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.
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.