In this paper, we consider how humans are drawn together into larger and larger settlements until we go from /Tribes of 150 people to cities such as NYC. The familiar economic multiplier is the key to understanding how communities grow. From this, we can see what forces draw people together until eventually they are drawn apart leading to the collapse of an empire.

We consider what sis the law of city building.  What causes humans to come together to form tribes, communities, and eventually cities?  The answer lies in human needs. We shall mention IX here, although the reader may think of more. No more than IX are necessary to explain how cities come to be formed such as London, New York, or Paris.

I shall list the IX human needs:

1.       Food (hunters; gathers; famers; divided labour)

2.       Work (Money; economy)

3.       Shelter (homes, work places; religious centres; schools etc.)

4.       Sex for the begetting of children (marriage)

5.       Child Rearing for continued survival of the species

6.       Intellectual stimulus which begets language and is enhanced by storytelling and education.

7.      Religion Life of the Soul (after life; hope)

8.      Funeral Rites (Burial)

9.      Medicine (health, death)

We have enough needs to put an equation to each of these major divisions.  Then we can solve the equations to see what we get (Figure 1).

·         (1)(2) Economic Equation   Y=C+I+G+NX

·         (3) Shelter =Space  PV/FV=Cusack Hinterland Factor=2? =E=Y    s=|E|t| sin 60°

·         (4,5) Children /Population growth Y=e^t

·         (6)  Looking Back (history); Looking forward (Education)  Y=2²⁰

·         (7)(8) Soul S.E.=t²-t-1=0

·         (9) Death Y=e^-t

Y=2²⁰=t²-t-1=1.0485

t^~1.618

Y=C+I+G

Y=C+(1-0.8415) +(14.28%)

Y=5.02-0.3018

C=4.7182

=2+e¹

=2 + population growth =2+children=Father and mother +children=Replacement rate +children

Y=e^-t=e^-1.618

=19829^~2  (replacement rate)

Pop-Y=e

Ln (pop.-Y)=Ln (4.7182-0.504)=14.38%=1/0.695

^~1/7 

=Economic Multiplier

The economic multiplier is the rate at which tribes, communities, and cities must increase to survive.

So, space s=|E||t| sin 60°

1.334=(2?)(t)0.866

t=0.246^~0.250=Period T

1/t=E

1/0.250=40=FV

0.400 x 1/7=5714^~1 rad=E=t

2?/4(.718-2)=Ln ?=t_max

Ln ?=23.1=Ln (pop-Y)

Pop-Y=?=23.1

23.1-PI=1995^~ 2

Ln 2=3=c

We’ve seen why humans come together; Now let us turn our attention to Empires and why the come apart (Table 1) [1-2].

e^-6.54=6922^~7

1/7 is the economic multiplier, again

F _attraction ? Market Value

F _Repulsion ? 1/FV =1/2x²

MV=1/FV

MV=1/2,68

FV=1592=1/2?

MV=1/FV=2?= Cusack Hinterland Factor

F att=F rep

2.68=1/(2x²)

2(2.68)x²=1

x=432

=1/2.315

=1/t

=E 

t=231(1789 -2020 AD )

We see that there is indeed a system of equations that explain growth of communities.

1.       Beinart J. Lectures theory of city form. Open Courseware, MIT. 2013.

2.       Cusack PTE. Teleological Universe (submitted).