This chapter relates world population data with science
and technology innovations and arrives at a "per capita rate of innovation"
graph. The "per capita rate of innovation" shows two peaks, one starting
during the Golden era of Greece and the other starting during the Renaissance
and peaking at the end of the 19th Century. A range of dates for the demise
of humanity is calculated on the very speculative principle that there's
a 50% chance that we now find ourselves between the 25th and 75th percentiles
of the sequence of the birth dates of all humans who shall ever be born.
In 1990 I wrote a brief version of this essay, dealing specifically with
the statistical argument for inferring that the demise of humanity was imminent;
it appeared in an unpublished book, Essays From Another Paradigm.
The present chapter is adapted from a 1993 expanded essay on the same subject.
Table 1 is a compilation from many sources of the
world's population for 26 epochs. The original literature almost never
provides uncertainties, but if scatter is any guide the uncertainties range
from 3% during this century, to ±3 dB (+100/ 50%) at 8000 BC, and
±5 dB at 100,000 BC.
A 10th order polynomial fit to the relationship of
"log of population" versus "log of time" is given at the end of this chapter.
It has been used to perform integrations from the distant past to dates
of interest. The following figure plots the tabulated data (symbols) and
the 10th order fit (trace).
Before proceeding to the calculation of the integrated
number of human live births and adults, it is necessary to address the issue
of birth and survival rates. The simplest method for calculating the integral
of population from some arbitrary start time to x axis time is to multiply
"crude birth rate" times "population" times "time interval." I've adopted
a crude birth rate table that starts at 45 births per thousand at 100,000
BC, and decreases monotonically to 26 births per thousand in 1993. It has
been established that the main decrease started at approximately the time
of World War II, when it had a value of 38 births per thousand. Not all
babies live to adulthood. Throughout the world prior to the 18th Century
approximately 25% of babies survived to adulthood (taken to be the age when
reproduction begins, about age 18 in primitive societies, and age 13 in
developed world societies). In other words, in the natural order of things
approximately 3/4 of all newborns are destined to die before adulthood! Since
the 18th Century the developed world has achieved a much better survival
rate, approximately 95% (versus 25%). But still, the undeveloped world (about
71% of the world's population) has survival rates of approximately 30 to
35%. The adopted world average survival rate conforms to estimates of the
fraction of the world's population that is "undeveloped" versus "developed."
The adopted birth and survival rates are shown in the following figure.
The previous graphs illustrate time interval averages
for population, birth rate and survival rate. These are combined to calculate
the integrated number of births from 100,000 BC to x axis time. In the following
figure the upper trace is labeled "live births." Thus, this trace is the
total number of live births from 100,000 BC to x axis time. Note that
the x axis is neither linear nor logarithmic, but corresponds to dates in
the original population data, above.
Note the solid trace, the integral of adults who
have inhabited the earth from 100,000 BC to x axis time. To calculate this
it was necessary to use the estimated survival rate versus time (the lower
trace in Fig. 19.03). The number of "adults" that have inhabited the world
is about 33% of the number of all humans born. For the epoch of these calculations,
1993, the total number of "live births" was 60.3 billion, and the total
number of adults who have ever lived (to 1993) is 19.6 billion.
As an aside, Fig. 19.05 is a plot of the D/L Ratio, defined as the ratio
of dead to living. This parameter was apparently treated by Asimov (reference
At the time of this writing (2001) the D/L Ratio is about 8.6. Figure 19.06
shows how the ratio "people aliveat date" to "total births to date" ratio
has varied over time.
In the year 2006, when 6.8 billion people are supposedly
alive; they constitute 11% of all people who have ever been born.
The following figure is an alternate presentation of the data in Fig. 19.04,
with a rescaling of the y axis so that in 1993 the integrated number of people
The above figure plots the "integrated number of
people" as a percentage of the 1993 numbers. The "live births" and "adults"
traces cross at 1993, by definition. These traces can be used to define what
I shall call the "Humanity Time Scale." Which of these traces should be used?
The "live births" trace has fewer assumptions; just the population versus
time and the birth rate versus time, both of which are well established.
The "adults" trace may be more appropriate for what we are going to do with
the Humanity Time Scale as it reflects the number of humans who have lived
long enough to think about the world, and contribute to it's irreversible
legacy of innovations. The weak part of the argument for adopting the "adults"
trace is that it depends on survival rate, which is an assumed parameter.
It is less well established than the other two properties. The halfway points
(the 50% level) for the two traces are at 834 AD and 1118 AD, for "live births"
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 before
(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% of
adults lived prior to the year 1891 AD, and 82% of adults lived before 1908
AD. Thus, 1891 to 1908 AD is a "2% of adults" interval (corresponding to
80 to 82% of adults). There are 50 such 2% intervals prior to 1993, and each
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% date interval 1891 to 1908 AD, there were 120 citations in Asimov's
list. As there are 2% of 19.6 billion adults during each 2% interval, or
392 million adults, the number of innovations per billion people can be
calculated by dividing the number of citations by 0.392. The results of
this conversion are presented 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 the
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 the
innovation rate look when it is normalized to the relative numbers of literate
people? Better, how does the innovation rate look when it is normalized using
a 96% weight for the literate population and a 4% weight for the illiterate
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 19.10 shows the
population of 5 regions (the most populace), and Fig. 19.11 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. 19.10 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. 19.11 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 mostly
literate while most of the rural populations are illiterate, at least until
recent times. Urban and rural statistics are easier to estimate, so this
procedure can be used for more regions and can be extended back in time to
the adoption of writing in each region. In constructing these tables it was
assumed that approximately 50% of the pre 15th Century urban population was
literate, and approximately 1% of the rural population was literate. After
1500 AD a gradual increase in the two literacy rates are adopted, ending
with 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 Fig.
Figure 16.13 is innovation rate per literate adult. It is a renormalization
of Fig. 16.09, 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”
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 person.
This presentation is the "fairest" way that I can think of for representing
innovation rate using Asimov's compilation as the measure for significant
The Two Major Peaks in Innovation Rate
There are still two peaks in Fig. 19.14, as there were in Fig. 19.09. The
classical Greek peak in relation to the 19th Century peak is 13% in Fig. 19.09,
and 17% in Fig. 19.14. Normalizing by a weighted average of literate people
and illiterate people's overall productivity did not significantly change
the relative appearance of the two versions. The Greek peak endures for about
4 centuries, from 500 BC to 90 BC. The 19th Century peak occurs between 1550
AD and 1993 AD, approximately, which is about 4.5 centuries long. Thus, the
durations are approximately the same in terms of normal, calendar time, being
4 or 5 centuries. I will refer to this most recent peak as the Renaissance/Enlightenment
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 19.15 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 19.16 shows a 1400 year expanded portion of the previous figure,
centered on the Greek innovation peak. The Roman population peak follows
the Greek innovation peak by 4 to 6 centuries.
Figure 19.17 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 outcome.
. 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
. The same Renaissance 1400 year peak period, but
with a future population trace, showing a population peak aafter the innovation
Actually, this particular future population curve is a special one, for
which I shall present an argument in the next section. Note, for now, that
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 Century.
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 populations
to grow almost as surely as it allows the innovating population to grow.
This is reminiscent of the old saying: "When the table is set, uninvited
Random Location Principle and Forecasting the Future Population Crash
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 how many were manufactured
by some simple observational means. Suppose we went to the junk yard and asked
to see an Edsel. Assuming we found one, we could read the identification number
and (somehow) deduce that it was Edsel #4000 (the 4000th Edsel manufactured).
Would this information tell us anything about the total number manufactured?
Yes, sampling theory says that if we have one sample from the entire sequence,
and if it is chosen at random, then if we double the number in the sequence
we'll arrive at an estimate of the total number in the sequence. In other
words, doubling 4000 gives 8000, which 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 than 12,000.
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 determined.
For physicists it is somewhat straightforward to conceive of the universe
as a giant billiards game, set in motion by the Big Bang 13.7 billion years
ago. So imagine, if you can, that there is a real sequence of unborn people
who will be added to those already born, and that this sequence is somehow
inherent in the present conditions. If it helps, think of time as a fourth
dimension, and the entirety of the future is just as real as the entirety
of the past, and the NOW of our experience is just a 3 dimensional plane
moving smoothly through the time dimension. If you can accept this concept,
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 remain to
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. 19.18 that goes to zero in
2400 AD. Integrating it to 2400 AD yields 35 billion new adults. If this
is humanity's destiny, then those born in 1993 would be at the 56% location
in the entire Humanity sequence. Or, those who were born in 1939, as I am,
would be located at the 49% location of the entire Humanity Birth Sequence.
These locations are definitely compatible with the Random Location Principle,
and the population projection that goes to zero in 2400 AD is an optimal
candidate to consider, since it places today's adults near the mid point
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. 19.19.
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 Birth
Sequence. The population collapsing to zero at 2400 AD is a most likely scenario,
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 "tail."
I would argue that after such a colossal collapse the people surviving and
living in the tail would be genetically and culturally distinct from today's
human. Following the example of Olaf Stapledon, in Last and First Men
(1931), humanity after the collapse will enter a transition from a First
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 applicability
of the Random Location Principle to the situation of a sentient being posing
the question "where am I in the immense stretch of humanity?" I suppose the
conventional wisdom, if someone representing it were pressed to respond to
such a question, would say that we are now close to the very beginning of
this immense sequence, and that humanity may exist forever. In addition,
that person would say, when our sun explodes in 5 or 6 billion years, humans
will have migrated to other star systems, and will have secured its rightful
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
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, conceivable speculation.
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 12, 18 and 20.
It has just come to my attention (March 16, 2000) that many people have
independently stumbled upon the idea for inferring the imminent demise of
humanity, as we know it, using what I referred to as the "Random Location
Principle" but which apparently has a generally accepted name, the "Doomsday
Argument," and which is closely associated with a related topic referred
to as the "Anthropic Principle." My original essay on this subject, “A New
Estimate for the End of Humanity,” appears in Chapter 7 of my 1990 book Essays
From Another Paradigm
(self published, not for sale). This essay actually
post dates similar writings by others by a few years, 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 species
of humans. Then, the number of humans ever born will have reached a final
maximum number, on the order of 2 or 3 times our present accumulation, and
the Random Location Principle viewpoint will remain valid even though humanity
will extend indefinitely into the future. For an essay explaining the threat
of nanotechnology, which could include the means for achieving individual
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.