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The article never mentions why folding in half is a good thing. It is, of course, but why half, and not fifths? The reason is that two is a good factor to work

The article never mentions why folding in half is a good thing. It is, of course, but why half, and not fifths? The reason is that two is a good factor to work with. Multiplying and dividing by two is more common than by five in a lot of domains. Three is pretty useful also. But the metric system is based on ten, which has factors two and five. Five is not such a great factor and often creates awkward numbers when dividing by two or three. The US measurement system, while inconsistent and arbitrary in many ways, but handles factors of two a lot better. Two cups in a pint, two pints in a quart, four quarts in a gallon. Better would be to have a consistent measurement system in base 12. Two twos and a three are a nice set of factors to work with. And twelve is still a nice "order of magnitude" that gives a good sense of scale. When it comes to distances, feet are actually pretty good in this regard. Degrees and time are base 60, which includes an extra five factor, so I guess it's combining all of them. The non-US world is smug about A4 and the metric system, but the very reasons that A4 is good shows why the metric system is not quite as brilliant as people like to think it is. (Obviously standardization and consistency have value, too. The metric system is good in that regard.)

katbyte 4y ago
all seems more complicated then just dropping down a unit in metric and doing whatever maths you need, without dealing won’t fractions or weird units.
throwaway744678 4y ago
Sheets of paper are not used to measure or calculate things, unlike the metric system.
monopoliessuck 4y ago
I agree with you, but think 16 would be a better base than 12 as it's binary reducible all the way down. It doesn't have a factor of three, which can be useful, but being able to natively understand and do math in a hex base would be such a boon, especially in the computer era. The Babylonians base 60 was quite a practical decision we partially inherited, but the metric 10 and Aztec 20 were probably just cavemen looking at their fingers (and toes). If you use your thumb to index the interphalangeal joints of your hand, you also get 16 which is super slick. A4 is a nice standard, but we really missed out on realizing base 16 metric.
- Beltalowda 4y ago
  Can't divide 16 by 3 though; the nice thing about 12 is that you get nice natural numbers for many common divisors: >>> 12/2, 12/3, 12/4, 12/5, 12/6, 12/7, 12/8 (6.0, 4.0, 3.0, 2.4, 2.0, 1.7142857142857142, 1.5) >>> 16/2, 16/3, 16/4, 16/5, 16/6, 16/7, 16/8 (8.0, 5.333333333333333, 4.0, 3.2, 2.6666666666666665, 2.2857142857142856, 2.0) With base-12, only 7 is awkward (and that's probably okay as it's not that common) and the non-natural numbers of 2.4 and 1.5 when dividing by 5 and 8 are still fairly easy to deal with. Dividing by the common figures of 2, 3, and 4 gives nice numbers. Base-16 has the "infinite number problem" for 3 and 6 that base-10 has, and only 2, 4, and 8 give natural numbers. This is probably why there are 12 months and why people used "a dozen" for a long time.
  - monopoliessuck 4y ago
    Sure and I agree with you, except base 16 is binary reducible all the way down which isn't a small thing. The Imperial or US standard systems of measure rounded the horses on halving in an awkward way because halving is intuitive. 1/2, 1/8, 1/16, 1/32 of an inch etc. and it's proven very useful. Splitting a meter into ten is less useful than splitting it in half and that half into half. Base ten doesn't half indefinitely across units bases. 1000cm, 500cm, 125cm, 62.5cm, 31.25, 15.625, 7.8125, 3.90625, 1.953125, 0.9765625... 4096cm, 2048cm, 1024cm, 512cm, 256, 128, 64, 32, 16, 8, 4, 2, 1 (which of course looks a lot better in base 16 notation) 1000, 800, 400, 200, 100, 80, 40, 20, 10, 8, 4, 2, 1 We could have had the best of both worlds. When SI was getting standardized there was a proposal for extra glyphs for base 12 and 16 that would have obviated our overloading of A-F too. Measuring in 1/256 of an inch would have been crazy simple while also getting the other metric goodies, IMO.
- int_19h 4y ago
  We're already long past the point where doing math in hex (or binary) is something that an average software engineer is likely to face. And outside of the industry, who ever cared?
  - monopoliessuck 4y ago
orthoxerox 4y ago
> Better would be to have a consistent measurement system in base 12. Or a system in base 60, where 12 and 5 are alternating: - 12 hairs = 1 graph square - 5 graph squares = 1 inch - 12 inches = 1 foot - 5 feet = 1 manlet - 12 manlets = 1 stone's throw - 5 stone's throws = 1 dash And so on
WastingMyTime89 4y ago
It’s a physical good. The reason is that it’s easy to fold in half and it offers a good enough granularity of size. Also having a measuring system in base 10 when you use base 10 for notation will always be more handy to calculate even it has less divisors. Your comment is the kind of comment which can only be made by someone who has never used metric.
Beltalowda 4y ago
I agree base-12 would be better (having 12 months is nice) in principle, but in practice I found it rarely to be an issue and I've paid special attention to it since I first heard this argument a few years ago because it sounded convincing at first. Stuff like easily using fractions (1.65m, and what's halfway between 6"4' and 6"5'?), division of things with fraction (what's half of 6"4'?), and converting from cm to m is much more common. So while metric does indeed make some things harder, it makes many common things easier. Overall, it seems like a fair trade-off.
int_19h 4y ago
It would be great to have a consistent measurement system in base-12 on top of base-12 numbers. But without this latter part, you end up with base-12 units computed in base-10 numbers, which creates more mess than having a few extra divisors remove. And, unfortunately, we're way too committed to base-10 to change it now. So metric it is.

katbyte 4y ago

all seems more complicated then just dropping down a unit in metric and doing whatever maths you need, without dealing won’t fractions or weird units.

throwaway744678 4y ago

Sheets of paper are not used to measure or calculate things, unlike the metric system.

monopoliessuck 4y ago

I agree with you, but think 16 would be a better base than 12 as it's binary reducible all the way down. It doesn't have a factor of three, which can be useful, but being able to natively understand and do math in a hex base would be such a boon, especially in the computer era. The Babylonians base 60 was quite a practical decision we partially inherited, but the metric 10 and Aztec 20 were probably just cavemen looking at their fingers (and toes). If you use your thumb to index the interphalangeal joints of your hand, you also get 16 which is super slick. A4 is a nice standard, but we really missed out on realizing base 16 metric.

Beltalowda 4y ago
Can't divide 16 by 3 though; the nice thing about 12 is that you get nice natural numbers for many common divisors: >>> 12/2, 12/3, 12/4, 12/5, 12/6, 12/7, 12/8 (6.0, 4.0, 3.0, 2.4, 2.0, 1.7142857142857142, 1.5) >>> 16/2, 16/3, 16/4, 16/5, 16/6, 16/7, 16/8 (8.0, 5.333333333333333, 4.0, 3.2, 2.6666666666666665, 2.2857142857142856, 2.0) With base-12, only 7 is awkward (and that's probably okay as it's not that common) and the non-natural numbers of 2.4 and 1.5 when dividing by 5 and 8 are still fairly easy to deal with. Dividing by the common figures of 2, 3, and 4 gives nice numbers. Base-16 has the "infinite number problem" for 3 and 6 that base-10 has, and only 2, 4, and 8 give natural numbers. This is probably why there are 12 months and why people used "a dozen" for a long time.
- monopoliessuck 4y ago
  Sure and I agree with you, except base 16 is binary reducible all the way down which isn't a small thing. The Imperial or US standard systems of measure rounded the horses on halving in an awkward way because halving is intuitive. 1/2, 1/8, 1/16, 1/32 of an inch etc. and it's proven very useful. Splitting a meter into ten is less useful than splitting it in half and that half into half. Base ten doesn't half indefinitely across units bases. 1000cm, 500cm, 125cm, 62.5cm, 31.25, 15.625, 7.8125, 3.90625, 1.953125, 0.9765625... 4096cm, 2048cm, 1024cm, 512cm, 256, 128, 64, 32, 16, 8, 4, 2, 1 (which of course looks a lot better in base 16 notation) 1000, 800, 400, 200, 100, 80, 40, 20, 10, 8, 4, 2, 1 We could have had the best of both worlds. When SI was getting standardized there was a proposal for extra glyphs for base 12 and 16 that would have obviated our overloading of A-F too. Measuring in 1/256 of an inch would have been crazy simple while also getting the other metric goodies, IMO.
int_19h 4y ago
We're already long past the point where doing math in hex (or binary) is something that an average software engineer is likely to face. And outside of the industry, who ever cared?
- monopoliessuck 4y ago

orthoxerox 4y ago

> Better would be to have a consistent measurement system in base 12. Or a system in base 60, where 12 and 5 are alternating: - 12 hairs = 1 graph square - 5 graph squares = 1 inch - 12 inches = 1 foot - 5 feet = 1 manlet - 12 manlets = 1 stone's throw - 5 stone's throws = 1 dash And so on

WastingMyTime89 4y ago

It’s a physical good. The reason is that it’s easy to fold in half and it offers a good enough granularity of size. Also having a measuring system in base 10 when you use base 10 for notation will always be more handy to calculate even it has less divisors. Your comment is the kind of comment which can only be made by someone who has never used metric.

Beltalowda 4y ago

I agree base-12 would be better (having 12 months is nice) in principle, but in practice I found it rarely to be an issue and I've paid special attention to it since I first heard this argument a few years ago because it sounded convincing at first. Stuff like easily using fractions (1.65m, and what's halfway between 6"4' and 6"5'?), division of things with fraction (what's half of 6"4'?), and converting from cm to m is much more common. So while metric does indeed make some things harder, it makes many common things easier. Overall, it seems like a fair trade-off.

int_19h 4y ago

It would be great to have a consistent measurement system in base-12 on top of base-12 numbers. But without this latter part, you end up with base-12 units computed in base-10 numbers, which creates more mess than having a few extra divisors remove. And, unfortunately, we're way too committed to base-10 to change it now. So metric it is.