Society and Math

With the recent announcement of parliament's dissolution and upcoming general elections, I see it fit to post a note on some crazy (and absurd) socioeconomic model by Plato.

In Laws, Plato suggests that the optimal number of citizens in a state to be 5040 because :

a) it is the product of 12, 20 and 21 (very significant in ancient Greek because of its properties)
b) the twelfth part of it can still be divided by 12 (5040 divisible by 144)
c) it has 59 divisors, including all the whole numbers from 1 to 12 (except 11, but 5038, which is very close is divisible by 11)

The choice of this number and its properties allow Plato to develop his socioeconomic vision. For instance, the state's land is divided into 5040 lots, with 420 such lots constituting the territory of each of the twelve 'tribes'. The people of the state themselves are divided into four social categories :

a) Free citizens
b) Slaves
c) permanent resident
d) visitors

Also note that in elections to the Council, members from all four property categories vote for ninety members from each class !! (14 votes each)

I wonder what ancient Greece would have been if Plato were a dictator back then !