WI: The metric system was duodecimal?

farwalker · Nov 15, 2012

What if, after the French Revolution, when deciding on a system of weights and measures the assembled learned men struck upon the "revolutionary" idea of using a base 12 system for counting because it makes so much more sense logically

... (opinions vary but it does make every day math simpler). For example using some variant of X for 10 and E for 11, the symbol doesn't really matter for these purposes.

Would it have seen as widespread adoption as OTL? Would we all be now counting in base 12?

Imladrik · Nov 15, 2012

farwalker said:
What if, after the French Revolution, when deciding on a system of weights and measures the assembled learned men struck upon the "revolutionary" idea of using a base 12 system for counting because it makes so much more sense logically ... (opinions vary but it does make every day math simpler). For example using some variant of X for 10 and E for 11, the symbol doesn't really matter for these purposes.

Would it have seen as widespread adoption as OTL? Would we all be now counting in base 12?

Eh. This is totally ASB. Previous systems were often in base 12 and it was seen that it wasn't logical. So why would they want another base 12 system (don't forget that the Metric System was pushed by scientist who wanted a unified base 10 system) ?

Kishan · Nov 15, 2012

The decimal system is the mathematical system based on the number 10 and it has no connection with the metric system. The decimal system is centuries old and it was adopted by the humans because we have ten fingers. Man started counting with fingers and naturally 10 became the base number. If the number of fingers were 12, then a base12 system would have evolved.
What the French experts who devised the metric system did was to design a system of measurements based on the existing base10 system. They were not directed to modify the present base10 system and they could not have done it.That is the jurisdiction of mathematicians and such a conversion from base10 to base12 will be a revolution which will throw not only the world of mathematics but the entire world of knowledge, including all sciences like physics, chemistry etc. and economics, statistics, geography, astronomy and in short, EVERYTHING into chaos.

farwalker · Nov 15, 2012

Imladrik said:
Eh. This is totally ASB. Previous systems were often in base 12 and it was seen that it wasn't logical. So why would they want another base 12 system (don't forget that the Metric System was pushed by scientist who wanted a unified base 10 system) ?

Well, they wanted a unified system. Base 10 was just the most common base used in Europe at the time. And as for crazy, they tried to push decimal time... these are people who liked to impose a system on everything simply because it was so much more logical (in their minds at least).

Oh and a base 12 system is actually more practical for everyday use than base 10. Seeing that Halves, Thirds and Quarters (the most common fractions) can all be represented by just one duodecimal place, becoming 0;6 0;3 and 0;4 respectively.

farwalker · Nov 15, 2012

Kishan said:
The decimal system is the mathematical system based on the number 10 and it has no connection with the metric system. The decimal system is centuries old and it was adopted by the humans because we have ten fingers. Man started counting with fingers and naturally 10 became the base number. If the number of fingers were 12, then a base12 system would have evolved.
What the French experts who devised the metric system did was to design a system of measurements based on the existing base10 system. They were not directed to modify the present base10 system and they could not have done it.That is the jurisdiction of mathematicians and such a conversion from base10 to base12 will be a revolution which will throw not only the world of mathematics but the entire world of knowledge, including all sciences like physics, chemistry etc. and economics, statistics, geography, astronomy and in short, EVERYTHING into chaos.

But the thing is different cultures have used different base systems for counting. Base 10 is merely the most common (yes because we have 10 fingers). But the Babylonians used a base 60 system because they thought it was the most useful number and many other cultures used a vigesimal system.

I am aware of what the metric system is and isn't. I'm asking what if these people who clearly trying to impose a more scientific outlook on the world looked at the numbering system and said: "Mais, pourquoi pas douze?"

Imladrik · Nov 15, 2012

farwalker said:
But the thing is different cultures have used different base systems for counting. Base 10 is merely the most common (yes because we have 10 fingers). But the Babylonians used a base 60 system because they thought it was the most useful number and many other cultures used a vigesimal system.

I am aware of what the metric system is and isn't. I'm asking what if these people who clearly trying to impose a more scientific outlook on the world looked at the numbering system and said: "Mais, pourquoi pas douze?"

"Parcequ'ils ont essayé de décimalisé le décompte du temps ?" They introduce the decimal time (which is not really crazy you know, or else the decimalization of '71 in the UK would be crazy too). Whether you wnat it or not, the trend was toward decimalization, not toward duodecimalization, because a duodecimal is less logical for humans than a decimal system, because we can use our hands for the decimal system. That's why the decimal system exist everywhere on earth while the duodecimal system was more restricted to some areas (and the vigesimal, because it's in fact a doubledecimal system in most case as in one native american language where 11 is we go below (to the feet)).

farwalker · Nov 15, 2012

Imladrik said:
"Parcequ'ils ont essayé de décimalisé le décompte du temps ?" They introduce the decimal time (which is not really crazy you know, or else the decimalization of '71 in the UK would be crazy too). Whether you wnat it or not, the trend was toward decimalization, not toward duodecimalization, because a duodecimal is less logical for humans than a decimal system, because we can use our hands for the decimal system. That's why the decimal system exist everywhere on earth while the duodecimal system was more restricted to some areas (and the vigesimal, because it's in fact a doubledecimal system in most case as in one native american language where 11 is we go below (to the feet)).

"Ils ont essayé de rationaliser le décompte du temps, c'est que leurs moyen de rationalisation était le système décimale."

You know you can count to twelve on one hand, just count your phalanges with your thumb. The thing is 12 is just a much more useful number not only for everyday uses but also in mathematics seeing as it has more common factors 2, 3 & 4 while the decimal system has only 2 and 5 (the later wouldn't be nearly so common in a non-decimal system).

I understand that decimal is the most common system, but we are dealing with people who love to implement their beautiful theories regardless of real-world conditions you know. (Not that I have a problem with that)

Imladrik · Nov 15, 2012

farwalker said:
You know you can count to twelve on one hand, just count your phalanges with your thumb. The thing is 12 is just a much more useful number not only for everyday uses but also in mathematics seeing as it has more common factors 2, 3 & 4 while the decimal system has only 2 and 5 (the later wouldn't be nearly so common in a non-decimal system).

You can count to 32 on one hand and to 1024 with two hands. But it's difficult. The only easy thing to do is to count to 10 with two hands.

Yes it's right about the common factor, but they never thought that way in those times. They wanted ten because ten was for normal people the most logical thing to do.

Alex Richards · Nov 15, 2012

Imladrik said:
You can count to 32 on one hand and to 1024 with two hands. But it's difficult. The only easy thing to do is to count to 10 with two hands.

Yes it's right about the common factor, but they never thought that way in those times. They wanted ten because ten was for normal people the most logical thing to do.

I'd argue that given that countries from India to Japan, to Western Europe and Ancient Rome used anything from Base 12, base 16, base 8, base 2, base 13 or base 20, but only rarely base 10 for currency, that anthropological research indicates that the earliest counting systems tend to be base 2, 3 or 4, that the Yan Tan Tethera system for counting that was common among shepherds across Britain was in base 20 and that there doesn't appear to be any culture in Eurasia which didn't use a 12 hour division for the day mean that this really isn't true.

carlton_bach · Nov 16, 2012

I thionk we are heading off into far too great complexity here. The system of counting - the numbers underlying every operation that the French reformers were aware of - was base 10. There is no particular reason for it to be base 10. It was, though, and as far as they were concerned, this was proper maths.

A lot of the measuring systems they were familiar with were not base 10, hence "unmathematical". They were more practical in everday applications, but that did not concern the developers except in that it was evidence of their primitiveness since it suited them to unmathematical minds.

Using base 12 for the metric system would only have been feasible if their system of mathematics had used base 12, because that was what they wanted the metric system to be more like.

farwalker · Nov 16, 2012

carlton_bach said:
I thionk we are heading off into far too great complexity here. The system of counting - the numbers underlying every operation that the French reformers were aware of - was base 10. There is no particular reason for it to be base 10. It was, though, and as far as they were concerned, this was proper maths.

A lot of the measuring systems they were familiar with were not base 10, hence "unmathematical". They were more practical in everday applications, but that did not concern the developers except in that it was evidence of their primitiveness since it suited them to unmathematical minds.

Using base 12 for the metric system would only have been feasible if their system of mathematics had used base 12, because that was what they wanted the metric system to be more like.

But that is what I'm saying. Instead of replacing the innumerable different measurement systems, a majority of them not decimal, they could have decided to reform the numbering system. Remember we're talking about some pretty smart guys here (Laplace, Condercet & Lavoisier among others). While they could be blinded by their prejudices towards those of lesser education, they are also fully capable of attacking the problem from different angles. The fact that they were trying to decimalise time shows they weren't too caught up on preserving existing conventions just because...

What we need now though is a series of prefixes denoting powers of 12, all we have in English is dozen, gross and great-gross. What would they call a twelfth of something?

LSCatilina · Nov 16, 2012

Why not 12? After all, as it was said it would have allowed an "unification" with previous system (that was roughly duodecimal) and neighbouring ones.

Well, there's some reasons :

-The roman numeral system was decimal. As Rome was sawn as the pinnacle of freedom (just remember how fashionable it was to rename yourself with a latin name or use roman symbols : Gracchus Babeuf, phrygian bonnet, it wouldn't have fit to use a duodecimal system.

-Why they would have interest into uniting or using systeme identified with oppressive and backward features? Ideologically, that doesn't make great sense.
It was intented to be a rupture with former systems.

-The scientific use of decimal system in the XVIII for mesurments in time or length probably played a great role into the decision made by the french comission.

Dathi THorfinnsson · Nov 16, 2012

Kishan said:
What the French experts who devised the metric system did was to design a system of measurements based on the existing base10 system. They were not directed to modify the present base10 system and they could not have done it.That is the jurisdiction of mathematicians and such a conversion from base10 to base12 will be a revolution which will throw not only the world of mathematics but the entire world of knowledge, including all sciences like physics, chemistry etc. and economics, statistics, geography, astronomy and in short, EVERYTHING into chaos.

Not really. Besides, changing the measuring system did all that anyway, we'd just be changing thinks to a DIFFERENT set of numbers than were changed to OTL.

Given the extremely radical positions of many behind the Revolution, I think a base 12 measuring system is well within the reach of possibility. It might make it more difficult to export. But on the other hand, it might make it easier. If you go with feet and inches, and pounds and ounces (Troy pounds already have 12 ounces), there'd be a lot of familiarity and continuity, and maybe less resistance to the change.

Gorm the Old · Nov 16, 2012

Dathi THorfinnsson said:
Not really. Besides, changing the measuring system did all that anyway, we'd just be changing thinks to a DIFFERENT set of numbers than were changed to OTL.

While I do agree that it does not seem out of the question that they might have attempted this, you do run into the problem of reading old documents. Any number above 9 in a document from before this duodecimalization could be read wrong by the inattentive person, or someone who was not aware when a document was produced. That is, unless you change the symbol of 0 when you add the symbol for 10 and 11.

You also have to change the name of some of the numbers. 1 to 10 is fine, but the names of 11 and 12 don't make much sense any more, and neither does a whole bunch of numbers following them. Still, not an impossible task, but certainly one where Paris would have to focus on getting it to stick for a least a generation, if not more.

Alex Richards · Nov 16, 2012

Gorm the Old said:
While I do agree that it does not seem out of the question that they might have attempted this, you do run into the problem of reading old documents. Any number above 9 in a document from before this duodecimalization could be read wrong by the inattentive person, or someone who was not aware when a document was produced. That is, unless you change the symbol of 0 when you add the symbol for 10 and 11.

You also have to change the name of some of the numbers. 1 to 10 is fine, but the names of 11 and 12 don't make much sense any more, and neither does a whole bunch of numbers following them. Still, not an impossible task, but certainly one where Paris would have to focus on getting it to stick for a least a generation, if not more.

Well, I don't know about other languages, but for English, French and German I don't think there's anything inherently implying '10+1' and '10+2' with Eleven, Twelve; Onze, Douze or Elf, Zwolf.

Falecius · Nov 16, 2012

Alex Richards said:
Well, I don't know about other languages, but for English, French and German I don't think there's anything inherently implying '10+1' and '10+2' with Eleven, Twelve; Onze, Douze or Elf, Zwolf.

"Onze" and "Douze" actually come from latin words which include the root for "ten". They share a recognizable structure with subsequent "Treize", "Quatorze" and so on. More or less the same for Italian and Spanish. There's a change after 15 in Spanish (I think in Portuguese as well but I am not sure) and after 16 in French and Italian. This is not the case in English and German, where you have the "teens" series actually starting with 13.

Dathi THorfinnsson · Nov 16, 2012

Gorm the Old said:
While I do agree that it does not seem out of the question that they might have attempted this, you do run into the problem of reading old documents.

That COULD be a feature, not a bug. If a radical regime wanted to inculcate 'modern' thought, changing the number system would help. Maybe the script, too.... Use Fraktur....

Falecius · Nov 16, 2012

Dathi THorfinnsson said:
That COULD be a feature, not a bug. If a radical regime wanted to inculcate 'modern' thought, changing the number system would help. Maybe the script, too.... Use Fraktur....

While they're at it, they could change French ortography into something reasonable, introducing a constructed phonetic alphabet. (I'd bet someone actually suggested that, but I doubt it was ever under serious consideration IOTL).

Falecius · Nov 16, 2012

One reason why most systems to write numbers I know of are more or less decimal is, of course, that in this way they somewhat visualize the pattern of the names of numbers in most languages. A doudecimal system of ciphers would lose this rough, but real, correspondence.
This in turn makes quite a strong case for a decimal system of measurements being fairly practical, though history cleary shows that THIS correspondence is far from universal since, for some everyday uses, doudecimal measurements have other apparent advantages.

The Kiat · Nov 16, 2012

farwalker said:
What if, after the French Revolution, when deciding on a system of weights and measures the assembled learned men struck upon the "revolutionary" idea of using a base 12 system for counting because it makes so much more sense logically

Where they anticipating we'd evolve an extra finger on each hand?

And everybody does realize that we have base-10 because we have ten fingers?