4 ms·

While I am no apologist for the measurement system we use here in the United States, I realized something interesting when trying to explain why almost all of o

While I am no apologist for the measurement system we use here in the United States, I realized something interesting when trying to explain why almost all of our units consist of easily divisible sub-units. Imagine you needed to split something up into halves, thirds, fourths, sixths, etc.. If you imagine doing this with paper, it's fairly easy. Now imagine Metric, and the need to split something into 10 even pieces. We can make this a little easier knowing that we just need to split into fifths first, and then halve each of those. Do you know how to fold a piece of paper into fifths? It can be done, and it's remarkable how to do this with a straight edge and a pencil. However it is definitely more time consuming than being able to fold using easily divisible numbers. To that end, once you have a decimal ruler you can just use that, but I can see why decimal based measurements were not more common in the past. All that being said, I really wish metrication had been completed here in the US before I was born.

deleted 2y ago
[deleted]
082349872349872 2y ago
The nice thing about geometry (as opposed to arithmetic) is that it's easy to guess something a little larger[0] than 1/10, repeat a series of ten of those units, and then line its end points up at an angle to your work and, letting similar triangles do their thing, transfer[1] from there... [0] eg, 1/8 would work, if you insist on subdivisions [1] assuming space-time is effectively euclidean at the scale you're doing this, which even on HN ought to be a safe bet?
- kragen 2y ago
  this presupposes a way to construct parallel lines to transfer your tenths back to the segment you wanted to subdivide; this can certainly be done to three significant figures of precision with a compass and straightedge (or string and sand table), but it's still extra effort and extra opportunities for error compared to simple perpendicular bisectors in some cases, it's not extra effort because you're doing a task that requires the construction of those parallel lines anyway, of course. laying out tiles on a floor or ripping a plank into smaller planks, for example. and if your desired parallel lines are perpendicular to the edge of your stela, the square that figures so prominently in the freemasons' logotype allows you to scribe them easily (then again, once you're going to the effort of making a square, you might as well rule it)
mitthrowaway2 2y ago
I don't think objections to US customary units are because of base-12 vs base-10. I think it's because it's 12 inches to 1 foot, 3 feet to 1 yard, 1760 yards to 1 mile, 3 tsp to 1 tbsp, 2 tbbsp to 1 fl. oz, 40 fl. oz per quart, 2 quarts per pint, 4 quarts per gallon, 31.5 gallons per barrel (or 42 if oil), 16 ounces per pound, 2000 pounds per ton (or 2240 if long ton), 1000 mil per inch, and so on. It's not just a base-12 system, it's pretty random across the board. And even just for "workshop" purposes, things like screw diameter (or sheet metal gauge, etc) are only listed in fractions-of-an-inch above certain sizes; below that it switches to a completely different numbering system, so you end up needing a reference chart anyway, which often just displays a decimal-inch figure like '#6 screw = 0.138 inch', and now you're looking up which fractional-markings that lies between on your ruler...
- bee_rider 2y ago
  This makes me wonder about an alternate universe where a mile has 2310 yards. At least we’d get a bunch of prime factors out of it. Although guess being able to repeatedly halve a mile is useful for splitting up properties?
- JoeAltmaier 2y ago
  Those conversions varied all over the place. But they originated in a system of doubling. Used to be two quarts per pottle, two pottles per gallon, and so on from there (peck, kenning, bushel, strike, coomb)
- davidgay 2y ago
  > 40 fl. oz per quart, That's the imperial quart. The US quart is 32 fl. oz. And, of course, the US fl. oz is slightly different from the imperial one. And neither is 1 (weight) oz of water (but at least the weight ozes are the same in US and imperial...).
  - deleted 2y ago
    [deleted]
  - saalweachter 2y ago
legitster 2y ago
Yeah, it's crazy to see my dad at work in his shop - the amount of intuition he has of fractional measurements is insane, but he can do the math so quickly. In that specific context, if you were to do the math with decimal measurements it would take longer and leave you with some funky units. It's hard to describe how you work with the fractions - but the lumber and the saw blades and the screws and even the finishes all come in these standardized fractional increments that are easy to work with. And the skill required of a project is directly related to the precision of the measurement you go down to - 1/8, 1/16, 1/32, etc. It all just kinda works.
- arlort 2y ago
  > if you were to do the math with decimal measurements You'd end up building the same intuitions and speed that you have with fractions. It's all just a matter of familiarity
itishappy 2y ago
> If you imagine doing this with paper, it's fairly easy. Halves and forths are easy. Thirds, fifths, and sixths are not. There are constructions for the odd fractions, but they're not particularly intuitive. https://abrashiorigami.com/dividing-paper-into-thirds-fifths-sevenths-and-so-on/ https://abrashiorigami.com/dividing-paper-into-thirds-fifths...
wongarsu 2y ago
> Now imagine Metric, and the need to split something into 10 even pieces That's only true if you assume that in metric everything starts out as 1, 10 or 100 units. But that's not really what happens. For example kitchen appliances and furniture basically works on multiples of 60cm: an oven or dishwasher fits in a 60cm slot, and accordingly your cabinets will be one appliance wide (60cm), two appliances wide (120cm) or half an appliance wide (30cm). And you will find that halfes, thirds, fourths or sixths of 60cm are easy to calculate. Lots of other furniture works on multiples of 80cm. Those don't have nice thirds, but halves, fourths, eights, sixteenths, doubles, triples, quadruples all work great. And this happens not only in furniture but in everything. Having things 1.2, 1.5 or 1.6 of whatever unit you are measuring is common and allows you to have nice fractions. We just never write them as fractions. And honestly 45 + 7.5 is so much easier to do that 3/8th + 1/16th (of 120)
- funnybeam 2y ago
  Kitchen appliances and furniture basically work on multiples of feet. 1 foot = 30cm, so the reason the standard appliance is 60cm is because that’s the metric equivalent of 2 feet
arlort 2y ago
> and the need to split something into 10 even pieces Why would you need to do that though?

deleted 2y ago

[deleted]

082349872349872 2y ago

The nice thing about geometry (as opposed to arithmetic) is that it's easy to guess something a little larger[0] than 1/10, repeat a series of ten of those units, and then line its end points up at an angle to your work and, letting similar triangles do their thing, transfer[1] from there... [0] eg, 1/8 would work, if you insist on subdivisions [1] assuming space-time is effectively euclidean at the scale you're doing this, which even on HN ought to be a safe bet?

kragen 2y ago
this presupposes a way to construct parallel lines to transfer your tenths back to the segment you wanted to subdivide; this can certainly be done to three significant figures of precision with a compass and straightedge (or string and sand table), but it's still extra effort and extra opportunities for error compared to simple perpendicular bisectors in some cases, it's not extra effort because you're doing a task that requires the construction of those parallel lines anyway, of course. laying out tiles on a floor or ripping a plank into smaller planks, for example. and if your desired parallel lines are perpendicular to the edge of your stela, the square that figures so prominently in the freemasons' logotype allows you to scribe them easily (then again, once you're going to the effort of making a square, you might as well rule it)

mitthrowaway2 2y ago

I don't think objections to US customary units are because of base-12 vs base-10. I think it's because it's 12 inches to 1 foot, 3 feet to 1 yard, 1760 yards to 1 mile, 3 tsp to 1 tbsp, 2 tbbsp to 1 fl. oz, 40 fl. oz per quart, 2 quarts per pint, 4 quarts per gallon, 31.5 gallons per barrel (or 42 if oil), 16 ounces per pound, 2000 pounds per ton (or 2240 if long ton), 1000 mil per inch, and so on. It's not just a base-12 system, it's pretty random across the board. And even just for "workshop" purposes, things like screw diameter (or sheet metal gauge, etc) are only listed in fractions-of-an-inch above certain sizes; below that it switches to a completely different numbering system, so you end up needing a reference chart anyway, which often just displays a decimal-inch figure like '#6 screw = 0.138 inch', and now you're looking up which fractional-markings that lies between on your ruler...

bee_rider 2y ago
This makes me wonder about an alternate universe where a mile has 2310 yards. At least we’d get a bunch of prime factors out of it. Although guess being able to repeatedly halve a mile is useful for splitting up properties?
JoeAltmaier 2y ago
Those conversions varied all over the place. But they originated in a system of doubling. Used to be two quarts per pottle, two pottles per gallon, and so on from there (peck, kenning, bushel, strike, coomb)
davidgay 2y ago
> 40 fl. oz per quart, That's the imperial quart. The US quart is 32 fl. oz. And, of course, the US fl. oz is slightly different from the imperial one. And neither is 1 (weight) oz of water (but at least the weight ozes are the same in US and imperial...).
- deleted 2y ago
  [deleted]
- saalweachter 2y ago

legitster 2y ago

Yeah, it's crazy to see my dad at work in his shop - the amount of intuition he has of fractional measurements is insane, but he can do the math so quickly. In that specific context, if you were to do the math with decimal measurements it would take longer and leave you with some funky units. It's hard to describe how you work with the fractions - but the lumber and the saw blades and the screws and even the finishes all come in these standardized fractional increments that are easy to work with. And the skill required of a project is directly related to the precision of the measurement you go down to - 1/8, 1/16, 1/32, etc. It all just kinda works.

arlort 2y ago
> if you were to do the math with decimal measurements You'd end up building the same intuitions and speed that you have with fractions. It's all just a matter of familiarity

itishappy 2y ago

> If you imagine doing this with paper, it's fairly easy. Halves and forths are easy. Thirds, fifths, and sixths are not. There are constructions for the odd fractions, but they're not particularly intuitive. https://abrashiorigami.com/dividing-paper-into-thirds-fifths-sevenths-and-so-on/ https://abrashiorigami.com/dividing-paper-into-thirds-fifths...

wongarsu 2y ago

> Now imagine Metric, and the need to split something into 10 even pieces That's only true if you assume that in metric everything starts out as 1, 10 or 100 units. But that's not really what happens. For example kitchen appliances and furniture basically works on multiples of 60cm: an oven or dishwasher fits in a 60cm slot, and accordingly your cabinets will be one appliance wide (60cm), two appliances wide (120cm) or half an appliance wide (30cm). And you will find that halfes, thirds, fourths or sixths of 60cm are easy to calculate. Lots of other furniture works on multiples of 80cm. Those don't have nice thirds, but halves, fourths, eights, sixteenths, doubles, triples, quadruples all work great. And this happens not only in furniture but in everything. Having things 1.2, 1.5 or 1.6 of whatever unit you are measuring is common and allows you to have nice fractions. We just never write them as fractions. And honestly 45 + 7.5 is so much easier to do that 3/8th + 1/16th (of 120)

funnybeam 2y ago
Kitchen appliances and furniture basically work on multiples of feet. 1 foot = 30cm, so the reason the standard appliance is 60cm is because that’s the metric equivalent of 2 feet

arlort 2y ago

> and the need to split something into 10 even pieces Why would you need to do that though?