A recent survey of ancient and contemporary societies
whose original ascendancy was followed by collapse
includes a chapter devoted to Easter Island

with its land area of 66 sq. miles and an estimated peak
human population (depending on the study surveyed) of
between 6,000 and 30,000 people
                     (See Jared Diamond's book Collapse, 2005)

Taking a mid-range peak population estimate of
approximately 15,000, the following mathematics
obtains: 


Assume that each person, while standing, is, on
average, approximately two feet width at shoulders
and 1.5 feet front to back, so that each individual
physically occupies (2) x (1.5)  =  approximately
3 sq. feet of space

Thus, 15,000 people x 3 sq. feet each would
occupy approximately  ~ 45,000 sq. feet.   

Since one square mile  =  27,878,400 sq. feet,
the total "empty space" on the island amounts
to

66 square miles times  27,878,400 for a total
island area of  ~ 1,839,974,400 sq. feet

 
Since a total of approximately 45,000 sq. feet is
physically occupied by the 15,000 residents,

45,000 sq feet divided by 1,839,974,400 sq. feet
(the total existing area) equals:  

             2.44568 x 10 ^-5   =  .000 02446
                                                or  .
                      2.45  / 1000ths  of  1%.

(a)  1% of 1,839,974,400   =  .01 x 1,839,974,400  = 18,399,744  sq. feet

(b)  1/10th of 1%:                .001 x  1,839,974,400   =  1,839,974  sq. feet

(c)  1/100th of 1%:           .000 1  x  1,839,974,400   =    183,997  sq. feet

(d)  1/1000th of 1%:           .000 01  x  1,839,974,400    = 18,399   sq. feet
(e)  3/1000ths of 1%:          .000 03  x  1,839,974,400   =  55,199  sq. feet

In addition, since 100%  minus 3/1000ths of 1%
                    equals  99.999 97 %

the total percentage of unoccupied "open space"
at the time of collapse was approximately
.
                            99.999 97 %.

Thus, Easter Island's human population, its
environment, and its society underwent
catastrophic collapse

even when .99.999 97 %. of the island
remained unoccupied.


In other words, collapse occurred even
               as "vast amounts of open-space" 
                 remained theoretically-available

In other words, we see still another history
that ended in collapse, this time involving a
human society confined to an island with
limited resources. 

In addition, the above collapse occurred
even as "vast amounts of open-space"
remained theoretically-available to the
island's human occupants

Footnote 1: 

Just like Easter Island, earth itself is, after all,
also an island (in space),

and though earth is many times larger in size
than Easter Island, so is the size of our
population

Footnote 2:  The similarity of our situation
and that of the peak population of Easter
Island is not perfect, however. 

The humans on Easter Island constituted
a pre-industrial society that could deforest
their environment, kill all of its birds and
most of its seabirds, and overexploit its
resources