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Economic growth in the former USSR. GDP data (Maddison, 2010) are compared with the hyperbolic fit. The growth was hyperbolic from AD 1 to 1870. From around 1870, shortly after the Industrial Revolution, economic growth started to be diverted to a slower trajectory. Epoch of stagnation did not exist in the economic growth. Industrial Revolution did not boost the economic growth. There was no takeoff from stagnation to growth because there was no stagnation but a steadily-increasing growth. Unified Growth Theory (Galor, 2005, 2008, 2011, 2012) is contradicted by the economic growth data.
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Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search for takeoffs from stagnation to...
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... It is my aim now to analyse mathematically distributions describing recent anthropogenic signatures in order to understand their dynamics. In my analysis I shall use the excellent compilation of data prepared and published by Ludwig (2014), with the exception of the data describing the growth of population and economic growth, because in the past few years I have carried out extensive investigation of these issues (Nielsen, 2014(Nielsen, , 2015(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016d(Nielsen, , 2016e, 2016f, 2016g, 2016h, 2016i, 2016j, 2016k, 2016l, 2016m, 2016n, 2016o, 2016p, 2017a(Nielsen, , 2017b(Nielsen, , 2017c(Nielsen, , 2017d. All this research was essential for the correct understanding of the Anthropocene. ...
... The recent fast-increasing economic growth had no mathematically determinable beginning, strongly suggesting that the recent fast increasing intensity of the combined effects of anthropogenic activities, which are reflected in the economic growth, also had no mathematically determinable beginning. Industrial Revolution had no impact on shaping economic growth trajectory, even in Western Europe and even in the United Kingdom (Nielsen, 2016b. There was no Great Acceleration around 1950. ...
Distributions of anthropogenic signatures (impacts and activities) are mathematically analysed. The aim is to understand the Anthropocene and to see whether anthropogenic signatures could be used to determine its beginning. A total of 23 signatures were analysed and results are presented in 31 diagrams. Some of these signatures contain undistinguishable natural component but most of them are of purely anthropogenic origin. Great care was taken to identify abrupt accelerations, which could be used to determine the beginning of the Anthropocene. Results of the analysis can be summarised in three conclusions. 1. Anthropogenic signatures cannot be used to determine the beginning of the Anthropocene. 2. There was no abrupt Great Acceleration around 1950 or around any other time. 3. Anthropogenic signatures are characterised by the Great Deceleration in the second half of the 20th century. The Great Deceleration indicates a gradual progress towards a sustainable future.
... When closely analysed, data show consistently that the growth of human population and the economic growth in the past 2,000,000 years were hyperbolic (Nielsen, 2016d(Nielsen, , 2016e, 2016f, 2016g, 2016h, 2016i, 2016j, 2017c(Nielsen, , 2017d. Hyperbolic growth started to be diverted gradually to slower, non-hyperbolic trajectories only recently, around 1950 (for the global growth of population and for the global economic growth) but the new trajectories are still close to the original hyperbolic trajectories. ...
... Growth of population and of the GDP during the AD era are shown in Figures 7 and 8. Data (Maddison, 2010) are compared with hyperbolic distributions. More extensive analysis is presented in separate publications (Nielsen, 2016d(Nielsen, , 2016e, 2016g, 2017c. ...
... 2. I have demonstrated that hyperbolic description of the growth of population applies not only to the growth of the world population, as studied by von Foerster, Mora and Amiot (1960), but also to the growth of regional populations (Nielsen, 2016g). 3. I have demonstrated that hyperbolic description of growth applies also to the economic growth, global and regional (Nielsen, 2016d). 4. I have extended the analysis of the growth of the world population to the BC era (over the past 12,000 years) and demonstrated that hyperbolic growth applies not only to the AD era, as pointed out by von Foerster, Mora and Amiot (1960), but also to the BC era (Nielsen, 2016e). ...
Growth of the world population and the world economic growth were hyperbolic in the past 2,000,000 years. Recently, from around 1950, they started to be diverted to slower trajectories but they are still close to the historical hyperbolic trajectories. Regional growth of population and regional economic growth were also hyperbolic. Hyperbolic growth can be slow over a long time and fast over a short time but it is still the same, monotonically increasing, growth. It is incorrect to interpret slow growth as stagnation and fast growth as explosion, each controlled by different mechanisms of growth. Hyperbolic growth has to be interpreted as a whole and the same mechanism has to be applied to the slow and to the fast growth. The Anthropocene is characterised by the rapid growth of population, rapid economic growth and rapid consumption of natural resources. The origin of the Anthropocene can be explained as the natural consequence of hyperbolic growth. However, while its dramatic impacts became apparent only recently its starting point cannot be mathematically determined. Its beginning could be traced to the dawn of the existence of hominines. Its future is insecure because it is dictated by many critical trends shaping the future or our planet, but notably because the size of the world population is predicted to continue to increase at least until the end of the current century to a possibly unsustainable level and because the world economic growth follows now an unsustainable trajectory.
... It should be also noticed that the point at AD 1000 in Figure 3 appears to be much further away from the fitted distribution then the point in Figure 1. The distributions are precisely the same but the display of reciprocal values magnifies the discrepancies between data and the calculated curve for small values (Nielsen, 2016b). The smaller are the values of the data and of the calculated distribution the larger is the magnification. ...
... There is no stagnation and no takeoff to a distinctly different regime of growth. Both, the GDP and the population increase hyperbolically (Nielsen, 2016b and thus monotonically. Consequently, their ratios increase also monotonically. Figure 6 presents the reciprocal values of the Gross Domestic Product (GDP) for Western Europe (Maddison, 2001) in the vicinity of the alleged takeoff. ...
... We shall now use exactly the same source of data and show that the Unified Growth Theory is scientifically unsustainable. For more extensive discussion of these issues see other publications (Nielsen, 2016a(Nielsen, , 2016b(Nielsen, , 2016d(Nielsen, , 2016e, 2016f, 2016g, 2016h, 2016i, 2016j, 2017a. ...
A simple but useful method of reciprocal values is introduced, explained and illustrated. This method simplifies the analysis of hyperbolic distributions, which are causing serious problems in the demographic and economic research. It allows for a unique identification of hyperbolic distributions and for unravelling components of more complicated trajectories. This method is illustrated by a few examples. They show that fundamental postulates of the demographic and economic research are contradicted by data, even by precisely the same data, which are used in this research. The generally accepted postulates are based on the incorrect understanding of hyperbolic distributions, which characterise the historical growth of population and the historical economic growth. In particular, data used, but never analysed, during the formulation of the Unified Growth Theory show that this theory is based on fundamentally incorrect premises and thus is fundamentally defective. Application of this simple method of analysis points to new directions in the demographic and economic research. It suggests simpler interpretations of the mechanism of growth. The concept or the evidence of the past primitive and difficult living conditions, which might be perhaps described as some kind of stagnation, is not questioned or disputed. It is only demonstrated that trajectories of the past economic growth and of the growth of population were not reflecting any form of stagnation and thus that they were not shaped by these primitive and difficult living conditions. The concept or evidence of an explosion in technology, medicine, education and in the improved living conditions is not questioned or disputed. It is only demonstrated that this possible explosion is not reflected in the trajectories of the economic growth and of the growth of population.
... This type of growth resembles hyperbolic growth, which characterises the historical economic growth and the growth of human population (von Foerster, Mora & Amiot, 1960;Nielsen, 2014Nielsen, , 2016cNielsen, , 2016d). Hyperbolic growth (or to be more precise, the first-order hyperbolic growth) is given by the following simple equation: ...
Mathematical method based on a direct or indirect analysis of growth rates is described. It is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. Only rudimentary knowledge of calculus is required. Projected trajectories based on such simple initial assumptions are easier to accept and to understand than alternative complicated projections based on more complicated assumptions and on more intricate computational procedures.
... His concepts can be only tested indirectly by showing that within the range of the mathematically-analysable data there was no stagnation, no sudden takeoffs, no "remarkable" or "stunning" escapes from the Malthusian trap (Galor, 2005a, pp. 177, 220) and no transition from stagnation to the so called sustained growth regime (Nielsen, 2014(Nielsen, , 2015a(Nielsen, , 2015b(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016d. Economic growth in the past was sustainable and secure, as indicated by the steadily-increasing hyperbolic trajectories, but now it is unsustainable and insecure (Nielsen, 2015b). ...
... We have already demonstrated (Nielsen, 2014(Nielsen, , 2015a(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016d) that Galor's Unified Growth Theory is fundamentally incorrect because it is based on fundamentally-incorrect ideas. We have shown that within the range of the mathematically-analysable data, historical economic growth and the growth of population were hyperbolic. ...
... In contrast, the accurate display of precisely the same data suggests entirely different interpretation. General features presented in Figure 1 are still maintained but now mathematical analysis of these data shows that the GDP/cap and the size of the population were increasing monotonically (Nielsen, 2014(Nielsen, , 2015a(Nielsen, , 2016a(Nielsen, , 2016d. There were no sudden takeoffs from stagnation to growth because there was no stagnation and because the acceleration was gradual along the entire range of these distributions. ...
The so-called great divergence in the income per capita is described in the Unified Growth Theory as one of the mind-boggling and unresolved mysteries about the growth process. This mystery has now been solved: the great divergence never happened. It was created by the manipulation of data. Economic growth in various regions is at different levels of development but it follows similar, non-divergent trajectories. Unified Growth Theory is not only scientifically unacceptable but also potentially dangerous because by promoting erroneous concepts it diverts attention from the urgent need to control the fast-increasing growth of income per capita. The distorted presentation of data supporting the concept of the great divergence shows that most regions follow the gently-increasing trajectories describing the growth of income per capita but mathematical analysis of data and even their undistorted presentations show that these trajectories are now increasing approximately vertically with time. So, while the distorted presentation of data used in the Unified Growth Theory suggests sustainable and secure economic growth, the undistorted presentation of data demonstrates that the growth is unsustainable and insecure. The concept of takeoffs from stagnation to the sustained-growth regime promoted in the Unified Growth Theory is also dangerously misleading because it suggests a sustainable and prosperous future while the mathematical analysis of data shows that the current economic growth is dangerously insecure and unsustainable.
... The aim of this publication is to present the direct proof that contrary to the fundamental postulate of the Unified Growth Theory (Galor, 2005a(Galor, , 2011 distributions describing historical growth of income per capita cannot be divided into three, distinctly-different regimes of growth governed by distinctly different mechanisms. The indirect proof was presented earlier (Nielsen, 2016a(Nielsen, , 2016c by showing that the historical growth of the Gross Domestic Product (GDP) and of human population were hyperbolic and that postulated by Galor three regimes of growth did not exist. Mathematical analysis of the latest data (Maddison, 2001(Maddison, , 2010) brings a new insight into the interpretation of the historical economic growth. ...
... Historical economic growth and historical growth of human population were hyperbolic (Nielsen, 2016a(Nielsen, , 2016d. Hyperbolic distributions are confusing and they are often misinterpreted in studies of economic growth and of the growth of human population. ...
... An example of such distorted and self-misleading presentations of data is shown in Figure 1. However now, the same data, when properly analysed, demonstrate that the Unified Growth Theory and other similar interpretations of economic growth or the growth of population are repeatedly contradicted by empirical evidence (Nielsen, 2014(Nielsen, , 2015(Nielsen, , 2016a(Nielsen, , 2016c(Nielsen, , 2016d. ...
Data describing historical growth of income per capita [Gross Domestic Product per capita (GDP/cap)] for the world economic growth and for the growth in Western Europe, Eastern Europe, Asia, former USSR, Africa and Latin America are analysed. They follow closely the linearly-modulated hyperbolic distributions represented by the ratios of hyperbolic distributions obtained by fitting the GDP and population data. Results of this analysis demonstrate that income per capita was increasing monotonically. There was no stagnation and there were no transitions from stagnation to growth. The usually postulated dramatic escapes from the Malthusian trap never happened because there was no trap. Unified Growth Theory is fundamentally incorrect because its central postulates are contradicted repeatedly by data, which were used but never analysed during the formulation of this theory. The large body of readily-available data opens new avenues for the economic and demographic research. They show that certain fundamental postulates revolving around the concept of Malthusian stagnation need to be replaced by the evidence-based interpretations. Within the range of analysable data, which for the growth of population extends down to 10,000 BC, growth of human population and economic growth were hyperbolic. There was no Malthusian stagnation and there were no transitions to distinctly faster trajectories. Industrial Revolution had no impact on changing growth trajectories.
... It shows that the growth of human population was increasing hyperbolically not only during the AD era, as observed by von Foerster, Mora and Amiot (1960), but also during the BC era. This analysis shows also that Industrial Revolution, 1760-1840 (Floud & McCloskey, 1994) did not boost the growth of human population, the result being in agreement with the analysis of the historical economic growth (Nielsen, 2016). ...
... It was not a dramatic takeoff but a transition to a slower hyperbolic trajectory. These features are important in relating the growth of population to the economic growth because contrary to the repeated claims presented in the Unified Growth Theory (Galor, 2005(Galor, , 2011 there was no stagnation and no dramatic takeoff in the growth of the GDP (Nielsen, 2016) or in the growth of the GDP/cap (Nielsen, 2015a). ...
... Again, there was no dramatic takeoff and no transition from stagnation to growth as claimed repeatedly by Galor (2005Galor ( , 2011. This hypothetical but non-existed takeoff, which was supposed to characterise not only the economic growth but also the growth of human population, is consistently contradicted by the analysis of the economic growth (Nielsen, 2015a(Nielsen, , 2016 and by the presented here analysis of the growth of the world population. ...
Abstract. Data describing the growth of the world population in the past 12,000 years are analysed. It is shown that population, if unchecked, does not increase exponentially, as expected by Malthus, but hyperbolically. This analysis reveals three episodes of hyperbolic growth: 10,000 - 500 BC, AD 500 - 1200 and AD 1400 -1950, representing the total of about 89% of the past 12,000 years. The remaining 11% were taken by three demographic transitions: 500 BC - AD 500, AD 1200 - 1400 and AD 1950 - present. The first two transitions were between sustained hyperbolic trajectories. The current transition is from a sustained hyperbolic growth to a yet unknown trajectory. The often claimed but never proven existence of Malthusian stagnation in the growth of human population is convincingly contradicted by the mathematical analysis of data. There was also never any form of a dramatic transition from stagnation to growth, described often as a takeoff, because there was no stagnation in the growth of the world population. The perceived takeoff is just the natural continuation of hyperbolic growth. Correct understanding of the historical growth of human population is essential in the correct interpretation of the historical growth of income per capita.
... O (Ashraf, 2009;Galor, 2005aGalor, , 2005bGalor, , 2007Galor, , 2008aGalor, , 2008bGalor, , 2008cGalor, , 2010Galor, , 2011Galor, , 2012aGalor, , 2012bGalor, , 2012cGalor & Moav, 2002;Snowdon & Galor, 2008). Historical economic growth and the growth of human population can be described using hyperbolic distributions (Nielsen, 2014(Nielsen, , 2015a(Nielsen, , 2015b(Nielsen, , 2015c(Nielsen, , 2015d(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016dvon Foerster, Mora & Amiot, 1960) Unlike the better-known exponential growth, which is easier to understand, hyperbolic distributions are strongly deceptive because they appear to be made of two distinctly different components, slow and fast, joined perhaps by a certain transition component. This illusion is so strong that even the most experienced researchers can be easily deceived particularly if their research is based on a limited body of data, as it was in the past. ...
... According to Galor, historical economic growth can be divided into three distinctly-different stages governed by three distinctly different mechanisms: (1) the Malthusian regime of stagnation, (2) the post-Malthusian regime, and (3) the sustained-growth regime. We have already demonstrated that this postulate of the three regimes of economic growth is contradicted by the data for Western Europe, Eastern Europe, Asia, countries of former USSR, Africa and Latin America (Nielsen, 2015a(Nielsen, , 2015b(Nielsen, , 2015c(Nielsen, , 2015d(Nielsen, , 2016b, ironically by the same data which were used but never analysed by Galor. This fundamental postulate of the three regimes of growth is used repeatedly throughout the narrative of the Unified Growth Theory and serves as the essential support for the discussed interpretations and explanations. ...
... Parameters describing the fitted distributions were determined by the mathematical analysis (Nielsen, 2016b) of Maddison's data (Maddison, 2010). ...
Data describing historical economic growth are analysed. They demonstrate
convincingly that the takeoffs from stagnation to growth, claimed in the
Unified Growth Theory, never happened. This theory is again contradicted by
data, which were used, but never properly analysed, during its formulation. The
absence of the claimed takeoffs demonstrates also that the postulate of the
differential takeoffs is contradicted by data.
... Hyperbolic distributions, which describe the historical economic growth (Nielsen, 2016a), are represented by the simple mathematical formula: ...
... The discussion presented here is the extension of the mathematical analysis of the historical economic growth (Nielsen, 2016a). We have already demonstrated that the historical economic growth was hyperbolic and thus that implicitly it gives no support for the doctrine of the three regimes of growth. ...
... Rigorous analysis of data shows convincingly that the past economic growth was sustained and secure because it followed the remarkably stable hyperbolic trajectories (Nielsen, 2016a). This conclusion is in harmony with the study of ecological footprints, which shows that until the late 1900s global ecological footprint was lower than the ecological capacity (WWF, 2010). ...
Economic growth in Western Europe, Eastern Europe, Asia, countries of the former USSR, Africa and Latin America were analysed. It is demonstrated that the fundamental postulate of the Unified Growth Theory about the existence of the three regimes of growth (Malthusian regime, post-Malthusian regime and sustained-growth regime) is contradicted by data. These regimes did not exist. In particular, there was no escape from the Malthusian trap because there was no trap. Economic growth in all these regions was not stagnant but hyperbolic. Unified Growth Theory is fundamentally incorrect. However, this theory is also dangerously misleading because it claims a transition from the endless epoch of stagnation to the new era of sustained economic growth, the interpretation creating the sense of security and a promise of prosperity. The data show that the opposite is true. Economic growth in the past was sustained and secure. Now, it is supported by the increasing ecological deficit. The long-term sustained and secure economic growth has yet to be created. It did not happen automatically, as suggested incorrectly by the Unified Growth Theory.
... We shall show that this question makes as much sense as the question, "Why is the Sun rotating around the Earth," and the answer to both of them is similar: the Sun does not rotate around the Earth and there was no sudden spurt in the growth rates of output per capita and population. There was also no takeoff from stagnation to growth (Nielsen, 2014(Nielsen, , 2015(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016d We have already demonstrated that the growth of human population and the growth of the Gross Domestic Product (GDP), global and regional, were hyperbolic (Nielsen, 2014(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016d. Hyperbolic growth is monotonic, and consequently it is also characterised by the monotonicallyincreasing growth rate. ...
... We shall show that this question makes as much sense as the question, "Why is the Sun rotating around the Earth," and the answer to both of them is similar: the Sun does not rotate around the Earth and there was no sudden spurt in the growth rates of output per capita and population. There was also no takeoff from stagnation to growth (Nielsen, 2014(Nielsen, , 2015(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016d We have already demonstrated that the growth of human population and the growth of the Gross Domestic Product (GDP), global and regional, were hyperbolic (Nielsen, 2014(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c(Nielsen, , 2016d. Hyperbolic growth is monotonic, and consequently it is also characterised by the monotonicallyincreasing growth rate. ...
... We have already discussed (Nielsen, 2014(Nielsen, , 2015(Nielsen, , 2016a(Nielsen, , 2016b(Nielsen, , 2016c various aspects of Galor's theory (Galor, 2005a(Galor, , 2011. We shall now focus our attention on the discussion of his unsubstantiated claims about the growth rates. ...
Galor discovered many mysteries of the growth process. He lists them in his Unified Growth Theory and wonders how they can be explained. Close inspection of his mysteries reveals that they are of his own creation. They do not exist. He created them by his habitually distorted presentation of data. One of his self-created mysteries is the mystery of the alleged sudden spurt in the growth rate of income per capita. This sudden spurt never happened. In order to understand the growth rate of income per capita, its mathematical properties are now explored and explained. The explanation is illustrated using the historical world economic growth. Galor also wonders about the sudden spurt in the growth rate of population. We show that this sudden spurt was also created by the distorted presentation of data. The mechanism of the historical economic growth and of the growth of human population is yet to be explained but it would be unproductive to try to explain the non-existing and self-created mysteries of the growth process described in the scientifically unacceptable Unified Growth Theory. However, the problem is much deeper than just the examination of this theory. Demographic Growth Theory is based on the incorrect but deeply entrenched postulates developed by accretion over many years and now generally accepted in the economic and demographic research, postulates revolving around the concept of Malthusian stagnation and around a transition from stagnation to growth. The study presented here and earlier similar publications show that these postulates need to be replaced by interpretations based on the mathematical analysis of data and on the correct understanding of hyperbolic distributions.
