Mar 072013
 
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In fact, we use both systems. I surely don’t have to explain the use of the decimal system. However, the use of the duodecimal system, i.e. counting to the base of 12, is hidden in our everyday life. When we are measuring or expressing time intervals, we do so by dividing 1 h by 60 to obtain minutes. For further accuracy we divide the minute again by 60 and call it a second. This division by 60 is in fact based on the duodecimal system, e.g. 5*12=60. If we want to measure time intervals below 1 second, we switch back to the decimal system.

The origin of the decimal system is due to the ten fingers, that each human has. But the numbers 12 and 60 are also present on our hands. If we use our thumb to count the single digits of all four of the remaining fingers, we can count to 12. After that we can use one finger of the other hand to indicate that we’ve already counted to 12 once. If we proceed in this manner, we can count up to 12 digits * 5 fingers, which sums up to 60.

During the french revolution, the supporters of the decimal system set the base for todays SI-unit system. Some purists among them even used decimal clocks and weeks consisting of 10 days.

Nowadays, nearly worldwide the decimal system is used. However, there are quite a few people that support the usage of the duodecimal system, as the number of divisors for 12 is higher, than for 10. 12 has 1,2,3,4,6 and 12 as divisors, whereas 10 only has 1,2,5 and 10. They propose that, when changing to the duodecimal system, mathematics would remain the same, but everyday applications would be easier. One third would not be expressed as 0.3333, but as a convenient 0.4.

Robert Lindner

Read more:

– The dozenal society of America.

– Georges Ifrah: Universalgeschichte der Zahlen, Glb Parkland, Cologne, 1998.

  2 Responses to “Why do we use the decimal and not the duodecimal system?”

  1. A fascinating discussion. I was thinking over the past few days which numerical system would do us best for the next 200 years.

    While I did toy with duodecimal, which seems like a great system to use because of the presence of the prime factor 3, the importance of division into three is probably one of the less important features of math.

    For sheer logic and number crunching, as well as working more effectively with the role that Binary has in our lives, my feeling is that a superior choice would be the Hexadecimal system.

    Programmers often become accustomed to certain special values within the Hex set and it’s a very powerful system for working with digital systems.

    16 x 16 = 256 = hex 100
    16 x 16 x 16 = 4096 = hex 1000
    16 x 16 x 16 x 16 = 65536 = hex 10000

    Anyone familiar with computers will be familiar with many key variant points within the system as well. Because it revolves around squares and squares of squares and squares of squares of squares, it’s a highly organized set of numbers.

    The biggest obstacle is that humans are brought up from an early age immersed in a decimal number set and adding characters can be hard for them to work with. Indeed, using letters for extending the set is convenient but perhaps not the best idea. A better idea might simply to set up Hex with a full symbol set. Perhaps related to alphabetic symbols to ease the transition, but with their own unique identity.

    I was thinking too that it might be fun to give them names and symbols from older non-decimal numeric systems as homage.

    Ultimately, it would require a concerted effort from educational centers to build this system up.

  2. Also remember, 12 inches per foot, 12 months per year, and 12 half-steps in every “octave”. Counting by the dozens makes things more convenient.

    If it were up to me, I wouldn’t even divide the hours into 60 minutes; I’d get rid of every trace of the decimal factor altogether! The most convenient way I can think of doing that, right now, is dividing every hour by 12 which gives us 5 minutes — but I’d call it another number such as 6 minutes. Then dividing each minute into either 3 dozen or 6 dozen seconds — at least the second-hand likely to tick only 3 dozen times per minute (b/c hearing it tick 6 dozen times a minute might get downright obnoxious!).

    Either way, think of each minute as 12 dozen (144) beats in rhythm — and I mean the fairly-recent pop and reggae tempo/measure length. Unlike time measurement as it is now, seemingly better geared to tempo/measure length WAY back when, in traditional America (and north Europe), the time measurement I’m proposing is in tune with the more-recent pop and reggae tempo/measure length. Heh, I stick with the times!. I’m averaging at about 173 beats per minute (of the current system), which would be measured as 12 dozen beats per minute of the new system.

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