Level 1_________ 1 ball
Level 2_________ 4
Level 3_________ 9
Level 4_________ 16
Level 5_________ 25
Level 6_________ 36
Level 7_________ 49
Level 8_________ 64
Level 9_________ 81
Level 10________ 100 balls
Total balls = 1+4+9+16+25+36+49+64+81+100 = 385 balls
In this modeling, the perfect human square pyramidal organization of 10 levels would have 385 human units.
Suppose the first level represents the apex ... the alpha human ... the head honcho
Suppose the next two levels represent the privileged classes (the blue bloods; the golden spoons; the associates)
Suppose the next three levels represent the minion classes (silver spoons; soldiers; securators; subprimators; sucklings)
Suppose the remaining four classes represent the slave classes (middle class; lower middle class; poor class)
Now, let's assume the capstone is the sigma of levels 1,2,3 ... then the population is 1+4+9 = 14 human units
Let's further assume that the ziggurat is the sigma of levels 4,5,6 ... then the population is 16+25+36 = 77 human units
Finally, assume that the base is the sigma of levels 7,8,9,10 ... then the population is 49+64+81+100 = 294 human units
To wit, if the perfect human pyramid of 10 levels comes even close to modeling the real organizational human pyramid ... then the base alone has a 294 to 91 or 3-to-1 advantage over the capstone and the ziggurat combined.
Extrapolating down to the smallest pyramid possible (e.g. three levels) ... capstone, ziggurat, base ... we have 1+4+9 = 14 human units. IOW, the base in this smallest pyramid has a 9 to (1+4) ratio or approx. 2-1 advantage over the capstone and the ziggurat combined. We note that the ratio favors the base increasingly as the height of the pyramid increases. At three levels, a 2 to 1 ratio ... at ten levels, a 3 to 1 ratio. The capstone would be further susceptible if the ziggurat ever decided to side with the base in any degree.
Question begs: how much of the ziggurat needs to be awakened so that it sides with the base (assuming that virtually all the base will be unified against the capstone once the grocery shelves run bare)? (Remember, in the worst case of the ten level pyramid, the base still has a 3-to-1 advantage over the sum of the capstone and the ziggurat.)
Anyways, thought I'd put that out to help illustrate the mathematics of the square pyramid.