Hard disagree on the fractional units. Using rational numbers for those things derives from the frequency with which people need to double and halve things in the fields that use those conventions. Doubling 3/8 to get 6/8 or 3/4 is much easier than doubling .375 to get .75
That one’s nothing to do with the metric system vs imperial, aside from the fields that rely on the convention being largely the ones that created imperial in the first place. If they all switched to metric tomorrow they’d just say they need 3/5 meter spacing.
From everything I’ve heard it’s a hodge podge, since the US, with the worst system, is the only one to use it consistently. Building plans would reference it by cm however.
What I was more referring to was from the perspective of the carpenter doing the work.
Fractions or decimals aren’t specific to us customary or metric. You see decimal inches perfectly often, or at least I do.
Fractions are a more convenient way of dealing with multiplying or dividing numbers without a lot of mental effort. 1/3 of .125 is gonna take a second to figure out. 1/3 of 1/8 is 1/24. 5 1/8 units is just ”5/8”, rather than the .625 in decimal.
It’s definitely less effective for numerical sorting in your head, but if I’m sorting screws or something, I’m probably gonna just look at them rather than compare the labels.
I understand the underlying principle, but I’m not sure if it actually shakes out that way for a few reasons:
If you asked a carpenter to cut something to 1/24", they’d be like “what?”. Sure, the math was easier, but the result is unusable. No measuring instrument has divisions of 24ths. The person making a cut would need it in terms of 8ths, 16ths, etc. Any time saved at the initial stage is lost when they need to convert it again to a useable denominator.
Secondly, what’s 3/32nds of 17/128ths?
The examples you give are harder in decimal form because nobody is going to make metric carpentry designs for things that are to the tenth of a millimeter, so 1.25cm isn’t even real.
I admit, there are a lot of specific scenarios where fractional convention is helpful. I just personally think they don’t outweigh the drawbacks.
It’s fair to not be as big of a fan. I’m also not saying that rational numbers are more useful in every situation.
I don’t think it’s to controversial to say that it’s generally easier to deal with rational numbers mentally than decimal numbers if you need to use fractional units. Metrics advantage is that you need to use fractional units less often.
Your example is indeed tricky, but it’s still easier than 0.09375 * 0.1328125. I’d much rather do 3 * 17 and 32 * 128.
People making metric designs for things is one thing, but people in metric countries definitely get cabinets built, and those need adjustments that are definitely smaller than a millimeter.
I feel like this is all getting away from the original point though. Fractions are useful when multiplying and dividing whole numbers. Metric did not change how carpenters or craftsmen actually do their work, and how they work is the entire reason people use those fractional units.
Metric and imperial don’t change the way carpenters work because in the case you mentioned of a sub-mm dimension, that’s in the 64th of an inch range. Carpenters don’t ever measure to that precision because of the fluidity of the material. Craftsman will at that point just cut to fit.
My point with those hard numbers wasn’t that metric would make those numbers easier, only that your examples were intrinsically favouring imperial measures. Maybe it’s easier to say:
What’s easier to figure out, 1/3 of 3cm or 1/3 of 1 93/512 inches? You can easily construct scenarios for a measure that are easy in one and obscene in the equivalent. It’s less about the notation and more about the measure. If you assume all of the initial measures are round in imperial units, then the math will automatically be easier. If your designs were designed in metric, they’ll be round to metric. If they’re in imperial, they’ll be round in imperial.
And when this degree of precision is actually important, imperial craftsmen (engineers, machinists) already use decimal. A “Mil” is a milli-inch.
Anyhow, again, I agree that for some very specific scenarios dealing with fractions is easier, especially when you’re doing any base 2 operation.
I just think that you would be surprised how infrequently the issues you’re imagining would actually manifest themselves, working with intrinsically metric designs, and that you’re underestimating the number of scenarios where not dealing with fractions actually would make your life easier.
“intuitive” in the sense you described just means “familiar”. One feels like one. Ten feels like ten.
The magic of metric isn’t that each base unit is somehow more valuable in metric. It isn’t. One will always feel like one.
The magic is how easy it is to convert from the “small one”, the “medium one” and the “big one”.
Also, the convention of fractional inches is ridiculous.
It should be trivial to order 27/64, 3/8, and 7/16. Don’t make me do that math.
Hard disagree on the fractional units. Using rational numbers for those things derives from the frequency with which people need to double and halve things in the fields that use those conventions. Doubling 3/8 to get 6/8 or 3/4 is much easier than doubling .375 to get .75
That one’s nothing to do with the metric system vs imperial, aside from the fields that rely on the convention being largely the ones that created imperial in the first place. If they all switched to metric tomorrow they’d just say they need 3/5 meter spacing.
Does Germany use 3/5m spacing?
I looked it up and they use 2/5 meter spacing. Some other countries nearby use 3/5th though.
And it’s described locally as 2/5 and 3/5, rather than 40 or 60 cm?
If so, I’m shocked, but delighted to have learned something unexpected
From everything I’ve heard it’s a hodge podge, since the US, with the worst system, is the only one to use it consistently. Building plans would reference it by cm however.
What I was more referring to was from the perspective of the carpenter doing the work.
Fractions or decimals aren’t specific to us customary or metric. You see decimal inches perfectly often, or at least I do.
Fractions are a more convenient way of dealing with multiplying or dividing numbers without a lot of mental effort. 1/3 of .125 is gonna take a second to figure out. 1/3 of 1/8 is 1/24. 5 1/8 units is just ”5/8”, rather than the .625 in decimal.
It’s definitely less effective for numerical sorting in your head, but if I’m sorting screws or something, I’m probably gonna just look at them rather than compare the labels.
I understand the underlying principle, but I’m not sure if it actually shakes out that way for a few reasons:
If you asked a carpenter to cut something to 1/24", they’d be like “what?”. Sure, the math was easier, but the result is unusable. No measuring instrument has divisions of 24ths. The person making a cut would need it in terms of 8ths, 16ths, etc. Any time saved at the initial stage is lost when they need to convert it again to a useable denominator.
Secondly, what’s 3/32nds of 17/128ths?
The examples you give are harder in decimal form because nobody is going to make metric carpentry designs for things that are to the tenth of a millimeter, so 1.25cm isn’t even real.
I admit, there are a lot of specific scenarios where fractional convention is helpful. I just personally think they don’t outweigh the drawbacks.
It’s fair to not be as big of a fan. I’m also not saying that rational numbers are more useful in every situation.
I don’t think it’s to controversial to say that it’s generally easier to deal with rational numbers mentally than decimal numbers if you need to use fractional units. Metrics advantage is that you need to use fractional units less often.
Your example is indeed tricky, but it’s still easier than 0.09375 * 0.1328125. I’d much rather do 3 * 17 and 32 * 128.
People making metric designs for things is one thing, but people in metric countries definitely get cabinets built, and those need adjustments that are definitely smaller than a millimeter.
I feel like this is all getting away from the original point though. Fractions are useful when multiplying and dividing whole numbers. Metric did not change how carpenters or craftsmen actually do their work, and how they work is the entire reason people use those fractional units.
Metric and imperial don’t change the way carpenters work because in the case you mentioned of a sub-mm dimension, that’s in the 64th of an inch range. Carpenters don’t ever measure to that precision because of the fluidity of the material. Craftsman will at that point just cut to fit.
My point with those hard numbers wasn’t that metric would make those numbers easier, only that your examples were intrinsically favouring imperial measures. Maybe it’s easier to say:
What’s easier to figure out, 1/3 of 3cm or 1/3 of 1 93/512 inches? You can easily construct scenarios for a measure that are easy in one and obscene in the equivalent. It’s less about the notation and more about the measure. If you assume all of the initial measures are round in imperial units, then the math will automatically be easier. If your designs were designed in metric, they’ll be round to metric. If they’re in imperial, they’ll be round in imperial.
And when this degree of precision is actually important, imperial craftsmen (engineers, machinists) already use decimal. A “Mil” is a milli-inch.
Anyhow, again, I agree that for some very specific scenarios dealing with fractions is easier, especially when you’re doing any base 2 operation.
I just think that you would be surprised how infrequently the issues you’re imagining would actually manifest themselves, working with intrinsically metric designs, and that you’re underestimating the number of scenarios where not dealing with fractions actually would make your life easier.