My most fundamental piece of theory

My editorial

I am returning to what seems to be my most fundamental piece of theory, namely the equilibrium between population, food and energy, or N = A*(E/N)µ*(F/N)1-µ, where N represents the headcount of local population, E/N stands for the consumption of energy per capita, F/N is the intake of food per capita, whilst ‘A’ and ‘µ’ are parameters. I am taking on two cases: United Kingdom, and Saudi Arabia. In United Kingdom, the issue of population, and more specifically that of immigration, has recently become a much disputed one, in the context of what is commonly called ‘Brexit’. In Table 1, below, you can find, first of all, the two types of ‘model population’ computed with the equation specified in my article ‘Settlement by Energy – Can Renewable Energies Sustain Our Civilisation?’. Thus, columns [2] and [3] provide that model size of population, in millions of people, computed on the grounds of constant alimentary intake equal to F/N = 1 219 100 kcal per person per year. More specifically, this particular variable was used in mega-calories per person year, thus F/N = 1219,1 Mcal per person per year. We have here one of the best fed populations on Earth. This factor is being combined with the current consumption of energy per capita, in tons of oil equivalent per person per year, as published by the World Bank. Column [2] provides the model size of population calculated as model(N) = (Energy consumption per person per year)0,52*(1219,1)1-0,52=0,48. For the sake of presentational convenience, let’s call it ‘Energy-based population’. Column [3] takes on the same logic, but introduces, as an estimate of the (E/N) variable, just the consumption of renewable energy per person per year, once again in tons of oil equivalent, and using the equation model(N) = (Renewable energy consumption per person per year)0,3*(1219,1)1-0,3=0,7.  This type of model population is going to be labelled ‘Renewables-based population’. Column [4] provides the real, current headcount of British population each year, and column [5] gives the estimation of net migration (immigration minus emigration), in a snapshot every five years. The ‘energy-based population’ starts, in 1990, slightly above the real one, with 3,597 tons of oil equivalent being consumed, on average, by one resident, per year, in the beautiful homeland of Shakespeare and The Beatles. That model population follows ascending trend, just as the real one, until 2003. Over that period of time, i.e. between 1990 and all through 2003, energy use per capita had been climbing, in a slightly hesitant manner, up to 3,732 tons of oil equivalent. The real headcount increased, during that period, by 2,58 millions of people, whilst the ‘energy-based’, model population climbed by 1,14 million. Starting from 2004, the British population starts saving energy. In 2013, its average consumption was of 2,978 tons of oil equivalent per capita. The real population has increased, since the last checkpoint in 2003, by 5,25 millions of people. Yet, the ‘energy-based’ population has decreased by 7,1 million people, conformingly to its underlying equation. Saving on the final consumption of energy, which really took place in United Kingdom, reduces the theoretically sustainable demographic base. The reader could say: this is not an equilibrium, if the model population matches the actual one just in a few years over the whole period since 1990 through 2013. Still, if you compute the average proportion (i.e. average over 1990 – 2013) between the real population, and the ‘energy based population’, like ‘real one divided by the energy-based one’, that average proportion is equal to A = 1,028560563. Quite a close match on the long run, isn’t it? This close match decomposes into two distinct phases. The first phase is that of increasing, energy-based sustainability of the population. The second one is the process of growing discrepancy between the real headcount, on the one hand, and what is sustainable in ‘energy-based’ terms, on the other hand.

Now, let’s have a look at column [3], thus at the model population based just on the consumption of renewable energy, alimentary intake held constant. This model population follows a different trend. In 1990, when my observation starts, and when the average resident of United Kingdom consumes, on average, just 0,02 tons of oil equivalent in renewable energy per year. At the time, the ‘renewables-based population’ is way below the real one, more specifically 10,37 million below. At my second checkpoint, in 2003, consumption of renewable energy in the UK doubles, up to 0,04 tons of oil equivalent per year per person. The ‘renewable-based’ population, in 2003, with 53,4 million people, is still below the real one by 6,45 million. In 2013, at my final checkpoint, the situation reverses. With 0,18 tons of oil equivalent per capita per year, in terms of renewable energy consumed, the ‘renewables-based’, model population of Britain makes 85,83 million, 21,5 million more than the real one. Interestingly, the ‘renewables-based’, model population started soaring up by 2007 – 2008, precisely when the global consumption of renewable energies started to grow really fast. Once again, some readers could have the legitimate doubt whether a model yielding that much difference is any kind of equilibrium. I had the same doubts when doing these maths, and the result surprised me. Over the whole period of 1990 – 2013, the ratio of real population divided by the ‘renewables-based’ one was A = 1,028817158, i.e. up to the third decimal point it is the same proportion as the one between the ‘energy-based’ population and the real one. I know that, at this point, it would be very easy to enter the tempting world of metaphysics. If the proportion between my femur and my humerus is X, and I find a piece of driftwood, which, compared to my femur, makes the same proportion, that piece of wood can easily become the fossilized bone of my distant ancestor etc. What holds me (relatively) close to real life is the fact that the recurrent proportion in question is the outcome of two equations with different input data and different values in parameters, and still with the same essential structure. This, in turn, makes me think that what I have found out are two processes, which make some kind of undertow in the country under scrutiny, i.e. United Kingdom in this precise occurrence. Being more and more profuse on the overall consumption of energy made the sustainable demographic base of UK swell, up to 2003, and then the fact of getting meaner on energy per capita contributed to make this demographic base less and less sustainable. In parallel, the systematic increase in the consumption of renewable energies consistently pumped up the demographic sustainability of the UK. Why am I talking about two distinct processes? Well, saving energy per capita means, essentially, more efficiency in using engines of all kinds, as well as high-power electronics (like big servers). On the other hand, shifting towards renewable energies is, respectively, one step and two steps upstream, in the chain of transformation. This type of change pertains essentially to trading combustion engines for electric ones, and switching the generation of electricity from fossil fuels to wind, water, sun etc.

At this point, my theoretical stance fundamentally differs from what the reader could find, for example, with the Club of Rome (see, for example: Meadows et al. 1972[1]). I develop a theoretical approach, where we, humans, are inherently prone to maximized our total intake of energy from environment. Those local equilibriums between population, food and energy mean that any such local population can be represented as a super-organism, absorbing energy, like one of those Australian, saltwater crocodiles, which grow up to the limits offered by their habitat, and there is no question of stopping before reaching those limits. The otherwise highly respectable, intellectual stance of the Club of Rome amounts to saying that we have to save energy in order to survive. I say that if this is the only way for us, humans, to survive, we can just as well start packing. The simple, straightforward saving of energy is simply not what we do. You could ask a white shark to turn vegan. Guess the result. On the other hand, what we can do is to change our technological base so as to have the same or greater an amount of directly consumable energy (motor power, heat, and functionality in our electronics) out of less burdening a basket of primary energies. The reader could object: “But the average resident of United Kingdom did save energy between 2003 and 2013”. Yes, they did, and their sustainable demographic shrunk accordingly. The robustness of any reasoning about demographics can be verified with data on net migration. Whatever I could calculate as the ‘demographic base’ of a country, the net inflow (or net outflow) of people in a given time and place is a sure indicator of how attractive said place is. Column [5] in table 1 provides the data published by the World Bank. These are snapshots, taken every five years: 1992, 1997, 2002, 2007, and 2012. At each of these checkpoints, net migration is way above the net increase in population. It means that immigrants are filling a space left by the otherwise shrinking domestic population. The place is becoming so attractive for newcomers that an effect of demographic crowding out is to notice.

As we move to the right, in table 1, column [6] introduces the ratio of fixed capital stock per one resident patent application. The reader can notice an almost continuous growth in this variable between 1990 and 2013. In terms of the theoretical stance I am developing in my research, that growth means an almost continuous change in the evolutionary function of selection between the incoming, new technologies. We can see a case of fixed capital accumulating faster than the capacity to create patentable invention. The female capitalist structures in the economy of United Kingdom are systematically increasing their capacity to absorb and recombine inventions. That means stronger incentives to invest in the development of new, technologically advanced businesses (the female, capitalistic function), which, in turn, creates an absorptive process: the capitalist structures are, in a sense, hungry for innovation. As the process unfolds, the growing, average amount of fixed assets per one patent application alleviates the pressure, on each individual invention, to be the toughest and the meanest dog in the pack. This, in turn, can be interpreted as lesser a pressure towards hierarchy-forming, in patentable invention, and stronger a pressure towards networking between inventions. One more step to the right side of table 1 brings into our focus the data on aggregate depreciation in fixed assets, as a fraction of the Gross Domestic Product; this is column [7]. We can observe some sort of waving cycle there: increase between 1990 and 1995, then a swing down the scale, between 1996 and 2003, just to give rise another surge, between 2004 and 2013. Growing values in the ratio of physical capital per one patent application seem to produce a cyclical stir in the depreciation of fixed assets. It is reasonable to assume that the pace of physical wear and tear is pretty constant over time, and the changing burden of amortizing fixed assets comes from moral obsolescence, thus from the pace of technological change. That pace of obsolescence, although displaying a tendency to cyclical change, follows an overall ascending trend. The more capital per one patent application, thus the less hierarchy and the more networking among patentable inventions, the greater the burden of technological change on the current aggregate income. A last step to the right, in table 1, leads to column [8], which provides information about the supply of money in the British economy, as a % of the GDP. Another wavy cycle can be noticed, which eventually leads to very high a supply of money, and very low a velocity in said money. Quick pace of technological change brings about the necessity, in the monetary system, to produce a growing number of alternative algorithms of response. That period between 1990 and 2013 shows quite well, how monetary systems can very literally learn to respond. At first, between 1990 and 1993, the monetary system responds, to an accelerating obsolescence in established technologies, by increasing the velocity of money. Starting from 1994, a different mechanism turns on: instead of increasing the velocity of circulation, the monetary system just accumulates monetary balances. It is accumulating monetary resources in reserve, or, in the lines of the Keynesian theory, it is accumulating speculative positions. In the presence of increasing uncertainty as for the actual lifecycle of our average technology, we build up the capacity to react pretty quickly (money allows such quick reaction) to any further technological change.

Table 1 – Selected data regarding United Kingdom

Year Model population, millions, based on energy consumption in general Model population, millions, based on the consumption of renewable energy Real population, millions Net migration, headcount Capital stock per one patent application, at current PPPs (in mil. 2011US$ Aggregate depreciation of fixed assets, as % of the GDP Supply of broad money, as % of the GDP
[1] [2] [3] [4] [5] [6] [7] [8]
1990 58,94 46,89 57,26   185,48 0,116 0,85
1991 59,88 46,37 57,42   191,39 0,124 0,821
1992 59,68 51,00 57,58 205443 201,54 0,13 0,565
1993 59,92 49,89 57,74   213,04 0,135 0,561
1994 60,08 54,27 57,90   232,57 0,145 0,574
1995 60,05 54,87 58,08   246,71 0,148 0,615
1996 61,30 53,62 58,26   270,95 0,147 0,66
1997 60,32 54,51 58,46 498998 281,41 0,139 0,788
1998 60,54 54,62 58,66   261,31 0,133 0,912
1999 60,51 53,28 58,87   236,04 0,124 0,914
2000 60,53 53,51 59,08   232,87 0,116 0,959
2001 60,52 51,98 59,30   242,77 0,113 1,006
2002 59,69 53,64 59,55 968350 251,42 0,109 1,01
2003 60,07 53,40 59,85   260,60 0,107 1,046
2004 59,76 56,35 60,21   302,57 0,109 1,094
2005 59,69 59,43 60,65   368,38 0,114 1,178
2006 58,95 61,36 61,15   407,57 0,119 1,274
2007 57,60 63,74 61,69 2030075 433,89 0,124 1,403
2008 56,89 68,72 62,22   512,68 0,137 1,617
2009 54,96 71,41 62,72   565,24 0,156 1,664
2010 55,68 76,37 63,16   643,84 0,173 1,672
2011 53,32 78,96 63,57   635,67 0,167 1,543
2012 53,89 81,20 63,96 990000 690,89 0,174 1,512
2013 53,42 85,83 64,33   777,86 0,178 1,486

Source: World Bank, Penn Tables 9.0

The case of United Kingdom is that of a relatively well fed society, which increases its demographic sustainability by shifting its technological base towards renewable energies. Presently, we can have a look at completely different a socio-economic environment: Saudi Arabia. Saudi Arabia is one of those countries, which seem to present a huge potential for socio-economic change, at the condition of increasing the use of renewable energies. In terms of the evolutionary selection function regarding new technologies, Saudi Arabia is a land of peace: the ratio of physical capital per one resident patent application is counted in dozens of billions of US dollars. Still, there seems to be more and more agitation in the backstage: this ratio, although very high, had been cut by seven between 1990 and 2013. There is a sneaky snake in that Eden garden. On the top of that, Saudi Arabia is one of those interesting societies with just a slight food deficit per capita: enough to make people alert, not enough to push them into the apathy of deep, chronical hunger. The average alimentary intake per capita, in Saudi Arabia, from 1990 through 2013, had been of F/N = 1087,7 mega calories per year. Table 2, below, provides the same type of quantitative profiling regarding Saudi Arabia as has been presented for United Kingdom. Whilst in the latter case, we deal with a population that had increased its headcount by some 11% between 1990 and 2013, Saudi Arabia presents completely different a calibre of demographic change: plus 83% during the same period. With this magnitude of demographic growth, the social structure in 2013 was likely to be very different from that in 1990. Interestingly, the final consumption of energy per capita per year had increased almost by the same gradient as population, i.e. by 79,5%. Even more interestingly, the ‘energy-based’, model population in Saudi Arabia, calculated with the empirical function model(N) = (Energy consumption per capita)0,72*(1087,7)1-0,72=0,38, never reaches that magnitude, although, on the long run, it is matched by the real population by the scale factor A = 1,026310231. The ‘energy-based’ population grows, over the whole window of observation, just by 52,4%. It is a good example of how the alimentary base of a society works. In comparison to United Kingdom, this base is just 10,8% thinner, and, in spite of almost doubling the absorption of non-edible energy, Saudi Arabia has trouble to develop a sustainable demographic base.

Saudi Arabia is one of those countries, where the absorption of renewable energies per capita had been consistently shrinking in our window of observation, from 1,35 kilograms of oil equivalent per year per capita, in 1990, to barely 0,41 kilograms in 2013.   The second version of model population, the ‘renewables-based’ one, computed as model(N) = (Renewable energy consumption per capita)0,27*(1087,7)1-0,27=0,73, had shrunk from 27,64 million in 1990, to 19,99 million in 2013. Let’s rephrase it, in order to grasp the phenomenon under scrutiny. With the amount of energy that the average Saudi resident consumed per capita in 1990, the country had a sustainable demographic base. Still, with the long-run alimentary intake at 1087,7 mega calories per year per person, the present population, exceeding 30 million people, is hardly sustainable, even with the soaring consumption of energy. Going back to 1990, once again, the amount of renewable energies consumed at the time, other variables held constant, could sustain a population much larger than the 16,89 million recorded in 1990. With the present consumption of renewables, the present population of Saudi Arabia looks anything but sustainable. As we have a look at net migration in Saudi Arabia (column [5] in table 2), a puzzling tendency appears: as long as the local population was robustly sustained by its energy consumption, the balance on migration was negative. When the local population started to drop wheels off its sustainable base, the balance on migration turned positive. Illogical? Maybe, and this is precisely why it is an intellectual challenge, and why I am trying to sort out my first puzzlement, regarding local equilibriums between population, food, and energy. A quick comparison with United Kingdom shows two, completely different paradigms of social change. In United Kingdom, the abundance of food allowed smooth shift towards renewable energies, so as to keep the place highly attractive in spite of saving on the overall energy consumption. In Saudi Arabia, with just slightly lower an alimentary intake, and highly problematic sustainability in population, domestic demographic growth stays way above the net migratory inflow.

Let’s have a look at technological change in Saudi Arabia. First, by having a look at column [7] in table 2, we can see that the relative burden of depreciation, i.e. of obsolescence in established technologies, is close to what is observable in United Kingdom. Thus, the basic pace of technological change can be assumed as nearly identical. Still, the economic system reacts to that change exactly in the opposite way to that observable in United Kingdom. At the starting point of our observation, in 1990, the Saudi economy is extremely abundant in physical capital, when denominated in resident patent applications (column [6]), and rather mean on money. In terms of my theory, it means very little competition between patentable inventions, very little hierarchy among them, and very little algorithms of response in the monetary system. As time passes, and as technological change speeds up (the share of depreciation in the GDP grows), the amount of physical capital per one patent application dramatically shrinks. It means increased effort in research and development, and quickly growing a competition, as well as quickly forming a hierarchy, between all those new inventions. Still, by comparison to the British monetary system, the Saudi one is far from being profuse. Not much is happening in terms of algorithms of response, as well as in terms of speculative positions, as regards the supply of money. In the presence of very nearly the same pace of technological change, and similar gradient of change in that pace, those two economic systems – United Kingdom and Saudi Arabia – develop completely different responses. United Kingdom gives some loose to its hierarchy of inventions, and to the competition between them, and adds a lot of liquidity in its monetary system. Saudi Arabia spurs competition between inventions, and barely adds to the supply of money. Of course, a lot of factors make the difference between those two societies: religion, institutions, historical track, natural resources, climate etc. Still, in terms of the theory I am forming, one difference is sharp like a razor: the difference in food base. United Kingdom has a secure, slightly superfluous alimentary regime, whilst Saudi Arabia is just below satiety. Can this single factor be the ultimate distinction, explaining all the other economic differences? My empirical findings strongly suggest that the answer is ‘yes’, and what I am trying to do now is to go more in depth of that distinction.

Table 2 Selected data regarding Saudi Arabia

Year Model population, millions, based on energy consumption in general Model population, millions, based on the consumption of renewable energy Real population, millions Net migration, headcount Capital stock per one patent application, at current PPPs (in mil. 2011US$ Aggregate depreciation of fixed assets, as % of the GDP Supply of broad money, as % of the GDP
[1] [2] [3] [4] [5] [6] [7] [8]
1990  17,62  27,64  16,89  75 767,78  0,13  0,43
1991  19,21  28,29  17,40    45 179,69  0,13  0,44
1992  20,66  25,37  17,89 -110000  58 512,83  0,12  0,43
1993  20,80  23,10  18,37    60 291,97  0,13  0,46
1994  21,16  27,96  18,85  39 192,54  0,14  0,46
1995  20,86  26,55  19,33    47 465,66  0,14  0,45
1996  21,52  20,58  19,81  49 895,93  0,13  0,44
1997  20,43  19,83  20,30 -350000  24 239,44  0,13  0,44
1998  21,01  20,44  20,83  31 785,39  0,14  0,52
1999  20,90  20,22  21,39    20 603,36  0,13  0,50
2000  21,17  20,14  22,01  20 231,88  0,12  0,45
2001  21,13  20,89  22,67    34 545,11  0,13  0,48
2002  22,27  20,79  23,36 730000  26 811,98  0,13  0,54
2003  21,98  20,44  24,06    30 481,69  0,13  0,51
2004  22,50  20,36  24,75  22 634,09  0,13  0,50
2005  22,41  20,07  25,42    16 913,35  0,12  0,45
2006  23,67  20,78  26,08  19 550,01  0,13  0,47
2007  23,79  20,30  26,74 995000  20 713,69  0,15  0,51
2008  25,28  20,24  27,41  n.a.  0,14  0,48
2009  25,98  20,29  28,09    n.a.  0,18  0,65
2010  27,57  20,09  28,79  12 904,10  0,17  0,55
2011  26,31  20,22  29,50    12 386,98  0,16  0,49
2012  28,14  20,42  30,20 1590000  n.a.  0,16  0,52
2013  26,85  19,99  30,89    10 065,90  0,18  0,56

Source: World Bank, Penn Tables 9.0

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[1] Donella H. Meadows, Dennis L. Meadows, Jorgen Randers, William W. Behrens III, 1972, The Limits to Growth. A report for The Club of Rome’s Project on the Predicament of Mankind, Published in the United States of America in 1972 by Universe Books, 381 Park Avenue South, New York, New York 10016, © 1972 by Dennis L. Meadows, ISBN 0-87663-165-0