26 февраля 2020


Proliferation of ignorance of the world around
us must also be supported by science.
Stanislaw Jerzy Lec

In 2005, an article by Huebner1, an American physicist, caused quite a stir among the public. In his article Huebner proposed a certain mankind innovation capability measure: the rate of innovation. He defined the rate as the number of important technological developments per year divided by the world population. We shall refer to Huebner's indicator as H-rate, whereby

H(t)= Q(t)/P(t), (1)


H(t) is H-rate in the year t;

Q(t) is quantity of scientific and technological developments for the year t; density thereof over time;

P(t) is population in the year t.

The H-rate can be calculated for a country or for the world in general.

Huebner argues that the H-rate reflects innovation capability of an average person. Implicit common opinion is that the innovation capability of an average person is practically constant through the centuries, i.e. the number of inventions always is in ratio to the population size. However, according to Huebner’s calculations, the H(t) function is not constant. The H-rate increased till the mid-19th century and was on the decline from then on, i.e. the H-rate plot is bell-shaped. Huebner predicted that by 2050 the H-rate would decline to the Middle Ages level, i.e. an average person of the mid-21st century would be no more inventive than a person of the Inquisition period. According to Huebner’s estimate of 2004, mankind had approached the innovations limit to be followed by a decline.

Six years have passed since 2004 and this estimate can be refined on the basis of new developments and population size statistics. Furthermore, certain assumptions of certain nations’ rate of innovation can be made.

Patents statistics

As Huebner rightly noted, scientific developments number over the latest one and a half - two centuries could be estimated as the number of patents issued. Despite a variety of shortcomings and restrictions inherent in the patents statistics, there hardly is a better quantitative innovation-capacity measure. Patents statistics for the countries that acceded to the Hague Conference have been maintained since 1883. It has been published by the World Intellectual Property Organization WIPO 2. The chart showing the number of patents issued as a function of time Q(t) based on the WIPO data is given below (Fig. 1).

Number of patents issued in the world

Fig. 1 – Number of patents issued in the world

Total quantity of patents issued in all countries Q(t) has been increasing steadily if tracked over the time intervals of approximately 50 years. For instance, about 28 thousand patents were issued in world in 1900, almost 59 thousand patents were issued in 1950 and 293 thousand in 2000. On the other hand, certain short sections of the Q(t) function are declining; the function decreases temporarily within these sections. An obvious explanation of the decline of the issued patents number is two world wars, changes in patents registration, disintegration of the Soviet Union, etc.

During the pre-war period and both world wars numerous countries (Germany, Japan, Great Britain, the USSR, Italy) went into self-isolation, classified their inventions, prohibited transfer of applications for discoveries to other countries. This resulted in a world-wide decline of patent registration numbers, which is shown by the Q(t) curve as two dips: from 1914 to 1921 and from 1933 to 1961.

Apparently, the dip associated with 1962 is related to the change of the international patent registration rules. In that and the previous years many national agencies did not differentiate between the resident and non-resident applications, although they did so prior to and after 1962.

The 1991 dip is associated with disintegration of the Soviet Union and suspension of registration of inventions (but not inventions itself) within its territory. Registration in the former Soviet Republics resumed in a few years: in 1992 in Russia, Latvia, Ukraine, in 1993 in Belarus, Uzbekistan and only in 1994 in Kirghizia. It took a while to reach the former Soviet level of the registrations.

Despite the absolute randomness, stochastic behavior of the invention process, its approximating Q’(t) function increases and, as it is believed generally, is governed by the exponential law.

Patents Statistics H-rate for the Last Two Hundred Years

Thus, the absolute number of patents issued in the world is on the increase. And what is the behavior of the relative H-rate? If during the latest years population of the planet increases much faster its intelligence, the H-rate should decrease. Let us check if this is correct using the H(t) graph (Fig. 2). The graph is plotted on the basis of the latest patents issued 2 and world population data 3, 4.

Number of Patents Issued Internationally Normalized to World Population

Population figure for the period of 1883 - 1949 is calculated as per 3, for the period of 1950 - 2008 – as per 4.

Fig. 2 – Number of Patents Issued Internationally Normalized to World Population

The H-rate curve shows the same dips as the Q(t) curve (Fig. 1). The curve is not bell-shaped as forecast by Huebner, and its approximating function is positive. For instance, in 1900 there were 17 patents per one million of the population, 23 in 1950 and as many as 48 patents in 2000. It means that an average person’s intelligence nearly tripled over a hundred years. Invention also continues to increase over the last decade. For the ten years from 1998 to 2008 invention increased for 53 to 60 patents per one million of the world population.

As the UN notes, a decline of the population growth rate and forecasts a further decline of the growth rate until 2050 4, it could be expected that growth of the H-rate could even accelerate as the denominator of the fraction (1) increases at a slower rate than the numerator. Hence, Huebner’s forecast of the H-rate decline has not come true and there are no prerequisites for such decline.

It also would be interesting to look back not just in the previous two hundred years but into more remote past, the Middle Ages, as Huebner did. We will use the same data but a different approach.

H-rate for Last Five Hundred Years

Unfortunately, there were no patent bureaus in the Middle Ages while the sovereigns and the Inquisition has poor understanding of statistics. Thus, we have no reliable statistics on innovation in those centuries. But we do have a splendid В«The History of Science and TechnologyВ» 5 by two authors, Bunch and Hellemans to which Huebner referred also. In the collection there are data from the Stone Age up to 2003. However, as it was already noted, the patent statistics will be more objective for last hundred years.

Certainly only the most significant inventions are visible to authors of the collection as well as all of us on a centuries-old distance from those events. Not all modern patents are worthy the same fame as the inventions mentioned in the collection. Obviously, historical weight of ordinary modern patents and world famous important inventions are various. Nevertheless, it is possible to give a rough estimate for a conversion coefficient from one weight in another that then to plot a curve of important inventions. The very important. The curve of the landmark inventions will unite famous inventions of the far past and patents of last century on the common time axis.

Let us look at the peaceful 1905. Patents procedure was already in place in the majority of the European countries and in the USA. WWI was still far away, there was no strict confidentiality, inventions were published and patents were issued. According to 5 there were 26 events in 1905. That year 44,273 patents were issued. It means that only one of approximately 1700 patents merited a mention in the Bunch and Hellemans 5. Now we apply the method below to superimpose the two curves: the patents curve and the landmark inventions curve. We cut a section of the patents curve above (Fig. 2) reflecting the 1905 - 2008 period and normalize the function by the importance of invention conversion ratio of importance of the invention, i.e. by 1,700. We then plot the landmark inventions curve on the same graph for 1450 - 1905 using the 5 data. The curves will converge at the 1905 mark (Fig. 3).

Number of landmark inventions normalized to the world population

The 1450 - 1905 section of the H(t) curve is based on the 5, data; the 1906 - 2008 section is based on the 2, data further normalized by the ratio of 1,700.

Fig. 3 – Number of landmark inventions normalized to the world population

The graph is not indicative of any decline of specific (per capita) invention of the humans for the last 558 years. The H-rate does not decline. Moreover, the H-rate increases exponentially and the increase continues over a large interval: from 1450 to 2008. Meanwhile, the increase is accelerated during the latest period of 2000-2008.

What did support Huebner�s concern with saturation of the invention curve? Most likely, Huebner’s apprehension was caused by the national US indicators rather that the international.

H-rate per Country

Form of the H-rate curves based on the national rather than the world data is quite different. Huebner plotted the H-rate curve for the patents granted to the US residents in 2004. Given the latest data 6-8 this curve was extended to 2008 (Fig. 4).

Number of patents issued to the US residents normalized to the population

Fig. 4 – Number of patents issued to the US residents normalized to the population

This curve, the US invention curve, cannot be described as steadily increasing or as steadily declining. Obviously, the curve’s dynamics caused Huebner’s pessimistic attitude to the overall invention capacity of the mankind.

On the contrary, the curves for Japan, Korea and China appear quite optimistic. The H-rate curve for Japan based on the patents statistics 2 and population 9s soars; it doesn't indicate any immediate decline. The H-rate curve for Korea based on the 2 and 10 data is similar in form (Fig. 5).

Number of the patents issued to the residents of Korea and Japan normalized to the population of the country

Fig. 5 – Number of the patents issued to the residents of Korea and Japan normalized to the population of the country

Thus, far from all national H-rate curves are upward, while some are really bell-shaped. Here, such bell-shaped curve is not always a Gauss curve. In other words, in certain countries specific invention has already reached its peak and is now declining while in other countries specific invention accelerates upwards. Is it possible to define a pattern? If nations exist in the same epoch, what is the reason for various perception of invention? Explanation of such national characteristic can be found in Gumilev’s ethnogenesis theory 11.

The Ethnogenesis Theory

Gumilev's ideas can be summarized as follows. Ethnogenesis is origination, development, decline and disappearance of an ethnos.

None of the ancient currently known ethnoses has been preserved in its integral form. The Sumerians, Etruscans, Romans, Hellenes, Phoenicians, Mayas, Egyptians, ancient Slavs, Persians left their traces only: romantic legends, magnificent ruins, clay tablets, crockery fragments, pyramids, parchments. Nothing is left of the ethnoses that appeared much earlier, at the very beginning of development of human culture. An ethnos appears as a result of a genetic mutation that alters the behavior stereotype, which becomes passionary1, i.e. passionate and sacrificial. «Passionarity is striving for action in the absence of any obvious purpose or for an illusory purpose. … A passionary cannot but act» 11.

Ethnoses appear, go through consecutive development phases and disappear; hence, ethnoses have an age: infancy, growth, maturity, aging and old age. It is only at the stage of maturity (according to Gumilev: breakdown and inertia) that the ethnos redirects its sacrificial energy. Such ethnos no longer asserts itself as a new nation and commences to assert itself in arts and science: «at low passionarity and sufficient abilities people manage quite well in the risk-free areas: arts, science, teaching and technical invention. During the previous phase they would have battled for their ideals and now they … experiment in the gravitation theory same as Newton and Galileo …» 11.

Gumilev proposed the ethnogenesis concept, i.e. a nation’s life cycle of about one and half thousand. Gumilev did not calculate the ancient ethnoses statistics. Such calculations based on the ancient ethnoses are presented in my previous article 12. The calculations confirm Gumilev's concept. Indeed, golden age of science and technology of the ancient nations that we know about covers only several centuries of the ethnogenesis. Absolute invention curves Q(t) for the Hellenes, Romans, Byzantines, Arab Moslems, Slavs 12 are other than zero only at the "mature" age of the ethnos while there are no traces of invention and creativity outside this period. Therefore, the ethnic invention curve Q(t) plotted as significantly normalized for a single ethnos that has gone through its infancy and its old age could be considered bell-shaped. It is obvious that the corresponding normalized ethnic curves H(t) also will be bell-shaped.

For example, the H-rate curve for the Roman ethnogenesis in the absence of considerable normalization for the period from inception to decline of the nation appears as a hummock (Fig. 6). This curve is plotted on the basis of the data of the Romans inventions 12 and the population of the Romans 13, 14.

Number of landmark inventions by the ancient Romans normalized to the population

Fig. 6 – Number of landmark inventions by the ancient Romans normalized to the population

Peak of the ancient Romans invention was in 250 BC while the enthnogenesis peak was in 400-500 BC. In other words, ethnic invention increases when the ethnogenesis is over its maximum. Ethnic invention level of a baby-ethnos and an old-man-ethnos equals zero. Hence, a strongly smoothed ethnic invention curve is bell-like. The Roman curve ideally illustrates the interrelation of the ethnic invention and the ethnogenesis.


Specific (per capita) invention rate of the mankind increases at an accelerated rate. There are no manifestations of or assumptions for its decrease in the nearest future. Statistical function of specific invention is approximated by exponent.

The strongly smoothed and averaged specific invention curve of a separate ethnos (nation) is bell-shaped if the curve is observed over 1.5-2 thousand years. As existence of an ethnos is practically always limited in time and the ethnos is incapable of invention outside its existence limits, the left and the right wings of the curve belong to the x-abscissa. An ethnos reached its invention peak in the ethnogenesis recession phase, in the life cycle recess cycle. Hence, the form of the ethnic invention curves Q(t) or H(t) can define the current phase of a living ethnos.


This article was written independently of any institutions or foundations. The views and conclusions are solely those of the author.

[1] Huebner J. A Possible Declining Trend for Worldwide Innovation, Technological Forecasting & Social Change, 72(8):988-995 Elsevier Inc. 2005.

[2] The World Intellectual Property Organization (WIPO). Statistics on Patents.

[3] U.S. Census Bureau (USCB). Historical Estimates of World Population, 2004.

[4] U.S. Census Bureau (USCB). Total Midyear Population for the World: 1950-2050, 2010.

[5] Bunch B., Hellemans A. The History of Science and Technology, Houghton Mifflin Co., New York, 2004.

[6] U.S. Census Bureau (USCB). 2000 Census of Population and Housing, Summary Population and Housing Counts. Series PHC-3-1, United States Summary. http://www.census.gov/census2000/pubs/phc-3.html

[7] U.S. Census Bureau (USCB). Monthly Population Estimates for the United States: April 1, 2000 to December 1, 2008 (NA-EST2008-01)"2000-2008. See www.census.gov/popest/national/tables

[8] U.S. Patent and Trademark Office. U.S. Patent Activity Calendar Years Since 1790 to the Present. 1790-2008 http://www.uspto.gov/web/offices/ac/ido/oeip/taf/h_counts.htm

[9] Statistics Bureau, Management and Coordination Agency. Population Estimates of Japan 1920-2000. 1920-2000 http://www.e-stat.go.jp/SG1/estat/ListE.do?bid=000000090004&cycode=0

[10] Population Statistic. http://populstat.info/Asia. Китай, Корея

[11] Гумилев Л. Н. Конец и вновь начало: Популярные лекции по народоведению – Москва:В АСТ, 2007.

[12] Немцов Э. Ф. Кривые Гумилева и кривые этнических достижений.

[13] California State University. Roman Census Figures.

[14] Turchin P., Scheidel W. Coin hoards speak of population declines in Ancient Rome, PNAS October 13, 2009 vol. 106 no. 41 17276-17279. http://www.pnas.org/content/106/41/17276.full.pdf+html.

Edward Nemtsov, PhD, Physics.
The article was published on this site in March, 2012 for the first time. It's the translation of my previous article into English. The second publication is in the book "Этногенез и изобретательность" on February 2014, Lambert Academic Publishing, ISBN 978-3-659-16364-7.
Авторские права на фотографии, статьи и рисунки принадлежат Эдварду Немцову, если это не оговорено особо.