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PLATO
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Of the occupied South
Dec 2002
time: 23:30
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quote:
Originally posted by Sava
that's wrong... according to a national geographic atlas I have... there have been an estimated 300 billion humans that have ever lived (homo sapiens)... the total number of people alive today is about 5% of all that have ever lived...  |
Well Sava, you are partially correct:
quote:
How many people have ever lived? Keyfitz's calculation updated
(done June 18, 1999)
This work was done at the request of Prof. Glen Paige
for his new book, "Non-killing Political Science"
A simple model of population growth is the exponential model where the population at time t, P(t), is given by Cert for some appropriate constants C and r. This model is broadly accurate, especially when an organism invades a new ecological niche and the environment seems to have infinite capacity for growth. This model accurately describes the initial growth of a bacterial culture in a fresh dish of growth medium, or the human population as it discovered agriculture. More refined models are needed as environmental and predatory constraints impinge, but this model works well with most human populations because many human populations rapidly shift from one environmental disequilibrium to another (and thus present a moving target that the environmental constraints fail to effectively constrain). It is of course never that simple: Black Death in Europe caused populations to drop dramatically for a few centuries.
Regardless of how one models P(t), the population at time t, P(t) may be used to estimate the total number of humans that have lived in a given time period. From a time A to a later time B, the integral of P(t) on [A,B] gives the total number of person-years for that time interval. If one has an estimate of the average lifespan, say 25 years as in Keyfitz's work, the number of people who lived from time A to time B is approximately (1/25) of the integral of P(t) on the [A,B].
Keyfitz assumed that exponential growth occured in various historical time intervals [A, B], but with possibly different constants C and r for each time interval. He chose C and r to match given values of P(t) at A and B. This requires solving two equations in 2 unknowns:
P(A)=C erA
P(B)=C erB
By standard algebra, P(B)/P(A)=er(B-A) and hence r={Ln[P(B)]-Ln[P(A)]}/(B-A). Once r is known, C is obtained immediately from C=P(A)e-rA. Note that Ln is the natural logarithm, the logarithm to the base e.
Keyfitz then integrates Cert on the interval [A,B]. An anti-derivative is (C/r)ert and the definite integral is the anti-derivative at B minus the anti-derivative at A. The total person-years from A to B is (C/r)[erB-erA]. By algebra, this is equal to (1/r)[P(B)-P(A)]. By substituting the value of r described just above,
the total person-years from A to B is [P(B)-P(A)](B-A)/{Ln[P(B)]-Ln[P(A)]}.
This formula is now applied to a system of time intervals from 1,000,000 BC to the present. The sum of the total person-years for all these intervals gives the total person-years for all human life. By dividing by the average lifespan, one obtains an estimate of how many people have ever lived. The data at ends of intervals are taken from a recent textbook on population, except for the first data point of 2 people at -1,000,000. That data point was proposed by Keyfitz.
Year People People-Years Since
Previous Data Point
-1000,000 2 0
-9000 7,500,000 4.91* 1011
0 300,000,000 7.14 * 1011
1650 507,500,000 6.51 * 1011
1750 795,000,000 6.41 * 1010
1800 969,000,000 4.40 * 1010
1850 1,265,000,000 5.55 * 1010
1900 1,656,000,000 7.26 * 1010
1950 2,513,000,000 1.027 * 1011
1960 3,027,000,000 2.76 * 1010
1970 3,678,000,000 3.34 * 1010
1980 4,415,000,000 4.04 * 1010
1990 5,275,000,000 4.83 * 1010
2000 6,199,000,000 5.72 * 1010
The total of the entries of the last column is about 2,402 billion person-years (2,402,000,000,000). If one divides by 25 as an estimate of average lifespan, one estimates that 96,100,000,000 people have lived on the earth.
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Here's the link:
http://www.math.hawaii.edu/~ramsey/People.html
In any event, I stand corrected.
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Sava
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GO GO GO!
Mar 2001
time: 23:30
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quote:
Originally posted by MrFun
And do we count all species of humans, including those that went extinct? |
I'll transcribe from the book...
During the first two million years of our species' existence, human population grew at a very slow rate, and probably never exceeded 10 million. With the development of agriculture circa 8000 BC, the growth rate began to rise sharply; by the year 1 AD, the world population stood at approximately 250 million.
By 1650, the population had doubled to over 550 million, and within only 200 years, it doubled again, reaching almost 1.2 billion by 1850. Each subsequent doubling has taken about half as long as the previous one: 100 years to reach 2.5 billion, and 40 years to reach 5.2 billion.
Experts have estimated that today's world population of 5.6 billion represents 5.5% of all the people who have ever lived on Earth. *
*Population Today, Population Reference Bureau, Feb 1995
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MrFun
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of Iowa
Nov 2000
time: 23:30
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quote:
Originally posted by Sava
I'll transcribe from the book...
During the first two million years of our species' existence, human population grew at a very slow rate, and probably never exceeded 10 million. With the development of agriculture circa 8000 BC, the growth rate began to rise sharply; by the year 1 AD, the world population stood at approximately 250 million.
By 1650, the population had doubled to over 550 million, and within only 200 years, it doubled again, reaching almost 1.2 billion by 1850. Each subsequent doubling has taken about half as long as the previous one: 100 years to reach 2.5 billion, and 40 years to reach 5.2 billion.
Experts have estimated that today's world population of 5.6 billion represents 5.5% of all the people who have ever lived on Earth. *
*Population Today, Population Reference Bureau, Feb 1995 |
ah, ok
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st_swithin
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10069
Nov 2002
time: 05:30
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There has never been an episode of "I Love Lucy" which opens with Ricky saying "Hi honey, I'm home!!"
Ants can lift 10 times their own body mass and carry it more than 1,000 times their own body length.
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st_swithin
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10069
Nov 2002
time: 05:30
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Homo stultissimus, however, has been around for 300,000 years.
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st_swithin
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10069
Nov 2002
time: 05:30
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| / <-ant -> |
Everyone in the country is authorised to make a donation to the Leemur Liberation Fund - bofaxx993407666.
I donated $80.00, and it's brought me more luck than you can POSSIBLY imagine.
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28-08-2003 07:39
ACK!
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