational ratio of √2:1. That's the opposite of what you want. [From wikipedia: The tritone is a restless interval, classed as a dissonance in Western music from the early Middle Ages through to the end of the common practice period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with the development of Guido of Arezzo's hexachordal system] If you divide the octave into "quarters" by going up three half-steps, you get a minor third. (Going for "thirds" by going up four half-steps will take you to mi and form a third [the name of the chord is not related to the idea of dividing an octave into three equal parts; it's called a "third" because "do re mi" is three notes], which is fine. But it's pretty clearly just a coincidence that that works out; the methodology of "there are twelve half-steps in the octave, so I'll divide that into equal parts and see what I get" just isn't related to the way you compose music.)

mdorazio 4y ago

I genuinely don't understand what you mean here, and I say that as an American who has done a fair amount of carpentry. I can't think of a single time I've thought to myself that using fractions was superior to measuring straight units in mm/cm/m.

throwway120385 4y ago
Because the ratios are pleasing to the eye.
22c 4y ago
I think GP means if you have a 12ft piece of lumber, you can cut in half to have 2 x 6ft, or cut it in thirds to have 3 x 4ft pieces. It doesn't really follow though, I think what's more important is the length of wood you start with. It's easier to divide 3m into 2 x 1.5m or 3 x 1m than it is to divide 9'10" into 2 x 4'11" or 3 x 3'3.333333333"
- uoaei 4y ago
  That would be true, except saw blades are not infinitely thin, so you still get these small unwieldy fractions pretty early on in your cut list. If your blade was e.g. 2mm thick instead of 1/16", I think it would be easier to manage.

billpg 4y ago

I would have a lot more respect for those units if it were consistent around 12. You mentioned the yard but that's equal to 3ft. What's the name of the 12 ft unit? Why isn't the mile equal to 12×12×12×12 ft? Why isn't an lb equal to 12 oz?

thaumasiotes 4y ago
> Why isn't an lb equal to 12 oz? It is; that's called Troy weight.
- billpg 4y ago
  Fair enough. Nonetheless, the 16 oz = 1 lb system is prevalent. I had never heard of "Troy" units until I read your response.
  - thaumasiotes 4y ago
    Troy weight is used for precious metals. It's important to the standard trick question "which weighs more, a pound of feathers or a pound of gold?"

thaumasiotes 4y ago

> I will say that having a base 12 length measuring system (in/ft/yd) is much nicer for carpentry than base 10 (m/cm), since it can be divided evenly by 2 and 3. It's the same reason why having 12 notes in a scale works for music. When would you want to divide an octave into two or three intervals like that? The normal way to divide an octave in "half" is at the fifth, which is a ratio of 3:2. If you instead go six half-steps up from the tonic, you'll be a half-step short of a fifth, at fi instead of so, with an irrational ratio of √2:1. That's the opposite of what you want. [From wikipedia: The tritone is a restless interval, classed as a dissonance in Western music from the early Middle Ages through to the end of the common practice period. This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with the development of Guido of Arezzo's hexachordal system] If you divide the octave into "quarters" by going up three half-steps, you get a minor third. (Going for "thirds" by going up four half-steps will take you to mi and form a third [the name of the chord is not related to the idea of dividing an octave into three equal parts; it's called a "third" because "do re mi" is three notes], which is fine. But it's pretty clearly just a coincidence that that works out; the methodology of "there are twelve half-steps in the octave, so I'll divide that into equal parts and see what I get" just isn't related to the way you compose music.)