Effects of a duodecimal system

And "count the whatmacallits on your fingers" is not as intuitive as "one finger, two finger, three fingers" for some reason.

Plus, why does it matter if it's easier to cut a cake (or whatever) into twelve pieces than ten? Twelve as ten+2 as opposed to . . . whatever you call twelve in duodecimal doesn't make it harder to cut things into convenient units.
 
And "count the whatmacallits on your fingers" is not as intuitive as "one finger, two finger, three fingers" for some reason.

Plus, why does it matter if it's easier to cut a cake (or whatever) into twelve pieces than ten? Twelve as ten+2 as opposed to . . . whatever you call twelve in duodecimal doesn't make it harder to cut things into convenient units.

It's easier to divide everything into thirds, quarters, sixths and twelfths.
While it's only easier to divide everything into fifths and tenths in decimal.
 
It's easier to divide everything into thirds, quarters, sixths and twelfths.
While it's only easier to divide everything into fifths and tenths in decimal.

Just because the system is base ten doesn't prevent me from cutting a pizza - or cheese wheel, but I cut more pizza than cheese wheels - into three (or four or sixth or twelve) pieces.

I don't see how making the system base twelve makes any impact on my ability to ensure everyone has a roughly even amount of pizza.
 
And "count the whatmacallits on your fingers" is not as intuitive as "one finger, two finger, three fingers" for some reason.

Plus, why does it matter if it's easier to cut a cake (or whatever) into twelve pieces than ten? Twelve as ten+2 as opposed to . . . whatever you call twelve in duodecimal doesn't make it harder to cut things into convenient units.

Who cares if its easier or not? Assume that it happens in antiquity for whatever reason, that's the POD.

I'd say more than half of AH threads are spent fighting the POD, even its a reasonable one with nothing ASB about it.
 
Well, the duodecimal system existed and was so wide-spread that it still has its effects today. Starting a system is not a big issue, but it has to prove useful over time or it will be replaced by a concurring one. Therefore it does matter how complicated a system is.

But then, as I mentioned above, there is not a big difference. Both systems work, and the important thing is using a digit-based system rather than other number systems. The POD we discuss here doesn't question this progress.

Consider the analogy of languages: You might argue that complicated languages don't spread so easily (assume there were an objective definition of "complicated"). Looking at actual history proves that people just learn any language once there is a sufficient pressure or motivation to do so. So theoretically, complicated languages might have a disadvantage, but in reality it hardly ever materializes.
 
Just because the system is base ten doesn't prevent me from cutting a pizza - or cheese wheel, but I cut more pizza than cheese wheels - into three (or four or sixth or twelve) pieces.

I don't see how making the system base twelve makes any impact on my ability to ensure everyone has a roughly even amount of pizza.

Not pizzas, but money and immaterial things.
 
After this last time base 10 and other possible alternatives were discussed (not too long before last Christmas), I spoke about this to my cousin, who is a trainee maths teacher.

He said one Egyptian culture had worked on a system of binary/doubling, and that this is used as a teaching method for those struggling with multiplication:

If you can't manage your seven times table, you double it, and again and again. This gives you something like this

1 2 4 8 16
7 14 28 56 112

If I then ask you to do 9x7, you look at you table. You have eight, and one, so add them together. This process can be used for long multipliction too, as doubling numbers is relatively simple. Simpler than trying to sort out 34x27. Using the above method, you get to thirty-two with 5 doubles, then add on your two.

Mark's been using this method on placement with a couple of kids, and says it's working wonders...
 
Who cares if its easier or not? Assume that it happens in antiquity for whatever reason, that's the POD.

I'd say more than half of AH threads are spent fighting the POD, even its a reasonable one with nothing ASB about it.

I care, because someone is arguing that it's easier. So I responded to that.

As far as the POD is concerned, I think if the only difference is that (for example) 1730 AD is some other number AD, it'd be pretty much the same as OTL. Certain concepts like percentages are going to be interesting in this system, but probably more a matter of detail than divergence, if that makes sense.

Joyeux: Same problem. I can divide 12 into even units in base 10, I can't divide X (using the Roman numeral) into even units whatever base system you pick.

So why does it matter? I mean, if X times X units of stuff has to be distributed among three people, who cares whether that's one dollar (100 cents) or (whatever the "percentage" is) of a dollar?
 
Joyeux: Same problem. I can divide 12 into even units in base 10, I can't divide X (using the Roman numeral) into even units whatever base system you pick.

So why does it matter? I mean, if X times X units of stuff has to be distributed among three people, who cares whether that's one dollar (100 cents) or (whatever the "percentage" is) of a dollar?

It doesn't matter all that much, it's just that we could have been using a somewhat more efficient system, but aren't.

1 dollar in a dozenal system would be 144 (100 in duodecimal numerals) cents. Divided by three would be 48 cents (40 in duodecimal numerals).
 
It doesn't matter all that much, it's just that we could have been using a somewhat more efficient system, but aren't.

1 dollar in a dozenal system would be 144 (100 in duodecimal numerals) cents. Divided by three would be 48 cents (40 in duodecimal numerals).

I don't think there's any reason a dollar would necessarily be 144 (base ten) cents. I mean, it's possible, but it was just as possible to do it with base ten.
 
I don't think there's any reason a dollar would necessarily be 144 (base ten) cents. I mean, it's possible, but it was just as possible to do it with base ten.

If the currency were duodecimal, it would be 144 cents to a dollar.
12 x 12 = 144

Just like how in decimal, it's 100 cents.
10 x 10 = 100
 
Yep, just look at the Sumerians and their 60 fingers.:rolleyes:

Arithmetic in a base-12 numbering system would be simpler.
For example, a third of 12 is 4 which is a nice number, unlike 33.33333...

Here is a handy video which explains the system, if anybody is interested.
http://m.youtube.com/watch?v=U6xJfP7-HCc
It's only simpler if you have an irrational fear of decimals. Fractions are no less complicated than repeating decimals. And duodecimal can still yield incredibly complicated results.

The Sumerian number system was base 60 because it was never meant to be practical. It was largely the domain of the priesthood, and for good reason it fell by the wayside. We've settled on base ten for a number of anthropological reasons, so this is a purely academic matter with all the significance of a game of Calvinball.
 
If the currency were duodecimal, it would be 144 cents to a dollar.
12 x 12 = 144

Just like how in decimal, it's 100 cents.
10 x 10 = 100

If the currency was, sure. But we could do that in base ten. We don't. We don't even have a consistent decimal system - 1, 5, 10, 25, 50, 100.

And that's looking at the US dollar.
 
It's only simpler if you have an irrational fear of decimals. Fractions are no less complicated than repeating decimals. And duodecimal can still yield incredibly complicated results.

The Sumerian number system was base 60 because it was never meant to be practical. It was largely the domain of the priesthood, and for good reason it fell by the wayside. We've settled on base ten for a number of anthropological reasons, so this is a purely academic matter with all the significance of a game of Calvinball.

Newsflash. Unless you have a working time machine I don't know about, so is every other bit of AH speculation on this site.
 
What if civilization gradually settles on a base 12 numbering system in antiquity instead of a base 10 system as OTL--would there by any significant effects? Ignore butterflies, I'm talking about intelligible effects....

Provided nothing butterflies away the concept of 0 and positional notation, I don't think things would be substantially different. Things might differ in the details -- a Roman century might have had a nominal duodecimal 100 (i.e., decimal 144) soldiers rather than a decimal 100 -- but at the macro level I don't think it would change things.
 
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