Decimal Vs Duodecimal System

I think that duodecimal (dozenal) system would be much more appropriate for architecture and let me explain you why. A big chunk of the design procedure is composed of dividing objects and distances into fractions, which is a mess in the decimal system. For example, we need to divide 20 m long Facade into thirds, which results in those funny numbers with infinite dividers: 6,666 and 13,333. Those numbers are not very useful on the construction site and no producer will make prefabricates in that sizes. We are forced to either use approximations (in this case 6 and 13) or to avoid certain dividers. First option creates some residueg and the second option is not really feasible, as simply too much of architectural design is composed of dividing geometric forms into fractions: halves, thirds, quarters, fifths, tenths, and so on.

 

2000px-cathedral_schematic_plan_en_vectorial-svg

Composition of a classical church, in this case squares are divided into rectangles.

 

Duodecimal system solves this problem by elegantly adding two extra numbers to the counting system. Instead of grouping numbers into tenths, we group them into twelfths.

1       2       3       4       5       6       7       8       9       10       (11)       (12)

1       2       3       4       5       6       7       8       9        ᘔ          Ɛ          10

Technically, number 10 gets a new symbol ᘔ (rotated number 2) and 11 gets Ɛ (rotated number 3). It is actually the oldest counting system, invented in the ancient Sumeria. At that time with the basis of 60 (4 x 12), which is still in use in measuring time. Ancient Sumerians found that this way they could simply divide a unit of crops into thirds and fourths for the purpose of taxation. The Germanic languages still have separate words for 11 and 12, and until the end of 19th century many traders used dozens as their preferred units of measurement.

The argument of having 10 fingers to count, well, it is only partially true. We have 3 bones in each finger, with 4 fingers it makes 12. Index finger is used for counting. Try it, it does work :).

duodecimal-hand

 

Let’s take a look at dividing into fractions. In the decimal system 1 meter is composed of 10 dm. Let’s divide it:

 

 

DECIMAL

1/1 of a meter =  10 dm

1/2 of a meter =  5 dm

1/3 of a meter = 3,333333 dm

1/4 of a meter = 2,5 dm

1/5 of a meter = 2 dm

1/6 of a meter = 1,6666666 dm

1/8 of a meter = 1,25 dm

1/10 of a meter = 1 dm

 

In the duodecimal system 1 meter is composed of 12 dm:

DUODECIMAL

1/1 of a meter =  12 dm

1/2 of a meter =  6 dm

1/3 of a meter = 4 dm

1/4 of a meter = 3 dm

1/5 of a meter = 2,4 dm

1/6 of a meter = 2 dm

1/8 of a meter = 1,5 dm

1/10 of a meter = 1,2 dm

1/12 of a meter =  1 dm

It is quite obvious that we got rid of those infinite  dividers (1,333, etc.) and that almost all numbers are natural numbers. Calculations are much easier, and have almost no residue.

That is why I almost always use as the basis for my plans 1,2 m (and not 1 m), as it is so easy to divide it into fractions. Do I have to extend a road for 1/3? I just add 0,4 m.  And I try to avoid the number 5, as it is a prime number and so non-dividable (numbers as 1’5, 0’5, etc.).

Am I a proponent of the duodecimal system? Yes. Do I think it is realistic to implement it? Of course not.

More on this here and here