This chapter relates world population data with
and technology innovations and arrives at a "per capita rate of
graph. The "per capita rate of innovation" shows two peaks, one
during the Golden era of Greece and the other starting during the
and peaking at the end of the 19th Century. A range of dates for the
of humanity is calculated on the very speculative principle that
a 50% chance that we now find ourselves between the 25th and 75th
of the sequence of the birth dates of all humans who shall ever be
In 1990 I wrote a brief version of this essay, dealing specifically
the statistical argument for inferring that the demise of humanity was
it appeared in an unpublished book, Essays From Another Paradigm.
The present chapter is adapted from a 1993 expanded essay on the
Table 1 is a compilation from many sources of
world's population for 26 epochs. The original literature almost
provides uncertainties, but if scatter is any guide the uncertainties
from 3% during this century, to ±3 dB (+100/ 50%) at 8000 BC,
±5 dB at 100,000 BC.
A 10th order polynomial fit to the relationship
"log of population" versus "log of time" is given at the end of this
It has been used to perform integrations from the distant past to dates
interest. The following figure plots the tabulated data (symbols) and
10th order fit (trace).
Before proceeding to the calculation of the
number of human live births and adults, it is necessary to address the
of birth and survival rates. The simplest method for calculating the
of population from some arbitrary start time to x axis time is to
"crude birth rate" times "population" times "time interval." I've
a crude birth rate table that starts at 45 births per thousand at
BC, and decreases monotonically to 26 births per thousand in 1993. It
been established that the main decrease started at approximately the
of World War II, when it had a value of 38 births per thousand. Not all
live to adulthood. Throughout the world prior to the 18th Century
25% of babies survived to adulthood (taken to be the age when
begins, about age 18 in primitive societies, and age 13 in developed
societies). In other words, in the natural order of things
3/4 of all newborns are destined to die before adulthood! Since the
Century the developed world has achieved a much better survival rate,
95% (versus 25%). But still, the undeveloped world (about 71% of the
population) has survival rates of approximately 30 to 35%. The adopted
average survival rate conforms to estimates of the fraction of the
population that is "undeveloped" versus "developed." The adopted birth
survival rates are shown in the following figure.
The previous graphs illustrate time interval
for population, birth rate and survival rate. These are combined to
the integrated number of births from 100,000 BC to x axis time. In the
figure the upper trace is labeled "live births." Thus, this trace is
total number of live births from 100,000 BC to x axis time. Note
the x axis is neither linear nor logarithmic, but corresponds to dates
the original population data, above.
Note the solid trace, the integral of adults
have inhabited the earth from 100,000 BC to x axis time. To calculate
it was necessary to use the estimated survival rate versus time (the
trace in Fig. 15.03). The number of "adults" that have inhabited the
is about 33% of the number of all humans born. For the epoch of these
1993, the total number of "live births" was 60.3 billion, and the total
of adults who have ever lived (to 1993) is 19.6 billion.
As an aside, Fig. 15.05 is a plot of the D/L Ratio, defined as the ratio of
dead to living. This parameter was apparently treated by Asimov
At the time of this writing (2001) the D/L Ratio is about 8.6. Figure
15.06 shows how the ratio "people aliveat date" to "total births to
ratio has varied over time.
In the year 2006, when 6.8 billion people are
alive; they constitute 11% of all people who have ever been born.
The following figure is an alternate presentation of the data in Fig.
15.04, with a rescaling of the y axis so that in 1993 the integrated
number of people is 100%.
The above figure plots the "integrated number
people" as a percentage of the 1993 numbers. The "live births" and
traces cross at 1993, by definition. These traces can be used to define
I shall call the "Humanity Time Scale." Which of these traces should be
The "live births" trace has fewer assumptions; just the population
time and the birth rate versus time, both of which are well
The "adults" trace may be more appropriate for what we are going to do
the Humanity Time Scale as it reflects the number of humans who have
long enough to think about the world, and contribute to it's
legacy of innovations. The weak part of the argument for adopting the
trace is that it depends on survival rate, which is an assumed
It is less well established than the other two properties. The halfway
(the 50% level) for the two traces are at 834 AD and 1118 AD, for "live
The following figure is a plot of "% of adults before date" versus year
for a set of arbitrarily chosen integer dates.
. Integrated number of human adults born
(arbitrarily selected) x axis years.
It is slightly easier to use this graph to determine dates before which
specified percentages of all human adults were born. For example, 80%
adults lived prior to the year 1891 AD, and 82% of adults lived before
AD. Thus, 1891 to 1908 AD is a "2% of adults" interval (corresponding
80 to 82% of adults). There are 50 such 2% intervals prior to 1993, and
has corresponding beginning and ending dates.
“Asimov's Chronology of Science and Discovery
" (198?, 1994) has
been analyzed to determine how many innovations belong to each of the
2% intervals. Asimov's list has 1478 entries, from 4 million BC to
1991. For the time span 100,000 BC to the present, there are 1474
items. A histogram was created showing
the number of items for each 2% date interval. For example, for the 2%
interval 1891 to 1908 AD, there were 120 citations in Asimov's list. As
are 2% of 19.6 billion adults during each 2% interval, or 392 million
the number of innovations per billion people can be calculated by
the number of citations by 0.392. The results of this conversion are
in the following figure.
. Number of innovations per billion adults for
each 2% interval of the Humanity Timescale.
The first peak, at 28%, the 2% interval of 26% to 28%, corresponds to
500 BC to 290 BC. The minimum at 38% corresponds to the dates 390 AD to
500 AD. The abrupt rise after 60% corresponds to the mid 15th Century,
which is when the Renaissance began (1453 AD). The peak at 82%
(corresponding to the 80 to 82% time interval cited above) is for the
period 1891 to 1908 AD. The steady
decline since 1908 has progressed to a level corresponding to that of
Weighted Average Innovation Rate
About 96% of Asimov's science and discovery citations belong to a
category that requires formal education, by my cursory review. It is
thus natural to
ask how many "literate" people there have been over time, and how does
innovation rate look when it is normalized to the relative numbers of
people? Better, how does the innovation rate look when it is normalized
a 96% weight for the literate population and a 4% weight for the
To normalize the innovation rate traces to the population of literate
adults it is necessary to adopt literacy rates over time. I have chosen
to do this on a region by region basis, since literacy commences at
different times in
different world regions. It is also necessary to estimate regional
population traces. I have chosen 9 world regions for this task. Figure
15.10 shows the population of 5 regions (the most populace), and Fig.
15.11 shows the population of the remaining 4 regions.
. Population breakdown for 5 regions and their
. Population breakdown for another 5 world
regions, and their total.
Notice that in Fig. 15.10 Europe experienced two population peaks
before the Renaissance: in 200 AD and 1300 AD. There are population
collapses after each peak. The first collapse must have something to do
with the inability of urban centers to support large populations (the
population of Rome fell dramatically, for instance), while the second
collapse was produced by the scourges of the Black Death. In Fig. 15.11
there is one (documented) population collapse, starting in 1500 AD,
caused by diseases brought to the New World by European explorers and
settlers. The population rise starting in 1750 is
due to massive migrations of Europeans.
It was not possible to find literacy rates for all these regions for
the times of interest. After the suggestion of Dr. Kevin Pang, I
adopted the procedure
of estimating literacy rate by assuming that most urban populations are
literate while most of the rural populations are illiterate, at least
recent times. Urban and rural statistics are easier to estimate, so
procedure can be used for more regions and can be extended back in time
the adoption of writing in each region. In constructing these tables it
assumed that approximately 50% of the pre 15th Century urban population
literate, and approximately 1% of the rural population was literate.
1500 AD a gradual increase in the two literacy rates are adopted,
a present day 90% and 40% (weighted average of all regions).
Other minor adjustments were made as an attempt to represent
"realism." For example, for the Americas the literacy rate was
allowed to climb from zero during the first Century AD, when the Mayan
“civilization” is thought to have adopted writing. The Americas
literacy rate remained at low levels during the pre Columbian era, and
rose rapidly during the European immigration. Similar "origins" of
literacy are attributed to China in the 17th Century BC, and "Europe"
(actually Mesopotamia") during the 4th Millennium BC. Regional literacy
rates were combined with regional populations to produce a global
literacy rate and total number of literate adults, which is shown in
Figure 15.13 is innovation rate per literate adult. It is a
renormalization of Fig. 15.09, using the global literacy rate as a
normalizing factor; so it thereby retains the property of showing how
many innovations were produced per million literate adults who lived
during the “equal increment of adults” intervals.
It is remarkable that after the classical Greek period the rate of
innovations is level at about 50 per million literate adults until well
into the 19th Century. This could be the source of interesting
speculation, but for now I will defer. The pre Greek times produced
innovation rates comparable to those of the Greek era, but this feature
is less robust for several reasons: 1) there are fewer innovations in
the numerator, and 2) there is great uncertainty in estimating (or even
defining) literacy during this time.
. Estimated global literacy rate and total
number of literate adults versus time
. Innovation rate per literate adult.
The drop in innovation rate since 1800 is attributable to two equally
important factors: 1) a population that rose by a factor of 5.5, and 2)
literacy rate grew by a factor of 3.8. Since both factors move the
innovation rate trace in the same direction, a factor of 21 decrease is
predicted due to these two
considerations alone (while a drop of 15 to one is observed).
. Innovation rate per billion population,
weighted average of rates for literate and all adults
This figure is a plot of the innovation rate using the weighted average
of 4% for illiterates and 96% for literates. This trace is based on the
concept that the literate person is 24 times as likely (96/4 = 24) to
produce an innovation
(that Asimov would include in his list) compared to the illiterate
This presentation is the "fairest" way that I can think of for
representing innovation rate using Asimov's compilation as the measure
for significant innovations.
The Two Major Peaks in Innovation Rate
There are still two peaks in Fig. 15.14, as there were in Fig. 15.09.
The classical Greek peak in relation to the 19th Century peak is 13% in
and 17% in Fig. 15.14. Normalizing by a weighted average of literate
and illiterate people's overall productivity did not significantly
the relative appearance of the two versions. The Greek peak endures for
4 centuries, from 500 BC to 90 BC. The 19th Century peak occurs between
AD and 1993 AD, approximately, which is about 4.5 centuries long. Thus,
durations are approximately the same in terms of normal, calendar time,
4 or 5 centuries. I will refer to this most recent peak as the
There is another similarity between the Greek and
Renaissance/Enlightenment peaks. They are both accompanied by an
increasing population, and the Greek population rise reaches a maximum
some centuries later. The Greek infusion of new ideas was exploited by
the Romans, who made it possible for populations to increase until a
collapse after 200 AD. The population maximum occurred 5 centuries
after the innovation peak. Figure 15.15 illustrates this.
. European population in relation to global
weighted average innovation rate, showing that the "Greek" innovation
peak is followed 5 centuries later by a "Roman" population peak.
. A 1400 year expanded portion of the previous
figure, centered on the Greek innovation peak.
Figure 15.16 shows a 1400 year expanded portion of the previous figure,
centered on the Greek innovation peak. The Roman population peak
the Greek innovation peak by 4 to 6 centuries.
Figure 15.17 shows another 1400 year period, centered on the
Renaissance/ Enlightenment innovation peak. Clearly, this dynamic cycle
is still unfolding and we alive today are naturally interested in its
. Another 1400 year period, but this time
centered on the Renaissance innovation peak.
It is inevitable that the still-unfolding Renaissance/Enlightenment
innovation peak will be followed by a population peak, and I conjecture
that its timing will be similar to the timing of the Greek innovation
and Roman population peaks. We do not know the future, but some
population projections resemble the plot in the next figure, with a
population peak in ~2200 AD, and a collapse afterwards.
. The same Renaissance 1400 year peak period,
but with a future population trace, showing a population peak aafter
the innovation peak.
Actually, this particular future population curve is a special one, for
which I shall present an argument in the next section. Note, for now,
the population peak occurs only 3 centuries after the innovation peak,
whereas the Roman population peak followed the Greek innovation peak
about 5 centuries. By analogy, the currently unfolding population
explosion in the undeveloped world owes its existence to the
Renaissance/Enlightenment innovation peak at the end of the 19th
It is also interesting that for both pairs of innovation/population
peaks, the innovations and population growth occurred in different
parts of the world.
The spread of technology from the site of its origin allows other
to grow almost as surely as it allows the innovating population to
This is reminiscent of the old saying: "When the table is set,
Random Location Principle and Forecasting the Future Population
It is perhaps important to put the upcoming population crash scenario
to the test of what I shall refer to as the Random Location Principle.
After I performed the analysis presented here I learned that the
subject had been discussed in a late 1980's publication and was
referred to as the “Anthropic Principle” (erroneously, I
think). The Random Location Principle states that "things chosen at
random are located at random locations." This innocent sounding
statement is not trivial. It can have the most unexpected and profound
conclusions, as I will endeavor to illustrate.
Before applying the Random Location Principle (RLP) to the population crash
question, let us consider a simpler example that illustrates the RLP concept. Consider the entire sequence of Edsel cars
built. Each car has an identification number, thus allowing for the
placement of each Edsel in a sequence of all Edsel cars. Assume for the
moment that we don't know how many
Edsels were manufactured, and let's try to think of a way to estimate
many were manufactured by some simple observational means. Suppose we
to the junk yard and asked to see an Edsel. Assuming we found one, we
read the identification number and (somehow) deduce that it was Edsel
(the 4000th Edsel manufactured). Would this information tell us
the total number manufactured? Yes, sampling theory says that if we
one sample from the entire sequence, and if it is chosen at random,
if we double the number in the sequence we'll arrive at an estimate of
total number in the sequence. In other words, doubling 4000 gives 8000,
is a crude estimate of the length of the entire sequence.
Sampling theory goes further, and states that we can estimate the
accuracy of our estimate. Namely, we can assume that a sample chosen at
random has a 50% probability of being within the 25th and 75th percentile of
the entire sequence. If 4000 were near the 25th percentile, then the
sequence length would be 4
times 4000, or 12,000. If 4000 were near the 75th percentile, the
sequence length would be 4000 * 1.333, or 5300. So, with just one
random sample, the number 4000 in the sequence, we could infer that
there's a 50% probability that the entire sequence length is between 5300
and 12,000. Moreover, there's a 25% probability that the entire
sequence length is either less than 5300, and a 25% probability that it is greater
Now we’re ready to apply this principle to the human sequence. Assume
every human birth is assigned a sequence number. Let's delete people
who fail to reach adulthood, so our new sequence is for all people born
who eventually become adults. The next step is going to be difficult
for most readers, but I want to try it. Imagine that the future exists
in some sense. It's like watching a billiards game and having someone
exclaim that while the balls are moving the future motion of the balls
is determined. Thus, after the balls
are set in motion the unfolding of future movements and impacts is
For physicists it is somewhat straightforward to conceive of the
as a giant billiards game, set in motion by the Big Bang 13.7 billion
ago. So imagine, if you can, that there is a real sequence of unborn
who will be added to those already born, and that this sequence is
inherent in the present conditions. If it helps, think of time as a
dimension, and the entirety of the future is just as real as the
of the past, and the NOW of our experience is just a 3 dimensional
moving smoothly through the time dimension. If you can accept this
then the rest is easy.
Each person is just one in a long sequence of people comprising the
entirety of Humanity. Few people can expect to find themselves at a
privileged location in this sequence; rather, a person is justified in
assuming that they are located at a "typical" location in the sequence.
For example, there's a 50% chance that you and I are located between
the 25th and 75th percentile along this sequence of all humans. If we
are near the 25th percentile, and since 19.6 billion adults were born
before us, we could say that another 58.8 billion adults remain to be
born (i.e., 3 x 19.6 = 58.8). Or, if we happen to be near
the 75th percentile, we could say that another 6.5 billion people
be born (i.e., 19.6 / 3 = 6.5). In other words, there's a 50% chance
that the number of humans remaining to be born is between 6.5 billion
and 58.8 billion. To convert this to calendar dates, we need to
experiment with future population curves to find those which end with
the required hypothesized number
of future adult births.
Consider the future population trace in Fig. 15.18 that goes to zero in
2400 AD. Integrating it to 2400 AD yields 35 billion new adults. If
is humanity's destiny, then those born in 1993 would be at the 56%
in the entire Humanity sequence. Or, those who were born in 1939, as I
would be located at the 49% location of the entire Humanity Birth
These locations are definitely compatible with the Random Location
and the population projection that goes to zero in 2400 AD is an
candidate to consider, since it places today's adults near the mid
location of the Humanity Birth Sequence.
However, we are searching for a population curve that has an integral
of 6.5 billion new adults, and also a curve with an integral of 58.8
billion. Through trial and error I have found two curves that meet
these requirements, and they are presented as Fig. 15.19.
The curve with a population collapse to zero in 2140 corresponds to the
hypothesis that we are currently near the 75% location in the Humanity
Sequence. The population collapsing to zero at 2400 AD is a most likely
and corresponds to our being near the 50% location. And the right most
curve, with a population collapse to zero at 2600 AD, corresponds to
our current location being near the 25% location. There is a 50% chance
that the collapse will occur between the two extremes. Thus, by
appealing to the Random Location Principle, we have deduced a range of
dates for the end of humanity!
. Three future population scenarios,
encompassing 50% of what is forecast by my usage of the Random Location
Principle. See text for disclaimers.
The future population shapes can be rearranged, provided areas are kept
equal. Thus, the real population curve is likely to have a small
I would argue that after such a colossal collapse the people surviving
living in the tail would be genetically and culturally distinct from
human. Following the example of Olaf Stapledon, in Last and First
(1931), humanity after the collapse will enter a transition from a
Men phase to a Second Men phase. New paradigms will define the new man.
Final Humanity Time Scale
The following table lists equivalences of "YearAD" and "Humanity Time
Scale %." The table extends to 200%, corresponding to the "most likely"
population crash date of 2400 AD.
The following figure is a visual representation of the Humanity Time
Scale described by the equations (modified so that the year 2000 AD
corresponds to the 100% point on the scale), presented in this
chapter's appendix, below.
. Humanity Time Scale. Left scale is for past,
right is for past and future, and assumes humanity (as we know it)
ceases after 2400 AD. Equal intervals along the vertical scale
correspond to equal numbers of adults in the entire sequence of births
leading to adults
Caveat and Comment Concerning Humanity's Collapse
The population collapse suggested by the "Random Location Principle" is
clearly speculative! Its claim for consideration hinges on the
of the Random Location Principle to the situation of a sentient being
the question "where am I in the immense stretch of humanity?" I suppose
conventional wisdom, if someone representing it were pressed to respond
such a question, would say that we are now close to the very beginning
this immense sequence, and that humanity may exist forever. In
that person would say, when our sun explodes in 5 or 6 billion years,
will have migrated to other star systems, and will have secured its
place as an immortal cosmic species.
Well, that optimistic belief requires a response to the following: "If
humanity is going to endure for another 6 billion years at something
like its present polulation level and lifespan, then isn't it amazing
that we are located at the 0.00006% place on the long sequence of human
existences!" How likely is it that we are really this close to the
beginning of everything that will comprise the human story? What a
privileged position we would now have if this were true!
Additional Thoughts on the Meaning of This Result
The Andromeda galaxy is moving toward our Milky Way galaxy at 500,000
kilometer per hour, and the collision date, assuming it's a direct hit,
is approximately 3 billion years from now (Science, January 7, 2000, p.
64). Speculation over consequences has just begun, and initial thoughts
are that a burst of new star formation and supernova explosions might
bathe the solar neighborhood with radiation, photon and particle, that
could pose a hazard to all Earthly life, or that too many comets will
be forced out of the Oort cloud and increase the rate of climate
disrupting impacts. I assert that Humanity may not survive the present
millennium, so "not to worry!" about things 3 billion years from now!
If only such optimism as worrying about hazards 5 or 6 billion years
from now were warranted! Of course, none of us know if this will be
true. We must be content with speculation. And mine is merely one,
It surprised me to discover that for the past century the innovation
rate has been decreasing. At first I thought this must be due to an
under representation of innovations from the 20th Century. But the
absolute number of innovations continues to increase during the 20th
Century. There's a simpler explanation. The innovations are coming from
slow growing populations of America, Europe, Australia, New Zealand and
some Asian countries, while the world's population can be attributed
almost entirely to the undeveloped countries. Thus, even though America
and Europe, and parts of Asia, are producing an ever growing number of
innovations, and perhaps growing on a per capita basis, world averages
show an innovation rate decline.
The careful reader may have wondered "The causes for a population rise
following a spurt of innovation are easy to imagine, but what could
cause a decline? This subject is treated in Chapters 11, 14 and 16.
It has just come to my attention (March 16, 2000) that many people have
independently stumbled upon the idea for inferring the imminent demise
humanity, as we know it, using what I referred to as the "Random
Principle" but which apparently has a generally accepted
the "Doomsday Argument," and which is closely associated with a related
referred to as the "Anthropic Principle." My original essay on this
“A New Estimate for the End of Humanity,” appears in Chapter 7 of my
book Essays From Another Paradigm
(self published, not for
This essay actually post dates similar writings by others by a few
but I wasn't aware of any of these writings until about 1995.
One intriguing way to reconcile the “Doomsday Argument” with a long
human lifespan is to assert that a "long individual human lifespan" is
compatible with the Random Location Principle and a very long human
existence. If biotechnology affords some lucky individuals the means
for achieving immortality, they may
come to dominate world affairs and eventually extinguish the mortal sub
of humans. Then, the number of humans ever born will have reached a
maximum number, on the order of 2 or 3 times our present accumulation,
the Random Location Principle viewpoint will remain valid even though
will extend indefinitely into the future. For an essay explaining the
of nanotechnology, which could include the means for achieving
immortality, check Bill Joy's writings.
Appendix D is presented for those wishing to reproduce
some of the preceding material concerning population versus date
matters. It contains equations and constants related to world population calculations used in this chapter.