7th International Conference of Sociocybernetics “TECHNOLOGY AND SOCIAL COMPLEXITY”

Rafael Pla-Lopez
Dpt.Applied Mathematics, Universitat de València, C/Dr.Moliner 50, 46100 Burjassot, Spain


In prior works, we developed a mathematical model about the duality East-West in Social Evolution. Thus, we introduced a feature of western individualism so that the evolution arrived to "collectivist" social systems in the “East”, to a "capitalist" social system in the “West”, and could further carry to an ecologic holocaust, to capitalism forever or to a free scientific society.

In order to introduce the duality North-South which also occurs in the real history of the humanity, we work now in a bidimensional space with a cylindrical topology, and make the relief between generations faster in the “South” and the learning of “young” subsystems faster in the “West”.

We need to re-calibrated the parameters in order to get an accurate simulation of the real social evolution of humanity until the present time, with a faster social evolution in the “North”, so that later collectivist systems arrived first in “North-East”, and "capitalist" system arrived first in “North-West”, and they only would appear in the South through a Cultural and Technological Diffusion.

When we got these results we'll be able to study if an eventual “free scientific society” can develop first in the South (like a “Socialism of the XXI Century” from Venezuela) or in the North, and if an eventual ecological holocaust would begin in the North or in the South.


In prior works (Nemiche&Pla-Lopez 2000, 2002a), we developed a model with a duality East-West in Social Evolution, particularly in the impact of the social repression:

The probability of satisfaction of a subsystem N with a social behaviour U is given by
E/E0≤1 measures the ecological destruction, π(U) the technical possibility of satisfaction, ρ(U,N) the derivation of consumption for recycling, and σ(U,N) the social repression, which decreases the probability of satisfaction and is given by
    σ(U,N)=U'≠U, N' Φ(U,N') sts(U',N') IMP(N',N) ,
Φ(U',N') is the scope of the social behaviour U' in a subsystem N', given by
        Φ(U',N')=P(U'|N')2/S ,
where P(U'|N') is the probability of the social behaviour U' in the subsystem N',
             P(U'|N')=F(U'|N')/B(N') so that B(N')=
U" F(U"|N')
and S is the number of active subsystems,
             S=n({N / B(N)≠0}) ,
sts(U',N') is the repressive capacity of the behaviour U' in the subsystem N' and IMP(N',N) is the impact of a subsystem N' on a subsystem N, given by
IMP(N',N)=U" P(U"|N') imp(U",d(N',N)) ,
imp(U",d(N',N)) is the impact of a behaviour U" at a distance d(N',N) between the subsystems N' and N.

 Thus, we introduced a feature of  western individualism (the repression only acts on other subsystems: imp(U,0)=0) and eastern gregariousness (the repression is stronger on the own subsystem: imp(U,0) is the maximum). With this model, we could simulate a dual social evolution, so that in the East the evolution arrived to a "collectivist" social systems U=6≡0110, and in the West it arrived to a "capitalist" social system, U=7≡0111 (individualism/gregariousness depends on the least significant bit).

Further on, the model could carry to an ecologic holocaust, to capitalism forever or to a free scientific society with U=F≡15≡1111 without repressive capacity, and we could study the features which favour one or another end of the social evolution. This model also could explain the emergence of
ephemeral anomalous social systems in situations of crisis, which we name Revolt Effect. Later, we introduced a "repressive solidarity", so that a subsystem increases its repressive capacity when other subsystem with the same social system-behaviour is repressed, in order to simulate the consequences of the 11S (Pla-Lopez&Nemiche 2002b).

The duality North-South

Nevertheless, this model did not consider the duality North-South which also occurs in the real history of the humanity. In order to introduce it, we work now in a bidimensional space with the cylindrical topology, resulting of supressing the poles in a spherical surface. Thus, we will indicate a subsystem by the pair (N,n), where N will express the "longitude" and n will express the "latitude". In our simulation, N=0:19 and n=0:9 so that N=0 and N=19 will be contiguous: the distance between the subsystems (N,n) amb (N',n') will be
Note that d(0,n,19,n)=10-|10-19|=1
(we could also consider N=0:20 so that N=20 and N=0 were equivalent: d(0,n,20,n)=10-|10-20|=0 ).

We make the parameter "tanatos"
variable with "latitude" n, so that it were lower in the South. This parameter regulates the occurrence of the relief between generations, so that the probability of relief depends on B/tanatos. Thus, the parameter "tanatos" can be related to the hope of life until a "natural death". Therefore, the probability of relief will be greater in the South, so that this relief will tend to occur before the behaviour of the subsystem were adapted by learning, and we can suppose that the social evolution through this learning were slower in the South.

In a first approximation, we will use a linear relation,
which will vary between 10000 and 28000, as it is indicated in Figure 1, a.

Also, the parameter "progress" regulates the technological progress, so that the probability of increase of the number of available behaviours depends on B/progress. In the previous model, tanatos=20000 and progress=tanatos/2=10000. Now, we will take progress(n)=10000 constant, so that the relation tanatos/progress will vary with the latitude n, between 1 and 2.8

On the other hand, the parameter "natal", which regulates initialization as a result of a relief, so that F(U|N,n)=natal(N) afther this relief, will depend on "longitude" N, so that the learning of young subsystems were faster in the West.

In a first approximation,
which will vary between 50 for N=5 (West) and 250 for N=15 (East), as it is indicated in Figure 1, b. Note that natal(20)=natal(0)=150 .

Figure 1
Figure 1
Variation of "tanatos" and "natal" as a function of the "latitude" and the "longitude", respectively.

Simulating the real history

But, although we begin the modelization from the values of the parameters of the former model, we need perhaps to re-calibrate these parameters in order to get an accurate simulation of the real social evolution of humanity until the present time, through different phases and with a different evolution between both East-West and North-South.

Particularly, the simulation should have to show a faster social evolution in the North, so that later collectivist systems arrived first in North-East, and "capitalist" system arrived first in North-West, while prior social systems remain in the South, and more complex "northern" social systems only would appear in the South through a Cultural and Technological Diffusion which can simulate the colonialism.

We execute the model with different values of some basic parameters. The most relevant are Ka, which indicates the adaptability of the produced repression to the suffered repression  ("adaptive pacifism"), Kr, which indicates the adaptability of the subjective satisfaction to the mean satisfaction ("resignation") and Ke, which indicates the adaptability of the recycling to the exhaustion of the environment ("adaptive ecologism"). These parameters regulate the delay of the adaptation, and so, in general, a lower value of them indicates a faster adaptation. Thus, we can analyze the influence of these factors on the social evolution, and estimate which values can correspond to the humanity on the Earth.

By changing only Ka and Kr, and using the same values of the other parameters from the former model, we can get an early appearance of some behaviours in the North, with a subsequent extension to the South, as the Figure 2 shows with the values Ka=10 and Kr=10 (which indicates a fast adaptive pacifism and resignation). Each sign correspond to a subsystem, with North up, South down, West at mid left and East at mid rigth, as usual (remember that the left limit n=0 and the right limit n=19 are contiguous). A number (in hexadecimal: F≡15) indicates a predominant behaviour. An hyfen "-" indicated that there is not any predominant behaviour. A white space indicates a destroyed subsystem.

We can interpret U=1≡0001 as the social behaviour of  "Slavery", U=3≡0011 as "Western Feudalism" and U=7≡0111 as "Capitalism". So, we observe that "Western Feudalism" appears first at North-West and later spread everywhere. Also, "Capitalism" appears first at North and later spread everywhere.

Nevertheless, by changing only the parameters Ka and Kr, we cannot simulate the appearance of gregarious social behaviours, as "Eastern Feudalism" U=2≡0010 or "State Socialism" U=6≡0010, at North-East. So, we need to re-calibrate other parameters in order to simulate the real history of the humanity on the Earth.


 33- - 11-1 -1 11 1
--333 111 1111 011-1
--33-3111 1 101---
1 3 1-111 1- -1 -
111111 11-1111 01 11
111-11111-11 101
- 1111 1 -11 -11 -
11 11111 1-1 1 11 11
1---111111 1 1-11--
3-3-11111 1 1-- 11

---- ---3-- --------
7-3-33--333-3- ---7-
-3333-3333-33-- ----
3 -333333 3333--- -
-33-33333---3---- --
--3-33-333-33 - - --
3--3-33 33--3- --- -
--333333 333--------
---33-33-3-3----- --

---- 77---- ------7-
7--7-37---3--- ----7
- 73----- ------- -
---7333---------- -7
---7-3-333--- - ----
----7-- 3----- --- -
----3-3--3------- --

7777 777777 -7------
7777777777-7-7 77---
7777777 777777- 77
77777777-77777--7 --
777-7-7777-77 77-777
7777777 7777-- 777 7
777777-7777777777 -7

Figure 2
Four steps in a simulation with Ka=10, Kr=10, Ke= 8, Ce= 4 and Qc=52

Forecasting the futur

When we got this simulation, we'll be able to study the conditions and the possibilities of later local emergency of ways to a free scientific society F≡15≡1111 in front of "capitalism forever" or ecologic holocaust, and if this alternative social system can develop first in the South or in the North. Also, in the case of the end of the social evolution were an ecological holocaust, we'd be able of  forecast if this would begin in the North or in the South. Thus, we'll be able to evaluate, for example, if the bolivarian project of the Socialism of the XXI Century from Venezuela, as different from the State Socialism of the XX Century, is an anomalous, local and ephemeral Revolt Effect, or it can be a feasible project with global significance.


Dieterich, H. (2001), "El Socialismo del Siglo XXI", Mexico, http://www.rebelion.org/dieterich/dieterich070802.pdf.

Engels, F. (1884), "Der Ursprung aus der Familie, der Privateigentum un der Staat", Zurich (translated to Spanish as "El Origen de la Familia, la Propiedad Privada y el Estado", Fundamentos, Madrid, 1970).

Godelier, M. (1970), "Schéms d'evolution des sociétés" (translated to Spanish as "Esquemas de evolución de las sociedades", Miguel Castellote Editor, aprox. in 1970).

Nemiche,M. & Pla-Lopez,R. (2000), "A Model of Dual Evolution of the Humanity", en 2nd International Conference on Sociocybernetics, Panticosa, 25-30 June, http://www.uv.es/~pla/models/MDEHabrid.htm.

Nemiche,M. & Pla-Lopez,R. (2002a), "A Learning Model for the Dual Evolution of Human Social Behaviors", en the 12th International WOSC Congress and the 4th IIGSS Workshop, Pittsburgh,  published in Kybernetes: The International Journal of Systems and Cybernetics, Volume 32 Number 5/6 2003, pp.679-691, Emerald, ISSN 0368-492X, http://www.uv.es/~pla/models/pittsburgh/.

Pla-Lopez,R. & Nemiche,M. (2002b), "Consecuencias del ataque a las Torres Gemelas para la Evolución de la Humanidad", in II Reunión Española de Ciencia de Sistemas (RECS-II), València, 12-14 June, published in Ciudad, sociedad, educación, control, caos y autoorganización, L.Ferrer, A.Caselles, J.Martínez, R.Pla, I.Martínez de Lejarza eds., Universitat de València-Departament de Matemàtica Aplicada, ISBN 84-370-5528-8, http://www.uv.es/~pla/models/torres.htm.