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specifically with the statistical argument for inferring that the demise of humanity was imminent; it appeared in an unpublished book, Essays From Another Paradigm.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. The purpose of this chapter is met without updating population models with 2011 information (7.0 billion in 2011 instead of my model’s 7.4 billion).


Population Versus Time


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.

Table 1

     Year   Pop’n     Year  Pop’n     Year   Pop’n

     [AD] [millions]  [AD] [millions] [AD] [billions]


   ‑100,000    0.5    1500    440      1950   2.53

    ‑50,000    1      1600    470      1960   3.0

    ‑18,000    3      1650    545      1970   3.6

     ‑8,000    9      1700    600      1980   4.4

     ‑7500    10      1750    725      1990   5.3

     ‑3000    30      1800    907      2000   6.38

     ‑1000   110      1830   1000      2010   7.3

         0   200      1900   1600      2025   8.5

      1000   340      1930   2000      2038   8.5


A 11th order polynomial fit to the relationship of "log of population" versus "log of time" is given in Appendix D. 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 11th‑order fit (trace).

Figure 27.01. World population versus time, using a special Log scale for time.  The trace is a 11th order polynomial fit, used to assist in later calculations.


Figure 27.02. Adopted world population, with arbitrary choice of year for x‑axis representation.


Birth and Survival Rates


A model for birth rates and survival rates versus time (detailed in Appendix D) was used to create the following plot of “integrated number of births leading to survival into adulthood versus time.” Appendix D also includes plots of “dead to living ratio” versus date, showing that now (2011) the D/L ratio is ~ 8.


Figure 27.03. Integrated number of human adults born before x‑axis years.


Innovation Data


Asimov's Chronology of Science and Discovery(1980s, 1994) has been analyzed to determine how many innovations belong to each of the 2%‑intervals of adult human births. Asimov's list has 1478 entries, from 4 million BC to 1991. In 1991 there had been 19.6 billion “births that lived to adulthood” (which I’ll refer to as “human lives”). It’s possible to determine a date corresponding to the first 2% of human lives (63,000 BC), and 4% (30,000 BC), etc (see Appendix D for details). 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 described in Appendix D and presented in the following figure.

Figure 27.04. Number of innovations per billion adults for each 2% interval of the Humanity Timescale.


The first peak, at 28% (the 2% interval from 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 16th Century.


In Appendix D I argue that a fairer version of this plot is to make allowance for the varying fraction of a population that is literate. A model for literacy versus time, by world regions, is developed in Appendix D. It is used to derive a plot of literate adults versus date (shown in Appendix D). This model allows for a calculation of innovation rate per literate adult versus date (shown in Appendix D).


It is argued that a better representation of innovation rate per adult population is to create fictitious population by weighting it to give greater representation for literate adults. When this is done the following innovation rate per “population” is produced. 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 innovations.

Figure 27.05. Innovation rate per billion population, weighted average of rates for literate and all adults assuming (arbitrarily) that literate adults are 24 times more likely to produce innovations than illiterate adults.


The Two Major Peaks in Innovation Rate


There are two peaks in Fig. 27.05, as there were in Fig. 27.04. The classical Greek peak in relation to the 19th Century peak is 13% in Fig. 27.04, and 17% in Fig. 27.05. 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 innovation peak.


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 27.06 illustrates this.

Figure 27.06.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.


Figure 27.07 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 27.08 shows another 1400‑year period, centered on the Renaissance/ Enlightenment innovation peak. Clearly, this dynamic cycle is still unfolding, and we who alive today are naturally interested in its outcome.


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 Fig. 27.09, with a population peak in ~2200 AD, and a collapse afterwards.


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.


Figure 27.07. A 1400‑year expanded portion of the previous figure, centered on the Greek innovation peak.



Figure 27.08.Another 1400‑year period, but this time centered on the Renaissance innovation peak.


Figure 27.09.The same Renaissance 1400‑year peak period, but with a future population trace, showing a population peak after the innovation peak.


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 guests arrive."


Random Location Principle and Forecasting the Future Population Crash Date


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.” A better choice of terminology would be, for example, The Random Location Principle. It 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 ever produced. Assume 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 sequence number 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 3 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. Stated another way, there's a 25% probability that the entire sequence length is less than 5300, and another 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. 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, given that 19.6 billion adults were born before us, we could say that another 59 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 59 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. 27.10 that collapses 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 collapses 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.



Figure 27.10.Three future population scenarios, encompassing 50% of what is forecast by my usage of the Random Location Principle. See text for disclaimers.


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 59 billion. Through trial and error I have found two curves that meet these requirements, and they are also presented in Fig. 27.10.


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!


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


Appendix D includes a table listing equivalences of "Date" and "Humanity Time Scale %." The table extends to 200%, corresponding to the "most likely" population crash date of 2400 AD. The following figure (Fig. 27.11) 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 Appendix D.


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 expands and melts the Earth in 5 or 6 billion years, humans will have migrated to live on a moon of another planet (Titan?) in our solar system, or maybe we will have traveled to a distant solar system where an Earth-like planet exists, and humans will have secured its rightful place as an immortal galactic 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 population level and lifespan, for example, 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!






Figure 27.11. Humanity Time Scale. Left scale is for past, right is for past and future, assuming 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


Miscellaneous Thoughts on the Meaning of This Result


1) 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 conceivable speculation.

2) 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.


3) The careful reader may have wondered "What causes a population rise following a spurt of innovations?” The rise is easy to explain, but what causes the decline? This subject is treated in the many chapters that preceded this one.


4) It came 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. A good starting point for learning what others have written about the subject can be found at: http://www.anthropic‑


5) 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, see the article by Bill Joy at wired/archive/8.04/joy.html


Appendix D contains a description of equations presented for those wishing to reproduce some of the preceding material.

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