A simple calculation about human population
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QUESTION:
The population of Earth is 6.5 billion (year 2003).
It is doubling about every 40 years.
The total surface area of the Earth (only counting habitable land,
e.g., not antartica and not lakes - counting ALL land would give 148
million square km. Land is about 20% snow/ice, 20% mountains, 10% land
with no topsoil...)
is about                                    14
          100 million square kilometers = 10  square meters.
Assume to grow enough food and produce enough resources 
for an average human to live off of, requires a 62meter X 62meter
square patch of land (about half the size of a football field).
HOW MANY years have we got (if this doubling rate continues) 
before humankind can no longer live?  

ANSWER:
    Only counting habitable land, 
    We have total land per person right now
           14            9
       = 10   / (6.5 * 10 ) = 15384.6 square meters.

    But supposing it takes a 62*62 meter plot (62*62=3844 square
    meters) to support an average person, that means the human
    population cannot grow by a factor of more than
           15384.6 / 3844 =  4.002237253
    before it is in deep trouble.

   Note 4.0022 is about 2*2, meaning we can double just TWICE before
   this.  If each doubling takes 40 years, that means we have 80 years left.

Obviously it is hard to be sure these input numbers are exactly right,
but you can see humankind is going to start getting into serious
problems in this century if we don't change our habits pretty damn
quick.

FOLLOW-UP QUESTION:
Certain people have made statements such as "I'm not worried because
predictions of doom have been made before and haven't panned out, and
humankind has been increasing exponentally for the past 200 years,
and no great problems have occurred (in fact, life expectancy has
increased and most resources have gotten cheaper)."  Do these people
have any logical basis?

ANSWER:
Unfortunately, that is not logically relevant. Consider the parable of
the lilies in the pond. The lilies double each day. After 29 days,
they fill half the pond. At that point the lily leader says "all
through lily history we have doubled each day, and still, a vast vista - as
much pond as has been occupied during all previous lily history,
remains open! Everything is cheaper now! Etc!"  Of course, the
very next day, the pond is full, and all the lilies die.

There has been no precedent for running out of an essential resource
on a worldwide scale before.  That is logically irrelevant to whether
it will happen.  In fact, exponential growth cannot continue very long
in a finite world.