We should all use the dozenal metric system
Instead of the US or British Imperials, or the metric using standard base, we should switch to dozenal metric. Why? The imperial system has the advantage of using certain logic of dozenal system, and the metric unit is inheritably superior for conversions. Imperial Units downfall is their needless complication of converting between units, and there is no universal expression for imperial measurements. Metric units using standard base downfall is their reduced divisibility in comparison with metric units using dozenal base. This makes dozenal metric ideals as it has all the advantages of both systems, and it eliminates downfalls of both.
To expand on the downfall of both system, let's start with the issue of imperial units. Suppose someone tells you to convert 200.375" to imperial decitectural form where feets are annotated, you'd have to start with feet annotation. You divide 200 by 12, and you get 16'. Then, you have to subtract 200 by 16*12 to get the inch integer which would be 4 and finally you have to create a fraction representing the remaining decimal and you get 3/8. Therefore, 200.375 inches = 16' - 4 3/8". It can also be expressed as 200 3/8".
The problem doesn't even end there. If someone asks you to express 7 yds, 4 feet, and 5. 6459 inches into decitectural form, well, good luck with that. 3.5 Mi to In requires you to do mental gymnastics, pen and pencil or calculator. In the metric system, 3.5 KM = 3,500 M, and that's very easy on the brain as it all involves just moving decimal points (More on that later). And let's not get into dead units like chains or ramsen's chain or poppy seeds in the imperial units. At this point, the issue with imperial system has been covered.
As for the issue with standard base, it has less divisibility than dozenal base. 10 in the standard base can only be divided into integers with 2,5 whereas in the dozenal system, 10 can be divided evenly in integer by 2,3, 4, and 6. Furthermore, 1 kilometer is 1000 meters is true in the dozenal metric system. As you can see, the usage of 10^x doesn't change by bases.
In scientific application, meter is defined as the length light travels at 1/8770X seconds according to the dozenal metric system, and that is far more cleaner than the base-10 version of metric. The issue here is that a lot of things would have to be redefined so that units and their relationship between variables would be consistent because base changes the very definition of some units that has been well-established by altering what defines 1 unit of something within that base.
Any comments?
And yes, I know this isn't feasible, but it's the best system there is.
To expand on the downfall of both system, let's start with the issue of imperial units. Suppose someone tells you to convert 200.375" to imperial decitectural form where feets are annotated, you'd have to start with feet annotation. You divide 200 by 12, and you get 16'. Then, you have to subtract 200 by 16*12 to get the inch integer which would be 4 and finally you have to create a fraction representing the remaining decimal and you get 3/8. Therefore, 200.375 inches = 16' - 4 3/8". It can also be expressed as 200 3/8".
The problem doesn't even end there. If someone asks you to express 7 yds, 4 feet, and 5. 6459 inches into decitectural form, well, good luck with that. 3.5 Mi to In requires you to do mental gymnastics, pen and pencil or calculator. In the metric system, 3.5 KM = 3,500 M, and that's very easy on the brain as it all involves just moving decimal points (More on that later). And let's not get into dead units like chains or ramsen's chain or poppy seeds in the imperial units. At this point, the issue with imperial system has been covered.
As for the issue with standard base, it has less divisibility than dozenal base. 10 in the standard base can only be divided into integers with 2,5 whereas in the dozenal system, 10 can be divided evenly in integer by 2,3, 4, and 6. Furthermore, 1 kilometer is 1000 meters is true in the dozenal metric system. As you can see, the usage of 10^x doesn't change by bases.
In scientific application, meter is defined as the length light travels at 1/8770X seconds according to the dozenal metric system, and that is far more cleaner than the base-10 version of metric. The issue here is that a lot of things would have to be redefined so that units and their relationship between variables would be consistent because base changes the very definition of some units that has been well-established by altering what defines 1 unit of something within that base.
Any comments?
And yes, I know this isn't feasible, but it's the best system there is.
Comments35
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"Why? The imperial system has the advantage of using certain logic of dozenal system"
Maybe it's because I did not grow up in a country using imperial, but I think imperial actually has little logic behind it and I don't understand how to use it. Metric seems to have more logic because, well, it's a metric system...
Maybe it's because I did not grow up in a country using imperial, but I think imperial actually has little logic behind it and I don't understand how to use it. Metric seems to have more logic because, well, it's a metric system...
"Metric" just means "pertaining to measurement" so literally any system of measurement units is a metric system. The "metric system" really gets its name from its basic unit of length, the meter. "Meter" just means "measure".
The real reason the metric system seems to have more logic is that its units were designed from the ground up to relate to each other in an easily computable way. Contrast that with the American and Imperial systems whose units were not. Many of them were derived from "average" sizes of human body parts, like the foot, or from practical considerations like the acre. (Roughly, an acre is the amount of land one man with a plough and ox team can get under till in one day. If you know how much land you have in acres, you know how much man-days you need to get the planting done. And yes, the size of an acre varied according to soil conditions. Officially, an acre is one chain by one furlong, a furlong being the length of a furrow in a standard 10-acre plot of land, and a chain being a standard 17th century surveying measure.)
Various attempts to standardize English measures over the centuries resulted in an unsystematic mess, apart from a half-hearted effort to relate them by multiples or fractions of 12, such as the 12 inches in a foot. (Originally, the inch was the width of a thumb. 12 inches were equated to a foot at a sufficiently early stage that its name is an Anglo-Saxon borrowing of the Latin word for 1/12.)
Internationally the situation was even worse because every country had its own peculiar system, usually with cognate or identical names, but which were all defined differently. There was a German "fuss", a French "pied", and an English "foot", but these were all of different sizes. The fuss wasn't even the same throughout all of Germany. The metric system was adopted to put an end to all that. But the rational method of relating metric units to each other is based on a place-based numerical system with a rather irrational basis: it's just the number of fingers on both human hands, which happens to be not arithmetically convenient at all. A truly rational system would have done away with that last primitive dependence on human anatomy as well, but it doesn't seem to have occurred to anyone.
The real reason the metric system seems to have more logic is that its units were designed from the ground up to relate to each other in an easily computable way. Contrast that with the American and Imperial systems whose units were not. Many of them were derived from "average" sizes of human body parts, like the foot, or from practical considerations like the acre. (Roughly, an acre is the amount of land one man with a plough and ox team can get under till in one day. If you know how much land you have in acres, you know how much man-days you need to get the planting done. And yes, the size of an acre varied according to soil conditions. Officially, an acre is one chain by one furlong, a furlong being the length of a furrow in a standard 10-acre plot of land, and a chain being a standard 17th century surveying measure.)
Various attempts to standardize English measures over the centuries resulted in an unsystematic mess, apart from a half-hearted effort to relate them by multiples or fractions of 12, such as the 12 inches in a foot. (Originally, the inch was the width of a thumb. 12 inches were equated to a foot at a sufficiently early stage that its name is an Anglo-Saxon borrowing of the Latin word for 1/12.)
Internationally the situation was even worse because every country had its own peculiar system, usually with cognate or identical names, but which were all defined differently. There was a German "fuss", a French "pied", and an English "foot", but these were all of different sizes. The fuss wasn't even the same throughout all of Germany. The metric system was adopted to put an end to all that. But the rational method of relating metric units to each other is based on a place-based numerical system with a rather irrational basis: it's just the number of fingers on both human hands, which happens to be not arithmetically convenient at all. A truly rational system would have done away with that last primitive dependence on human anatomy as well, but it doesn't seem to have occurred to anyone.
> Internationally the situation was even worse because every country had its own peculiar system, usually with cognate or identical names, but which were all defined differently.
I think you forgot to mention differences US imperial and British Imperial. They're similar, but not defined the same.
I think you forgot to mention differences US imperial and British Imperial. They're similar, but not defined the same.
I didn't forget. It was relatively unimportant compared to what was going on in Europe.
I frequently point out in other contexts that the US and Imperial systems are not identical, usually when someone calls the US system "Imperial". But the difference is mainly in units of volume. The US standardized on the ale gallon, divided into 8 pints of 16 ounces each. The Imperial system standardized on a gallon closer to (but slightly different from) the wine gallon, divided into 8 pints of 20 oz each. Therefore, the Imperial ounce is slightly smaller, but all bigger units are slightly larger, than the US. Most other units are identical, or close enough where it makes no practical difference.
I frequently point out in other contexts that the US and Imperial systems are not identical, usually when someone calls the US system "Imperial". But the difference is mainly in units of volume. The US standardized on the ale gallon, divided into 8 pints of 16 ounces each. The Imperial system standardized on a gallon closer to (but slightly different from) the wine gallon, divided into 8 pints of 20 oz each. Therefore, the Imperial ounce is slightly smaller, but all bigger units are slightly larger, than the US. Most other units are identical, or close enough where it makes no practical difference.
"Various attempts to standardize English measures over the centuries resulted in an unsystematic mess, apart from a half-hearted effort to relate them by multiples or fractions of 12, such as the 12 inches in a foot."
Makes sense to me, and it sounds like it works just as well as base 10.
The problem with that is... people count up to ten, not up to twelve. Are we really going to start counting 1-2-...-9-10-A-B, or something like that, just for the sake of whatever benefits the dozenal metric system has?
Makes sense to me, and it sounds like it works just as well as base 10.
The problem with that is... people count up to ten, not up to twelve. Are we really going to start counting 1-2-...-9-10-A-B, or something like that, just for the sake of whatever benefits the dozenal metric system has?
No, we're too used to counting on our fingers. I'm just explaining why base-10 isn't particularly rational, if rationality is to be the argument for the metric system.
If you were raised counting in base-12, you'd be accustomed to it and would do it without even thinking. Many other bases are possible. 10 is only "natural" to us because we're raised with it. mentalfloss.com/article/31879/…
If you were raised counting in base-12, you'd be accustomed to it and would do it without even thinking. Many other bases are possible. 10 is only "natural" to us because we're raised with it. mentalfloss.com/article/31879/…
There are many theories as to why 10 is the actual standard. Unfortunately I have no sources at hand which discuss these things but I do remember many other theories besides being raised by it. Besides it is the system that could hold its ground against other bases such as the 60 base of Babylon, which were probably the first system used for mathematical purpose. It just hints that it might be the one base that has the best ratio of uses to problems.
Astrological speaking, base 12 would be the best systems, for some reasons.
But thats the thing I guess. Every field of science would have a base that benefits it uses the most. Computerscience i.e. works the best with bases 2 and 16. And so it might be, that base 10 is the best base for the everyday purpose. Besides changing it now would be a tremendous amount of work that will probably not be worth it.
Astrological speaking, base 12 would be the best systems, for some reasons.
But thats the thing I guess. Every field of science would have a base that benefits it uses the most. Computerscience i.e. works the best with bases 2 and 16. And so it might be, that base 10 is the best base for the everyday purpose. Besides changing it now would be a tremendous amount of work that will probably not be worth it.
No, there aren't many theories. It's entirely because we have 10 fingers. Even the word "digit" is derived from a word for finger.
The advantage of 12 as a base has nothing to do with astrology. It's the other way around. There are 12 astrological signs because the Babylonians counted in base-60. (12 is 60/5, so base 60 gives additional factors of 5)
The advantage of 12 as a base has nothing to do with astrology. It's the other way around. There are 12 astrological signs because the Babylonians counted in base-60. (12 is 60/5, so base 60 gives additional factors of 5)
Base-30 has that benefit of 5 with the sacrifice of 4. It's probably easier to use base-30 than it is to use base-60.
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Base 12 has more divisibility than Base 10, and it's the lowest number with the most acceptable amount of divisible number from the scientific perspective. Base 2 has the very issue of having large number to quantify something like 184045345, and Base 16 has less divisibility than base 12. Yes, it is the best system for most application. Base 10 is only used because of our fingers.
Imperial uses 12 because it is a highly composite number. That's the main reason why a lot of people advocate imperial unit. Not that I agree because imperial unit is still a base-10 system with usability of divisions of 2,3,4,6 with conversion being its own demise, and lack of scientific accessibility as units doesn't have interchangeable relationship is also its own very demise. It's much harder to convert from cubic yard to cubic inch than it is to convert between litres and cubic x-meters.
“In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie1 of energy to heat up by one degree centigrade—which is 1 percent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it. Whereas in the American system, the answer to ‘How much energy does it take to boil a room-temperature gallon of water?’ is ‘Go fuck yourself,’ because you can’t directly relate any of those quantities.” Wild Thing by Josh Bazell.
That explains what I mean.
“In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie1 of energy to heat up by one degree centigrade—which is 1 percent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it. Whereas in the American system, the answer to ‘How much energy does it take to boil a room-temperature gallon of water?’ is ‘Go fuck yourself,’ because you can’t directly relate any of those quantities.” Wild Thing by Josh Bazell.
That explains what I mean.
I guess I just don't see the value in relearning a whole new base system just for the sake of... cleaner... divisions?
The cleaner division actually makes sense from certain perspective. Like were if you want to cut 1/3 of a wood, and the wood is 100 centimeter, you get the issue of 33.3333333, but dozenal system would make it 40 centimeter. Even division by 5 isn't a major problem since the error of margin is slightly below .01, and for almost all intents and purpose, 10/5 can be truncated to 2.5 in the dozenal system.
But realistically, when are you ever going to need that precise a measurement when cutting wood?
You don't, but it kinda tells the issue with the base 10 system.
You are not the first person to point out that 12 is a much more sensible counting base than 10. The Babylonians knew it, after all. But I'm afraid base 10 is embedded now and we're stuck with it.
Well, there might be changes in the future, but we'll be dead by then.
If we could start completely new from the beginning, I'd agree with you. We would need new words for the new numbers, and we would need to teach maths new to children, but if taught from the start it wouldn't be exactly more difficult or anything. So, after the inevitable downfall of civilization, we should definitely use another system there.
We could also use a hexadecimal system though, which would work well with what computer science has been doing all the time. Or does anything speak against it? I'd even think it has even more advantages than a dozenal system. Maybe we should decide after discovering how many fingers we will have on each hand after all the nuclear downfall after the apocalypse I have been speaking of.
We could also use a hexadecimal system though, which would work well with what computer science has been doing all the time. Or does anything speak against it? I'd even think it has even more advantages than a dozenal system. Maybe we should decide after discovering how many fingers we will have on each hand after all the nuclear downfall after the apocalypse I have been speaking of.
Base 12 has already been given all the symbols it would need and I wouldn’t worry too much about how we’d teach it to kids as it makes arithmetic easier. As I understand it, all of mathematics works the same way under base 12, it’s just easier to do calculations. I don’t think there are any ethical or legal issues to consider. No serious person would suggest we just make the switch over night. It would be a phased transition. Really, the only argument for not using it is that it will never be used, which is pretty retarded reasoning.
I am aware that mathematics would be basically the same. With "teaching maths new to children" I didn't actually mean math but counting. I would also not think there could be ethical or legal issues. What kind even? But what speaks against base 16? I'd think, if we make the step, base 16 would be the way to go. Or does it count as a disadvantage that we can't divide 16 by uneven numbers into integers?
Actually, that reminds me of another reason to go with base 12: we’re already familiar with using it (i.e., the foot, the number of hours per day, months per year, etc.).
I haven’t thought about base 16, but I’m pretty sure that that fact that it isn’t divisible by 3 means it doesn’t work the way base 12 does with thirds (i.e., resolving the infinite digit chain you get when dividing by 3 in the dicimal system). Also, we could teach counting under base 12 quite easily. Most of us have four fingers with three segments per finger. Count by segment. You can get to twelve on one hand. I can’t think of a similarly elegant way to count to sixteen.
Base 12 seems more useful and intuitive for those outside of comp-sci and it’s unclear to me how useful base 16 would be to those in comp-sci. I don’t know, how you think that would work?
I haven’t thought about base 16, but I’m pretty sure that that fact that it isn’t divisible by 3 means it doesn’t work the way base 12 does with thirds (i.e., resolving the infinite digit chain you get when dividing by 3 in the dicimal system). Also, we could teach counting under base 12 quite easily. Most of us have four fingers with three segments per finger. Count by segment. You can get to twelve on one hand. I can’t think of a similarly elegant way to count to sixteen.
Base 12 seems more useful and intuitive for those outside of comp-sci and it’s unclear to me how useful base 16 would be to those in comp-sci. I don’t know, how you think that would work?
I wouldn't say I'm familiar with the foot, but the calendar I accept as an argument for base 12, yes.
As for counting to 16, you could use the four fingers of each hand to count to 8 and for further counting fold them away again. Not the most elegant, but it works. For the segments you would have to actually remember where you are, but with the upfolding and downfolding (I hope this makes sense to say, it sounds weird) of fingers you would know exactly where you are at any point by just looking at the hands without needing to remember it. If you use always the same order of folding in and out. But I guess the whole easily divisible by 3 part is pretty neat with base 12.
I haven't actually ever thought about the pros and cons of any base before, so everything I have been saying here and will be saying is just a spur of the moment thing. I just thought that the reason for base 16 usage in comp-sci may be a reason why it could be useful in general. I don't actually know the reason, except that it translates well into base 2 but is easier to relate to for people used to base 10 than base 2 is.
As for counting to 16, you could use the four fingers of each hand to count to 8 and for further counting fold them away again. Not the most elegant, but it works. For the segments you would have to actually remember where you are, but with the upfolding and downfolding (I hope this makes sense to say, it sounds weird) of fingers you would know exactly where you are at any point by just looking at the hands without needing to remember it. If you use always the same order of folding in and out. But I guess the whole easily divisible by 3 part is pretty neat with base 12.
I haven't actually ever thought about the pros and cons of any base before, so everything I have been saying here and will be saying is just a spur of the moment thing. I just thought that the reason for base 16 usage in comp-sci may be a reason why it could be useful in general. I don't actually know the reason, except that it translates well into base 2 but is easier to relate to for people used to base 10 than base 2 is.
I actually thought of a idea of base 16. Split the palm of your hand to 2, and use your entire segments. You get 16. Another way, you can use two sides of your hand.
What's an entire segment here?
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