So this is an argument for the Imperial system. It's never stated in the post, but if you don't like the Metric system then what are you arguing for? There's only the Imperial system left. Here is why the Imperial system is bad:
- It's not consistently base 2 (or base 12), it's more like base random.
- Imperial calculations still use base 10 numbers for representation! This is the worst of both worlds. You can argue that base 10 is inefficient but at least the Metric system aligns perfectly with it, as compared to the Imperial system which uses base random and base 10 numbers which cannot perfectly model many Imperial system values.
> Metric’s entire foundation is a bad base.
You're stuck with base 10 numbers. Don't blame the base, pick a better system.
I agree but it's more important that we share a common system and it's incredibly expensive to switch (not just monetarily). For better or worse, if there's gonna be one system it will be decimal. Take heart that decimal time didn't catch on.
100 hour days are exactly what I think of the metric system. It's good for science and engineering, so you're not constantly converting bases; but when it comes to daily, human-scaled activity, I want numbers that are small and easy to divide. 1 / 4 == 3 is a lot nicer than 1 / 4 == 25.
If we were using a base 12, 24 or 60 from the start, the metric system would had used those bases. It is not about the metric system, is about our numeric system.
Metric may be not perfect, but is not in the same category of mess that is the imperial one, specially if he is complaining about proportions between different units of measurements.
Base 10 is an excellent base for exactly one reason: we all know it and use it. All bases have trade-offs but a common language/base beats any slight technical reason that another base should be put into general use.
We can celebrate the fact that our notion of numbers is flexible enough that we can easily represent other bases without significant reach. Eg: Imagine trying to express another base with Roman numerals.
"it is the most divisional number under 100" implies there's some committee of Hammurabi where "they" evaluated all the possibilities and decided "60 is the best".
My understanding is that it's "finger bones between knuckles reachable by thumb" and "count of times counted through all knuckles". Meaning you count to 12 with one hand (thumb incrementing through finger bones) and then count 13-60 by incrementing the other.
It just so happens that 12 * 5 ends up having a fantastic number of divisors.
> "it is the most divisional number under 100" implies there's some committee of Hammurabi where "they" evaluated all the possibilities and decided "60 is the best".
OP didn't say or imply anything about the origins of the Sumerians' use of base 60, they just observed that it has nice properties.
From the article itself it is clear that it was not a pure base 60 system. It was basically a base 10 system where the symbol changed at 10 and not 60. A pure base would be like Hexadecimal where we use 16 symbols and 16 is equivalent to 10.
I guess most of the human civilisation ended up using base 10 numbers because we have 10 finger. If we had 8 fingers, we would probably be using base 8. 64 would be our 100.
Base 60 (like the Babylonians and Sumerians) is actually a terrific base for daily use. Base 12 is similarly good, and more functional.
60 and 12 are both divisible by 2, 3, 4, and 6, which are some of the most common divisions that people need in daily life.
Base 60 has the additional advantage of being divisible by 5, 10, 15, and 20 as well. Note that we still use bases 60 and 24 for our timekeeping, and it's extremely convenient to be able to divide up the hour or day evenly into these chunks.
The metric system is great for scientific purposes, but the properties that make it good for scientific use are not terribly relevant to household or daily use.
I don't think there's anything in the metric system that actually requires using base 10. Anything will work the same with base 12 or any other base. The only thing we need is consistency, which is the hardest part in this matter.
Base 10 is not bad for day to day use because you can just round there. Metric system is especially good in cooking because you do not need n ways to measure thing. Just one kitchen scale.
Given how this very short rant of a blog post is technically right that 10 is not a very integer-division-friendly base and how it uses imperial measures to illustrate the point—the pain point with imperial measures is not that they don't take base ten, the point is that it takes a plethora of multiplicators between commensurate units and that none of those multiplicators lines up with the way we say and write numbers. The obstacle from switching from colloquial "four in the afternoon" to "16:00" (not e.g. "14:00" which for a learner would be the obvious but wrong answer) is not to blame on the multiplicator, it's the fact that the multiplicator is not the base of our counting. Another obstacle in adding up seconds, minutes and hours and to say the results in terms of days, hours and so on is that several multiplicators—12, 60 and 24—are involved, none of which is a power or at least a multiple of the base that we use for expressing the results.
Of course none of this even touches about the great utility of a system where one liter equals a thousand cubic centimeters, with water weighing (OK, "massing") one kilogram (at standard conditions, imagine all the hedges), and where all mass measurements are based on the kilogram, all lengths on the meter and so on. In imperial, the horizontal distance from you to that tower is given in miles, yrds or feet depending on your habits and how far away you are; the height of the tower will most likely be given in feet, the vertical distance to a plane high in the sky curiously in feet, too, but the distance to the ISS in miles. In metric you do something similar in choosing between centimeters, meters, kilometers as you see fit, but crucially the digits remain the same, only the decimal point shifts somewhere else. This is what they wanted when they initially proposed the metric system near the end of the 18th century; SI is building upon this and greatly expands the system.
Let's try to phase it in gradually. We'll petition congress to move to base 12, but will compromise, and use base 11 for a while. Then, if people are still not ready for base 12, we can move on to base 11.1 for a few years, then 11.2, and so forth. Maybe once we get to 11.5, we can start a sliding scale where the base increases slightly every day, so people aren't inconvenienced.
We could use genetic engineering so people have six fingers. However better would be to genetically engineer humans to have four arms and ditch the pinky, then we could use base 16.
Cultures that counted in base 12 used each finger segment (there are 12 on a hand), and used their thumb as a pointer. So we already have all the biological tools needed.
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- It's not consistently base 2 (or base 12), it's more like base random.
- Imperial calculations still use base 10 numbers for representation! This is the worst of both worlds. You can argue that base 10 is inefficient but at least the Metric system aligns perfectly with it, as compared to the Imperial system which uses base random and base 10 numbers which cannot perfectly model many Imperial system values.
> Metric’s entire foundation is a bad base.
You're stuck with base 10 numbers. Don't blame the base, pick a better system.
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Metric may be not perfect, but is not in the same category of mess that is the imperial one, specially if he is complaining about proportions between different units of measurements.
We can celebrate the fact that our notion of numbers is flexible enough that we can easily represent other bases without significant reach. Eg: Imagine trying to express another base with Roman numerals.
Is what I thought you were going to say. But I do sometimes wish we had 12
If we can convince everyone to have 12 fingers, maybe we can convince them to switch to dozenal.
Sumerians used Base 60.
https://en.wikipedia.org/wiki/Sexagesimal
It’s the most divisional number under 100. Hence why 60 is still used today for so many things (clocks, degrees, etc).
My understanding is that it's "finger bones between knuckles reachable by thumb" and "count of times counted through all knuckles". Meaning you count to 12 with one hand (thumb incrementing through finger bones) and then count 13-60 by incrementing the other.
It just so happens that 12 * 5 ends up having a fantastic number of divisors.
OP didn't say or imply anything about the origins of the Sumerians' use of base 60, they just observed that it has nice properties.
So in some ways it's not entirely coincidental.
In fact, 12 is derived the same way, 4 fingers times 3 knuckles, so the only coincidence is that 4 is divisible by 2.
60 and 12 are both divisible by 2, 3, 4, and 6, which are some of the most common divisions that people need in daily life.
Base 60 has the additional advantage of being divisible by 5, 10, 15, and 20 as well. Note that we still use bases 60 and 24 for our timekeeping, and it's extremely convenient to be able to divide up the hour or day evenly into these chunks.
The metric system is great for scientific purposes, but the properties that make it good for scientific use are not terribly relevant to household or daily use.
But yes, having a standard everyone agrees on is way more important than how well thought out the standard is.
30 is not divisible by 4.
Given how this very short rant of a blog post is technically right that 10 is not a very integer-division-friendly base and how it uses imperial measures to illustrate the point—the pain point with imperial measures is not that they don't take base ten, the point is that it takes a plethora of multiplicators between commensurate units and that none of those multiplicators lines up with the way we say and write numbers. The obstacle from switching from colloquial "four in the afternoon" to "16:00" (not e.g. "14:00" which for a learner would be the obvious but wrong answer) is not to blame on the multiplicator, it's the fact that the multiplicator is not the base of our counting. Another obstacle in adding up seconds, minutes and hours and to say the results in terms of days, hours and so on is that several multiplicators—12, 60 and 24—are involved, none of which is a power or at least a multiple of the base that we use for expressing the results.
Of course none of this even touches about the great utility of a system where one liter equals a thousand cubic centimeters, with water weighing (OK, "massing") one kilogram (at standard conditions, imagine all the hedges), and where all mass measurements are based on the kilogram, all lengths on the meter and so on. In imperial, the horizontal distance from you to that tower is given in miles, yrds or feet depending on your habits and how far away you are; the height of the tower will most likely be given in feet, the vertical distance to a plane high in the sky curiously in feet, too, but the distance to the ISS in miles. In metric you do something similar in choosing between centimeters, meters, kilometers as you see fit, but crucially the digits remain the same, only the decimal point shifts somewhere else. This is what they wanted when they initially proposed the metric system near the end of the 18th century; SI is building upon this and greatly expands the system.
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