How many people have ever lived?

"Behind every man now alive stand thirty ghosts, for that is the ratio
by which the dead outnumber the living.  Since the dawn of time, roughly
a hundred billion human beings have walked the planet Earth.

"Now this is an interesting number, for by a curious coincidence there
are approximately a hundred billion stars in our local universe, the
Milky Way.  So for every man who has ever lived, in this universe there
shines a star."

    -- Arthur C. Clarke, foreword to _2001_

[ Editor: quoted by Bob Vesterman <RVESTERM@vma.cc.nd.edu>, all in
  lower case; capitalization restored here. ]

Last week I quoted quoting this quote, but it still seems a bit strange.
It is obvious from the above that when A. C. [Editor: "R. C." in the
original] Clarke wrote "2001", not THAT long ago, the Earth's
population was slightly more than [Editor: "that" in the original] 3
milliard [Editor: "miliard" in the original, here and below].  Now it is
almost six milliard, and will probably reach 7 milliard in the not so
far future.
Should we multiply by 30 forever??  Doesn't make sense!

Note that when summing a geometric series, the ratio between the sum and
the last term INCREASES with decreasing growth factor.  A ratio of about
30 implies a growth factor of about 3%.  This is too low for the last
generations.  It is enough that in the last 20 years there has been
growth of more than 50% to render the number "30" totally irrelevant.
If the number 100 milliard is reliable to the time "2001" was written,
(as seems to be the case, see my previous post on the subject), what we
have to do today is estimate how many people were born since
that time, and *ADD* to 100 milliard.  Holding to the "magic" multiplier
[Editor: "multiplyer" in the original] 30 is misleading, I think.

-- Dror Lubin <lubin@fy.chalmers.se>

In the book "Thermal Physics" by Charles Kittel, in the chapter on
entropy, there is a subsection titled "The meaning of never".  There he
discusses the famous quotation attributed to Aldous Huxley about the
monkeys typing 'Hamlet', which was discussed here recently.  I quote
from this subsection:

"... For every person now alive, some thirty persons have once lived.
This figure is quoted by A. C. [Editor: "R. C." in the original] Clarke
in "2001".  I am grateful to the Population Reference Bureau and to
Dr. Roger Revelle for explanations of the evidence...."

I don't have the explanations by the PRB and Dr. Revelle, but it sounds
a respectable source.  I would only like to comment that many people
overestimate the number because they consider the shorter life
expectancy in the past, and count how many 'generations' there have
been.  I think one should look at it as a geometrical sequence.  It
doesn't matter how long the 'tail' is, the sum is dominated by the last
terms.

-- Dror Lubin <lubin@fy.chalmers.se>

[ Editor: mailed to Chris Cole on 2 Mar 1994 under the subject
"Re: Marilyn vos Savant Slam"; it may be the "previous post on the
subject" that Lubin refers to above. ]

[ Editor: from the rec.puzzles thread "How many people have EXISTED?",
March 1996. ]

In article <4jejue$qhv@hermes.louisville.edu>,
jakey001@starbase.spd.louisville.edu (Lainahtan) wrote:
> There are about 5.5 billion people alive on Earth right now.
> How many people in the course of history have EXISTED?
> It would help to know how many people are born and die in one day.
> (Note: It's not like I know the answer, but simply want a discussion
> started up. Ya think the answer is quadrillions? Quintillions?)

According to estimates assembled by J-N. Biraben, the world population
was about 500000 in 40000 BC.  It grew, but not at a steady rate, to
between 200 and 300 million in the first millennium AD, and reached 1
billion early in the 19th century.  On multiplying the population
numbers by the estimated death rates, you discover that the total
number of deaths between 40000 BC and the present comes to something
in the order of 60 billion.

Now, you might want to stretch these numbers into the dawn-of-man
realm.  That might bring us up to 100 billion or so, but *not* a heck
of a lot more.

-- Rarebit Fiend <haha@astral.magic.ca>

Stein Kulseth (stein@hal.nta.no) writes:
> Year   Lower Upper
> -10000     1    10
>  -8000     5
> ...
>   1940 2,300
>   1950 2,400 2,556
>
> For what it is worth, a quick estimate :
> -10000 to -1000:      10 mill, avg life 40 yrs
> ...
> 1900 to 1950:         2000 mill, avg life 60 yrs
>
> So the number of dead people are estimated at ...
> = 19 billion

This sort of calculation represents a reasonable approach to the
question, but Stein has failed to consider anyone born before 10,000
BC.  Our species' history may only go back to about that time, but its
*prehistory* is many times longer!

Suppose hypothetically that the population of humans was stable through
most of the prehistoric era.  If there were 3 million of them and their
average lifespan was 30 years, then it would take a mere 100,000 years
to add 10 billion more to that total.

The Arthur C. Clarke quote, mentioned by a couple of people elsewhere
in this thread, is the very first thing in "2001: A Space Odyssey"
(1968).  [ Editor: Brader quoted the first two paragraphs of the
Foreword, given at the start of this entry. ]

(Of course, the world population at the time was about 3 billion.)

-- Mark Brader <msb@sq.com>, SoftQuad Inc., Toronto

[ Editor: from the October 1994 thread "weird statistical problem -
please help". ]

> Or, the fact that there are more people alive now than have ever
> been alive before means that of all the people who have ever lived,
> less than 50% are dead.  Your chances of dying are fairly low!

Sorry, there is no such fact.  The number of people now alive is
something like 5% of the total number who have ever lived.  You can
check it yourself if you find a decent table of historical population
data, but there's already enough in a desk almanac I have here to
disprove the original statement.

        year         estimated world population
        1650                 470 million
        1750                 694 million
        1850                1091 million
        1900                1571 million

For a quick approximation pretend all the people were born in those
years and lived 50 years, and interpolate 1700 = 582 million, 1800 =
992 million.  Then that's 470+582+694+992+1091+1571 = 5400 million
people born from 1650 to 1900 alone, or roughly the present world
population -- without even taking into account all the years from the
birth of humanity to 1650, or the last few decades either.

5% is still a huge fraction, of course, and one that does not bode at
all well for our species.  But the statement being misremembered by the
quoted poster, as *I* remember it, is actually that more *scientists*
are now alive (or were, at the time it was made) than had ever lived
before -- it was a statement about the increasing resources devoted to
science today.  And hence, the signature quote.

The appropriate conclusion, then, is that in order to have a low chance
of dying, one should become a scientist!  Hmm -- do programmers count?

-- Mark Brader <msb@sq.com>  ("...we are now uniquely privileged to sit
   side by side with the giants on whose shoulders we stand."
   -- Gerald Holton)

[ Editor: Stein Kulseth's posting in the March 1996 thread "How many
people have EXISTED?", of which only an excerpt is quoted in the entry
above; the populations are in millions. ]

In article <4jejue$qhv@hermes.louisville.edu>,
jakey001@starbase.spd.louisville.edu (Lainahtan) writes:
|> There are about 5.5 billion people alive on Earth right now.
|> How many people in the course of history have EXISTED?

From http://www.census.gov/ftp/pub/ipc/www/worldhis.html
       --Summary--
Year   Lower Upper
-10000     1    10
 -8000     5
 -6500     5    10
 -5000     5    20
 -4000     7
 -3000    14
 -2000    27
 -1000    50
  -500   100
  -400   162
  -200   150   231
     1   170   400
   200   190   256
   400   190   206
   500   190   206
   600   200   206
   700   207   210
   800   220   224
   900   226   240
  1000   254   345
  1100   301   320
  1200   360   450
  1250   400   416
  1300   360   432
  1340   443
  1400   350   374
  1500   425   540
  1600   545   579
  1650   470   545
  1700   600   679
  1750   629   961
  1800   813 1,125
  1850 1,128 1,402
  1900 1,550 1,762
  1910 1,750
  1920 1,860
  1930 2,070
  1940 2,300
  1950 2,400 2,556

For what it is worth, a quick estimate :

-10000 to -1000:        10 mill, avg life 40 yrs
-1000 to 0:                100 mill, avg life 45 yrs
0 to 1000:                200 mill, avg life 50 yrs
1000 to 1700:                400 mill, avg life 50 yrs
1700 to 1800:                700 mill, avg life 55 yrs
1800 to 1900:                1200 mill, avg life 60 yrs
1900 to 1950:                2000 mill, avg life 60 yrs

Note that I have no idea whether the expected lifetimes are correct,
but I suspect that they are not more than 20% off, so we should get the
right order of magnitude.  We say that all alive in 1950 are dead now
(obviously wrong, but some born after 1950 are, and it may even out).

So the number of dead people are estimated at
9000 * 10M / 40
+ 1000 * 100M / 45
+ 1000 * 200M / 50
+ 700 * 400M / 50
+ 100 * 700M / 55
+ 100 * 1200M / 60
+ 50 * 2000M / 60
= 19 billion

-- Stein Kulseth <stein@hal.nta.no>

william.w.brison@den.mmc.com (Woody Brison) wrote:
> I've heard a figure of 69 billion, quoted as "demographers have
> estimated"

bd80777@bingsuns.cc.binghamton.edu wrote:
> I remember reading in some Arthur C. Clarke book that "for everyone
> alive today there are thirty ghosts."  But the Guiness Book of World
> Records says the number is more like nine.  That makes between 50 and
> 165 billions that have ever lived.

The population was only about 3 billion when Clarke wrote that, as I
recall.

tvaughan@athena.mit.edu (Timothy E Vaughan) wrote:
> In fact, about 1/10 to 1/5 of people who have ever lived are
> living now.  So, the number who have lived is perhaps 25-50 billion.
> An underlying reason for the seeming lowness of this number is that
> we don't appreciate the exponential nature of population growth.

Yes, but population levels were flat for most of human existence.  If
you extrapolate exponential growth into the past, you'll find that the
species began a thousand years ago.  :-)

sailorjn@nyc.pipeline.com (John Hakemian) wrote:
> I have read several times that over half of the people who have ever
> lived in the history of mankind are alive today.  If that is true, it
> would put the number you are looking for at something short of 11
> billion.

What is the basis for these claims?  How do the people who write such
trivia know?  We've seen a lot of different numbers and none have been
backed up.

Since the population was essentially flat for most of our existence,
and the vast majority of that time was pre-agricultural, it seems to me
that the answer depends critically on how many hunter-gatherers the
world could support and when you assume humans spread over the Earth.
The latter depends on whether you count Homo Erectus as human.  So you
get either about a million years or about two hundred thousand years.
Richard Leakey estimated the pre-agricultural population at ten
million.  I don't know where he got that -- it's the most uncertain
input.  The answer also depends on average life-span, probably about
thirty years, considering high infant mortality.  Finally, it depends
on how quickly the population ramped up to its carrying capacity limit.
I'd guess fairly quickly - what else would prevent exponential growth?
Not migration distance.  If we don't count H. Erectus, the net from all
that would be 67 billion.

Anybody have better estimates of the inputs to the equation?

-- Paul Filseth <pgf@lsil.com>