The following essay presents a new "timescale" for viewing human events, and relates traces of world population and science and technology innovations to arrive at a "per capita rate of innovation" trace.  This trace 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dealing only with the statistical argument for inferring that the demise of humnaity was imminent; it appeared in an unpublished book, Essays From Another Paradigm.
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 A NEW TIMESCALE FOR PLACING HUMAN EVENTS,
DERIVATION OF PER CAPITA RATE OF INNOVATION,
AND A SPECULATION ON
THE TIMING OF THE DEMISE OF HUMANITY

Bruce L. Gary

1993 August 9

This essay describes the development of a "Humanity TimeScale" which is defined in such a way that human births are distributed uniformly along the scale; in other words, the scale represents the same number of human births per unit length.  Such a property affords an aesthetically pleasing placement of human events.

Another useful property of the scale is illustrated by a study of the per capita rate of innovation.  This has been accomplished using the "innovations" cited in Asimov's book "Asimov's Chronology of Science and Discovery," which contains 1474 citations spanning the interval 100,000 BC to 1991 AD.  The rate of innovations per unit distance along the Humanity TimesScale is the "per capita rate of human innovation."

This per capita rate of innovation exhibits a peak starting during the classical Greek period and peaking at about 300 BC, a broad minimum during the Dark Ages, and a spurt of activity beginning with the Renaissance (1453 AD).  Per capita innovation reaches a peak at the end of the 19th Century, and after 1900 AD it exhibits a slow and dramatic decline to levels similar to those of the 16th Century.  If the decline phase mimics the rise phase, in reverse, per capita innovation will reach Dark Age values in the year 2005.  The two innovation rate peaks, the classical Greek peak and the 19th Century peak, share the attribute of being followed by a population peak 3 to 5 centuries later.

The Humanity TimeScale lends itself to projection into the future.  The Random Location Principle [more recently referred to as the Anthropic Principle] is used to argue that the world's population has a 50% chance of crashing irreversibly sometime between 2140 AD and 2600 AD.  The most-likely crash date of 2400 AD is used to extend the Humanity TimeScale into the future, providing a smooth conversion from date to location on the time scale, which renders the new Humanity TimeScale useful for the placement of all past events and all future ones belonging to this phase of human existence.

Population Versus Time

The following is a compilation from many sources of the world's population for 26 epochs:

           YEAR      Population            YEAR      Population                 YEAR      Population
            [AD]        [millions]               [AD]        [millions]                    [AD]        [millions]

      -100,000     0.5         1500      440            1950     2530
    -50,000     1           1600      470            1960     3000
    -18,000     3           1650      545            1970     3600
     -8,000     9           1700      600            1980     4400
      -7500    10           1750      725            1990     5300
      -3000    30           1800      907            2000    (6380)
      -1000   110           1830     1000            2010    (7300)
          0   200           1900     1600            2025    (8500)
       1000   340           1930     2000            2038    (8500)

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.  I fitted a 10th order polynomial to the relationship of "log of population" versus "log of time."  The equation (available from the author) was useful in performing integrations, described below.  The following figure plots the tabulated data (symbols) and the 10th-order fit (trace).

Figure 1:  World population versus time, using a special Log scale for time.  The green trace is a 10th order polynomial fit, used to assist in later calculations.

Figure 2:  Adopted world population, with arbitrary choice of year for x-axis representation.

Birth and survival Rates

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 population 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%.  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.

Figure 3:  Adopted crude birth rate (red) and surival rate (green).

Integrated Population Versus Time

The previous graphs illustrate time interval averages for population, birth rate and survival rate. These are combioned to calculate the integrated number of births from 100,000 BC to x-axis time.  In the following figure the upper trace is labelled "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.)

Fig. 4:  Integrated number of live births and integrated number of humans reaching adulthood.

Note the green 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. 3).  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 lived was 19.6 billion.

The following figure merely rescales the y-axis so that in 1993 the integrated number of people is 100%.

Figure 5:  Integrated number of human live births humans reaching adulthood, normalized so that 1993 has 100% of the integrated numbers.

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 am calling 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 one more assumed property versus time:  survival rate.  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" and "adults."

The following figure is a plot of "% of adults before date" versus year for a set of arbitrarily chosen integer dates.

Figure 6:  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.

Innovation Data

"Asimov's Chronology of Science and Discovery" 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 is presented in Fig. 7.

Figure 7:  Number of innovations per billion adults for each 2% interval of the Humanity Timescale.

The first peak, at 28%, corresponds to the 2% interval of 26% to 28%, which corresponds to 500 BC to 290 BC.  The minimum at 38% corresponds to the dates 390 AD to 500 AD.  The abrupt rise beginning at 58% 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.

Weighted Average Innovation Rate

About 96% of Asimov's science and discovery citations belong to a category that requires formal eduction, 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 4% weight for the literate population and a 96% weight for the illiterate population?

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 8 shows the population of 5 regions (the most populace), and Figure 9 shows the population of the remaining 4 regions.

Figure 8:  Population breakdown for 5 world regions in the old world, and their total.

Figure 9:  Population breakdown for another 5 world regions, and their total.

Notice in Fig. 8 that Europe experienced two population peaks before the Renaissance, in 200 AD and 1300 AD.  There are population collapses afterward 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.9 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 poplations 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 as 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-Coulmbian 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 Millenium 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 the following figure.

Figure 10:  Estimated global literacy rate and total number of literate adults versus time.

Figure 11 is innovation rate per literate adult.  It is a renormalization of Fig. 7, 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 that lived during the equal adults intervals.

Figure 11:  Innovation rate per literate adult.

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) since there are fewer innovations in the numerator, and 2) there is great unceratinty in estimating (or even defining) literacy during teh millenia BC.  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) a literacy rate that 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 thse two considerations alone (while a drop of 15 to one is observed).

Figure 12 is a plot of the innovation rate using the weighted average of 4% for illiterates and 96% for literates.  In other words, this trace is based on the concept that the literate person is 24 times as likely to produce an innovation (that Asimov would include in his list) compared to the illiterate person (note that 96/4 = 24).  This figure is the "fairest" plot that I know how to produce for representing innovation rate, using Asimov's compilation as the measure for significant innovations.

Figure 12:  Innovation rate per billion population, weighted average of rates for literate and all adults.

The Two Major Peaks in Innovation Rate

There are still two peaks in Fig. 12, as there were in Fig. 7.  The classical Greek peak in relation to the 19th Century peak is 13% in Fig. 7, and 17% in Fig. 12.  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 occurs between 500 BC and 90 BC, for a duration of about 4 centuries.  The 19th Century peak occurs between 1550 AD and 1993 AD, approximately, for a duration of about 4.5 centuries.  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 13 illustrates this.

Figure 13:  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.

The following figure shows a 1400-year expanded portion of the previous figure, centrered on the Greek innovation peak. The Roman population peak follws the Greek innovation peak by 4 to 6 centuries.

Figure 14:  A 1400-year expanded portion of the previous figure, centrered on the Greek innovation peak.

The next figure shows another 1400-year period, but this time centered on the Renaissance/Enlightenment innovation peak, which has not yet completed its decline.

Figure 15:  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 2100 AD, and a collapse afterwards.

Figure 16:  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, 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 which culminated 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 guests appear."

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 the Random Location Principle, also known as the "Principle of Mediocrity" by astronomers.  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 to the population crash question, let us consider a simpler example that illustrates the Random Location Principle 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% chance of being withing the 25th percentile 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 that was number 4000 in the sequence we could infer that there's a 50% chance theat the entire sequence length is between 5300 and 12,000; and that there's a 50% chance that the entire sequence length is greater than 8000 (or less than 8000).

Now, assume every person born is assigned a sequence number.  Let's delete persons who fail to reach adulthood, so our new sequence is for all persons 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 motions 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 stratightforward to concieve of the universe as a giant billiards game, set in motion by the Big Bang 13 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 (and past) 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.

A 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. 32 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. 17.

Figure 17:  Three future population scenarios, encompassing 50% of what is forecast by my usage of the Random Location Principle.  See text for disclaimers.

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 (New York: Dover Publications, 1937), 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 TimeScale

The following table lists equivalences of "YearAD" and "Humanity TimeScale %."  The table extends to 200%, corresponding to the "most likely" population crash date of 2400 AD.
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EQUIVALENCE OF HUMANITY TIMESCALE % AND YEAR

  ...PAST...    ..FUTURE..
  %  YearAD       % YearAD

  0 -100000     100   1993
  2  -63000     102   2000
  4  -30000     104   2006
  6  -17500     106   2013
  8  -10600     108   2020
 10   -7000     110   2026
 12   -5500     112   2033
 14   -4100     114   2038
 16   -3300     116   2044
 18   -2400     118   2050
 20   -1880     120   2055
 22   -1450     122   2060
 24   -1100     124   2065
 26    -800     126   2070
 28    -540     128   2075
 30    -310     130   2080
 32    -120     132   2086
 34      20     134   2091
 36     175     136   2096
 38     310     138   2101
 40     460     140   2106
 42     600     142   2110
 44     740     144   2115
 46     870     146   2120
 48     990     148   2125
 50    1100     150   2150
 52    1200     152   2135
 54    1280     154   2140
 56    1370     156   2145
 58    1445     158   2150
 60    1510     160   2155
 62    1572     162   2160
 64    1630     164   2166
 66    1683     166   2172
 68    1728     168   2177
 70    1765     170   2183
 72    1796     172   2188
 74    1822     174   2194
 76    1848     176   2199
 78    1867     178   2205
 80    1885     180   2211
 82    1903     182   2218
 84    1917     184   2225
 86    1931     186   2232
 88    1942     188   2240
 90    1953     190   2250
 92    1962     192   2260
 94    1970     194   2272
 96    1979     196   2286
 98    1985     198   2306
                200   2400
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EQUATIONS FOR DERIVING X POPULATION (ADULTS) VERSUS YEAR

    FOR 100,000 BC TO 1993 AD (0% TO 100%):

         PCT [%] = C0 + C1*X + C2*X^2 + C3*X^3 + ... + Cl1*X^1l

                 where x = 3.6 - LOG10 (2500 AD - YearAD)

         RMS error from fit to table is 0.17%

      0    21.78
      1    47.54
      2    65.86
      3    -0.059
      4  -229.01
      5   -79.95
      6   573.42
      7   228.253
      8  -687.085
      9  -289.926
     10   342.044
     11   179.91

    FOR 1993 AD TO 2400 AD (100 TO 200%):

         PCT [%] = CO + C1*X + C2*X^2 + C3*X^3 + ... + C11*X^8

                 where X = YearAD

          RMS error from table fit is 0.15%

         0   145.94
         1     0.4045
         2    -0.000134
         3    -2.496E-06
         4     1.023E-08
         5    -1.206E-10
         6    -2.488E-13
         7     4.631E-15
         8    -9.375E-18
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The following figure is a visual representation of the Humanity TimeScale described by the above equations (modified so that the year 2000 AD corresponds to the 100% point on the scale).

                                    HUMANITY TIMESCALE

Figure 18:  Humanity TimeScale.  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.  This figure adopts 2000 AD for the 100% point on the scale.

Caveat and Closing Comment

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.  When our sun explodes in 3 to 5 billion years, humans will have migrated to other star systems, and will have secured its rightful place as an immortal cosmic species.

[Note added, 2000 March 4:  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 [worrying about hazards 3 to 5 billion years from now] were warranted!  Of course, none of us know if this will be true.  We must be content with speculation.  And what I have presented is merely one, concievable 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 form slow-growing populations of American and European 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 "What causes a population crash after an innovation peak?"  The causes for a population rise following a spurt of innovation are easy to imagine, but what could cause a decline?  This is the subject of annother essay.  There may be many candidates for population declines, such as climate change, invasion by barbarians (with a low population density culture), and increased opportunity for decimation by diseases that require high population densities.  My favorite speculations hypothesize that success often breeds the seeds of failure from within, not without, and that a successful unfolding of innovations by productive people sets the stage for parasitic opportunists who inevitably kill the "productive geese that laid the golden eggs."  For this speculation, click on Producers and Paraistes, which has links to more outlandish speculations.

[Note added July 24, 2000:  One intriguing way to reconcile the Anthropic Principle with a long human lifespan is to invoke just that, a "long individual human lifespan."  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 Anthropic Principle will remian 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 following article by Bill Joy:  http://www.wired.com/wired/archive/8.04/joy.html ]

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My original essay describing this concept is A New Estimate for the End of Humanity, which 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, but I wasn't aware of any other similar writings until about 1995.

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 "Anthropic Principle."  The following web site is a good starting point for learning what others have written about the subject:  http://www.anthropic-principle.com/profiles.html .

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This site opened:  October 14, 1998.  Last Update:  July 24, 2000.