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-I*mSHjjjjjjjjJjjjjj:,k.jZkGllllllllllllllll4m)ljll%. SOCIAL AND ECOLOGICAL CONSEQUENCES
OF ADAPTIVE PACIFISM AND UNSUBMISSION
(from a Mathematical Model)
RAFAEL PLA-LPEZ
Dpt.Applied Mathematics
Universitat de Valncia
C/Dr.Moliner, 50
46100 Burjassot (Valncia)
e-mail pla@vm.ci.uv.es
URL http://www.uv.es/~pla
Spain
ABSTRACT
We work with a mathematical model of Social Evolution from a Learning General Theory. In prior works, we studied the conditions of transition to a Full Repressive Society or to a Free Scientific Society, depending on the adaptivity of produced repression to suffered repression and on the "resignation" to mean satisfaction. Then, we varied repression adaptability and resignation depending on social behaviour, and introduced geographical factors, such as ecological boundaries, natural differences and distances between subsystems. In this paper, we present a statistical study of the influence of repression adaptability and resignation on ecological destruction and social evolution.
RSUM
Nous travaillons avec un modle mathmatique de l'volution Social, d'aprs une Thorie Gnral d'Apprentissage. Dans des travaux prcdents, nous avons tudi les conditions de transition vers une Societ Pleinement Rpressive ou vers une Societ Scientifique Libre, en fonction de la capacit d'adaptation de la rpression produite a la rpression subie et de la "rsignation" a la satisfaction moyenne. Aprs, nous avons vari la capacit d'adaptation de la rpression et la rsignation en fonction de la conduite sociale, et ajoutant facteurs gographiques comme bornes cologiques, diffrences naturelles et distances entre subsystmes. En ce travail, nous exposons une tude statistique de l'influence de l'adaptativit de la rpression et la rsignation en la destruction cologique et l'volution social.
1. A MODEL OF ADAPTIVE, HISTORICAL, GEOGRAPHICAL AND MULTIDIMENSIONAL SOCIAL LEARNING WITH RESIGNATION
We work with an Adaptive, Historical, Geographical and Multidimensional Model with Resignation 1,2,3,4 built from a General Learning Theory 5 which is formulated in terms of General Systems Theory 6. By means of this Mathematical Model, we have studied the possible paths of evolution from a Full Repressive Society to a Free Scientific Society with a multidimensional state-variable which values characterize social behaviours.
The Model is composed by means of the interaction of several mathematical Systems, which express the relations between the variables involved:
The core of the Model is the Learning System, through positive and negative reinforcement: the probability (P) of each social behaviour (U), in each individual subsystem (N) of a social population, increases when his goal is fulfilled and decreases when it is not fulfilled from this social behaviour. If no social behaviour available to an individual subsystem produces goal fulfilment, then this subsystem can be destroyed. The fulfilment probability (PG) depends on its technical possibility (), which is weighted by a factor determined by the social organization (1-).
This factor is generated by a Repression System: each social behaviour, according to its scope () in each individual subsystem, the impact (IMP) of this on different individual subsystems, and its repressive capacity (sts), produces a decrease of this factor for the different social behaviours. Thus, each social behaviour represses the other social behaviours, by decreasing its goal fulfilment.
A Relay System produces a random () substitution () of an individual subsystem for a "child subsystem" with initial equiprobability (ntl) of every available social behaviour. A "child subsystem" can also occupy (A) the niche of a destroyed subsystem. Thus, relay causes the loss of the information accumulated in the substituted individual subsystem.
Also, a Science System determines the probability of learning (PL) for each social behaviour in each subsystem: the probability of the experience of other subsystems, which is weighted by factors of emission (EM), reception (RE) and impact IMP, is added to its own experience. This System expresses the relations of "intellectual communication" between different individual subsystems.
A Historic System simulates historical evolution through the random () increase () of the dimension (m) of the state-variable in each subsystem, and therefore of the number of its available social behaviours. The probability of evolution is increased (b) by the existence of social behaviours which were theoretically not available but are forced by the Science System from the experience of other subsystems. This System expresses technological progress, and also technological diffusion (we characterize a technologically higher society by a greater capacity of choice between different social behaviours).
An Adaptive System determines the dynamic evolution (Ta) of the repressive capacity in a subsystem, from an initial value (st) -when it is a "child subsystem"- which depends on the might () and ferocity () of the social behaviour-, toward its suffered repression (). The Adaptation Time Ta expresses the delay in the adaptation of produced repression (sts) to suffered repression (): thus, with a low delay Ta, the produced repression equals quickly the suffered repression; on the contrary, with a high delay Ta, produced repression remains approximately constant.
A Resignation System expresses the influence of subjective factors through a tendency to a statistical normalization of the reinforcement from satisfaction and dissatisfaction; we name this tendency "resignation", and express it by a time of delay (Tr) according to a model of Systems Dynamics.
Moreover, a Delay System expresses the decrease of Adaptation Time Ta with might and the increase of Resignation Time Tr with ferocity , by means of the parameters ka and kr respectively.
An Impact System expresses how the impact IMP on repression and intellectual communication depends on might and distance (d) between subsystems.
A Natural System expresses a diversity of initial conditions ntl of the individual subsystems. In its first version, this System is a rigid System, without feedback nor evolution.
Finally, an Ecological System expresses a Ecological Destruction (ec<1) through a decrease in the technical possibilities of satisfaction when the sum of the repressive capacities sts and the technical possibilities of satisfaction (cannons and butter) on every subsystem surpasses the maximum size (NP) of the population of subsystems. Ecological destruction can be reversed only when some individual subsystem is destroyed.
The mathematical relations are set out in the Table 1.
2. SPECIFICATION OF THE MODEL
We have implemented our model in language C and executed it on the IBM 9021/500 of the SIUV (Servei Informtic de la Universitat de Valncia). You can find the source code in http://www.uv.es/~pla/MODAPRHG.C
We work with NP=100 individual subsystems, a maximum dimension mm=4 and binary components Uj_{0,1} of social behaviour U.
With this specification, U=0000 would correspond to a Primitive Society with a technical possibility of satisfaction equal to 0, without scientific communication, and which has ferocity but not might, and therefore has no repressive capacity.
In the same way, U=0111=7 can correspond to a Full Repressive Society with some technical possibility of satisfaction, some scientific communication and full repressive capacity.
Finally, U=1111=15=F corresponds to a Free Scientific Society with full technical possibility of satisfaction, full scientific communication and null repressive capacity.
The specification of the model is also included in Table 1.
We have studied 2,3,4 the end of evolution from a Primitive Society with different values of initialization (ntl) of the "child subsystems" and different values for the Adaptation Time (Ta) of the repressive capacity and for the Resignation Time (Tr): high ntl produces a faster learning in young subsystems, low Ta produces a faster evolution of the repressive capacity toward suffered repression, and low Tr produces a faster resignation to the mean satisfaction.
We speak about predominance of a state U if its probability is the majority (P>0.5) in a relative majority of subsystems. And we speak about strong predominance if moreover its probability of satisfaction (PG) is the maximum.
3. A STATISTICAL STUDY
In previous works 2,3,4, we have studied the probability of reaching and overcoming a Full Repressive Society. But we pointed out that a more extensive study had to be made to obtain conclusive statistical results.
Thus, we have executed our model 10000 times, by varying ka and kr between 1 and 100.
We are especially interested in evolution processes with strong predominance of Full Repressive Society U=7 by considering that only such processes can simulate real social evolution on the planet Earth, from the present New World Order. Therefore, only in these processes have we recorded the results.
In order to study how the results of evolutionary processes depend on kr and ka, we use the REGINT 7 program to explore the type of functional relation of different variables with kr and with ka, respectively. We then use an own program to study the linear regression of these variables on these functions of kr and ka.
For the statistical study, we aggregate values in squares of 1010 .
Bearing in mind that high values of ka and kr involve slow adaptability to repression and resignation, respectively. Thus, an Adaptive Pacifism (disarmament due to a lack of enemies) can be expressed by low values of ka, and Unsubmission can be expressed by high values of kr.
3.1. From a Full Repressive Society towards a Free Scientific Society
The proportion of arrival at a strong predominance of a Full Repressive Society U=7 is
%SP7 134.579/kr + 2.44898 ln(ka) -5.074690 (29)
with a correlation coefficient of _=0.946392 .
By averaging on a variable and studying the linear regression on a function of the other variable, we obtain
%SP7 134.579/kr + 3.838159 (30)
with a correlation coefficient of _=0.991922 , and
%SP7 2.44898 ln(ka) + 0.667151 (31)
with a correlation coefficient of _=0.874173 .
In sum, there is a strong correlation with both parameters, especially with resignation: faster resignation facilitates the arisal of a Full Repressive Society, and faster peaceful adaptation hinders it.
On the other hand, the proportion of final predominance of a Full Repressive Society U=7 is %FP7 124.839/kr + 3.00700 ln(ka) - 8.849998 . (32)
The correlations (0.992126 and 0.939859) are similar to those above.
Henceforth, we will treat only the cases with strong predominance of U=7, and we will study the proportion or the mean of different variables on these cases. To this end, we have had to execute the model over 200 times until we found a case with kr between 91 and 100 and ka between 1 to 10, in order to avoid dividing by zero.
Thus, the proportion that overcome a Full Repressive Society U=7 towards a Free Scientific Society U=F is
%O7F -36.51747 e-kr/10 + 419.3677/ka + 17.872488 (33)
with a strong correlation (0.994890) with Adaptive Pacifism, and a weaker correlation (0.795396) with Unsubmission.
3.2. Survival and Ecological Destruction
The mean number of surviving individual subsystems S is
99.984218 + 0.0001684962 kr -5.672475 log(ka) (34)
with a strong correlation (0.985135) with Adaptive Pacifism, and very scarce correlation (0.698171) with Unsubmission.
Finally, the mean of the remaining Ecology ec is
c 0.680313 - 0.4112817/kr - 0.001473373 cos(0.211111ka) (35)
with a strong correlation (0.979376) with Unsubmission, and no correlation with Adaptive Pacifism.
4. CONCLUSION
According to our Model, Adaptive Pacifism and Unsubmission would need to be promoted in order to survive in a Free Scientific Society without Ecological Destruction.
REFERENCES
1. R. Pla-Lpez, "Model of Multidimensional Historical Evolution", in R.Trappl ed, Cybernetics and Systems'90, World Scientific, Singapore, 575-582 (1990).
2. R. Pla-Lpez, "Model of Adaptive, Historical and Multidimensional Social Learning", in R.Trappl ed, Cybernetics and Systems Research'92, World Scientific, Singapore, 1005-1012 (1992).
3. R. Pla-Lpez, "The Role of Subjective Factor in Social Evolution", Second European Congress on Systems Science, Prague (1993).
4. R. Pla-Lpez and V.Castellar-Bus, "Model of Historical-Geographical Evolution", in R.Trappl ed., Cybernetics and Systems'94, World Scientific, Singapore, vol.I, 1049-1056 (1994).
5. R. Pla-Lpez, "Introduction to a Learning General Theory", Cybernetics and Systems: An International Journal 19, 411-429 (1988).
6. G.J. Klir, "An approach to General Systems Theory", D.Van Nostrand Co., London (1969).
7. A. Caselles, "REGINT", program in C language, Department of Applied Mathematics, Universitat de Valncia, Spain
(e-mail Antonio.Caselles@uv.es, URL http://www.uv.es/~caselles/regint.exe).
Table 1
Mathematical relations in the model of Adaptive, Historical, Geographical and Multidimensional Social Learning with Resignation
General conditions:
m(N)mm=4, Uj{0,1}, U=(U3,U2,U1,U0)=j=0m(N) Uj 2 j{0,1,...,15}, M(N)=maximum of U=2 m(N) -1 MM=15
NP=maximum number of individual subsystems=100, N{0,1,2,3,...,99}, tnt=20000, prg=10000 (0)
(it continues at the next page)
Table 1 (continuation)
Mathematical relations in the model of Adaptive, Historical, Geographical
and Multidimensional Social Learning with Resignation
Learning System:
P(U/N)=F(U/N)/B(N) such that B(N)= U' F(U'/N) (1)
<1 Ft+100(U/N) = Ft(U/N) + 200[PGt(U,N)-PRt(N)]PLt(U/N)SR0(N)/SRt(N) or 0 if negative (2)
1 if UM(N), F(U/N)=ntl, else F(U/N)=0 (3)
PG(U)=(U)(1-(U)) , 0(U)=(U)= j j(Uj) = j Uj/4 1 (4)
Repression System:
(U,N') = U'U N (U',N)sts(U',N)IMP(N,N') (5)
(U,N) = P(U/N)/S such that S=n({ N / B(N)0 }) (6)
Science System:
PL(U/N) = P(U/N) + RE(N) N'N P(U/N')EM(N')IMP(N',N) (7)
EM(N)= U P(U/N)em(U) , em(U) = j emj(Uj) = j Uj 2 j/MM = U/15 (8)
RE(N) = U P(U/N)re(U) , re(U) = j rej(Uj) = j Uj 2 j/MM = U/15 (9)
Relay System:
= + A(N) + [1-A(N)]B(N)/tnt , random [0,1[ (10)
A(N) = U P(U/N)a(U) = U P(U/N) 0.09(1-2U/MM) = 0.09 - 0.012 U P(U/N) U (11)
Historic System:
1 m(N)tM(N) P(U/N) (13)
Adaptation System:
<1 stst+100(U,N) = stst(U,N) + 100[(U)-stst(U,N)]/Ta (14)
1 sts(U,N) = st(U), st(U)=(U)(U) (15)
(U) = j j(Uj) = j Uj 2 j/(2mm-1-1) = U/7 (16)
(U) = 1- j [1- j(Uj) ] = 1- j [1- (1-Uj)j/(mm-1) ] = 1- j/Uj=0 (3-j)/3 (17)
Resignation System:
PGM(N) = U PG(U,N)PL(U/N) / U PL(U/N) (18)
SPG(N) = ( U PG(U,N) PL(U/N) / U PL(U/N) - PGM(N) ) (19)
<1 PRt+100(N) = PRt(N) + 100 [ PGMt(N) - PRt(N) ] / Tr (20)
SRt+100(N) = SRt(N) + 100 [ SPGt(N) - SRt(N) ] / Tr
1 PR(N)=PR0(m(N))= UM(N) (U) / (M(N)+1) (21)
SR(N)=SR0(N)= ( UM(N) (U)/(M(N)+1) - PR0(m(N)) )
Delay System:
Ta(N) = ka 100 M/U (U) P(U/N) = ka 1500/U U P(U/N) / M=maximum of = 15/7 (22)
Tr(N) = kr 100 U ((U)+1) P(U/N) (23)
Impact System:
IMP(N,N') = U P(U/N) imp(U,d) (24)
imp(U,d) = mimp + (dm>d)(Mimp-mimp)(dm-d)/dm , d=NP/2-|NP/2-|N-N'|| = 50-|50-|N-N'||
mimp= (>1)(-1)/(M-1) = (>1)(-1)7/8 , Mimp= (2-mimp)((1)/+(>1)) (25)
dm=Md((<1)+(1)) / Md=maximum of d(N,N')= 50
Natural System:
ntl(N) = Mntl - d(N,MN)(Mntl-mntl)/Md = 150 - |50-|N-25|| (26)
Mntl=maximum of ntl=150, mntl=minimum of ntl=50, MN=individual subsystem with maximum of ntl=75
Ecological System:
t+100(U) = t(U) dect revt , ec0=1, ect+100 = ect dect revt (27)
dec = min(1,(NP-K2)/K1) , revt+100 = max(1,min(St/St+100,1/ect))
K1 = N U (U) P(U/N) , K2 = N U sts(U,N) P(U/N) (28)
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